From f3da6201f8f57177150326997655fddc244c7932 Mon Sep 17 00:00:00 2001
From: Jakub Marcowski <chubercikbattle@gmail.com>
Date: Thu, 15 May 2025 23:06:54 +0200
Subject: [PATCH] manifold: Update to 3.1.1

---
 COPYRIGHT.txt                                 |   2 +-
 modules/csg/SCsub                             |   2 +
 thirdparty/README.md                          |   4 +-
 thirdparty/manifold/include/manifold/common.h |  59 +-
 thirdparty/manifold/include/manifold/linalg.h | 741 +++++++++---------
 .../manifold/include/manifold/manifold.h      | 148 +++-
 .../include/manifold/optional_assert.h        |   4 +
 .../manifold/include/manifold/polygon.h       |   9 +-
 .../manifold/include/manifold/vec_view.h      |  36 +-
 thirdparty/manifold/src/boolean3.cpp          | 443 ++++-------
 thirdparty/manifold/src/boolean3.h            |   7 +-
 thirdparty/manifold/src/boolean_result.cpp    | 239 +++---
 thirdparty/manifold/src/collider.h            | 121 ++-
 thirdparty/manifold/src/constructors.cpp      |  68 +-
 .../src/cross_section/cross_section.cpp       |  23 +-
 thirdparty/manifold/src/csg_tree.cpp          | 217 +++--
 thirdparty/manifold/src/csg_tree.h            |  20 +-
 thirdparty/manifold/src/edge_op.cpp           | 639 ++++++++++-----
 thirdparty/manifold/src/face_op.cpp           | 217 ++---
 thirdparty/manifold/src/hashtable.h           |  40 +-
 thirdparty/manifold/src/impl.cpp              | 706 +++++++++--------
 thirdparty/manifold/src/impl.h                | 230 +++---
 thirdparty/manifold/src/iters.h               |  27 +-
 thirdparty/manifold/src/manifold.cpp          | 169 ++--
 thirdparty/manifold/src/mesh_fixes.h          |   2 +-
 thirdparty/manifold/src/parallel.h            | 214 ++---
 thirdparty/manifold/src/polygon.cpp           | 250 +++---
 thirdparty/manifold/src/properties.cpp        | 235 +++---
 thirdparty/manifold/src/quickhull.cpp         |   9 +-
 thirdparty/manifold/src/quickhull.h           |   4 +-
 thirdparty/manifold/src/sdf.cpp               |  38 +-
 thirdparty/manifold/src/shared.h              |  34 +-
 thirdparty/manifold/src/smoothing.cpp         | 321 ++++----
 thirdparty/manifold/src/sort.cpp              | 191 +++--
 thirdparty/manifold/src/subdivision.cpp       | 146 ++--
 thirdparty/manifold/src/svd.h                 | 110 ++-
 thirdparty/manifold/src/tree2d.cpp            |  59 ++
 thirdparty/manifold/src/tree2d.h              |  85 ++
 thirdparty/manifold/src/tri_dist.h            |   1 +
 thirdparty/manifold/src/utils.h               |  21 +-
 thirdparty/manifold/src/vec.h                 |  58 +-
 41 files changed, 3224 insertions(+), 2725 deletions(-)
 create mode 100644 thirdparty/manifold/src/tree2d.cpp
 create mode 100644 thirdparty/manifold/src/tree2d.h

diff --git a/COPYRIGHT.txt b/COPYRIGHT.txt
index cdc49bb9ed..5a7e274f2b 100644
--- a/COPYRIGHT.txt
+++ b/COPYRIGHT.txt
@@ -391,7 +391,7 @@ License: BSD-3-clause
 
 Files: thirdparty/manifold/*
 Comment: Manifold
-Copyright: 2020-2024, The Manifold Authors
+Copyright: 2020-2025, The Manifold Authors
 License: Apache-2.0
 
 Files: thirdparty/mbedtls/*
diff --git a/modules/csg/SCsub b/modules/csg/SCsub
index 32bc240a82..a6515b8c92 100644
--- a/modules/csg/SCsub
+++ b/modules/csg/SCsub
@@ -25,9 +25,11 @@ thirdparty_sources = [
     "src/polygon.cpp",
     "src/properties.cpp",
     "src/quickhull.cpp",
+    "src/sdf.cpp",
     "src/smoothing.cpp",
     "src/sort.cpp",
     "src/subdivision.cpp",
+    "src/tree2d.cpp",
 ]
 
 thirdparty_sources = [thirdparty_dir + file for file in thirdparty_sources]
diff --git a/thirdparty/README.md b/thirdparty/README.md
index cd2232166a..ab4e306498 100644
--- a/thirdparty/README.md
+++ b/thirdparty/README.md
@@ -624,12 +624,12 @@ See `linuxbsd_headers/README.md`.
 ## manifold
 
 - Upstream: https://github.com/elalish/manifold
-- Version: 3.0.1 (98b8142519d35c13e0e25cfa9fd6e3a271403be6, 2024)
+- Version: 3.1.1 (2f4741e0b1de44d6d461b869e481351335340b44, 2025)
 - License: Apache 2.0
 
 File extracted from upstream source:
 
-- `src/` and `include/`, except from `CMakeLists.txt`, `cross_section.cpp` and `meshIO.{cpp,h}`
+- `src/` and `include/`, except from `CMakeLists.txt`, `cross_section.h` and `meshIO.{cpp,h}`
 - `AUTHORS`, `LICENSE`
 
 
diff --git a/thirdparty/manifold/include/manifold/common.h b/thirdparty/manifold/include/manifold/common.h
index f1200f4654..6975cc3de5 100644
--- a/thirdparty/manifold/include/manifold/common.h
+++ b/thirdparty/manifold/include/manifold/common.h
@@ -20,7 +20,8 @@
 #include <chrono>
 #endif
 
-#include "manifold/linalg.h"
+#include "linalg.h"
+#include "optional_assert.h"
 
 namespace manifold {
 /** @addtogroup Math
@@ -548,7 +549,7 @@ class Quality {
     int nSegL = 2.0 * radius * kPi / circularEdgeLength_;
     int nSeg = fmin(nSegA, nSegL) + 3;
     nSeg -= nSeg % 4;
-    return std::max(nSeg, 3);
+    return std::max(nSeg, 4);
   }
 
   /**
@@ -577,21 +578,62 @@ struct ExecutionParams {
   /// Perform extra sanity checks and assertions on the intermediate data
   /// structures.
   bool intermediateChecks = false;
-  /// Verbose output primarily of the Boolean, including timing info and vector
-  /// sizes.
-  bool verbose = false;
+  /// Perform 3D mesh self-intersection test on intermediate boolean results to
+  /// test for ϵ-validity. For debug purposes only.
+  bool selfIntersectionChecks = false;
   /// If processOverlaps is false, a geometric check will be performed to assert
   /// all triangles are CCW.
   bool processOverlaps = true;
   /// Suppresses printed errors regarding CW triangles. Has no effect if
   /// processOverlaps is true.
   bool suppressErrors = false;
-  /// Perform optional but recommended triangle cleanups in SimplifyTopology()
+  /// Deprecated! This value no longer has any effect, as cleanup now only
+  /// occurs on intersected triangles.
   bool cleanupTriangles = true;
+  /// Verbose level:
+  /// - 0 for no verbose output
+  /// - 1 for verbose output for the Boolean, including timing info and vector
+  /// sizes.
+  /// - 2 for verbose output with triangulator action as well.
+  int verbose = 0;
 };
 /** @} */
 
 #ifdef MANIFOLD_DEBUG
+template <class T>
+std::ostream& operator<<(std::ostream& out, const la::vec<T, 1>& v) {
+  return out << '{' << v[0] << '}';
+}
+template <class T>
+std::ostream& operator<<(std::ostream& out, const la::vec<T, 2>& v) {
+  return out << '{' << v[0] << ',' << v[1] << '}';
+}
+template <class T>
+std::ostream& operator<<(std::ostream& out, const la::vec<T, 3>& v) {
+  return out << '{' << v[0] << ',' << v[1] << ',' << v[2] << '}';
+}
+template <class T>
+std::ostream& operator<<(std::ostream& out, const la::vec<T, 4>& v) {
+  return out << '{' << v[0] << ',' << v[1] << ',' << v[2] << ',' << v[3] << '}';
+}
+
+template <class T, int M>
+std::ostream& operator<<(std::ostream& out, const la::mat<T, M, 1>& m) {
+  return out << '{' << m[0] << '}';
+}
+template <class T, int M>
+std::ostream& operator<<(std::ostream& out, const la::mat<T, M, 2>& m) {
+  return out << '{' << m[0] << ',' << m[1] << '}';
+}
+template <class T, int M>
+std::ostream& operator<<(std::ostream& out, const la::mat<T, M, 3>& m) {
+  return out << '{' << m[0] << ',' << m[1] << ',' << m[2] << '}';
+}
+template <class T, int M>
+std::ostream& operator<<(std::ostream& out, const la::mat<T, M, 4>& m) {
+  return out << '{' << m[0] << ',' << m[1] << ',' << m[2] << ',' << m[3] << '}';
+}
+
 inline std::ostream& operator<<(std::ostream& stream, const Box& box) {
   return stream << "min: " << box.min << ", "
                 << "max: " << box.max;
@@ -602,6 +644,11 @@ inline std::ostream& operator<<(std::ostream& stream, const Rect& box) {
                 << "max: " << box.max;
 }
 
+inline std::ostream& operator<<(std::ostream& stream, const Smoothness& s) {
+  return stream << "halfedge: " << s.halfedge << ", "
+                << "smoothness: " << s.smoothness;
+}
+
 /**
  * Print the contents of this vector to standard output. Only exists if compiled
  * with MANIFOLD_DEBUG flag.
diff --git a/thirdparty/manifold/include/manifold/linalg.h b/thirdparty/manifold/include/manifold/linalg.h
index dfcd305ba8..12f484fa1c 100644
--- a/thirdparty/manifold/include/manifold/linalg.h
+++ b/thirdparty/manifold/include/manifold/linalg.h
@@ -37,17 +37,10 @@
 
 #include <array>        // For std::array
 #include <cmath>        // For various unary math functions, such as std::sqrt
-#include <cstdint>      // For implementing namespace linalg::aliases
 #include <cstdlib>      // To resolve std::abs ambiguity on clang
 #include <functional>   // For std::hash declaration
-#include <iosfwd>       // For forward definitions of std::ostream
 #include <type_traits>  // For std::enable_if, std::is_same, std::declval
 
-#ifdef MANIFOLD_DEBUG
-#include <iomanip>
-#include <iostream>
-#endif
-
 // In Visual Studio 2015, `constexpr` applied to a member function implies
 // `const`, which causes ambiguous overload resolution
 #if defined(_MSC_VER) && (_MSC_VER <= 1900)
@@ -96,27 +89,27 @@ struct ord {
   T a, b;
 };
 template <class T>
-constexpr bool operator==(const ord<T> &o, std::nullptr_t) {
+constexpr bool operator==(const ord<T>& o, std::nullptr_t) {
   return o.a == o.b;
 }
 template <class T>
-constexpr bool operator!=(const ord<T> &o, std::nullptr_t) {
+constexpr bool operator!=(const ord<T>& o, std::nullptr_t) {
   return !(o.a == o.b);
 }
 template <class T>
-constexpr bool operator<(const ord<T> &o, std::nullptr_t) {
+constexpr bool operator<(const ord<T>& o, std::nullptr_t) {
   return o.a < o.b;
 }
 template <class T>
-constexpr bool operator>(const ord<T> &o, std::nullptr_t) {
+constexpr bool operator>(const ord<T>& o, std::nullptr_t) {
   return o.b < o.a;
 }
 template <class T>
-constexpr bool operator<=(const ord<T> &o, std::nullptr_t) {
+constexpr bool operator<=(const ord<T>& o, std::nullptr_t) {
   return !(o.b < o.a);
 }
 template <class T>
-constexpr bool operator>=(const ord<T> &o, std::nullptr_t) {
+constexpr bool operator>=(const ord<T>& o, std::nullptr_t) {
   return !(o.a < o.b);
 }
 
@@ -126,21 +119,21 @@ struct any_compare {};
 template <class T>
 struct any_compare<vec<T, 1>, vec<T, 1>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const vec<T, 1> &a, const vec<T, 1> &b) const {
+  constexpr ord<T> operator()(const vec<T, 1>& a, const vec<T, 1>& b) const {
     return ord<T>{a.x, b.x};
   }
 };
 template <class T>
 struct any_compare<vec<T, 2>, vec<T, 2>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const vec<T, 2> &a, const vec<T, 2> &b) const {
+  constexpr ord<T> operator()(const vec<T, 2>& a, const vec<T, 2>& b) const {
     return !(a.x == b.x) ? ord<T>{a.x, b.x} : ord<T>{a.y, b.y};
   }
 };
 template <class T>
 struct any_compare<vec<T, 3>, vec<T, 3>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const vec<T, 3> &a, const vec<T, 3> &b) const {
+  constexpr ord<T> operator()(const vec<T, 3>& a, const vec<T, 3>& b) const {
     return !(a.x == b.x)   ? ord<T>{a.x, b.x}
            : !(a.y == b.y) ? ord<T>{a.y, b.y}
                            : ord<T>{a.z, b.z};
@@ -149,7 +142,7 @@ struct any_compare<vec<T, 3>, vec<T, 3>> {
 template <class T>
 struct any_compare<vec<T, 4>, vec<T, 4>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const vec<T, 4> &a, const vec<T, 4> &b) const {
+  constexpr ord<T> operator()(const vec<T, 4>& a, const vec<T, 4>& b) const {
     return !(a.x == b.x)   ? ord<T>{a.x, b.x}
            : !(a.y == b.y) ? ord<T>{a.y, b.y}
            : !(a.z == b.z) ? ord<T>{a.z, b.z}
@@ -159,24 +152,24 @@ struct any_compare<vec<T, 4>, vec<T, 4>> {
 template <class T, int M>
 struct any_compare<mat<T, M, 1>, mat<T, M, 1>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const mat<T, M, 1> &a,
-                              const mat<T, M, 1> &b) const {
+  constexpr ord<T> operator()(const mat<T, M, 1>& a,
+                              const mat<T, M, 1>& b) const {
     return compare(a.x, b.x);
   }
 };
 template <class T, int M>
 struct any_compare<mat<T, M, 2>, mat<T, M, 2>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const mat<T, M, 2> &a,
-                              const mat<T, M, 2> &b) const {
+  constexpr ord<T> operator()(const mat<T, M, 2>& a,
+                              const mat<T, M, 2>& b) const {
     return a.x != b.x ? compare(a.x, b.x) : compare(a.y, b.y);
   }
 };
 template <class T, int M>
 struct any_compare<mat<T, M, 3>, mat<T, M, 3>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const mat<T, M, 3> &a,
-                              const mat<T, M, 3> &b) const {
+  constexpr ord<T> operator()(const mat<T, M, 3>& a,
+                              const mat<T, M, 3>& b) const {
     return a.x != b.x   ? compare(a.x, b.x)
            : a.y != b.y ? compare(a.y, b.y)
                         : compare(a.z, b.z);
@@ -185,8 +178,8 @@ struct any_compare<mat<T, M, 3>, mat<T, M, 3>> {
 template <class T, int M>
 struct any_compare<mat<T, M, 4>, mat<T, M, 4>> {
   using type = ord<T>;
-  constexpr ord<T> operator()(const mat<T, M, 4> &a,
-                              const mat<T, M, 4> &b) const {
+  constexpr ord<T> operator()(const mat<T, M, 4>& a,
+                              const mat<T, M, 4>& b) const {
     return a.x != b.x   ? compare(a.x, b.x)
            : a.y != b.y ? compare(a.y, b.y)
            : a.z != b.z ? compare(a.z, b.z)
@@ -201,28 +194,28 @@ struct getter;
 template <>
 struct getter<0> {
   template <class A>
-  constexpr auto operator()(A &a) const -> decltype(a.x) {
+  constexpr auto operator()(A& a) const -> decltype(a.x) {
     return a.x;
   }
 };
 template <>
 struct getter<1> {
   template <class A>
-  constexpr auto operator()(A &a) const -> decltype(a.y) {
+  constexpr auto operator()(A& a) const -> decltype(a.y) {
     return a.y;
   }
 };
 template <>
 struct getter<2> {
   template <class A>
-  constexpr auto operator()(A &a) const -> decltype(a.z) {
+  constexpr auto operator()(A& a) const -> decltype(a.z) {
     return a.z;
   }
 };
 template <>
 struct getter<3> {
   template <class A>
-  constexpr auto operator()(A &a) const -> decltype(a.w) {
+  constexpr auto operator()(A& a) const -> decltype(a.w) {
     return a.w;
   }
 };
@@ -255,12 +248,12 @@ struct make_seq_impl<A, 4> {
 template <int A, int B>
 using make_seq = typename make_seq_impl<A, B - A>::type;
 template <class T, int M, int... I>
-vec<T, sizeof...(I)> constexpr swizzle(const vec<T, M> &v, seq<I...> i) {
+vec<T, sizeof...(I)> constexpr swizzle(const vec<T, M>& v, seq<I...>) {
   return {getter<I>{}(v)...};
 }
 template <class T, int M, int N, int... I, int... J>
-mat<T, sizeof...(I), sizeof...(J)> constexpr swizzle(const mat<T, M, N> &m,
-                                                     seq<I...> i, seq<J...> j) {
+mat<T, sizeof...(I), sizeof...(J)> constexpr swizzle(const mat<T, M, N>& m,
+                                                     seq<I...> i, seq<J...>) {
   return {swizzle(getter<J>{}(m), i)...};
 }
 
@@ -291,7 +284,7 @@ struct apply<F, scalars_t<>, vec<A, M>> {
   using type = vec<ret_t<F, A>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, const vec<A, M> &a) {
+  static constexpr type impl(seq<I...>, F f, const vec<A, M>& a) {
     return {f(getter<I>{}(a))...};
   }
 };
@@ -300,8 +293,8 @@ struct apply<F, scalars_t<>, vec<A, M>, vec<B, M>> {
   using type = vec<ret_t<F, A, B>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, const vec<A, M> &a,
-                             const vec<B, M> &b) {
+  static constexpr type impl(seq<I...>, F f, const vec<A, M>& a,
+                             const vec<B, M>& b) {
     return {f(getter<I>{}(a), getter<I>{}(b))...};
   }
 };
@@ -310,7 +303,7 @@ struct apply<F, scalars_t<B>, vec<A, M>, B> {
   using type = vec<ret_t<F, A, B>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, const vec<A, M> &a, B b) {
+  static constexpr type impl(seq<I...>, F f, const vec<A, M>& a, B b) {
     return {f(getter<I>{}(a), b)...};
   }
 };
@@ -319,7 +312,7 @@ struct apply<F, scalars_t<A>, A, vec<B, M>> {
   using type = vec<ret_t<F, A, B>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, A a, const vec<B, M> &b) {
+  static constexpr type impl(seq<I...>, F f, A a, const vec<B, M>& b) {
     return {f(a, getter<I>{}(b))...};
   }
 };
@@ -328,8 +321,8 @@ struct apply<F, scalars_t<>, vec<A, M>, vec<B, M>, vec<C, M>> {
   using type = vec<ret_t<F, A, B, C>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, const vec<A, M> &a,
-                             const vec<B, M> &b, const vec<C, M> &c) {
+  static constexpr type impl(seq<I...>, F f, const vec<A, M>& a,
+                             const vec<B, M>& b, const vec<C, M>& c) {
     return {f(getter<I>{}(a), getter<I>{}(b), getter<I>{}(c))...};
   }
 };
@@ -338,8 +331,8 @@ struct apply<F, scalars_t<C>, vec<A, M>, vec<B, M>, C> {
   using type = vec<ret_t<F, A, B, C>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, const vec<A, M> &a,
-                             const vec<B, M> &b, C c) {
+  static constexpr type impl(seq<I...>, F f, const vec<A, M>& a,
+                             const vec<B, M>& b, C c) {
     return {f(getter<I>{}(a), getter<I>{}(b), c)...};
   }
 };
@@ -348,8 +341,8 @@ struct apply<F, scalars_t<B>, vec<A, M>, B, vec<C, M>> {
   using type = vec<ret_t<F, A, B, C>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, const vec<A, M> &a, B b,
-                             const vec<C, M> &c) {
+  static constexpr type impl(seq<I...>, F f, const vec<A, M>& a, B b,
+                             const vec<C, M>& c) {
     return {f(getter<I>{}(a), b, getter<I>{}(c))...};
   }
 };
@@ -358,7 +351,7 @@ struct apply<F, scalars_t<B, C>, vec<A, M>, B, C> {
   using type = vec<ret_t<F, A, B, C>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, const vec<A, M> &a, B b, C c) {
+  static constexpr type impl(seq<I...>, F f, const vec<A, M>& a, B b, C c) {
     return {f(getter<I>{}(a), b, c)...};
   }
 };
@@ -367,8 +360,8 @@ struct apply<F, scalars_t<A>, A, vec<B, M>, vec<C, M>> {
   using type = vec<ret_t<F, A, B, C>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, A a, const vec<B, M> &b,
-                             const vec<C, M> &c) {
+  static constexpr type impl(seq<I...>, F f, A a, const vec<B, M>& b,
+                             const vec<C, M>& c) {
     return {f(a, getter<I>{}(b), getter<I>{}(c))...};
   }
 };
@@ -377,7 +370,7 @@ struct apply<F, scalars_t<A, C>, A, vec<B, M>, C> {
   using type = vec<ret_t<F, A, B, C>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, A a, const vec<B, M> &b, C c) {
+  static constexpr type impl(seq<I...>, F f, A a, const vec<B, M>& b, C c) {
     return {f(a, getter<I>{}(b), c)...};
   }
 };
@@ -386,7 +379,7 @@ struct apply<F, scalars_t<A, B>, A, B, vec<C, M>> {
   using type = vec<ret_t<F, A, B, C>, M>;
   enum { size = M, mm = 0 };
   template <int... I>
-  static constexpr type impl(seq<I...>, F f, A a, B b, const vec<C, M> &c) {
+  static constexpr type impl(seq<I...>, F f, A a, B b, const vec<C, M>& c) {
     return {f(a, b, getter<I>{}(c))...};
   }
 };
@@ -395,7 +388,7 @@ struct apply<F, scalars_t<>, mat<A, M, N>> {
   using type = mat<ret_t<F, A>, M, N>;
   enum { size = N, mm = 0 };
   template <int... J>
-  static constexpr type impl(seq<J...>, F f, const mat<A, M, N> &a) {
+  static constexpr type impl(seq<J...>, F f, const mat<A, M, N>& a) {
     return {apply<F, void, vec<A, M>>::impl(make_seq<0, M>{}, f,
                                             getter<J>{}(a))...};
   }
@@ -405,8 +398,8 @@ struct apply<F, scalars_t<>, mat<A, M, N>, mat<B, M, N>> {
   using type = mat<ret_t<F, A, B>, M, N>;
   enum { size = N, mm = 1 };
   template <int... J>
-  static constexpr type impl(seq<J...>, F f, const mat<A, M, N> &a,
-                             const mat<B, M, N> &b) {
+  static constexpr type impl(seq<J...>, F f, const mat<A, M, N>& a,
+                             const mat<B, M, N>& b) {
     return {apply<F, void, vec<A, M>, vec<B, M>>::impl(
         make_seq<0, M>{}, f, getter<J>{}(a), getter<J>{}(b))...};
   }
@@ -416,7 +409,7 @@ struct apply<F, scalars_t<B>, mat<A, M, N>, B> {
   using type = mat<ret_t<F, A, B>, M, N>;
   enum { size = N, mm = 0 };
   template <int... J>
-  static constexpr type impl(seq<J...>, F f, const mat<A, M, N> &a, B b) {
+  static constexpr type impl(seq<J...>, F f, const mat<A, M, N>& a, B b) {
     return {apply<F, void, vec<A, M>, B>::impl(make_seq<0, M>{}, f,
                                                getter<J>{}(a), b)...};
   }
@@ -426,7 +419,7 @@ struct apply<F, scalars_t<A>, A, mat<B, M, N>> {
   using type = mat<ret_t<F, A, B>, M, N>;
   enum { size = N, mm = 0 };
   template <int... J>
-  static constexpr type impl(seq<J...>, F f, A a, const mat<B, M, N> &b) {
+  static constexpr type impl(seq<J...>, F f, A a, const mat<B, M, N>& b) {
     return {apply<F, void, A, vec<B, M>>::impl(make_seq<0, M>{}, f, a,
                                                getter<J>{}(b))...};
   }
@@ -471,8 +464,8 @@ struct select {
 };
 struct lerp {
   template <class A, class B, class C>
-  constexpr auto operator()(A a, B b,
-                            C c) const -> decltype(a * (1 - c) + b * c) {
+  constexpr auto operator()(A a, B b, C c) const
+      -> decltype(a * (1 - c) + b * c) {
     return a * (1 - c) + b * c;
   }
 };
@@ -855,16 +848,16 @@ template <class T>
 struct vec<T, 1> {
   T x;
   constexpr vec() : x() {}
-  constexpr vec(const T &x_) : x(x_) {}
+  constexpr vec(const T& x_) : x(x_) {}
   // NOTE: vec<T,1> does NOT have a constructor from pointer, this can conflict
   // with initializing its single element from zero
   template <class U>
-  constexpr explicit vec(const vec<U, 1> &v) : vec(static_cast<T>(v.x)) {}
-  constexpr const T &operator[](int i) const { return x; }
-  LINALG_CONSTEXPR14 T &operator[](int i) { return x; }
+  constexpr explicit vec(const vec<U, 1>& v) : vec(static_cast<T>(v.x)) {}
+  constexpr const T& operator[](int) const { return x; }
+  LINALG_CONSTEXPR14 T& operator[](int) { return x; }
 
   template <class U, class = detail::conv_t<vec, U>>
-  constexpr vec(const U &u) : vec(converter<vec, U>{}(u)) {}
+  constexpr vec(const U& u) : vec(converter<vec, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, vec>>
   constexpr operator U() const {
     return converter<U, vec>{}(*this);
@@ -874,21 +867,21 @@ template <class T>
 struct vec<T, 2> {
   T x, y;
   constexpr vec() : x(), y() {}
-  constexpr vec(const T &x_, const T &y_) : x(x_), y(y_) {}
-  constexpr explicit vec(const T &s) : vec(s, s) {}
-  constexpr explicit vec(const T *p) : vec(p[0], p[1]) {}
+  constexpr vec(const T& x_, const T& y_) : x(x_), y(y_) {}
+  constexpr explicit vec(const T& s) : vec(s, s) {}
+  constexpr explicit vec(const T* p) : vec(p[0], p[1]) {}
   template <class U, int N>
-  constexpr explicit vec(const vec<U, N> &v)
+  constexpr explicit vec(const vec<U, N>& v)
       : vec(static_cast<T>(v.x), static_cast<T>(v.y)) {
     static_assert(
         N >= 2,
         "You must give extra arguments if your input vector is shorter.");
   }
-  constexpr const T &operator[](int i) const { return i == 0 ? x : y; }
-  LINALG_CONSTEXPR14 T &operator[](int i) { return i == 0 ? x : y; }
+  constexpr const T& operator[](int i) const { return i == 0 ? x : y; }
+  LINALG_CONSTEXPR14 T& operator[](int i) { return i == 0 ? x : y; }
 
   template <class U, class = detail::conv_t<vec, U>>
-  constexpr vec(const U &u) : vec(converter<vec, U>{}(u)) {}
+  constexpr vec(const U& u) : vec(converter<vec, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, vec>>
   constexpr operator U() const {
     return converter<U, vec>{}(*this);
@@ -898,30 +891,30 @@ template <class T>
 struct vec<T, 3> {
   T x, y, z;
   constexpr vec() : x(), y(), z() {}
-  constexpr vec(const T &x_, const T &y_, const T &z_) : x(x_), y(y_), z(z_) {}
-  constexpr vec(const vec<T, 2> &xy, const T &z_) : vec(xy.x, xy.y, z_) {}
-  constexpr explicit vec(const T &s) : vec(s, s, s) {}
-  constexpr explicit vec(const T *p) : vec(p[0], p[1], p[2]) {}
+  constexpr vec(const T& x_, const T& y_, const T& z_) : x(x_), y(y_), z(z_) {}
+  constexpr vec(const vec<T, 2>& xy, const T& z_) : vec(xy.x, xy.y, z_) {}
+  constexpr explicit vec(const T& s) : vec(s, s, s) {}
+  constexpr explicit vec(const T* p) : vec(p[0], p[1], p[2]) {}
   template <class U, int N>
-  constexpr explicit vec(const vec<U, N> &v)
+  constexpr explicit vec(const vec<U, N>& v)
       : vec(static_cast<T>(v.x), static_cast<T>(v.y), static_cast<T>(v.z)) {
     static_assert(
         N >= 3,
         "You must give extra arguments if your input vector is shorter.");
   }
-  constexpr const T &operator[](int i) const {
+  constexpr const T& operator[](int i) const {
     return i == 0 ? x : i == 1 ? y : z;
   }
-  LINALG_CONSTEXPR14 T &operator[](int i) {
+  LINALG_CONSTEXPR14 T& operator[](int i) {
     return i == 0 ? x : i == 1 ? y : z;
   }
-  constexpr const vec<T, 2> &xy() const {
-    return *reinterpret_cast<const vec<T, 2> *>(this);
+  constexpr const vec<T, 2>& xy() const {
+    return *reinterpret_cast<const vec<T, 2>*>(this);
   }
-  vec<T, 2> &xy() { return *reinterpret_cast<vec<T, 2> *>(this); }
+  vec<T, 2>& xy() { return *reinterpret_cast<vec<T, 2>*>(this); }
 
   template <class U, class = detail::conv_t<vec, U>>
-  constexpr vec(const U &u) : vec(converter<vec, U>{}(u)) {}
+  constexpr vec(const U& u) : vec(converter<vec, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, vec>>
   constexpr operator U() const {
     return converter<U, vec>{}(*this);
@@ -931,39 +924,39 @@ template <class T>
 struct vec<T, 4> {
   T x, y, z, w;
   constexpr vec() : x(), y(), z(), w() {}
-  constexpr vec(const T &x_, const T &y_, const T &z_, const T &w_)
+  constexpr vec(const T& x_, const T& y_, const T& z_, const T& w_)
       : x(x_), y(y_), z(z_), w(w_) {}
-  constexpr vec(const vec<T, 2> &xy, const T &z_, const T &w_)
+  constexpr vec(const vec<T, 2>& xy, const T& z_, const T& w_)
       : vec(xy.x, xy.y, z_, w_) {}
-  constexpr vec(const vec<T, 3> &xyz, const T &w_)
+  constexpr vec(const vec<T, 3>& xyz, const T& w_)
       : vec(xyz.x, xyz.y, xyz.z, w_) {}
-  constexpr explicit vec(const T &s) : vec(s, s, s, s) {}
-  constexpr explicit vec(const T *p) : vec(p[0], p[1], p[2], p[3]) {}
+  constexpr explicit vec(const T& s) : vec(s, s, s, s) {}
+  constexpr explicit vec(const T* p) : vec(p[0], p[1], p[2], p[3]) {}
   template <class U, int N>
-  constexpr explicit vec(const vec<U, N> &v)
+  constexpr explicit vec(const vec<U, N>& v)
       : vec(static_cast<T>(v.x), static_cast<T>(v.y), static_cast<T>(v.z),
             static_cast<T>(v.w)) {
     static_assert(
         N >= 4,
         "You must give extra arguments if your input vector is shorter.");
   }
-  constexpr const T &operator[](int i) const {
+  constexpr const T& operator[](int i) const {
     return i == 0 ? x : i == 1 ? y : i == 2 ? z : w;
   }
-  LINALG_CONSTEXPR14 T &operator[](int i) {
+  LINALG_CONSTEXPR14 T& operator[](int i) {
     return i == 0 ? x : i == 1 ? y : i == 2 ? z : w;
   }
-  constexpr const vec<T, 2> &xy() const {
-    return *reinterpret_cast<const vec<T, 2> *>(this);
+  constexpr const vec<T, 2>& xy() const {
+    return *reinterpret_cast<const vec<T, 2>*>(this);
   }
-  constexpr const vec<T, 3> &xyz() const {
-    return *reinterpret_cast<const vec<T, 3> *>(this);
+  constexpr const vec<T, 3>& xyz() const {
+    return *reinterpret_cast<const vec<T, 3>*>(this);
   }
-  vec<T, 2> &xy() { return *reinterpret_cast<vec<T, 2> *>(this); }
-  vec<T, 3> &xyz() { return *reinterpret_cast<vec<T, 3> *>(this); }
+  vec<T, 2>& xy() { return *reinterpret_cast<vec<T, 2>*>(this); }
+  vec<T, 3>& xyz() { return *reinterpret_cast<vec<T, 3>*>(this); }
 
   template <class U, class = detail::conv_t<vec, U>>
-  constexpr vec(const U &u) : vec(converter<vec, U>{}(u)) {}
+  constexpr vec(const U& u) : vec(converter<vec, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, vec>>
   constexpr operator U() const {
     return converter<U, vec>{}(*this);
@@ -1067,20 +1060,20 @@ functions, as well as a set of standard reductions.
  */
 template <class T, int M>
 struct mat<T, M, 1> {
-  typedef vec<T, M> V;
+  using V = vec<T, M>;
   V x;
   constexpr mat() : x() {}
-  constexpr mat(const V &x_) : x(x_) {}
-  constexpr explicit mat(const T &s) : x(s) {}
-  constexpr explicit mat(const T *p) : x(p + M * 0) {}
+  constexpr mat(const V& x_) : x(x_) {}
+  constexpr explicit mat(const T& s) : x(s) {}
+  constexpr explicit mat(const T* p) : x(p + M * 0) {}
   template <class U>
-  constexpr explicit mat(const mat<U, M, 1> &m) : mat(V(m.x)) {}
+  constexpr explicit mat(const mat<U, M, 1>& m) : mat(V(m.x)) {}
   constexpr vec<T, 1> row(int i) const { return {x[i]}; }
-  constexpr const V &operator[](int j) const { return x; }
-  LINALG_CONSTEXPR14 V &operator[](int j) { return x; }
+  constexpr const V& operator[](int) const { return x; }
+  LINALG_CONSTEXPR14 V& operator[](int) { return x; }
 
   template <class U, class = detail::conv_t<mat, U>>
-  constexpr mat(const U &u) : mat(converter<mat, U>{}(u)) {}
+  constexpr mat(const U& u) : mat(converter<mat, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, mat>>
   constexpr operator U() const {
     return converter<U, mat>{}(*this);
@@ -1088,22 +1081,22 @@ struct mat<T, M, 1> {
 };
 template <class T, int M>
 struct mat<T, M, 2> {
-  typedef vec<T, M> V;
+  using V = vec<T, M>;
   V x, y;
   constexpr mat() : x(), y() {}
-  constexpr mat(const V &x_, const V &y_) : x(x_), y(y_) {}
-  constexpr explicit mat(const T &s) : x(s), y(s) {}
-  constexpr explicit mat(const T *p) : x(p + M * 0), y(p + M * 1) {}
+  constexpr mat(const V& x_, const V& y_) : x(x_), y(y_) {}
+  constexpr explicit mat(const T& s) : x(s), y(s) {}
+  constexpr explicit mat(const T* p) : x(p + M * 0), y(p + M * 1) {}
   template <class U, int N, int P>
-  constexpr explicit mat(const mat<U, N, P> &m) : mat(V(m.x), V(m.y)) {
+  constexpr explicit mat(const mat<U, N, P>& m) : mat(V(m.x), V(m.y)) {
     static_assert(P >= 2, "Input matrix dimensions must be at least as big.");
   }
   constexpr vec<T, 2> row(int i) const { return {x[i], y[i]}; }
-  constexpr const V &operator[](int j) const { return j == 0 ? x : y; }
-  LINALG_CONSTEXPR14 V &operator[](int j) { return j == 0 ? x : y; }
+  constexpr const V& operator[](int j) const { return j == 0 ? x : y; }
+  LINALG_CONSTEXPR14 V& operator[](int j) { return j == 0 ? x : y; }
 
   template <class U, class = detail::conv_t<mat, U>>
-  constexpr mat(const U &u) : mat(converter<mat, U>{}(u)) {}
+  constexpr mat(const U& u) : mat(converter<mat, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, mat>>
   constexpr operator U() const {
     return converter<U, mat>{}(*this);
@@ -1111,29 +1104,29 @@ struct mat<T, M, 2> {
 };
 template <class T, int M>
 struct mat<T, M, 3> {
-  typedef vec<T, M> V;
+  using V = vec<T, M>;
   V x, y, z;
   constexpr mat() : x(), y(), z() {}
-  constexpr mat(const V &x_, const V &y_, const V &z_) : x(x_), y(y_), z(z_) {}
-  constexpr mat(const mat<T, M, 2> &m_, const V &z_)
+  constexpr mat(const V& x_, const V& y_, const V& z_) : x(x_), y(y_), z(z_) {}
+  constexpr mat(const mat<T, M, 2>& m_, const V& z_)
       : x(m_.x), y(m_.y), z(z_) {}
-  constexpr explicit mat(const T &s) : x(s), y(s), z(s) {}
-  constexpr explicit mat(const T *p)
+  constexpr explicit mat(const T& s) : x(s), y(s), z(s) {}
+  constexpr explicit mat(const T* p)
       : x(p + M * 0), y(p + M * 1), z(p + M * 2) {}
   template <class U, int N, int P>
-  constexpr explicit mat(const mat<U, N, P> &m) : mat(V(m.x), V(m.y), V(m.z)) {
+  constexpr explicit mat(const mat<U, N, P>& m) : mat(V(m.x), V(m.y), V(m.z)) {
     static_assert(P >= 3, "Input matrix dimensions must be at least as big.");
   }
   constexpr vec<T, 3> row(int i) const { return {x[i], y[i], z[i]}; }
-  constexpr const V &operator[](int j) const {
+  constexpr const V& operator[](int j) const {
     return j == 0 ? x : j == 1 ? y : z;
   }
-  LINALG_CONSTEXPR14 V &operator[](int j) {
+  LINALG_CONSTEXPR14 V& operator[](int j) {
     return j == 0 ? x : j == 1 ? y : z;
   }
 
   template <class U, class = detail::conv_t<mat, U>>
-  constexpr mat(const U &u) : mat(converter<mat, U>{}(u)) {}
+  constexpr mat(const U& u) : mat(converter<mat, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, mat>>
   constexpr operator U() const {
     return converter<U, mat>{}(*this);
@@ -1141,32 +1134,32 @@ struct mat<T, M, 3> {
 };
 template <class T, int M>
 struct mat<T, M, 4> {
-  typedef vec<T, M> V;
+  using V = vec<T, M>;
   V x, y, z, w;
   constexpr mat() : x(), y(), z(), w() {}
-  constexpr mat(const V &x_, const V &y_, const V &z_, const V &w_)
+  constexpr mat(const V& x_, const V& y_, const V& z_, const V& w_)
       : x(x_), y(y_), z(z_), w(w_) {}
-  constexpr mat(const mat<T, M, 3> &m_, const V &w_)
+  constexpr mat(const mat<T, M, 3>& m_, const V& w_)
       : x(m_.x), y(m_.y), z(m_.z), w(w_) {}
-  constexpr explicit mat(const T &s) : x(s), y(s), z(s), w(s) {}
-  constexpr explicit mat(const T *p)
+  constexpr explicit mat(const T& s) : x(s), y(s), z(s), w(s) {}
+  constexpr explicit mat(const T* p)
       : x(p + M * 0), y(p + M * 1), z(p + M * 2), w(p + M * 3) {}
   template <class U, int N, int P>
-  constexpr explicit mat(const mat<U, N, P> &m)
+  constexpr explicit mat(const mat<U, N, P>& m)
       : mat(V(m.x), V(m.y), V(m.z), V(m.w)) {
     static_assert(P >= 4, "Input matrix dimensions must be at least as big.");
   }
 
   constexpr vec<T, 4> row(int i) const { return {x[i], y[i], z[i], w[i]}; }
-  constexpr const V &operator[](int j) const {
+  constexpr const V& operator[](int j) const {
     return j == 0 ? x : j == 1 ? y : j == 2 ? z : w;
   }
-  LINALG_CONSTEXPR14 V &operator[](int j) {
+  LINALG_CONSTEXPR14 V& operator[](int j) {
     return j == 0 ? x : j == 1 ? y : j == 2 ? z : w;
   }
 
   template <class U, class = detail::conv_t<mat, U>>
-  constexpr mat(const U &u) : mat(converter<mat, U>{}(u)) {}
+  constexpr mat(const U& u) : mat(converter<mat, U>{}(u)) {}
   template <class U, class = detail::conv_t<U, mat>>
   constexpr operator U() const {
     return converter<U, mat>{}(*this);
@@ -1228,35 +1221,35 @@ constexpr identity_t identity{1};
  *  @{
  */
 template <class F, class A, class B>
-constexpr A fold(F f, A a, const vec<B, 1> &b) {
+constexpr A fold(F f, A a, const vec<B, 1>& b) {
   return f(a, b.x);
 }
 template <class F, class A, class B>
-constexpr A fold(F f, A a, const vec<B, 2> &b) {
+constexpr A fold(F f, A a, const vec<B, 2>& b) {
   return f(f(a, b.x), b.y);
 }
 template <class F, class A, class B>
-constexpr A fold(F f, A a, const vec<B, 3> &b) {
+constexpr A fold(F f, A a, const vec<B, 3>& b) {
   return f(f(f(a, b.x), b.y), b.z);
 }
 template <class F, class A, class B>
-constexpr A fold(F f, A a, const vec<B, 4> &b) {
+constexpr A fold(F f, A a, const vec<B, 4>& b) {
   return f(f(f(f(a, b.x), b.y), b.z), b.w);
 }
 template <class F, class A, class B, int M>
-constexpr A fold(F f, A a, const mat<B, M, 1> &b) {
+constexpr A fold(F f, A a, const mat<B, M, 1>& b) {
   return fold(f, a, b.x);
 }
 template <class F, class A, class B, int M>
-constexpr A fold(F f, A a, const mat<B, M, 2> &b) {
+constexpr A fold(F f, A a, const mat<B, M, 2>& b) {
   return fold(f, fold(f, a, b.x), b.y);
 }
 template <class F, class A, class B, int M>
-constexpr A fold(F f, A a, const mat<B, M, 3> &b) {
+constexpr A fold(F f, A a, const mat<B, M, 3>& b) {
   return fold(f, fold(f, fold(f, a, b.x), b.y), b.z);
 }
 template <class F, class A, class B, int M>
-constexpr A fold(F f, A a, const mat<B, M, 4> &b) {
+constexpr A fold(F f, A a, const mat<B, M, 4>& b) {
   return fold(f, fold(f, fold(f, fold(f, a, b.x), b.y), b.z), b.w);
 }
 /** @} */
@@ -1286,20 +1279,20 @@ using scalar_t =
 // apply(f,...) applies the provided function in an elementwise fashion to its
 // arguments, producing an object of the same dimensions
 template <class F, class... A>
-constexpr apply_t<F, A...> apply(F func, const A &...args) {
+constexpr apply_t<F, A...> apply(F func, const A&... args) {
   return detail::apply<F, void, A...>::impl(
       detail::make_seq<0, detail::apply<F, void, A...>::size>{}, func, args...);
 }
 
 // map(a,f) is equivalent to apply(f,a)
 template <class A, class F>
-constexpr apply_t<F, A> map(const A &a, F func) {
+constexpr apply_t<F, A> map(const A& a, F func) {
   return apply(func, a);
 }
 
 // zip(a,b,f) is equivalent to apply(f,a,b)
 template <class A, class B, class F>
-constexpr apply_t<F, A, B> zip(const A &a, const B &b, F func) {
+constexpr apply_t<F, A, B> zip(const A& a, const B& b, F func) {
   return apply(func, a, b);
 }
 /** @} */
@@ -1311,38 +1304,38 @@ constexpr apply_t<F, A, B> zip(const A &a, const B &b, F func) {
  *  @{
  */
 template <class A, class B>
-constexpr typename detail::any_compare<A, B>::type compare(const A &a,
-                                                           const B &b) {
+constexpr typename detail::any_compare<A, B>::type compare(const A& a,
+                                                           const B& b) {
   return detail::any_compare<A, B>()(a, b);
 }
 template <class A, class B>
-constexpr auto operator==(const A &a,
-                          const B &b) -> decltype(compare(a, b) == 0) {
+constexpr auto operator==(const A& a, const B& b)
+    -> decltype(compare(a, b) == 0) {
   return compare(a, b) == 0;
 }
 template <class A, class B>
-constexpr auto operator!=(const A &a,
-                          const B &b) -> decltype(compare(a, b) != 0) {
+constexpr auto operator!=(const A& a, const B& b)
+    -> decltype(compare(a, b) != 0) {
   return compare(a, b) != 0;
 }
 template <class A, class B>
-constexpr auto operator<(const A &a,
-                         const B &b) -> decltype(compare(a, b) < 0) {
+constexpr auto operator<(const A& a, const B& b)
+    -> decltype(compare(a, b) < 0) {
   return compare(a, b) < 0;
 }
 template <class A, class B>
-constexpr auto operator>(const A &a,
-                         const B &b) -> decltype(compare(a, b) > 0) {
+constexpr auto operator>(const A& a, const B& b)
+    -> decltype(compare(a, b) > 0) {
   return compare(a, b) > 0;
 }
 template <class A, class B>
-constexpr auto operator<=(const A &a,
-                          const B &b) -> decltype(compare(a, b) <= 0) {
+constexpr auto operator<=(const A& a, const B& b)
+    -> decltype(compare(a, b) <= 0) {
   return compare(a, b) <= 0;
 }
 template <class A, class B>
-constexpr auto operator>=(const A &a,
-                          const B &b) -> decltype(compare(a, b) >= 0) {
+constexpr auto operator>=(const A& a, const B& b)
+    -> decltype(compare(a, b) >= 0) {
   return compare(a, b) >= 0;
 }
 /** @} */
@@ -1353,38 +1346,38 @@ constexpr auto operator>=(const A &a,
  *  @{
  */
 template <class A>
-constexpr bool any(const A &a) {
+constexpr bool any(const A& a) {
   return fold(detail::op_or{}, false, a);
 }
 template <class A>
-constexpr bool all(const A &a) {
+constexpr bool all(const A& a) {
   return fold(detail::op_and{}, true, a);
 }
 template <class A>
-constexpr scalar_t<A> sum(const A &a) {
+constexpr scalar_t<A> sum(const A& a) {
   return fold(detail::op_add{}, scalar_t<A>(0), a);
 }
 template <class A>
-constexpr scalar_t<A> product(const A &a) {
+constexpr scalar_t<A> product(const A& a) {
   return fold(detail::op_mul{}, scalar_t<A>(1), a);
 }
 template <class A>
-constexpr scalar_t<A> minelem(const A &a) {
+constexpr scalar_t<A> minelem(const A& a) {
   return fold(detail::min{}, a.x, a);
 }
 template <class A>
-constexpr scalar_t<A> maxelem(const A &a) {
+constexpr scalar_t<A> maxelem(const A& a) {
   return fold(detail::max{}, a.x, a);
 }
 template <class T, int M>
-int argmin(const vec<T, M> &a) {
+int argmin(const vec<T, M>& a) {
   int j = 0;
   for (int i = 1; i < M; ++i)
     if (a[i] < a[j]) j = i;
   return j;
 }
 template <class T, int M>
-int argmax(const vec<T, M> &a) {
+int argmax(const vec<T, M>& a) {
   int j = 0;
   for (int i = 1; i < M; ++i)
     if (a[i] > a[j]) j = i;
@@ -1398,19 +1391,19 @@ int argmax(const vec<T, M> &a) {
  *  @{
  */
 template <class A>
-constexpr apply_t<detail::op_pos, A> operator+(const A &a) {
+constexpr apply_t<detail::op_pos, A> operator+(const A& a) {
   return apply(detail::op_pos{}, a);
 }
 template <class A>
-constexpr apply_t<detail::op_neg, A> operator-(const A &a) {
+constexpr apply_t<detail::op_neg, A> operator-(const A& a) {
   return apply(detail::op_neg{}, a);
 }
 template <class A>
-constexpr apply_t<detail::op_cmp, A> operator~(const A &a) {
+constexpr apply_t<detail::op_cmp, A> operator~(const A& a) {
   return apply(detail::op_cmp{}, a);
 }
 template <class A>
-constexpr apply_t<detail::op_not, A> operator!(const A &a) {
+constexpr apply_t<detail::op_not, A> operator!(const A& a) {
   return apply(detail::op_not{}, a);
 }
 /** @} */
@@ -1424,108 +1417,108 @@ constexpr apply_t<detail::op_not, A> operator!(const A &a) {
  *  @{
  */
 template <class A, class B>
-constexpr apply_t<detail::op_add, A, B> operator+(const A &a, const B &b) {
+constexpr apply_t<detail::op_add, A, B> operator+(const A& a, const B& b) {
   return apply(detail::op_add{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_sub, A, B> operator-(const A &a, const B &b) {
+constexpr apply_t<detail::op_sub, A, B> operator-(const A& a, const B& b) {
   return apply(detail::op_sub{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_mul, A, B> cmul(const A &a, const B &b) {
+constexpr apply_t<detail::op_mul, A, B> cmul(const A& a, const B& b) {
   return apply(detail::op_mul{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_div, A, B> operator/(const A &a, const B &b) {
+constexpr apply_t<detail::op_div, A, B> operator/(const A& a, const B& b) {
   return apply(detail::op_div{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_mod, A, B> operator%(const A &a, const B &b) {
+constexpr apply_t<detail::op_mod, A, B> operator%(const A& a, const B& b) {
   return apply(detail::op_mod{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_un, A, B> operator|(const A &a, const B &b) {
+constexpr apply_t<detail::op_un, A, B> operator|(const A& a, const B& b) {
   return apply(detail::op_un{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_xor, A, B> operator^(const A &a, const B &b) {
+constexpr apply_t<detail::op_xor, A, B> operator^(const A& a, const B& b) {
   return apply(detail::op_xor{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_int, A, B> operator&(const A &a, const B &b) {
+constexpr apply_t<detail::op_int, A, B> operator&(const A& a, const B& b) {
   return apply(detail::op_int{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_lsh, A, B> operator<<(const A &a, const B &b) {
+constexpr apply_t<detail::op_lsh, A, B> operator<<(const A& a, const B& b) {
   return apply(detail::op_lsh{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_rsh, A, B> operator>>(const A &a, const B &b) {
+constexpr apply_t<detail::op_rsh, A, B> operator>>(const A& a, const B& b) {
   return apply(detail::op_rsh{}, a, b);
 }
 
 // Binary `operator *` represents the algebraic matrix product - use cmul(a, b)
 // for the Hadamard (component-wise) product.
 template <class A, class B>
-constexpr auto operator*(const A &a, const B &b) {
+constexpr auto operator*(const A& a, const B& b) {
   return mul(a, b);
 }
 
 // Binary assignment operators a $= b is always defined as though it were
 // explicitly written a = a $ b
 template <class A, class B>
-constexpr auto operator+=(A &a, const B &b) -> decltype(a = a + b) {
+constexpr auto operator+=(A& a, const B& b) -> decltype(a = a + b) {
   return a = a + b;
 }
 template <class A, class B>
-constexpr auto operator-=(A &a, const B &b) -> decltype(a = a - b) {
+constexpr auto operator-=(A& a, const B& b) -> decltype(a = a - b) {
   return a = a - b;
 }
 template <class A, class B>
-constexpr auto operator*=(A &a, const B &b) -> decltype(a = a * b) {
+constexpr auto operator*=(A& a, const B& b) -> decltype(a = a * b) {
   return a = a * b;
 }
 template <class A, class B>
-constexpr auto operator/=(A &a, const B &b) -> decltype(a = a / b) {
+constexpr auto operator/=(A& a, const B& b) -> decltype(a = a / b) {
   return a = a / b;
 }
 template <class A, class B>
-constexpr auto operator%=(A &a, const B &b) -> decltype(a = a % b) {
+constexpr auto operator%=(A& a, const B& b) -> decltype(a = a % b) {
   return a = a % b;
 }
 template <class A, class B>
-constexpr auto operator|=(A &a, const B &b) -> decltype(a = a | b) {
+constexpr auto operator|=(A& a, const B& b) -> decltype(a = a | b) {
   return a = a | b;
 }
 template <class A, class B>
-constexpr auto operator^=(A &a, const B &b) -> decltype(a = a ^ b) {
+constexpr auto operator^=(A& a, const B& b) -> decltype(a = a ^ b) {
   return a = a ^ b;
 }
 template <class A, class B>
-constexpr auto operator&=(A &a, const B &b) -> decltype(a = a & b) {
+constexpr auto operator&=(A& a, const B& b) -> decltype(a = a & b) {
   return a = a & b;
 }
 template <class A, class B>
-constexpr auto operator<<=(A &a, const B &b) -> decltype(a = a << b) {
+constexpr auto operator<<=(A& a, const B& b) -> decltype(a = a << b) {
   return a = a << b;
 }
 template <class A, class B>
-constexpr auto operator>>=(A &a, const B &b) -> decltype(a = a >> b) {
+constexpr auto operator>>=(A& a, const B& b) -> decltype(a = a >> b) {
   return a = a >> b;
 }
 /** @} */
 
-/** @addtogroup swizzles
+/** @defgroup swizzles Swizzles
+ * Swizzles and subobjects.
  * @ingroup LinAlg
- * @brief Swizzles and subobjects.
- *  @{
+ * @{
  */
 /**
  * @brief Returns a vector containing the specified ordered indices, e.g.
  * linalg::swizzle<1, 2, 0>(vec4(4, 5, 6, 7)) == vec3(5, 6, 4)
  */
 template <int... I, class T, int M>
-constexpr vec<T, sizeof...(I)> swizzle(const vec<T, M> &a) {
+constexpr vec<T, sizeof...(I)> swizzle(const vec<T, M>& a) {
   return {detail::getter<I>{}(a)...};
 }
 /**
@@ -1533,7 +1526,7 @@ constexpr vec<T, sizeof...(I)> swizzle(const vec<T, M> &a) {
  * linalg::subvec<1, 4>(vec4(4, 5, 6, 7)) == vec3(5, 6, 7)
  */
 template <int I0, int I1, class T, int M>
-constexpr vec<T, I1 - I0> subvec(const vec<T, M> &a) {
+constexpr vec<T, I1 - I0> subvec(const vec<T, M>& a) {
   return detail::swizzle(a, detail::make_seq<I0, I1>{});
 }
 /**
@@ -1541,7 +1534,7 @@ constexpr vec<T, I1 - I0> subvec(const vec<T, M> &a) {
  * linalg::submat<rowStart, colStart, rowEnd, colEnd>
  */
 template <int I0, int J0, int I1, int J1, class T, int M, int N>
-constexpr mat<T, I1 - I0, J1 - J0> submat(const mat<T, M, N> &a) {
+constexpr mat<T, I1 - I0, J1 - J0> submat(const mat<T, M, N>& a) {
   return detail::swizzle(a, detail::make_seq<I0, I1>{},
                          detail::make_seq<J0, J1>{});
 }
@@ -1553,79 +1546,79 @@ constexpr mat<T, I1 - I0, J1 - J0> submat(const mat<T, M, N> &a) {
  *  @{
  */
 template <class A>
-constexpr apply_t<detail::std_isfinite, A> isfinite(const A &a) {
+constexpr apply_t<detail::std_isfinite, A> isfinite(const A& a) {
   return apply(detail::std_isfinite{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_abs, A> abs(const A &a) {
+constexpr apply_t<detail::std_abs, A> abs(const A& a) {
   return apply(detail::std_abs{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_floor, A> floor(const A &a) {
+constexpr apply_t<detail::std_floor, A> floor(const A& a) {
   return apply(detail::std_floor{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_ceil, A> ceil(const A &a) {
+constexpr apply_t<detail::std_ceil, A> ceil(const A& a) {
   return apply(detail::std_ceil{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_exp, A> exp(const A &a) {
+constexpr apply_t<detail::std_exp, A> exp(const A& a) {
   return apply(detail::std_exp{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_log, A> log(const A &a) {
+constexpr apply_t<detail::std_log, A> log(const A& a) {
   return apply(detail::std_log{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_log2, A> log2(const A &a) {
+constexpr apply_t<detail::std_log2, A> log2(const A& a) {
   return apply(detail::std_log2{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_log10, A> log10(const A &a) {
+constexpr apply_t<detail::std_log10, A> log10(const A& a) {
   return apply(detail::std_log10{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_sqrt, A> sqrt(const A &a) {
+constexpr apply_t<detail::std_sqrt, A> sqrt(const A& a) {
   return apply(detail::std_sqrt{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_sin, A> sin(const A &a) {
+constexpr apply_t<detail::std_sin, A> sin(const A& a) {
   return apply(detail::std_sin{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_cos, A> cos(const A &a) {
+constexpr apply_t<detail::std_cos, A> cos(const A& a) {
   return apply(detail::std_cos{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_tan, A> tan(const A &a) {
+constexpr apply_t<detail::std_tan, A> tan(const A& a) {
   return apply(detail::std_tan{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_asin, A> asin(const A &a) {
+constexpr apply_t<detail::std_asin, A> asin(const A& a) {
   return apply(detail::std_asin{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_acos, A> acos(const A &a) {
+constexpr apply_t<detail::std_acos, A> acos(const A& a) {
   return apply(detail::std_acos{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_atan, A> atan(const A &a) {
+constexpr apply_t<detail::std_atan, A> atan(const A& a) {
   return apply(detail::std_atan{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_sinh, A> sinh(const A &a) {
+constexpr apply_t<detail::std_sinh, A> sinh(const A& a) {
   return apply(detail::std_sinh{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_cosh, A> cosh(const A &a) {
+constexpr apply_t<detail::std_cosh, A> cosh(const A& a) {
   return apply(detail::std_cosh{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_tanh, A> tanh(const A &a) {
+constexpr apply_t<detail::std_tanh, A> tanh(const A& a) {
   return apply(detail::std_tanh{}, a);
 }
 template <class A>
-constexpr apply_t<detail::std_round, A> round(const A &a) {
+constexpr apply_t<detail::std_round, A> round(const A& a) {
   return apply(detail::std_round{}, a);
 }
 /** @} */
@@ -1637,19 +1630,19 @@ constexpr apply_t<detail::std_round, A> round(const A &a) {
  *  @{
  */
 template <class A, class B>
-constexpr apply_t<detail::std_fmod, A, B> fmod(const A &a, const B &b) {
+constexpr apply_t<detail::std_fmod, A, B> fmod(const A& a, const B& b) {
   return apply(detail::std_fmod{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::std_pow, A, B> pow(const A &a, const B &b) {
+constexpr apply_t<detail::std_pow, A, B> pow(const A& a, const B& b) {
   return apply(detail::std_pow{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::std_atan2, A, B> atan2(const A &a, const B &b) {
+constexpr apply_t<detail::std_atan2, A, B> atan2(const A& a, const B& b) {
   return apply(detail::std_atan2{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::std_copysign, A, B> copysign(const A &a, const B &b) {
+constexpr apply_t<detail::std_copysign, A, B> copysign(const A& a, const B& b) {
   return apply(detail::std_copysign{}, a, b);
 }
 /** @} */
@@ -1661,27 +1654,27 @@ constexpr apply_t<detail::std_copysign, A, B> copysign(const A &a, const B &b) {
  *  @{
  */
 template <class A, class B>
-constexpr apply_t<detail::op_eq, A, B> equal(const A &a, const B &b) {
+constexpr apply_t<detail::op_eq, A, B> equal(const A& a, const B& b) {
   return apply(detail::op_eq{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_ne, A, B> nequal(const A &a, const B &b) {
+constexpr apply_t<detail::op_ne, A, B> nequal(const A& a, const B& b) {
   return apply(detail::op_ne{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_lt, A, B> less(const A &a, const B &b) {
+constexpr apply_t<detail::op_lt, A, B> less(const A& a, const B& b) {
   return apply(detail::op_lt{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_gt, A, B> greater(const A &a, const B &b) {
+constexpr apply_t<detail::op_gt, A, B> greater(const A& a, const B& b) {
   return apply(detail::op_gt{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_le, A, B> lequal(const A &a, const B &b) {
+constexpr apply_t<detail::op_le, A, B> lequal(const A& a, const B& b) {
   return apply(detail::op_le{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::op_ge, A, B> gequal(const A &a, const B &b) {
+constexpr apply_t<detail::op_ge, A, B> gequal(const A& a, const B& b) {
   return apply(detail::op_ge{}, a, b);
 }
 /** @} */
@@ -1693,19 +1686,19 @@ constexpr apply_t<detail::op_ge, A, B> gequal(const A &a, const B &b) {
  *  @{
  */
 template <class A, class B>
-constexpr apply_t<detail::min, A, B> min(const A &a, const B &b) {
+constexpr apply_t<detail::min, A, B> min(const A& a, const B& b) {
   return apply(detail::min{}, a, b);
 }
 template <class A, class B>
-constexpr apply_t<detail::max, A, B> max(const A &a, const B &b) {
+constexpr apply_t<detail::max, A, B> max(const A& a, const B& b) {
   return apply(detail::max{}, a, b);
 }
 /**
  * @brief Clamps the components of x between l and h, provided l[i] < h[i].
  */
 template <class X, class L, class H>
-constexpr apply_t<detail::clamp, X, L, H> clamp(const X &x, const L &l,
-                                                const H &h) {
+constexpr apply_t<detail::clamp, X, L, H> clamp(const X& x, const L& l,
+                                                const H& h) {
   return apply(detail::clamp{}, x, l, h);
 }
 /**
@@ -1713,8 +1706,8 @@ constexpr apply_t<detail::clamp, X, L, H> clamp(const X &x, const L &l,
  * true and from b otherwise.
  */
 template <class P, class A, class B>
-constexpr apply_t<detail::select, P, A, B> select(const P &p, const A &a,
-                                                  const B &b) {
+constexpr apply_t<detail::select, P, A, B> select(const P& p, const A& a,
+                                                  const B& b) {
   return apply(detail::select{}, p, a, b);
 }
 /**
@@ -1722,36 +1715,36 @@ constexpr apply_t<detail::select, P, A, B> select(const P &p, const A &a,
  * [a, b] will result if t is outside [0, 1].
  */
 template <class A, class B, class T>
-constexpr apply_t<detail::lerp, A, B, T> lerp(const A &a, const B &b,
-                                              const T &t) {
+constexpr apply_t<detail::lerp, A, B, T> lerp(const A& a, const B& b,
+                                              const T& t) {
   return apply(detail::lerp{}, a, b, t);
 }
 /** @} */
 
-/** @addtogroup vec_algebra
+/** @defgroup vec_algebra Vector Algebra
+ * Support for vector algebra.
  * @ingroup LinAlg
- * @brief Support for vector algebra.
  *  @{
  */
 /**
  * @brief shorthand for `cross({a.x,a.y,0}, {b.x,b.y,0}).z`
  */
 template <class T>
-constexpr T cross(const vec<T, 2> &a, const vec<T, 2> &b) {
+constexpr T cross(const vec<T, 2>& a, const vec<T, 2>& b) {
   return a.x * b.y - a.y * b.x;
 }
 /**
  * @brief shorthand for `cross({0,0,a.z}, {b.x,b.y,0}).xy()`
  */
 template <class T>
-constexpr vec<T, 2> cross(T a, const vec<T, 2> &b) {
+constexpr vec<T, 2> cross(T a, const vec<T, 2>& b) {
   return {-a * b.y, a * b.x};
 }
 /**
  * @brief shorthand for `cross({a.x,a.y,0}, {0,0,b.z}).xy()`
  */
 template <class T>
-constexpr vec<T, 2> cross(const vec<T, 2> &a, T b) {
+constexpr vec<T, 2> cross(const vec<T, 2>& a, T b) {
   return {a.y * b, -a.x * b};
 }
 /**
@@ -1759,7 +1752,7 @@ constexpr vec<T, 2> cross(const vec<T, 2> &a, T b) {
  * product](https://en.wikipedia.org/wiki/Cross_product) of vectors `a` and `b`
  */
 template <class T>
-constexpr vec<T, 3> cross(const vec<T, 3> &a, const vec<T, 3> &b) {
+constexpr vec<T, 3> cross(const vec<T, 3>& a, const vec<T, 3>& b) {
   return {a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x};
 }
 /**
@@ -1767,21 +1760,21 @@ constexpr vec<T, 3> cross(const vec<T, 3> &a, const vec<T, 3> &b) {
  * vectors `a` and `b`
  */
 template <class T, int M>
-constexpr T dot(const vec<T, M> &a, const vec<T, M> &b) {
+constexpr T dot(const vec<T, M>& a, const vec<T, M>& b) {
   return sum(a * b);
 }
 /**
  * @brief *square* of the length or magnitude of vector `a`
  */
 template <class T, int M>
-constexpr T length2(const vec<T, M> &a) {
+constexpr T length2(const vec<T, M>& a) {
   return dot(a, a);
 }
 /**
  * @brief length or magnitude of a vector `a`
  */
 template <class T, int M>
-T length(const vec<T, M> &a) {
+T length(const vec<T, M>& a) {
   return std::sqrt(length2(a));
 }
 /**
@@ -1790,7 +1783,7 @@ T length(const vec<T, M> &a) {
 
  */
 template <class T, int M>
-vec<T, M> normalize(const vec<T, M> &a) {
+vec<T, M> normalize(const vec<T, M>& a) {
   return a / length(a);
 }
 /**
@@ -1799,7 +1792,7 @@ vec<T, M> normalize(const vec<T, M> &a) {
  * `a` and `b`
  */
 template <class T, int M>
-constexpr T distance2(const vec<T, M> &a, const vec<T, M> &b) {
+constexpr T distance2(const vec<T, M>& a, const vec<T, M>& b) {
   return length2(b - a);
 }
 /**
@@ -1807,14 +1800,14 @@ constexpr T distance2(const vec<T, M> &a, const vec<T, M> &b) {
  * between points `a` and `b`
  */
 template <class T, int M>
-T distance(const vec<T, M> &a, const vec<T, M> &b) {
+T distance(const vec<T, M>& a, const vec<T, M>& b) {
   return length(b - a);
 }
 /**
  * @brief Return the angle in radians between two unit vectors.
  */
 template <class T, int M>
-T uangle(const vec<T, M> &a, const vec<T, M> &b) {
+T uangle(const vec<T, M>& a, const vec<T, M>& b) {
   T d = dot(a, b);
   return d > 1 ? 0 : std::acos(d < -1 ? -1 : d);
 }
@@ -1822,7 +1815,7 @@ T uangle(const vec<T, M> &a, const vec<T, M> &b) {
  * @brief Return the angle in radians between two non-unit vectors.
  */
 template <class T, int M>
-T angle(const vec<T, M> &a, const vec<T, M> &b) {
+T angle(const vec<T, M>& a, const vec<T, M>& b) {
   return uangle(normalize(a), normalize(b));
 }
 /**
@@ -1830,7 +1823,7 @@ T angle(const vec<T, M> &a, const vec<T, M> &b) {
  * [radians](https://en.wikipedia.org/wiki/Radian)
  */
 template <class T>
-vec<T, 2> rot(T a, const vec<T, 2> &v) {
+vec<T, 2> rot(T a, const vec<T, 2>& v) {
   const T s = std::sin(a), c = std::cos(a);
   return {v.x * c - v.y * s, v.x * s + v.y * c};
 }
@@ -1839,7 +1832,7 @@ vec<T, 2> rot(T a, const vec<T, 2> &v) {
  * [radians](https://en.wikipedia.org/wiki/Radian) around the X axis
  */
 template <class T>
-vec<T, 3> rotx(T a, const vec<T, 3> &v) {
+vec<T, 3> rotx(T a, const vec<T, 3>& v) {
   const T s = std::sin(a), c = std::cos(a);
   return {v.x, v.y * c - v.z * s, v.y * s + v.z * c};
 }
@@ -1848,7 +1841,7 @@ vec<T, 3> rotx(T a, const vec<T, 3> &v) {
  * [radians](https://en.wikipedia.org/wiki/Radian) around the Y axis
  */
 template <class T>
-vec<T, 3> roty(T a, const vec<T, 3> &v) {
+vec<T, 3> roty(T a, const vec<T, 3>& v) {
   const T s = std::sin(a), c = std::cos(a);
   return {v.x * c + v.z * s, v.y, -v.x * s + v.z * c};
 }
@@ -1857,7 +1850,7 @@ vec<T, 3> roty(T a, const vec<T, 3> &v) {
  * [radians](https://en.wikipedia.org/wiki/Radian) around the Z axis
  */
 template <class T>
-vec<T, 3> rotz(T a, const vec<T, 3> &v) {
+vec<T, 3> rotz(T a, const vec<T, 3>& v) {
   const T s = std::sin(a), c = std::cos(a);
   return {v.x * c - v.y * s, v.x * s + v.y * c, v.z};
 }
@@ -1865,7 +1858,7 @@ vec<T, 3> rotz(T a, const vec<T, 3> &v) {
  * @brief shorthand for `normalize(lerp(a,b,t))`
  */
 template <class T, int M>
-vec<T, M> nlerp(const vec<T, M> &a, const vec<T, M> &b, T t) {
+vec<T, M> nlerp(const vec<T, M>& a, const vec<T, M>& b, T t) {
   return normalize(lerp(a, b, t));
 }
 /**
@@ -1874,7 +1867,7 @@ vec<T, M> nlerp(const vec<T, M> &a, const vec<T, M> &b, T t) {
  * parameter `t`
  */
 template <class T, int M>
-vec<T, M> slerp(const vec<T, M> &a, const vec<T, M> &b, T t) {
+vec<T, M> slerp(const vec<T, M>& a, const vec<T, M>& b, T t) {
   T th = uangle(a, b);
   return th == 0 ? a
                  : a * (std::sin(th * (1 - t)) / std::sin(th)) +
@@ -1882,10 +1875,10 @@ vec<T, M> slerp(const vec<T, M> &a, const vec<T, M> &b, T t) {
 }
 /** @} */
 
-/** @addtogroup quaternions
+/** @defgroup quaternions Quaternions
+ * Support for quaternion algebra using 4D vectors of
+ * arbitrary length, representing xi + yj + zk + w.
  * @ingroup LinAlg
- * @brief Support for quaternion algebra using 4D vectors of arbitrary length,
- * representing xi + yj + zk + w.
  *  @{
  */
 /**
@@ -1894,7 +1887,7 @@ vec<T, M> slerp(const vec<T, M> &a, const vec<T, M> &b, T t) {
  * of quaternion `q`
  */
 template <class T>
-constexpr vec<T, 4> qconj(const vec<T, 4> &q) {
+constexpr vec<T, 4> qconj(const vec<T, 4>& q) {
   return {-q.x, -q.y, -q.z, q.w};
 }
 /**
@@ -1903,7 +1896,7 @@ constexpr vec<T, 4> qconj(const vec<T, 4> &q) {
  * of quaternion `q` (undefined for zero-length quaternions)
  */
 template <class T>
-vec<T, 4> qinv(const vec<T, 4> &q) {
+vec<T, 4> qinv(const vec<T, 4>& q) {
   return qconj(q) / length2(q);
 }
 /**
@@ -1912,7 +1905,7 @@ vec<T, 4> qinv(const vec<T, 4> &q) {
  * of quaternion `q`
  */
 template <class T>
-vec<T, 4> qexp(const vec<T, 4> &q) {
+vec<T, 4> qexp(const vec<T, 4>& q) {
   const auto v = q.xyz();
   const auto vv = length(v);
   return std::exp(q.w) *
@@ -1924,7 +1917,7 @@ vec<T, 4> qexp(const vec<T, 4> &q) {
  * of quaternion `q`
  */
 template <class T>
-vec<T, 4> qlog(const vec<T, 4> &q) {
+vec<T, 4> qlog(const vec<T, 4>& q) {
   const auto v = q.xyz();
   const auto vv = length(v), qq = length(q);
   return {v * (vv > 0 ? std::acos(q.w / qq) / vv : 0), std::log(qq)};
@@ -1933,7 +1926,7 @@ vec<T, 4> qlog(const vec<T, 4> &q) {
  * @brief quaternion `q` raised to the exponent `p`
  */
 template <class T>
-vec<T, 4> qpow(const vec<T, 4> &q, const T &p) {
+vec<T, 4> qpow(const vec<T, 4>& q, const T& p) {
   const auto v = q.xyz();
   const auto vv = length(v), qq = length(q), th = std::acos(q.w / qq);
   return std::pow(qq, p) *
@@ -1945,7 +1938,7 @@ vec<T, 4> qpow(const vec<T, 4> &q, const T &p) {
  * quaternions `a` and `b`
  */
 template <class T>
-constexpr vec<T, 4> qmul(const vec<T, 4> &a, const vec<T, 4> &b) {
+constexpr vec<T, 4> qmul(const vec<T, 4>& a, const vec<T, 4>& b) {
   return {a.x * b.w + a.w * b.x + a.y * b.z - a.z * b.y,
           a.y * b.w + a.w * b.y + a.z * b.x - a.x * b.z,
           a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x,
@@ -1955,21 +1948,21 @@ constexpr vec<T, 4> qmul(const vec<T, 4> &a, const vec<T, 4> &b) {
  * @brief Multiply as many input quaternions together as desired.
  */
 template <class T, class... R>
-constexpr vec<T, 4> qmul(const vec<T, 4> &a, R... r) {
+constexpr vec<T, 4> qmul(const vec<T, 4>& a, R... r) {
   return qmul(a, qmul(r...));
 }
 /** @} */
 
-/** @addtogroup quaternion_rotation
+/** @defgroup quaternion_rotation Quaternion Rotations
+ * Support for 3D spatial rotations using normalized quaternions.
  * @ingroup LinAlg
- * @brief Support for 3D spatial rotations using normalized quaternions.
  *  @{
  */
 /**
  * @brief efficient shorthand for `qrot(q, {1,0,0})`
  */
 template <class T>
-constexpr vec<T, 3> qxdir(const vec<T, 4> &q) {
+constexpr vec<T, 3> qxdir(const vec<T, 4>& q) {
   return {q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z,
           (q.x * q.y + q.z * q.w) * 2, (q.z * q.x - q.y * q.w) * 2};
 }
@@ -1977,7 +1970,7 @@ constexpr vec<T, 3> qxdir(const vec<T, 4> &q) {
  * @brief efficient shorthand for `qrot(q, {0,1,0})`
  */
 template <class T>
-constexpr vec<T, 3> qydir(const vec<T, 4> &q) {
+constexpr vec<T, 3> qydir(const vec<T, 4>& q) {
   return {(q.x * q.y - q.z * q.w) * 2,
           q.w * q.w - q.x * q.x + q.y * q.y - q.z * q.z,
           (q.y * q.z + q.x * q.w) * 2};
@@ -1986,7 +1979,7 @@ constexpr vec<T, 3> qydir(const vec<T, 4> &q) {
  * @brief efficient shorthand for `qrot(q, {0,0,1})`
  */
 template <class T>
-constexpr vec<T, 3> qzdir(const vec<T, 4> &q) {
+constexpr vec<T, 3> qzdir(const vec<T, 4>& q) {
   return {(q.z * q.x + q.y * q.w) * 2, (q.y * q.z - q.x * q.w) * 2,
           q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z};
 }
@@ -1994,14 +1987,14 @@ constexpr vec<T, 3> qzdir(const vec<T, 4> &q) {
  * @brief Create an equivalent mat3 rotation matrix from the input quaternion.
  */
 template <class T>
-constexpr mat<T, 3, 3> qmat(const vec<T, 4> &q) {
+constexpr mat<T, 3, 3> qmat(const vec<T, 4>& q) {
   return {qxdir(q), qydir(q), qzdir(q)};
 }
 /**
  * @brief Rotate a vector by a quaternion.
  */
 template <class T>
-constexpr vec<T, 3> qrot(const vec<T, 4> &q, const vec<T, 3> &v) {
+constexpr vec<T, 3> qrot(const vec<T, 4>& q, const vec<T, 3>& v) {
   return qxdir(q) * v.x + qydir(q) * v.y + qzdir(q) * v.z;
 }
 /**
@@ -2009,7 +2002,7 @@ constexpr vec<T, 3> qrot(const vec<T, 4> &q, const vec<T, 3> &v) {
  * input normalized quaternion.
  */
 template <class T>
-T qangle(const vec<T, 4> &q) {
+T qangle(const vec<T, 4>& q) {
   return std::atan2(length(q.xyz()), q.w) * 2;
 }
 /**
@@ -2017,7 +2010,7 @@ T qangle(const vec<T, 4> &q) {
  * input normalized quaternion.
  */
 template <class T>
-vec<T, 3> qaxis(const vec<T, 4> &q) {
+vec<T, 3> qaxis(const vec<T, 4>& q) {
   return normalize(q.xyz());
 }
 /**
@@ -2025,14 +2018,14 @@ vec<T, 3> qaxis(const vec<T, 4> &q) {
  * geometrically sensible, consider qslerp instead.
  */
 template <class T>
-vec<T, 4> qnlerp(const vec<T, 4> &a, const vec<T, 4> &b, T t) {
+vec<T, 4> qnlerp(const vec<T, 4>& a, const vec<T, 4>& b, T t) {
   return nlerp(a, dot(a, b) < 0 ? -b : b, t);
 }
 /**
  * @brief Spherical linear interpolation that takes the shortest path.
  */
 template <class T>
-vec<T, 4> qslerp(const vec<T, 4> &a, const vec<T, 4> &b, T t) {
+vec<T, 4> qslerp(const vec<T, 4>& a, const vec<T, 4>& b, T t) {
   return slerp(a, dot(a, b) < 0 ? -b : b, t);
 }
 /**
@@ -2040,7 +2033,7 @@ vec<T, 4> qslerp(const vec<T, 4> &a, const vec<T, 4> &b, T t) {
  * radians about the provided axis.
  */
 template <class T>
-vec<T, 4> constexpr rotation_quat(const vec<T, 3> &axis, T angle) {
+vec<T, 4> constexpr rotation_quat(const vec<T, 3>& axis, T angle) {
   return {axis * std::sin(angle / 2), std::cos(angle / 2)};
 }
 /**
@@ -2048,13 +2041,13 @@ vec<T, 4> constexpr rotation_quat(const vec<T, 3> &axis, T angle) {
  * from orig vector to dest vector.
  */
 template <class T>
-vec<T, 4> rotation_quat(const vec<T, 3> &orig, const vec<T, 3> &dest);
+vec<T, 4> rotation_quat(const vec<T, 3>& orig, const vec<T, 3>& dest);
 /**
  * @brief Returns a normalized quaternion representing the input rotation
  * matrix, which should be orthonormal.
  */
 template <class T>
-vec<T, 4> rotation_quat(const mat<T, 3, 3> &m);
+vec<T, 4> rotation_quat(const mat<T, 3, 3>& m);
 /** @} */
 
 /** @addtogroup mat_algebra
@@ -2063,167 +2056,167 @@ vec<T, 4> rotation_quat(const mat<T, 3, 3> &m);
  *  @{
  */
 template <class T, int M>
-constexpr vec<T, M> mul(const vec<T, M> &a, const T &b) {
+constexpr vec<T, M> mul(const vec<T, M>& a, const T& b) {
   return cmul(a, b);
 }
 template <class T, int M>
-constexpr vec<T, M> mul(const T &b, const vec<T, M> &a) {
+constexpr vec<T, M> mul(const T& b, const vec<T, M>& a) {
   return cmul(b, a);
 }
 template <class T, int M, int N>
-constexpr mat<T, M, N> mul(const mat<T, M, N> &a, const T &b) {
+constexpr mat<T, M, N> mul(const mat<T, M, N>& a, const T& b) {
   return cmul(a, b);
 }
 template <class T, int M, int N>
-constexpr mat<T, M, N> mul(const T &b, const mat<T, M, N> &a) {
+constexpr mat<T, M, N> mul(const T& b, const mat<T, M, N>& a) {
   return cmul(b, a);
 }
 template <class T, int M>
-constexpr vec<T, M> mul(const vec<T, M> &a, const vec<T, M> &b) {
+constexpr vec<T, M> mul(const vec<T, M>& a, const vec<T, M>& b) {
   return cmul(a, b);
 }
 template <class T, int M>
-constexpr vec<T, M> mul(const mat<T, M, 1> &a, const vec<T, 1> &b) {
+constexpr vec<T, M> mul(const mat<T, M, 1>& a, const vec<T, 1>& b) {
   return a.x * b.x;
 }
 template <class T, int M>
-constexpr vec<T, M> mul(const mat<T, M, 2> &a, const vec<T, 2> &b) {
+constexpr vec<T, M> mul(const mat<T, M, 2>& a, const vec<T, 2>& b) {
   return a.x * b.x + a.y * b.y;
 }
 template <class T, int M>
-constexpr vec<T, M> mul(const mat<T, M, 3> &a, const vec<T, 3> &b) {
+constexpr vec<T, M> mul(const mat<T, M, 3>& a, const vec<T, 3>& b) {
   return a.x * b.x + a.y * b.y + a.z * b.z;
 }
 template <class T, int M>
-constexpr vec<T, M> mul(const mat<T, M, 4> &a, const vec<T, 4> &b) {
+constexpr vec<T, M> mul(const mat<T, M, 4>& a, const vec<T, 4>& b) {
   return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
 }
 template <class T, int M, int N>
-constexpr mat<T, M, 1> mul(const mat<T, M, N> &a, const mat<T, N, 1> &b) {
+constexpr mat<T, M, 1> mul(const mat<T, M, N>& a, const mat<T, N, 1>& b) {
   return {mul(a, b.x)};
 }
 template <class T, int M, int N>
-constexpr mat<T, M, 2> mul(const mat<T, M, N> &a, const mat<T, N, 2> &b) {
+constexpr mat<T, M, 2> mul(const mat<T, M, N>& a, const mat<T, N, 2>& b) {
   return {mul(a, b.x), mul(a, b.y)};
 }
 template <class T, int M, int N>
-constexpr mat<T, M, 3> mul(const mat<T, M, N> &a, const mat<T, N, 3> &b) {
+constexpr mat<T, M, 3> mul(const mat<T, M, N>& a, const mat<T, N, 3>& b) {
   return {mul(a, b.x), mul(a, b.y), mul(a, b.z)};
 }
 template <class T, int M, int N>
-constexpr mat<T, M, 4> mul(const mat<T, M, N> &a, const mat<T, N, 4> &b) {
+constexpr mat<T, M, 4> mul(const mat<T, M, N>& a, const mat<T, N, 4>& b) {
   return {mul(a, b.x), mul(a, b.y), mul(a, b.z), mul(a, b.w)};
 }
 template <class T, int M, int N, int P>
-constexpr vec<T, M> mul(const mat<T, M, N> &a, const mat<T, N, P> &b,
-                        const vec<T, P> &c) {
+constexpr vec<T, M> mul(const mat<T, M, N>& a, const mat<T, N, P>& b,
+                        const vec<T, P>& c) {
   return mul(mul(a, b), c);
 }
 template <class T, int M, int N, int P, int Q>
-constexpr mat<T, M, Q> mul(const mat<T, M, N> &a, const mat<T, N, P> &b,
-                           const mat<T, P, Q> &c) {
+constexpr mat<T, M, Q> mul(const mat<T, M, N>& a, const mat<T, N, P>& b,
+                           const mat<T, P, Q>& c) {
   return mul(mul(a, b), c);
 }
 template <class T, int M, int N, int P, int Q>
-constexpr vec<T, M> mul(const mat<T, M, N> &a, const mat<T, N, P> &b,
-                        const mat<T, P, Q> &c, const vec<T, Q> &d) {
+constexpr vec<T, M> mul(const mat<T, M, N>& a, const mat<T, N, P>& b,
+                        const mat<T, P, Q>& c, const vec<T, Q>& d) {
   return mul(mul(a, b, c), d);
 }
 template <class T, int M, int N, int P, int Q, int R>
-constexpr mat<T, M, R> mul(const mat<T, M, N> &a, const mat<T, N, P> &b,
-                           const mat<T, P, Q> &c, const mat<T, Q, R> &d) {
+constexpr mat<T, M, R> mul(const mat<T, M, N>& a, const mat<T, N, P>& b,
+                           const mat<T, P, Q>& c, const mat<T, Q, R>& d) {
   return mul(mul(a, b, c), d);
 }
 template <class T, int M>
-constexpr mat<T, M, 1> outerprod(const vec<T, M> &a, const vec<T, 1> &b) {
+constexpr mat<T, M, 1> outerprod(const vec<T, M>& a, const vec<T, 1>& b) {
   return {a * b.x};
 }
 template <class T, int M>
-constexpr mat<T, M, 2> outerprod(const vec<T, M> &a, const vec<T, 2> &b) {
+constexpr mat<T, M, 2> outerprod(const vec<T, M>& a, const vec<T, 2>& b) {
   return {a * b.x, a * b.y};
 }
 template <class T, int M>
-constexpr mat<T, M, 3> outerprod(const vec<T, M> &a, const vec<T, 3> &b) {
+constexpr mat<T, M, 3> outerprod(const vec<T, M>& a, const vec<T, 3>& b) {
   return {a * b.x, a * b.y, a * b.z};
 }
 template <class T, int M>
-constexpr mat<T, M, 4> outerprod(const vec<T, M> &a, const vec<T, 4> &b) {
+constexpr mat<T, M, 4> outerprod(const vec<T, M>& a, const vec<T, 4>& b) {
   return {a * b.x, a * b.y, a * b.z, a * b.w};
 }
 template <class T>
-constexpr vec<T, 1> diagonal(const mat<T, 1, 1> &a) {
+constexpr vec<T, 1> diagonal(const mat<T, 1, 1>& a) {
   return {a.x.x};
 }
 template <class T>
-constexpr vec<T, 2> diagonal(const mat<T, 2, 2> &a) {
+constexpr vec<T, 2> diagonal(const mat<T, 2, 2>& a) {
   return {a.x.x, a.y.y};
 }
 template <class T>
-constexpr vec<T, 3> diagonal(const mat<T, 3, 3> &a) {
+constexpr vec<T, 3> diagonal(const mat<T, 3, 3>& a) {
   return {a.x.x, a.y.y, a.z.z};
 }
 template <class T>
-constexpr vec<T, 4> diagonal(const mat<T, 4, 4> &a) {
+constexpr vec<T, 4> diagonal(const mat<T, 4, 4>& a) {
   return {a.x.x, a.y.y, a.z.z, a.w.w};
 }
 template <class T, int N>
-constexpr T trace(const mat<T, N, N> &a) {
+constexpr T trace(const mat<T, N, N>& a) {
   return sum(diagonal(a));
 }
 template <class T, int M>
-constexpr mat<T, M, 1> transpose(const mat<T, 1, M> &m) {
+constexpr mat<T, M, 1> transpose(const mat<T, 1, M>& m) {
   return {m.row(0)};
 }
 template <class T, int M>
-constexpr mat<T, M, 2> transpose(const mat<T, 2, M> &m) {
+constexpr mat<T, M, 2> transpose(const mat<T, 2, M>& m) {
   return {m.row(0), m.row(1)};
 }
 template <class T, int M>
-constexpr mat<T, M, 3> transpose(const mat<T, 3, M> &m) {
+constexpr mat<T, M, 3> transpose(const mat<T, 3, M>& m) {
   return {m.row(0), m.row(1), m.row(2)};
 }
 template <class T, int M>
-constexpr mat<T, M, 4> transpose(const mat<T, 4, M> &m) {
+constexpr mat<T, M, 4> transpose(const mat<T, 4, M>& m) {
   return {m.row(0), m.row(1), m.row(2), m.row(3)};
 }
 template <class T, int M>
-constexpr mat<T, 1, M> transpose(const vec<T, M> &m) {
+constexpr mat<T, 1, M> transpose(const vec<T, M>& m) {
   return transpose(mat<T, M, 1>(m));
 }
 template <class T>
-constexpr mat<T, 1, 1> adjugate(const mat<T, 1, 1> &a) {
+constexpr mat<T, 1, 1> adjugate(const mat<T, 1, 1>&) {
   return {vec<T, 1>{1}};
 }
 template <class T>
-constexpr mat<T, 2, 2> adjugate(const mat<T, 2, 2> &a) {
+constexpr mat<T, 2, 2> adjugate(const mat<T, 2, 2>& a) {
   return {{a.y.y, -a.x.y}, {-a.y.x, a.x.x}};
 }
 template <class T>
-constexpr mat<T, 3, 3> adjugate(const mat<T, 3, 3> &a);
+constexpr mat<T, 3, 3> adjugate(const mat<T, 3, 3>& a);
 template <class T>
-constexpr mat<T, 4, 4> adjugate(const mat<T, 4, 4> &a);
+constexpr mat<T, 4, 4> adjugate(const mat<T, 4, 4>& a);
 template <class T, int N>
-constexpr mat<T, N, N> comatrix(const mat<T, N, N> &a) {
+constexpr mat<T, N, N> comatrix(const mat<T, N, N>& a) {
   return transpose(adjugate(a));
 }
 template <class T>
-constexpr T determinant(const mat<T, 1, 1> &a) {
+constexpr T determinant(const mat<T, 1, 1>& a) {
   return a.x.x;
 }
 template <class T>
-constexpr T determinant(const mat<T, 2, 2> &a) {
+constexpr T determinant(const mat<T, 2, 2>& a) {
   return a.x.x * a.y.y - a.x.y * a.y.x;
 }
 template <class T>
-constexpr T determinant(const mat<T, 3, 3> &a) {
+constexpr T determinant(const mat<T, 3, 3>& a) {
   return a.x.x * (a.y.y * a.z.z - a.z.y * a.y.z) +
          a.x.y * (a.y.z * a.z.x - a.z.z * a.y.x) +
          a.x.z * (a.y.x * a.z.y - a.z.x * a.y.y);
 }
 template <class T>
-constexpr T determinant(const mat<T, 4, 4> &a);
+constexpr T determinant(const mat<T, 4, 4>& a);
 template <class T, int N>
-constexpr mat<T, N, N> inverse(const mat<T, N, N> &a) {
+constexpr mat<T, N, N> inverse(const mat<T, N, N>& a) {
   return adjugate(a) / determinant(a);
 }
 /** @} */
@@ -2234,35 +2227,35 @@ constexpr mat<T, N, N> inverse(const mat<T, N, N> &a) {
  *  @{
  */
 template <class T, int M>
-T *begin(vec<T, M> &a) {
+T* begin(vec<T, M>& a) {
   return &a.x;
 }
 template <class T, int M>
-const T *begin(const vec<T, M> &a) {
+const T* begin(const vec<T, M>& a) {
   return &a.x;
 }
 template <class T, int M>
-T *end(vec<T, M> &a) {
+T* end(vec<T, M>& a) {
   return begin(a) + M;
 }
 template <class T, int M>
-const T *end(const vec<T, M> &a) {
+const T* end(const vec<T, M>& a) {
   return begin(a) + M;
 }
 template <class T, int M, int N>
-vec<T, M> *begin(mat<T, M, N> &a) {
+vec<T, M>* begin(mat<T, M, N>& a) {
   return &a.x;
 }
 template <class T, int M, int N>
-const vec<T, M> *begin(const mat<T, M, N> &a) {
+const vec<T, M>* begin(const mat<T, M, N>& a) {
   return &a.x;
 }
 template <class T, int M, int N>
-vec<T, M> *end(mat<T, M, N> &a) {
+vec<T, M>* end(mat<T, M, N>& a) {
   return begin(a) + N;
 }
 template <class T, int M, int N>
-const vec<T, M> *end(const mat<T, M, N> &a) {
+const vec<T, M>* end(const mat<T, M, N>& a) {
   return begin(a) + N;
 }
 /** @} */
@@ -2282,30 +2275,30 @@ enum z_range {
   zero_to_one
 };  // Should projection matrices map z into the range of [-1,1] or [0,1]?
 template <class T>
-mat<T, 4, 4> translation_matrix(const vec<T, 3> &translation) {
+mat<T, 4, 4> translation_matrix(const vec<T, 3>& translation) {
   return {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {translation, 1}};
 }
 template <class T>
-mat<T, 4, 4> rotation_matrix(const vec<T, 4> &rotation) {
+mat<T, 4, 4> rotation_matrix(const vec<T, 4>& rotation) {
   return {{qxdir(rotation), 0},
           {qydir(rotation), 0},
           {qzdir(rotation), 0},
           {0, 0, 0, 1}};
 }
 template <class T>
-mat<T, 4, 4> scaling_matrix(const vec<T, 3> &scaling) {
+mat<T, 4, 4> scaling_matrix(const vec<T, 3>& scaling) {
   return {{scaling.x, 0, 0, 0},
           {0, scaling.y, 0, 0},
           {0, 0, scaling.z, 0},
           {0, 0, 0, 1}};
 }
 template <class T>
-mat<T, 4, 4> pose_matrix(const vec<T, 4> &q, const vec<T, 3> &p) {
+mat<T, 4, 4> pose_matrix(const vec<T, 4>& q, const vec<T, 3>& p) {
   return {{qxdir(q), 0}, {qydir(q), 0}, {qzdir(q), 0}, {p, 1}};
 }
 template <class T>
-mat<T, 4, 4> lookat_matrix(const vec<T, 3> &eye, const vec<T, 3> &center,
-                           const vec<T, 3> &view_y_dir, fwd_axis fwd = neg_z);
+mat<T, 4, 4> lookat_matrix(const vec<T, 3>& eye, const vec<T, 3>& center,
+                           const vec<T, 3>& view_y_dir, fwd_axis fwd = neg_z);
 template <class T>
 mat<T, 4, 4> frustum_matrix(T x0, T x1, T y0, T y1, T n, T f,
                             fwd_axis a = neg_z, z_range z = neg_one_to_one);
@@ -2325,82 +2318,46 @@ mat<T, 4, 4> perspective_matrix(T fovy, T aspect, T n, T f, fwd_axis a = neg_z,
  */
 template <class T>
 struct converter<vec<T, 1>, std::array<T, 1>> {
-  vec<T, 1> operator()(const std::array<T, 1> &a) const { return {a[0]}; }
+  vec<T, 1> operator()(const std::array<T, 1>& a) const { return {a[0]}; }
 };
 template <class T>
 struct converter<vec<T, 2>, std::array<T, 2>> {
-  vec<T, 2> operator()(const std::array<T, 2> &a) const { return {a[0], a[1]}; }
+  vec<T, 2> operator()(const std::array<T, 2>& a) const { return {a[0], a[1]}; }
 };
 template <class T>
 struct converter<vec<T, 3>, std::array<T, 3>> {
-  vec<T, 3> operator()(const std::array<T, 3> &a) const {
+  vec<T, 3> operator()(const std::array<T, 3>& a) const {
     return {a[0], a[1], a[2]};
   }
 };
 template <class T>
 struct converter<vec<T, 4>, std::array<T, 4>> {
-  vec<T, 4> operator()(const std::array<T, 4> &a) const {
+  vec<T, 4> operator()(const std::array<T, 4>& a) const {
     return {a[0], a[1], a[2], a[3]};
   }
 };
 
 template <class T>
 struct converter<std::array<T, 1>, vec<T, 1>> {
-  std::array<T, 1> operator()(const vec<T, 1> &a) const { return {a[0]}; }
+  std::array<T, 1> operator()(const vec<T, 1>& a) const { return {a[0]}; }
 };
 template <class T>
 struct converter<std::array<T, 2>, vec<T, 2>> {
-  std::array<T, 2> operator()(const vec<T, 2> &a) const { return {a[0], a[1]}; }
+  std::array<T, 2> operator()(const vec<T, 2>& a) const { return {a[0], a[1]}; }
 };
 template <class T>
 struct converter<std::array<T, 3>, vec<T, 3>> {
-  std::array<T, 3> operator()(const vec<T, 3> &a) const {
+  std::array<T, 3> operator()(const vec<T, 3>& a) const {
     return {a[0], a[1], a[2]};
   }
 };
 template <class T>
 struct converter<std::array<T, 4>, vec<T, 4>> {
-  std::array<T, 4> operator()(const vec<T, 4> &a) const {
+  std::array<T, 4> operator()(const vec<T, 4>& a) const {
     return {a[0], a[1], a[2], a[3]};
   }
 };
 /** @} */
-
-#ifdef MANIFOLD_DEBUG
-template <class T>
-std::ostream &operator<<(std::ostream &out, const vec<T, 1> &v) {
-  return out << '{' << v[0] << '}';
-}
-template <class T>
-std::ostream &operator<<(std::ostream &out, const vec<T, 2> &v) {
-  return out << '{' << v[0] << ',' << v[1] << '}';
-}
-template <class T>
-std::ostream &operator<<(std::ostream &out, const vec<T, 3> &v) {
-  return out << '{' << v[0] << ',' << v[1] << ',' << v[2] << '}';
-}
-template <class T>
-std::ostream &operator<<(std::ostream &out, const vec<T, 4> &v) {
-  return out << '{' << v[0] << ',' << v[1] << ',' << v[2] << ',' << v[3] << '}';
-}
-
-template <class T, int M>
-std::ostream &operator<<(std::ostream &out, const mat<T, M, 1> &m) {
-  return out << '{' << m[0] << '}';
-}
-template <class T, int M>
-std::ostream &operator<<(std::ostream &out, const mat<T, M, 2> &m) {
-  return out << '{' << m[0] << ',' << m[1] << '}';
-}
-template <class T, int M>
-std::ostream &operator<<(std::ostream &out, const mat<T, M, 3> &m) {
-  return out << '{' << m[0] << ',' << m[1] << ',' << m[2] << '}';
-}
-template <class T, int M>
-std::ostream &operator<<(std::ostream &out, const mat<T, M, 4> &m) {
-  return out << '{' << m[0] << ',' << m[1] << ',' << m[2] << ',' << m[3] << '}';
-}
-#endif
 }  // namespace linalg
 
 namespace std {
@@ -2411,28 +2368,28 @@ namespace std {
  */
 template <class T>
 struct hash<linalg::vec<T, 1>> {
-  std::size_t operator()(const linalg::vec<T, 1> &v) const {
+  std::size_t operator()(const linalg::vec<T, 1>& v) const {
     std::hash<T> h;
     return h(v.x);
   }
 };
 template <class T>
 struct hash<linalg::vec<T, 2>> {
-  std::size_t operator()(const linalg::vec<T, 2> &v) const {
+  std::size_t operator()(const linalg::vec<T, 2>& v) const {
     std::hash<T> h;
     return h(v.x) ^ (h(v.y) << 1);
   }
 };
 template <class T>
 struct hash<linalg::vec<T, 3>> {
-  std::size_t operator()(const linalg::vec<T, 3> &v) const {
+  std::size_t operator()(const linalg::vec<T, 3>& v) const {
     std::hash<T> h;
     return h(v.x) ^ (h(v.y) << 1) ^ (h(v.z) << 2);
   }
 };
 template <class T>
 struct hash<linalg::vec<T, 4>> {
-  std::size_t operator()(const linalg::vec<T, 4> &v) const {
+  std::size_t operator()(const linalg::vec<T, 4>& v) const {
     std::hash<T> h;
     return h(v.x) ^ (h(v.y) << 1) ^ (h(v.z) << 2) ^ (h(v.w) << 3);
   }
@@ -2440,28 +2397,28 @@ struct hash<linalg::vec<T, 4>> {
 
 template <class T, int M>
 struct hash<linalg::mat<T, M, 1>> {
-  std::size_t operator()(const linalg::mat<T, M, 1> &v) const {
+  std::size_t operator()(const linalg::mat<T, M, 1>& v) const {
     std::hash<linalg::vec<T, M>> h;
     return h(v.x);
   }
 };
 template <class T, int M>
 struct hash<linalg::mat<T, M, 2>> {
-  std::size_t operator()(const linalg::mat<T, M, 2> &v) const {
+  std::size_t operator()(const linalg::mat<T, M, 2>& v) const {
     std::hash<linalg::vec<T, M>> h;
     return h(v.x) ^ (h(v.y) << M);
   }
 };
 template <class T, int M>
 struct hash<linalg::mat<T, M, 3>> {
-  std::size_t operator()(const linalg::mat<T, M, 3> &v) const {
+  std::size_t operator()(const linalg::mat<T, M, 3>& v) const {
     std::hash<linalg::vec<T, M>> h;
     return h(v.x) ^ (h(v.y) << M) ^ (h(v.z) << (M * 2));
   }
 };
 template <class T, int M>
 struct hash<linalg::mat<T, M, 4>> {
-  std::size_t operator()(const linalg::mat<T, M, 4> &v) const {
+  std::size_t operator()(const linalg::mat<T, M, 4>& v) const {
     std::hash<linalg::vec<T, M>> h;
     return h(v.x) ^ (h(v.y) << M) ^ (h(v.z) << (M * 2)) ^ (h(v.w) << (M * 3));
   }
@@ -2471,7 +2428,7 @@ struct hash<linalg::mat<T, M, 4>> {
 
 // Definitions of functions too long to be defined inline
 template <class T>
-constexpr linalg::mat<T, 3, 3> linalg::adjugate(const mat<T, 3, 3> &a) {
+constexpr linalg::mat<T, 3, 3> linalg::adjugate(const mat<T, 3, 3>& a) {
   return {{a.y.y * a.z.z - a.z.y * a.y.z, a.z.y * a.x.z - a.x.y * a.z.z,
            a.x.y * a.y.z - a.y.y * a.x.z},
           {a.y.z * a.z.x - a.z.z * a.y.x, a.z.z * a.x.x - a.x.z * a.z.x,
@@ -2481,7 +2438,7 @@ constexpr linalg::mat<T, 3, 3> linalg::adjugate(const mat<T, 3, 3> &a) {
 }
 
 template <class T>
-constexpr linalg::mat<T, 4, 4> linalg::adjugate(const mat<T, 4, 4> &a) {
+constexpr linalg::mat<T, 4, 4> linalg::adjugate(const mat<T, 4, 4>& a) {
   return {{a.y.y * a.z.z * a.w.w + a.w.y * a.y.z * a.z.w +
                a.z.y * a.w.z * a.y.w - a.y.y * a.w.z * a.z.w -
                a.z.y * a.y.z * a.w.w - a.w.y * a.z.z * a.y.w,
@@ -2533,7 +2490,7 @@ constexpr linalg::mat<T, 4, 4> linalg::adjugate(const mat<T, 4, 4> &a) {
 }
 
 template <class T>
-constexpr T linalg::determinant(const mat<T, 4, 4> &a) {
+constexpr T linalg::determinant(const mat<T, 4, 4>& a) {
   return a.x.x * (a.y.y * a.z.z * a.w.w + a.w.y * a.y.z * a.z.w +
                   a.z.y * a.w.z * a.y.w - a.y.y * a.w.z * a.z.w -
                   a.z.y * a.y.z * a.w.w - a.w.y * a.z.z * a.y.w) +
@@ -2549,8 +2506,8 @@ constexpr T linalg::determinant(const mat<T, 4, 4> &a) {
 }
 
 template <class T>
-linalg::vec<T, 4> linalg::rotation_quat(const vec<T, 3> &orig,
-                                        const vec<T, 3> &dest) {
+linalg::vec<T, 4> linalg::rotation_quat(const vec<T, 3>& orig,
+                                        const vec<T, 3>& dest) {
   T cosTheta = dot(orig, dest);
   if (cosTheta >= 1 - std::numeric_limits<T>::epsilon()) {
     return {0, 0, 0, 1};
@@ -2568,7 +2525,7 @@ linalg::vec<T, 4> linalg::rotation_quat(const vec<T, 3> &orig,
 }
 
 template <class T>
-linalg::vec<T, 4> linalg::rotation_quat(const mat<T, 3, 3> &m) {
+linalg::vec<T, 4> linalg::rotation_quat(const mat<T, 3, 3>& m) {
   const vec<T, 4> q{m.x.x - m.y.y - m.z.z, m.y.y - m.x.x - m.z.z,
                     m.z.z - m.x.x - m.y.y, m.x.x + m.y.y + m.z.z},
       s[]{{1, m.x.y + m.y.x, m.z.x + m.x.z, m.y.z - m.z.y},
@@ -2579,9 +2536,9 @@ linalg::vec<T, 4> linalg::rotation_quat(const mat<T, 3, 3> &m) {
 }
 
 template <class T>
-linalg::mat<T, 4, 4> linalg::lookat_matrix(const vec<T, 3> &eye,
-                                           const vec<T, 3> &center,
-                                           const vec<T, 3> &view_y_dir,
+linalg::mat<T, 4, 4> linalg::lookat_matrix(const vec<T, 3>& eye,
+                                           const vec<T, 3>& center,
+                                           const vec<T, 3>& view_y_dir,
                                            fwd_axis a) {
   const vec<T, 3> f = normalize(center - eye), z = a == pos_z ? f : -f,
                   x = normalize(cross(view_y_dir, z)), y = cross(z, x);
diff --git a/thirdparty/manifold/include/manifold/manifold.h b/thirdparty/manifold/include/manifold/manifold.h
index 9c59d7367a..8764771a01 100644
--- a/thirdparty/manifold/include/manifold/manifold.h
+++ b/thirdparty/manifold/include/manifold/manifold.h
@@ -13,12 +13,9 @@
 // limitations under the License.
 
 #pragma once
+#include <cstdint>  // uint32_t, uint64_t
 #include <functional>
-#include <memory>
-
-#ifdef MANIFOLD_EXPORT
-#include <iostream>
-#endif
+#include <memory>  // needed for shared_ptr
 
 #include "manifold/common.h"
 #include "manifold/vec_view.h"
@@ -46,11 +43,71 @@ class CsgLeafNode;
  * @brief Mesh input/output suitable for pushing directly into graphics
  * libraries.
  *
- * This may not be manifold since the verts are duplicated along property
- * boundaries that do not match. The additional merge vectors store this missing
- * information, allowing the manifold to be reconstructed. MeshGL is an alias
- * for the standard single-precision version. Use MeshGL64 to output the full
- * double precision that Manifold uses internally.
+ * The core (non-optional) parts of MeshGL are the triVerts indices buffer and
+ * the vertProperties interleaved vertex buffer, which follow the conventions of
+ * OpenGL (and other graphic libraries') buffers and are therefore generally
+ * easy to map directly to other applications' data structures.
+ *
+ * The triVerts vector has a stride of 3 and specifies triangles as
+ * vertex indices. For triVerts = [2, 4, 5, 3, 1, 6, ...], the triangles are [2,
+ * 4, 5], [3, 1, 6], etc. and likewise the halfedges are [2, 4], [4, 5], [5, 2],
+ * [3, 1], [1, 6], [6, 3], etc.
+ *
+ * The triVerts indices should form a manifold mesh: each of the 3 halfedges of
+ * each triangle should have exactly one paired halfedge in the list, defined as
+ * having the first index of one equal to the second index of the other and
+ * vice-versa. However, this is not always possible - consider e.g. a cube with
+ * normal-vector properties. Shared vertices would turn the cube into a ball by
+ * interpolating normals - the common solution is to duplicate each corner
+ * vertex into 3, each with the same position, but different normals
+ * corresponding to each face. This is exactly what should be done in MeshGL,
+ * however we request two additional vectors in this case: mergeFromVert and
+ * mergeToVert. Each vertex mergeFromVert[i] is merged into vertex
+ * mergeToVert[i], avoiding unreliable floating-point comparisons to recover the
+ * manifold topology. These merges are simply a union, so which is from and to
+ * doesn't matter.
+ *
+ * If you don't have merge vectors, you can create them with the Merge() method,
+ * however this will fail if the mesh is not already manifold within the set
+ * tolerance. For maximum reliablility, always store the merge vectors with the
+ * mesh, e.g. using the EXT_mesh_manifold extension in glTF.
+ *
+ * You can have any number of arbitrary floating-point properties per vertex,
+ * and they will all be interpolated as necessary during operations. It is up to
+ * you to keep track of which channel represents what type of data. A few of
+ * Manifold's methods allow you to specify the channel where normals data
+ * starts, in order to update it automatically for transforms and such. This
+ * will be easier if your meshes all use the same channels for properties, but
+ * this is not a requirement. Operations between meshes with different numbers
+ * of peroperties will simply use the larger numProp and pad the smaller one
+ * with zeroes.
+ *
+ * On output, the triangles are sorted into runs (runIndex, runOriginalID,
+ * runTransform) that correspond to different mesh inputs. Other 3D libraries
+ * may refer to these runs as primitives of a mesh (as in glTF) or draw calls,
+ * as they often represent different materials on different parts of the mesh.
+ * It is generally a good idea to maintain a map of OriginalIDs to materials to
+ * make it easy to reapply them after a set of Boolean operations. These runs
+ * can also be used as input, and thus also ensure a lossless roundtrip of data
+ * through MeshGL.
+ *
+ * As an example, with runIndex = [0, 6, 18, 21] and runOriginalID = [1, 3, 3],
+ * there are 7 triangles, where the first two are from the input mesh with ID 1,
+ * the next 4 are from an input mesh with ID 3, and the last triangle is from a
+ * different copy (instance) of the input mesh with ID 3. These two instances
+ * can be distinguished by their different runTransform matrices.
+ *
+ * You can reconstruct polygonal faces by assembling all the triangles that are
+ * from the same run and share the same faceID. These faces will be planar
+ * within the output tolerance.
+ *
+ * The halfedgeTangent vector is used to specify the weighted tangent vectors of
+ * each halfedge for the purpose of using the Refine methods to create a
+ * smoothly-interpolated surface. They can also be output when calculated
+ * automatically by the Smooth functions.
+ *
+ * MeshGL is an alias for the standard single-precision version. Use MeshGL64 to
+ * output the full double precision that Manifold uses internally.
  */
 template <typename Precision, typename I = uint32_t>
 struct MeshGLP {
@@ -62,7 +119,7 @@ struct MeshGLP {
   I numProp = 3;
   /// Flat, GL-style interleaved list of all vertex properties: propVal =
   /// vertProperties[vert * numProp + propIdx]. The first three properties are
-  /// always the position x, y, z.
+  /// always the position x, y, z. The stride of the array is numProp.
   std::vector<Precision> vertProperties;
   /// The vertex indices of the three triangle corners in CCW (from the outside)
   /// order, for each triangle.
@@ -93,10 +150,11 @@ struct MeshGLP {
   /// This matrix is stored in column-major order and the length of the overall
   /// vector is 12 * runOriginalID.size().
   std::vector<Precision> runTransform;
-  /// Optional: Length NumTri, contains the source face ID this
-  /// triangle comes from. When auto-generated, this ID will be a triangle index
-  /// into the original mesh. This index/ID is purely for external use (e.g.
-  /// recreating polygonal faces) and will not affect Manifold's algorithms.
+  /// Optional: Length NumTri, contains the source face ID this triangle comes
+  /// from. Simplification will maintain all edges between triangles with
+  /// different faceIDs. Input faceIDs will be maintained to the outputs, but if
+  /// none are given, they will be filled in with Manifold's coplanar face
+  /// calculation based on mesh tolerance.
   std::vector<I> faceID;
   /// Optional: The X-Y-Z-W weighted tangent vectors for smooth Refine(). If
   /// non-empty, must be exactly four times as long as Mesh.triVerts. Indexed
@@ -263,6 +321,7 @@ class Manifold {
     RunIndexWrongLength,
     FaceIDWrongLength,
     InvalidConstruction,
+    ResultTooLarge,
   };
 
   /** @name Information
@@ -311,6 +370,7 @@ class Manifold {
   Manifold Warp(std::function<void(vec3&)>) const;
   Manifold WarpBatch(std::function<void(VecView<vec3>)>) const;
   Manifold SetTolerance(double) const;
+  Manifold Simplify(double tolerance = 0) const;
   ///@}
 
   /** @name Boolean
@@ -368,22 +428,68 @@ class Manifold {
   static Manifold Hull(const std::vector<vec3>& pts);
   ///@}
 
+  /** @name Debugging I/O
+   * Self-contained mechanism for reading and writing high precision Manifold
+   * data.  Write function creates special-purpose OBJ files, and Read function
+   * reads them in.  Be warned these are not (and not intended to be)
+   * full-featured OBJ importers/exporters.  Their primary use is to extract
+   * accurate Manifold data for debugging purposes - writing out any info
+   * needed to accurately reproduce a problem case's state.  Consequently, they
+   * may store and process additional data in comments that other OBJ parsing
+   * programs won't understand.
+   *
+   * The "format" read and written by these functions is not guaranteed to be
+   * stable from release to release - it will be modified as needed to ensure
+   * it captures information needed for debugging.  The only API guarantee is
+   * that the ReadOBJ method in a given build/release will read in the output
+   * of the WriteOBJ method produced by that release.
+   *
+   * To work with a file, the caller should prepare the ifstream/ostream
+   * themselves, as follows:
+   *
+   * Reading:
+   * @code
+   * std::ifstream ifile;
+   * ifile.open(filename);
+   * if (ifile.is_open()) {
+   *   Manifold obj_m = Manifold::ReadOBJ(ifile);
+   *   ifile.close();
+   *   if (obj_m.Status() != Manifold::Error::NoError) {
+   *      std::cerr << "Failed reading " << filename << ":\n";
+   *      std::cerr << Manifold::ToString(ob_m.Status()) << "\n";
+   *   }
+   *   ifile.close();
+   * }
+   * @endcode
+   *
+   * Writing:
+   * @code
+   * std::ofstream ofile;
+   * ofile.open(filename);
+   * if (ofile.is_open()) {
+   *    if (!m.WriteOBJ(ofile)) {
+   *       std::cerr << "Failed writing to " << filename << "\n";
+   *    }
+   * }
+   * ofile.close();
+   * @endcode
+   */
+#ifdef MANIFOLD_DEBUG
+  static Manifold ReadOBJ(std::istream& stream);
+  bool WriteOBJ(std::ostream& stream) const;
+#endif
+
   /** @name Testing Hooks
    *  These are just for internal testing.
    */
   ///@{
   bool MatchesTriNormals() const;
   size_t NumDegenerateTris() const;
-  size_t NumOverlaps(const Manifold& second) const;
   double GetEpsilon() const;
   ///@}
 
   struct Impl;
 
-#ifdef MANIFOLD_EXPORT
-  static Manifold ImportMeshGL64(std::istream& stream);
-#endif
-
  private:
   Manifold(std::shared_ptr<CsgNode> pNode_);
   Manifold(std::shared_ptr<Impl> pImpl_);
@@ -429,6 +535,8 @@ inline std::string ToString(const Manifold::Error& error) {
       return "Face ID Wrong Length";
     case Manifold::Error::InvalidConstruction:
       return "Invalid Construction";
+    case Manifold::Error::ResultTooLarge:
+      return "Result Too Large";
     default:
       return "Unknown Error";
   };
diff --git a/thirdparty/manifold/include/manifold/optional_assert.h b/thirdparty/manifold/include/manifold/optional_assert.h
index 905746cca3..d08a6318fc 100644
--- a/thirdparty/manifold/include/manifold/optional_assert.h
+++ b/thirdparty/manifold/include/manifold/optional_assert.h
@@ -15,6 +15,7 @@
 #pragma once
 
 #ifdef MANIFOLD_DEBUG
+#include <iomanip>
 #include <iostream>
 #include <sstream>
 #include <stdexcept>
@@ -33,6 +34,9 @@ struct geometryErr : public virtual std::runtime_error {
   using std::runtime_error::runtime_error;
 };
 using logicErr = std::logic_error;
+#endif
+
+#if defined(MANIFOLD_ASSERT) && defined(MANIFOLD_DEBUG)
 
 template <typename Ex>
 void AssertFail(const char* file, int line, const char* cond, const char* msg) {
diff --git a/thirdparty/manifold/include/manifold/polygon.h b/thirdparty/manifold/include/manifold/polygon.h
index 2902524ce4..35968ad045 100644
--- a/thirdparty/manifold/include/manifold/polygon.h
+++ b/thirdparty/manifold/include/manifold/polygon.h
@@ -52,11 +52,10 @@ using PolygonsIdx = std::vector<SimplePolygonIdx>;
  * @brief Polygon triangulation
  *  @{
  */
-std::vector<ivec3> TriangulateIdx(const PolygonsIdx &polys,
-                                  double epsilon = -1);
+std::vector<ivec3> TriangulateIdx(const PolygonsIdx& polys, double epsilon = -1,
+                                  bool allowConvex = true);
 
-std::vector<ivec3> Triangulate(const Polygons &polygons, double epsilon = -1);
-
-ExecutionParams &PolygonParams();
+std::vector<ivec3> Triangulate(const Polygons& polygons, double epsilon = -1,
+                               bool allowConvex = true);
 /** @} */
 }  // namespace manifold
diff --git a/thirdparty/manifold/include/manifold/vec_view.h b/thirdparty/manifold/include/manifold/vec_view.h
index 4dc5f73445..b5fcc8288e 100644
--- a/thirdparty/manifold/include/manifold/vec_view.h
+++ b/thirdparty/manifold/include/manifold/vec_view.h
@@ -31,22 +31,22 @@ namespace manifold {
 template <typename T>
 class VecView {
  public:
-  using Iter = T *;
-  using IterC = const T *;
+  using Iter = T*;
+  using IterC = const T*;
 
   VecView() : ptr_(nullptr), size_(0) {}
 
-  VecView(T *ptr, size_t size) : ptr_(ptr), size_(size) {}
+  VecView(T* ptr, size_t size) : ptr_(ptr), size_(size) {}
 
-  VecView(const std::vector<std::remove_cv_t<T>> &v)
+  VecView(const std::vector<std::remove_cv_t<T>>& v)
       : ptr_(v.data()), size_(v.size()) {}
 
-  VecView(const VecView &other) {
+  VecView(const VecView& other) {
     ptr_ = other.ptr_;
     size_ = other.size_;
   }
 
-  VecView &operator=(const VecView &other) {
+  VecView& operator=(const VecView& other) {
     ptr_ = other.ptr_;
     size_ = other.size_;
     return *this;
@@ -55,12 +55,12 @@ class VecView {
   // allows conversion to a const VecView
   operator VecView<const T>() const { return {ptr_, size_}; }
 
-  inline const T &operator[](size_t i) const {
+  inline const T& operator[](size_t i) const {
     ASSERT(i < size_, std::out_of_range("Vec out of range"));
     return ptr_[i];
   }
 
-  inline T &operator[](size_t i) {
+  inline T& operator[](size_t i) {
     ASSERT(i < size_, std::out_of_range("Vec out of range"));
     return ptr_[i];
   }
@@ -74,25 +74,25 @@ class VecView {
   Iter begin() { return ptr_; }
   Iter end() { return ptr_ + size_; }
 
-  const T &front() const {
+  const T& front() const {
     ASSERT(size_ != 0,
            std::out_of_range("Attempt to take the front of an empty vector"));
     return ptr_[0];
   }
 
-  const T &back() const {
+  const T& back() const {
     ASSERT(size_ != 0,
            std::out_of_range("Attempt to take the back of an empty vector"));
     return ptr_[size_ - 1];
   }
 
-  T &front() {
+  T& front() {
     ASSERT(size_ != 0,
            std::out_of_range("Attempt to take the front of an empty vector"));
     return ptr_[0];
   }
 
-  T &back() {
+  T& back() {
     ASSERT(size_ != 0,
            std::out_of_range("Attempt to take the back of an empty vector"));
     return ptr_[size_ - 1];
@@ -106,8 +106,7 @@ class VecView {
                   size_t length = std::numeric_limits<size_t>::max()) {
     if (length == std::numeric_limits<size_t>::max())
       length = this->size_ - offset;
-    ASSERT(length >= 0, std::out_of_range("Vec::view out of range"));
-    ASSERT(offset + length <= this->size_ && offset >= 0,
+    ASSERT(offset + length <= this->size_,
            std::out_of_range("Vec::view out of range"));
     return VecView<T>(this->ptr_ + offset, length);
   }
@@ -117,8 +116,7 @@ class VecView {
       size_t length = std::numeric_limits<size_t>::max()) const {
     if (length == std::numeric_limits<size_t>::max())
       length = this->size_ - offset;
-    ASSERT(length >= 0, std::out_of_range("Vec::cview out of range"));
-    ASSERT(offset + length <= this->size_ && offset >= 0,
+    ASSERT(offset + length <= this->size_,
            std::out_of_range("Vec::cview out of range"));
     return VecView<const T>(this->ptr_ + offset, length);
   }
@@ -129,9 +127,9 @@ class VecView {
     return cview(offset, length);
   }
 
-  T *data() { return this->ptr_; }
+  T* data() { return this->ptr_; }
 
-  const T *data() const { return this->ptr_; }
+  const T* data() const { return this->ptr_; }
 
 #ifdef MANIFOLD_DEBUG
   void Dump() const {
@@ -144,7 +142,7 @@ class VecView {
 #endif
 
  protected:
-  T *ptr_ = nullptr;
+  T* ptr_ = nullptr;
   size_t size_ = 0;
 };
 
diff --git a/thirdparty/manifold/src/boolean3.cpp b/thirdparty/manifold/src/boolean3.cpp
index 1fca99db45..ba92f77ae4 100644
--- a/thirdparty/manifold/src/boolean3.cpp
+++ b/thirdparty/manifold/src/boolean3.cpp
@@ -12,11 +12,15 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "./boolean3.h"
+#include "boolean3.h"
 
 #include <limits>
 
-#include "./parallel.h"
+#include "parallel.h"
+
+#if (MANIFOLD_PAR == 1)
+#include <tbb/combinable.h>
+#endif
 
 using namespace manifold;
 
@@ -38,12 +42,12 @@ vec2 Interpolate(vec3 pL, vec3 pR, double x) {
   if (!std::isfinite(lambda) || !std::isfinite(dLR.y) || !std::isfinite(dLR.z))
     return vec2(pL.y, pL.z);
   vec2 yz;
-  yz[0] = fma(lambda, dLR.y, useL ? pL.y : pR.y);
-  yz[1] = fma(lambda, dLR.z, useL ? pL.z : pR.z);
+  yz[0] = lambda * dLR.y + (useL ? pL.y : pR.y);
+  yz[1] = lambda * dLR.z + (useL ? pL.z : pR.z);
   return yz;
 }
 
-vec4 Intersect(const vec3 &pL, const vec3 &pR, const vec3 &qL, const vec3 &qR) {
+vec4 Intersect(const vec3& pL, const vec3& pR, const vec3& qL, const vec3& qR) {
   const double dyL = qL.y - pL.y;
   const double dyR = qR.y - pR.y;
   DEBUG_ASSERT(dyL * dyR <= 0, logicErr,
@@ -53,53 +57,17 @@ vec4 Intersect(const vec3 &pL, const vec3 &pR, const vec3 &qL, const vec3 &qR) {
   double lambda = (useL ? dyL : dyR) / (dyL - dyR);
   if (!std::isfinite(lambda)) lambda = 0.0;
   vec4 xyzz;
-  xyzz.x = fma(lambda, dx, useL ? pL.x : pR.x);
+  xyzz.x = lambda * dx + (useL ? pL.x : pR.x);
   const double pDy = pR.y - pL.y;
   const double qDy = qR.y - qL.y;
   const bool useP = fabs(pDy) < fabs(qDy);
-  xyzz.y = fma(lambda, useP ? pDy : qDy,
-               useL ? (useP ? pL.y : qL.y) : (useP ? pR.y : qR.y));
-  xyzz.z = fma(lambda, pR.z - pL.z, useL ? pL.z : pR.z);
-  xyzz.w = fma(lambda, qR.z - qL.z, useL ? qL.z : qR.z);
+  xyzz.y = lambda * (useP ? pDy : qDy) +
+           (useL ? (useP ? pL.y : qL.y) : (useP ? pR.y : qR.y));
+  xyzz.z = lambda * (pR.z - pL.z) + (useL ? pL.z : pR.z);
+  xyzz.w = lambda * (qR.z - qL.z) + (useL ? qL.z : qR.z);
   return xyzz;
 }
 
-template <const bool inverted>
-struct CopyFaceEdges {
-  const SparseIndices &p1q1;
-  // x can be either vert or edge (0 or 1).
-  SparseIndices &pXq1;
-  VecView<const Halfedge> halfedgesQ;
-  const size_t offset;
-
-  void operator()(const size_t i) {
-    int idx = 3 * (i + offset);
-    int pX = p1q1.Get(i, inverted);
-    int q2 = p1q1.Get(i, !inverted);
-
-    for (const int j : {0, 1, 2}) {
-      const int q1 = 3 * q2 + j;
-      const Halfedge edge = halfedgesQ[q1];
-      int a = pX;
-      int b = edge.IsForward() ? q1 : edge.pairedHalfedge;
-      if (inverted) std::swap(a, b);
-      pXq1.Set(idx + static_cast<size_t>(j), a, b);
-    }
-  }
-};
-
-SparseIndices Filter11(const Manifold::Impl &inP, const Manifold::Impl &inQ,
-                       const SparseIndices &p1q2, const SparseIndices &p2q1) {
-  ZoneScoped;
-  SparseIndices p1q1(3 * p1q2.size() + 3 * p2q1.size());
-  for_each_n(autoPolicy(p1q2.size(), 1e5), countAt(0_uz), p1q2.size(),
-             CopyFaceEdges<false>({p1q2, p1q1, inQ.halfedge_, 0_uz}));
-  for_each_n(autoPolicy(p2q1.size(), 1e5), countAt(0_uz), p2q1.size(),
-             CopyFaceEdges<true>({p2q1, p1q1, inP.halfedge_, p1q2.size()}));
-  p1q1.Unique();
-  return p1q1;
-}
-
 inline bool Shadows(double p, double q, double dir) {
   return p == q ? dir < 0 : p < q;
 }
@@ -107,16 +75,16 @@ inline bool Shadows(double p, double q, double dir) {
 inline std::pair<int, vec2> Shadow01(
     const int p0, const int q1, VecView<const vec3> vertPosP,
     VecView<const vec3> vertPosQ, VecView<const Halfedge> halfedgeQ,
-    const double expandP, VecView<const vec3> normalP, const bool reverse) {
+    const double expandP, VecView<const vec3> normal, const bool reverse) {
   const int q1s = halfedgeQ[q1].startVert;
   const int q1e = halfedgeQ[q1].endVert;
   const double p0x = vertPosP[p0].x;
   const double q1sx = vertPosQ[q1s].x;
   const double q1ex = vertPosQ[q1e].x;
-  int s01 = reverse ? Shadows(q1sx, p0x, expandP * normalP[q1s].x) -
-                          Shadows(q1ex, p0x, expandP * normalP[q1e].x)
-                    : Shadows(p0x, q1ex, expandP * normalP[p0].x) -
-                          Shadows(p0x, q1sx, expandP * normalP[p0].x);
+  int s01 = reverse ? Shadows(q1sx, p0x, expandP * normal[q1s].x) -
+                          Shadows(q1ex, p0x, expandP * normal[q1e].x)
+                    : Shadows(p0x, q1ex, expandP * normal[p0].x) -
+                          Shadows(p0x, q1sx, expandP * normal[p0].x);
   vec2 yz01(NAN);
 
   if (s01 != 0) {
@@ -126,70 +94,26 @@ inline std::pair<int, vec2> Shadow01(
       const double start2 = la::dot(diff, diff);
       diff = vertPosQ[q1e] - vertPosP[p0];
       const double end2 = la::dot(diff, diff);
-      const double dir = start2 < end2 ? normalP[q1s].y : normalP[q1e].y;
+      const double dir = start2 < end2 ? normal[q1s].y : normal[q1e].y;
       if (!Shadows(yz01[0], vertPosP[p0].y, expandP * dir)) s01 = 0;
     } else {
-      if (!Shadows(vertPosP[p0].y, yz01[0], expandP * normalP[p0].y)) s01 = 0;
+      if (!Shadows(vertPosP[p0].y, yz01[0], expandP * normal[p0].y)) s01 = 0;
     }
   }
   return std::make_pair(s01, yz01);
 }
 
-// https://github.com/scandum/binary_search/blob/master/README.md
-// much faster than standard binary search on large arrays
-size_t monobound_quaternary_search(VecView<const int64_t> array, int64_t key) {
-  if (array.size() == 0) {
-    return std::numeric_limits<size_t>::max();
-  }
-  size_t bot = 0;
-  size_t top = array.size();
-  while (top >= 65536) {
-    size_t mid = top / 4;
-    top -= mid * 3;
-    if (key < array[bot + mid * 2]) {
-      if (key >= array[bot + mid]) {
-        bot += mid;
-      }
-    } else {
-      bot += mid * 2;
-      if (key >= array[bot + mid]) {
-        bot += mid;
-      }
-    }
-  }
-
-  while (top > 3) {
-    size_t mid = top / 2;
-    if (key >= array[bot + mid]) {
-      bot += mid;
-    }
-    top -= mid;
-  }
-
-  while (top--) {
-    if (key == array[bot + top]) {
-      return bot + top;
-    }
-  }
-  return -1;
-}
-
 struct Kernel11 {
-  VecView<vec4> xyzz;
-  VecView<int> s;
   VecView<const vec3> vertPosP;
   VecView<const vec3> vertPosQ;
   VecView<const Halfedge> halfedgeP;
   VecView<const Halfedge> halfedgeQ;
   const double expandP;
   VecView<const vec3> normalP;
-  const SparseIndices &p1q1;
 
-  void operator()(const size_t idx) {
-    const int p1 = p1q1.Get(idx, false);
-    const int q1 = p1q1.Get(idx, true);
-    vec4 &xyzz11 = xyzz[idx];
-    int &s11 = s[idx];
+  std::pair<int, vec4> operator()(int p1, int q1) {
+    vec4 xyzz11 = vec4(NAN);
+    int s11 = 0;
 
     // For pRL[k], qRL[k], k==0 is the left and k==1 is the right.
     int k = 0;
@@ -201,10 +125,8 @@ struct Kernel11 {
 
     const int p0[2] = {halfedgeP[p1].startVert, halfedgeP[p1].endVert};
     for (int i : {0, 1}) {
-      const auto syz01 = Shadow01(p0[i], q1, vertPosP, vertPosQ, halfedgeQ,
-                                  expandP, normalP, false);
-      const int s01 = syz01.first;
-      const vec2 yz01 = syz01.second;
+      const auto [s01, yz01] = Shadow01(p0[i], q1, vertPosP, vertPosQ,
+                                        halfedgeQ, expandP, normalP, false);
       // If the value is NaN, then these do not overlap.
       if (std::isfinite(yz01[0])) {
         s11 += s01 * (i == 0 ? -1 : 1);
@@ -219,10 +141,8 @@ struct Kernel11 {
 
     const int q0[2] = {halfedgeQ[q1].startVert, halfedgeQ[q1].endVert};
     for (int i : {0, 1}) {
-      const auto syz10 = Shadow01(q0[i], p1, vertPosQ, vertPosP, halfedgeP,
-                                  expandP, normalP, true);
-      const int s10 = syz10.first;
-      const vec2 yz10 = syz10.second;
+      const auto [s10, yz10] = Shadow01(q0[i], p1, vertPosQ, vertPosP,
+                                        halfedgeP, expandP, normalP, true);
       // If the value is NaN, then these do not overlap.
       if (std::isfinite(yz10[0])) {
         s11 += s10 * (i == 0 ? -1 : 1);
@@ -251,42 +171,22 @@ struct Kernel11 {
 
       if (!Shadows(xyzz11.z, xyzz11.w, expandP * dir)) s11 = 0;
     }
+
+    return std::make_pair(s11, xyzz11);
   }
 };
 
-std::tuple<Vec<int>, Vec<vec4>> Shadow11(SparseIndices &p1q1,
-                                         const Manifold::Impl &inP,
-                                         const Manifold::Impl &inQ,
-                                         double expandP) {
-  ZoneScoped;
-  Vec<int> s11(p1q1.size());
-  Vec<vec4> xyzz11(p1q1.size());
-
-  for_each_n(autoPolicy(p1q1.size(), 1e4), countAt(0_uz), p1q1.size(),
-             Kernel11({xyzz11, s11, inP.vertPos_, inQ.vertPos_, inP.halfedge_,
-                       inQ.halfedge_, expandP, inP.vertNormal_, p1q1}));
-
-  p1q1.KeepFinite(xyzz11, s11);
-
-  return std::make_tuple(s11, xyzz11);
-};
-
 struct Kernel02 {
-  VecView<int> s;
-  VecView<double> z;
   VecView<const vec3> vertPosP;
   VecView<const Halfedge> halfedgeQ;
   VecView<const vec3> vertPosQ;
   const double expandP;
   VecView<const vec3> vertNormalP;
-  const SparseIndices &p0q2;
   const bool forward;
 
-  void operator()(const size_t idx) {
-    const int p0 = p0q2.Get(idx, !forward);
-    const int q2 = p0q2.Get(idx, forward);
-    int &s02 = s[idx];
-    double &z02 = z[idx];
+  std::pair<int, double> operator()(int p0, int q2) {
+    int s02 = 0;
+    double z02 = 0.0;
 
     // For yzzLR[k], k==0 is the left and k==1 is the right.
     int k = 0;
@@ -342,47 +242,21 @@ struct Kernel02 {
           s02 = 0;
       }
     }
+    return std::make_pair(s02, z02);
   }
 };
 
-std::tuple<Vec<int>, Vec<double>> Shadow02(const Manifold::Impl &inP,
-                                           const Manifold::Impl &inQ,
-                                           SparseIndices &p0q2, bool forward,
-                                           double expandP) {
-  ZoneScoped;
-  Vec<int> s02(p0q2.size());
-  Vec<double> z02(p0q2.size());
-
-  auto vertNormalP = forward ? inP.vertNormal_ : inQ.vertNormal_;
-  for_each_n(autoPolicy(p0q2.size(), 1e4), countAt(0_uz), p0q2.size(),
-             Kernel02({s02, z02, inP.vertPos_, inQ.halfedge_, inQ.vertPos_,
-                       expandP, vertNormalP, p0q2, forward}));
-
-  p0q2.KeepFinite(z02, s02);
-
-  return std::make_tuple(s02, z02);
-};
-
 struct Kernel12 {
-  VecView<int> x;
-  VecView<vec3> v;
-  VecView<const int64_t> p0q2;
-  VecView<const int> s02;
-  VecView<const double> z02;
-  VecView<const int64_t> p1q1;
-  VecView<const int> s11;
-  VecView<const vec4> xyzz11;
   VecView<const Halfedge> halfedgesP;
   VecView<const Halfedge> halfedgesQ;
   VecView<const vec3> vertPosP;
   const bool forward;
-  const SparseIndices &p1q2;
+  Kernel02 k02;
+  Kernel11 k11;
 
-  void operator()(const size_t idx) {
-    int p1 = p1q2.Get(idx, !forward);
-    int q2 = p1q2.Get(idx, forward);
-    int &x12 = x[idx];
-    vec3 &v12 = v[idx];
+  std::pair<int, vec3> operator()(int p1, int q2) {
+    int x12 = 0;
+    vec3 v12 = vec3(NAN);
 
     // For xzyLR-[k], k==0 is the left and k==1 is the right.
     int k = 0;
@@ -396,18 +270,15 @@ struct Kernel12 {
     const Halfedge edge = halfedgesP[p1];
 
     for (int vert : {edge.startVert, edge.endVert}) {
-      const int64_t key = forward ? SparseIndices::EncodePQ(vert, q2)
-                                  : SparseIndices::EncodePQ(q2, vert);
-      const size_t idx = monobound_quaternary_search(p0q2, key);
-      if (idx != std::numeric_limits<size_t>::max()) {
-        const int s = s02[idx];
+      const auto [s, z] = k02(vert, q2);
+      if (std::isfinite(z)) {
         x12 += s * ((vert == edge.startVert) == forward ? 1 : -1);
         if (k < 2 && (k == 0 || (s != 0) != shadows)) {
           shadows = s != 0;
           xzyLR0[k] = vertPosP[vert];
           std::swap(xzyLR0[k].y, xzyLR0[k].z);
           xzyLR1[k] = xzyLR0[k];
-          xzyLR1[k][1] = z02[idx];
+          xzyLR1[k][1] = z;
           k++;
         }
       }
@@ -417,17 +288,11 @@ struct Kernel12 {
       const int q1 = 3 * q2 + i;
       const Halfedge edge = halfedgesQ[q1];
       const int q1F = edge.IsForward() ? q1 : edge.pairedHalfedge;
-      const int64_t key = forward ? SparseIndices::EncodePQ(p1, q1F)
-                                  : SparseIndices::EncodePQ(q1F, p1);
-      const size_t idx = monobound_quaternary_search(p1q1, key);
-      if (idx !=
-          std::numeric_limits<size_t>::max()) {  // s is implicitly zero for
-                                                 // anything not found
-        const int s = s11[idx];
+      const auto [s, xyzz] = forward ? k11(p1, q1F) : k11(q1F, p1);
+      if (std::isfinite(xyzz[0])) {
         x12 -= s * (edge.IsForward() ? 1 : -1);
         if (k < 2 && (k == 0 || (s != 0) != shadows)) {
           shadows = s != 0;
-          const vec4 xyzz = xyzz11[idx];
           xzyLR0[k][0] = xyzz.x;
           xzyLR0[k][1] = xyzz.z;
           xzyLR0[k][2] = xyzz.y;
@@ -448,60 +313,146 @@ struct Kernel12 {
       v12.y = xzyy[2];
       v12.z = xzyy[1];
     }
+    return std::make_pair(x12, v12);
   }
 };
 
-std::tuple<Vec<int>, Vec<vec3>> Intersect12(
-    const Manifold::Impl &inP, const Manifold::Impl &inQ, const Vec<int> &s02,
-    const SparseIndices &p0q2, const Vec<int> &s11, const SparseIndices &p1q1,
-    const Vec<double> &z02, const Vec<vec4> &xyzz11, SparseIndices &p1q2,
-    bool forward) {
+struct Kernel12Tmp {
+  Vec<std::array<int, 2>> p1q2_;
+  Vec<int> x12_;
+  Vec<vec3> v12_;
+};
+
+struct Kernel12Recorder {
+  using Local = Kernel12Tmp;
+  Kernel12& k12;
+  VecView<const TmpEdge> tmpedges;
+  bool forward;
+
+#if MANIFOLD_PAR == 1
+  tbb::combinable<Kernel12Tmp> store;
+  Local& local() { return store.local(); }
+#else
+  Kernel12Tmp localStore;
+  Local& local() { return localStore; }
+#endif
+
+  void record(int queryIdx, int leafIdx, Local& tmp) {
+    queryIdx = tmpedges[queryIdx].halfedgeIdx;
+    const auto [x12, v12] = k12(queryIdx, leafIdx);
+    if (std::isfinite(v12[0])) {
+      if (forward)
+        tmp.p1q2_.push_back({queryIdx, leafIdx});
+      else
+        tmp.p1q2_.push_back({leafIdx, queryIdx});
+      tmp.x12_.push_back(x12);
+      tmp.v12_.push_back(v12);
+    }
+  }
+
+  Kernel12Tmp get() {
+#if MANIFOLD_PAR == 1
+    Kernel12Tmp result;
+    std::vector<Kernel12Tmp> tmps;
+    store.combine_each(
+        [&](Kernel12Tmp& data) { tmps.emplace_back(std::move(data)); });
+    std::vector<size_t> sizes;
+    size_t total_size = 0;
+    for (const auto& tmp : tmps) {
+      sizes.push_back(total_size);
+      total_size += tmp.x12_.size();
+    }
+    result.p1q2_.resize(total_size);
+    result.x12_.resize(total_size);
+    result.v12_.resize(total_size);
+    for_each_n(ExecutionPolicy::Seq, countAt(0), tmps.size(), [&](size_t i) {
+      std::copy(tmps[i].p1q2_.begin(), tmps[i].p1q2_.end(),
+                result.p1q2_.begin() + sizes[i]);
+      std::copy(tmps[i].x12_.begin(), tmps[i].x12_.end(),
+                result.x12_.begin() + sizes[i]);
+      std::copy(tmps[i].v12_.begin(), tmps[i].v12_.end(),
+                result.v12_.begin() + sizes[i]);
+    });
+    return result;
+#else
+    return localStore;
+#endif
+  }
+};
+
+std::tuple<Vec<int>, Vec<vec3>> Intersect12(const Manifold::Impl& inP,
+                                            const Manifold::Impl& inQ,
+                                            Vec<std::array<int, 2>>& p1q2,
+                                            double expandP, bool forward) {
   ZoneScoped;
-  Vec<int> x12(p1q2.size());
-  Vec<vec3> v12(p1q2.size());
+  // a: 1 (edge), b: 2 (face)
+  const Manifold::Impl& a = forward ? inP : inQ;
+  const Manifold::Impl& b = forward ? inQ : inP;
 
-  for_each_n(
-      autoPolicy(p1q2.size(), 1e4), countAt(0_uz), p1q2.size(),
-      Kernel12({x12, v12, p0q2.AsVec64(), s02, z02, p1q1.AsVec64(), s11, xyzz11,
-                inP.halfedge_, inQ.halfedge_, inP.vertPos_, forward, p1q2}));
+  Kernel02 k02{a.vertPos_, b.halfedge_,     b.vertPos_,
+               expandP,    inP.vertNormal_, forward};
+  Kernel11 k11{inP.vertPos_,  inQ.vertPos_, inP.halfedge_,
+               inQ.halfedge_, expandP,      inP.vertNormal_};
 
-  p1q2.KeepFinite(v12, x12);
+  Vec<TmpEdge> tmpedges = CreateTmpEdges(a.halfedge_);
+  Vec<Box> AEdgeBB(tmpedges.size());
+  for_each_n(autoPolicy(tmpedges.size(), 1e5), countAt(0), tmpedges.size(),
+             [&](const int e) {
+               AEdgeBB[e] = Box(a.vertPos_[tmpedges[e].first],
+                                a.vertPos_[tmpedges[e].second]);
+             });
+  Kernel12 k12{a.halfedge_, b.halfedge_, a.vertPos_, forward, k02, k11};
+  Kernel12Recorder recorder{k12, tmpedges, forward, {}};
 
+  b.collider_.Collisions<false, Box, Kernel12Recorder>(AEdgeBB.cview(),
+                                                       recorder);
+
+  Kernel12Tmp result = recorder.get();
+  p1q2 = std::move(result.p1q2_);
+  auto x12 = std::move(result.x12_);
+  auto v12 = std::move(result.v12_);
+  // sort p1q2
+  Vec<size_t> i12(p1q2.size());
+  sequence(i12.begin(), i12.end());
+  stable_sort(i12.begin(), i12.end(), [&](int a, int b) {
+    return p1q2[a][0] < p1q2[b][0] ||
+           (p1q2[a][0] == p1q2[b][0] && p1q2[a][1] < p1q2[b][1]);
+  });
+  Permute(p1q2, i12);
+  Permute(x12, i12);
+  Permute(v12, i12);
   return std::make_tuple(x12, v12);
 };
 
-Vec<int> Winding03(const Manifold::Impl &inP, Vec<int> &vertices, Vec<int> &s02,
-                   bool reverse) {
+Vec<int> Winding03(const Manifold::Impl& inP, const Manifold::Impl& inQ,
+                   double expandP, bool forward) {
   ZoneScoped;
   // verts that are not shadowed (not in p0q2) have winding number zero.
-  Vec<int> w03(inP.NumVert(), 0);
-  if (vertices.size() <= 1e5) {
-    for_each_n(ExecutionPolicy::Seq, countAt(0), s02.size(),
-               [&w03, &vertices, &s02, reverse](const int i) {
-                 w03[vertices[i]] += s02[i] * (reverse ? -1 : 1);
-               });
-  } else {
-    for_each_n(ExecutionPolicy::Par, countAt(0), s02.size(),
-               [&w03, &vertices, &s02, reverse](const int i) {
-                 AtomicAdd(w03[vertices[i]], s02[i] * (reverse ? -1 : 1));
-               });
-  }
+  // a: 0 (vertex), b: 2 (face)
+  const Manifold::Impl& a = forward ? inP : inQ;
+  const Manifold::Impl& b = forward ? inQ : inP;
+  Vec<int> w03(a.NumVert(), 0);
+  Kernel02 k02{a.vertPos_, b.halfedge_,     b.vertPos_,
+               expandP,    inP.vertNormal_, forward};
+  auto f = [&](int a, int b) {
+    const auto [s02, z02] = k02(a, b);
+    if (std::isfinite(z02)) AtomicAdd(w03[a], s02 * (!forward ? -1 : 1));
+  };
+  auto recorder = MakeSimpleRecorder(f);
+  b.collider_.Collisions<false>(a.vertPos_.cview(), recorder);
   return w03;
 };
 }  // namespace
 
 namespace manifold {
-Boolean3::Boolean3(const Manifold::Impl &inP, const Manifold::Impl &inQ,
+Boolean3::Boolean3(const Manifold::Impl& inP, const Manifold::Impl& inQ,
                    OpType op)
     : inP_(inP), inQ_(inQ), expandP_(op == OpType::Add ? 1.0 : -1.0) {
   // Symbolic perturbation:
   // Union -> expand inP
   // Difference, Intersection -> contract inP
-
-#ifdef MANIFOLD_DEBUG
-  Timer broad;
-  broad.Start();
-#endif
+  constexpr size_t INT_MAX_SZ =
+      static_cast<size_t>(std::numeric_limits<int>::max());
 
   if (inP.IsEmpty() || inQ.IsEmpty() || !inP.bBox_.DoesOverlap(inQ.bBox_)) {
     PRINT("No overlap, early out");
@@ -510,88 +461,34 @@ Boolean3::Boolean3(const Manifold::Impl &inP, const Manifold::Impl &inQ,
     return;
   }
 
-  // Level 3
-  // Find edge-triangle overlaps (broad phase)
-  p1q2_ = inQ_.EdgeCollisions(inP_);
-  p2q1_ = inP_.EdgeCollisions(inQ_, true);  // inverted
-
-  p1q2_.Sort();
-  PRINT("p1q2 size = " << p1q2_.size());
-
-  p2q1_.Sort();
-  PRINT("p2q1 size = " << p2q1_.size());
-
-  // Level 2
-  // Find vertices that overlap faces in XY-projection
-  SparseIndices p0q2 = inQ.VertexCollisionsZ(inP.vertPos_);
-  p0q2.Sort();
-  PRINT("p0q2 size = " << p0q2.size());
-
-  SparseIndices p2q0 = inP.VertexCollisionsZ(inQ.vertPos_, true);  // inverted
-  p2q0.Sort();
-  PRINT("p2q0 size = " << p2q0.size());
-
-  // Find involved edge pairs from Level 3
-  SparseIndices p1q1 = Filter11(inP_, inQ_, p1q2_, p2q1_);
-  PRINT("p1q1 size = " << p1q1.size());
-
 #ifdef MANIFOLD_DEBUG
-  broad.Stop();
   Timer intersections;
   intersections.Start();
 #endif
 
-  // Level 2
-  // Build up XY-projection intersection of two edges, including the z-value for
-  // each edge, keeping only those whose intersection exists.
-  Vec<int> s11;
-  Vec<vec4> xyzz11;
-  std::tie(s11, xyzz11) = Shadow11(p1q1, inP, inQ, expandP_);
-  PRINT("s11 size = " << s11.size());
-
-  // Build up Z-projection of vertices onto triangles, keeping only those that
-  // fall inside the triangle.
-  Vec<int> s02;
-  Vec<double> z02;
-  std::tie(s02, z02) = Shadow02(inP, inQ, p0q2, true, expandP_);
-  PRINT("s02 size = " << s02.size());
-
-  Vec<int> s20;
-  Vec<double> z20;
-  std::tie(s20, z20) = Shadow02(inQ, inP, p2q0, false, expandP_);
-  PRINT("s20 size = " << s20.size());
-
   // Level 3
   // Build up the intersection of the edges and triangles, keeping only those
   // that intersect, and record the direction the edge is passing through the
   // triangle.
-  std::tie(x12_, v12_) =
-      Intersect12(inP, inQ, s02, p0q2, s11, p1q1, z02, xyzz11, p1q2_, true);
+  std::tie(x12_, v12_) = Intersect12(inP, inQ, p1q2_, expandP_, true);
   PRINT("x12 size = " << x12_.size());
 
-  std::tie(x21_, v21_) =
-      Intersect12(inQ, inP, s20, p2q0, s11, p1q1, z20, xyzz11, p2q1_, false);
+  std::tie(x21_, v21_) = Intersect12(inP, inQ, p2q1_, expandP_, false);
   PRINT("x21 size = " << x21_.size());
 
-  s11.clear();
-  xyzz11.clear();
-  z02.clear();
-  z20.clear();
+  if (x12_.size() > INT_MAX_SZ || x21_.size() > INT_MAX_SZ) {
+    valid = false;
+    return;
+  }
 
-  Vec<int> p0 = p0q2.Copy(false);
-  p0q2.Resize(0);
-  Vec<int> q0 = p2q0.Copy(true);
-  p2q0.Resize(0);
   // Sum up the winding numbers of all vertices.
-  w03_ = Winding03(inP, p0, s02, false);
-
-  w30_ = Winding03(inQ, q0, s20, true);
+  w03_ = Winding03(inP, inQ, expandP_, true);
+  w30_ = Winding03(inP, inQ, expandP_, false);
 
 #ifdef MANIFOLD_DEBUG
   intersections.Stop();
 
   if (ManifoldParams().verbose) {
-    broad.Print("Broad phase");
     intersections.Print("Intersections");
   }
 #endif
diff --git a/thirdparty/manifold/src/boolean3.h b/thirdparty/manifold/src/boolean3.h
index 7ee2ee1230..745403f78d 100644
--- a/thirdparty/manifold/src/boolean3.h
+++ b/thirdparty/manifold/src/boolean3.h
@@ -13,11 +13,11 @@
 // limitations under the License.
 
 #pragma once
-#include "./impl.h"
+#include "impl.h"
 
 #ifdef MANIFOLD_DEBUG
 #define PRINT(msg) \
-  if (ManifoldParams().verbose) std::cout << msg << std::endl;
+  if (ManifoldParams().verbose > 0) std::cout << msg << std::endl;
 #else
 #define PRINT(msg)
 #endif
@@ -53,8 +53,9 @@ class Boolean3 {
  private:
   const Manifold::Impl &inP_, &inQ_;
   const double expandP_;
-  SparseIndices p1q2_, p2q1_;
+  Vec<std::array<int, 2>> p1q2_, p2q1_;
   Vec<int> x12_, x21_, w03_, w30_;
   Vec<vec3> v12_, v21_;
+  bool valid = true;
 };
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/boolean_result.cpp b/thirdparty/manifold/src/boolean_result.cpp
index 2921dde906..4ea3303741 100644
--- a/thirdparty/manifold/src/boolean_result.cpp
+++ b/thirdparty/manifold/src/boolean_result.cpp
@@ -16,9 +16,9 @@
 #include <array>
 #include <map>
 
-#include "./boolean3.h"
-#include "./parallel.h"
-#include "./utils.h"
+#include "boolean3.h"
+#include "parallel.h"
+#include "utils.h"
 
 #if (MANIFOLD_PAR == 1) && __has_include(<tbb/concurrent_map.h>)
 #define TBB_PREVIEW_CONCURRENT_ORDERED_CONTAINERS 1
@@ -37,7 +37,7 @@ using namespace manifold;
 
 template <>
 struct std::hash<std::pair<int, int>> {
-  size_t operator()(const std::pair<int, int> &p) const {
+  size_t operator()(const std::pair<int, int>& p) const {
     return std::hash<int>()(p.first) ^ std::hash<int>()(p.second);
   }
 };
@@ -83,12 +83,12 @@ struct CountNewVerts {
   VecView<int> countP;
   VecView<int> countQ;
   VecView<const int> i12;
-  const SparseIndices &pq;
+  const Vec<std::array<int, 2>>& pq;
   VecView<const Halfedge> halfedges;
 
   void operator()(const int idx) {
-    int edgeP = pq.Get(idx, inverted);
-    int faceQ = pq.Get(idx, !inverted);
+    int edgeP = pq[idx][inverted ? 1 : 0];
+    int faceQ = pq[idx][inverted ? 0 : 1];
     int inclusion = std::abs(i12[idx]);
 
     if (atomic) {
@@ -106,10 +106,10 @@ struct CountNewVerts {
 };
 
 std::tuple<Vec<int>, Vec<int>> SizeOutput(
-    Manifold::Impl &outR, const Manifold::Impl &inP, const Manifold::Impl &inQ,
-    const Vec<int> &i03, const Vec<int> &i30, const Vec<int> &i12,
-    const Vec<int> &i21, const SparseIndices &p1q2, const SparseIndices &p2q1,
-    bool invertQ) {
+    Manifold::Impl& outR, const Manifold::Impl& inP, const Manifold::Impl& inQ,
+    const Vec<int>& i03, const Vec<int>& i30, const Vec<int>& i12,
+    const Vec<int>& i21, const Vec<std::array<int, 2>>& p1q2,
+    const Vec<std::array<int, 2>>& p2q1, bool invertQ) {
   ZoneScoped;
   Vec<int> sidesPerFacePQ(inP.NumTri() + inQ.NumTri(), 0);
   // note: numFaceR <= facePQ2R.size() = sidesPerFacePQ.size() + 1
@@ -154,7 +154,7 @@ std::tuple<Vec<int>, Vec<int>> SizeOutput(
   int numFaceR = facePQ2R.back();
   facePQ2R.resize(inP.NumTri() + inQ.NumTri());
 
-  outR.faceNormal_.resize(numFaceR);
+  outR.faceNormal_.resize_nofill(numFaceR);
 
   Vec<size_t> tmpBuffer(outR.faceNormal_.size());
   auto faceIds = TransformIterator(countAt(0_uz), [&sidesPerFacePQ](size_t i) {
@@ -196,8 +196,9 @@ std::tuple<Vec<int>, Vec<int>> SizeOutput(
 }
 
 struct EdgePos {
-  int vert;
   double edgePos;
+  int vert;
+  int collisionId;
   bool isStart;
 };
 
@@ -212,8 +213,8 @@ void AddNewEdgeVerts(
     // we need concurrent_map because we will be adding things concurrently
     concurrent_map<int, std::vector<EdgePos>> &edgesP,
     concurrent_map<std::pair<int, int>, std::vector<EdgePos>> &edgesNew,
-    const SparseIndices &p1q2, const Vec<int> &i12, const Vec<int> &v12R,
-    const Vec<Halfedge> &halfedgeP, bool forward) {
+    const Vec<std::array<int, 2>> &p1q2, const Vec<int> &i12, const Vec<int> &v12R,
+    const Vec<Halfedge> &halfedgeP, bool forward, size_t offset) {
   ZoneScoped;
   // For each edge of P that intersects a face of Q (p1q2), add this vertex to
   // P's corresponding edge vector and to the two new edges, which are
@@ -222,8 +223,8 @@ void AddNewEdgeVerts(
   // the output vert index. When forward is false, all is reversed.
   auto process = [&](std::function<void(size_t)> lock,
                      std::function<void(size_t)> unlock, size_t i) {
-    const int edgeP = p1q2.Get(i, !forward);
-    const int faceQ = p1q2.Get(i, forward);
+    const int edgeP = p1q2[i][forward ? 0 : 1];
+    const int faceQ = p1q2[i][forward ? 1 : 0];
     const int vert = v12R[i];
     const int inclusion = i12[i];
 
@@ -236,21 +237,22 @@ void AddNewEdgeVerts(
 
     bool direction = inclusion < 0;
     std::hash<std::pair<int, int>> pairHasher;
-    std::array<std::tuple<bool, size_t, std::vector<EdgePos> *>, 3> edges = {
+    std::array<std::tuple<bool, size_t, std::vector<EdgePos>*>, 3> edges = {
         std::make_tuple(direction, std::hash<int>{}(edgeP), &edgesP[edgeP]),
         std::make_tuple(direction ^ !forward,  // revert if not forward
                         pairHasher(keyRight), &edgesNew[keyRight]),
         std::make_tuple(direction ^ forward,  // revert if forward
                         pairHasher(keyLeft), &edgesNew[keyLeft])};
-    for (const auto &tuple : edges) {
+    for (const auto& tuple : edges) {
       lock(std::get<1>(tuple));
       for (int j = 0; j < std::abs(inclusion); ++j)
-        std::get<2>(tuple)->push_back({vert + j, 0.0, std::get<0>(tuple)});
+        std::get<2>(tuple)->push_back(
+            {0.0, vert + j, static_cast<int>(i + offset), std::get<0>(tuple)});
       unlock(std::get<1>(tuple));
       direction = !direction;
     }
   };
-#if (MANIFOLD_PAR == 1) && __has_include(<tbb/tbb.h>)
+#if (MANIFOLD_PAR == 1) && __has_include(<tbb/concurrent_map.h>)
   // parallelize operations, requires concurrent_map so we can only enable this
   // with tbb
   if (p1q2.size() > kParallelThreshold) {
@@ -264,19 +266,19 @@ void AddNewEdgeVerts(
         std::placeholders::_1);
     tbb::parallel_for(
         tbb::blocked_range<size_t>(0_uz, p1q2.size(), 32),
-        [&](const tbb::blocked_range<size_t> &range) {
+        [&](const tbb::blocked_range<size_t>& range) {
           for (size_t i = range.begin(); i != range.end(); i++) processFun(i);
         },
         ap);
     return;
   }
 #endif
-  auto processFun = std::bind(
-      process, [](size_t _) {}, [](size_t _) {}, std::placeholders::_1);
+  auto processFun =
+      std::bind(process, [](size_t) {}, [](size_t) {}, std::placeholders::_1);
   for (size_t i = 0; i < p1q2.size(); ++i) processFun(i);
 }
 
-std::vector<Halfedge> PairUp(std::vector<EdgePos> &edgePos) {
+std::vector<Halfedge> PairUp(std::vector<EdgePos>& edgePos) {
   // Pair start vertices with end vertices to form edges. The choice of pairing
   // is arbitrary for the manifoldness guarantee, but must be ordered to be
   // geometrically valid. If the order does not go start-end-start-end... then
@@ -289,7 +291,11 @@ std::vector<Halfedge> PairUp(std::vector<EdgePos> &edgePos) {
                                [](EdgePos x) { return x.isStart; });
   DEBUG_ASSERT(static_cast<size_t>(middle - edgePos.begin()) == nEdges,
                topologyErr, "Non-manifold edge!");
-  auto cmp = [](EdgePos a, EdgePos b) { return a.edgePos < b.edgePos; };
+  auto cmp = [](EdgePos a, EdgePos b) {
+    return a.edgePos < b.edgePos ||
+           // we also sort by collisionId to make things deterministic
+           (a.edgePos == b.edgePos && a.collisionId < b.collisionId);
+  };
   std::stable_sort(edgePos.begin(), middle, cmp);
   std::stable_sort(middle, edgePos.end(), cmp);
   std::vector<Halfedge> edges;
@@ -298,11 +304,11 @@ std::vector<Halfedge> PairUp(std::vector<EdgePos> &edgePos) {
   return edges;
 }
 
-void AppendPartialEdges(Manifold::Impl &outR, Vec<char> &wholeHalfedgeP,
-                        Vec<int> &facePtrR,
-                        concurrent_map<int, std::vector<EdgePos>> &edgesP,
-                        Vec<TriRef> &halfedgeRef, const Manifold::Impl &inP,
-                        const Vec<int> &i03, const Vec<int> &vP2R,
+void AppendPartialEdges(Manifold::Impl& outR, Vec<char>& wholeHalfedgeP,
+                        Vec<int>& facePtrR,
+                        concurrent_map<int, std::vector<EdgePos>>& edgesP,
+                        Vec<TriRef>& halfedgeRef, const Manifold::Impl& inP,
+                        const Vec<int>& i03, const Vec<int>& vP2R,
                         const Vec<int>::IterC faceP2R, bool forward) {
   ZoneScoped;
   // Each edge in the map is partially retained; for each of these, look up
@@ -310,15 +316,15 @@ void AppendPartialEdges(Manifold::Impl &outR, Vec<char> &wholeHalfedgeP,
   // while remapping them to the output using vP2R. Use the verts position
   // projected along the edge vector to pair them up, then distribute these
   // edges to their faces.
-  Vec<Halfedge> &halfedgeR = outR.halfedge_;
-  const Vec<vec3> &vertPosP = inP.vertPos_;
-  const Vec<Halfedge> &halfedgeP = inP.halfedge_;
+  Vec<Halfedge>& halfedgeR = outR.halfedge_;
+  const Vec<vec3>& vertPosP = inP.vertPos_;
+  const Vec<Halfedge>& halfedgeP = inP.halfedge_;
 
-  for (auto &value : edgesP) {
+  for (auto& value : edgesP) {
     const int edgeP = value.first;
-    std::vector<EdgePos> &edgePosP = value.second;
+    std::vector<EdgePos>& edgePosP = value.second;
 
-    const Halfedge &halfedge = halfedgeP[edgeP];
+    const Halfedge& halfedge = halfedgeP[edgeP];
     wholeHalfedgeP[edgeP] = false;
     wholeHalfedgeP[halfedge.pairedHalfedge] = false;
 
@@ -326,13 +332,13 @@ void AppendPartialEdges(Manifold::Impl &outR, Vec<char> &wholeHalfedgeP,
     const int vEnd = halfedge.endVert;
     const vec3 edgeVec = vertPosP[vEnd] - vertPosP[vStart];
     // Fill in the edge positions of the old points.
-    for (EdgePos &edge : edgePosP) {
+    for (EdgePos& edge : edgePosP) {
       edge.edgePos = la::dot(outR.vertPos_[edge.vert], edgeVec);
     }
 
     int inclusion = i03[vStart];
-    EdgePos edgePos = {vP2R[vStart],
-                       la::dot(outR.vertPos_[vP2R[vStart]], edgeVec),
+    EdgePos edgePos = {la::dot(outR.vertPos_[vP2R[vStart]], edgeVec),
+                       vP2R[vStart], std::numeric_limits<int>::max(),
                        inclusion > 0};
     for (int j = 0; j < std::abs(inclusion); ++j) {
       edgePosP.push_back(edgePos);
@@ -340,8 +346,8 @@ void AppendPartialEdges(Manifold::Impl &outR, Vec<char> &wholeHalfedgeP,
     }
 
     inclusion = i03[vEnd];
-    edgePos = {vP2R[vEnd], la::dot(outR.vertPos_[vP2R[vEnd]], edgeVec),
-               inclusion < 0};
+    edgePos = {la::dot(outR.vertPos_[vP2R[vEnd]], edgeVec), vP2R[vEnd],
+               std::numeric_limits<int>::max(), inclusion < 0};
     for (int j = 0; j < std::abs(inclusion); ++j) {
       edgePosP.push_back(edgePos);
       ++edgePos.vert;
@@ -359,8 +365,8 @@ void AppendPartialEdges(Manifold::Impl &outR, Vec<char> &wholeHalfedgeP,
     // reference is now to the endVert instead of the startVert, which is one
     // position advanced CCW. This is only valid if this is a retained vert; it
     // will be ignored later if the vert is new.
-    const TriRef forwardRef = {forward ? 0 : 1, -1, faceLeftP};
-    const TriRef backwardRef = {forward ? 0 : 1, -1, faceRightP};
+    const TriRef forwardRef = {forward ? 0 : 1, -1, faceLeftP, -1};
+    const TriRef backwardRef = {forward ? 0 : 1, -1, faceRightP, -1};
 
     for (Halfedge e : edges) {
       const int forwardEdge = facePtrR[faceLeft]++;
@@ -379,18 +385,18 @@ void AppendPartialEdges(Manifold::Impl &outR, Vec<char> &wholeHalfedgeP,
 }
 
 void AppendNewEdges(
-    Manifold::Impl &outR, Vec<int> &facePtrR,
-    concurrent_map<std::pair<int, int>, std::vector<EdgePos>> &edgesNew,
-    Vec<TriRef> &halfedgeRef, const Vec<int> &facePQ2R, const int numFaceP) {
+    Manifold::Impl& outR, Vec<int>& facePtrR,
+    concurrent_map<std::pair<int, int>, std::vector<EdgePos>>& edgesNew,
+    Vec<TriRef>& halfedgeRef, const Vec<int>& facePQ2R, const int numFaceP) {
   ZoneScoped;
   // Pair up each edge's verts and distribute to faces based on indices in key.
-  Vec<Halfedge> &halfedgeR = outR.halfedge_;
-  Vec<vec3> &vertPosR = outR.vertPos_;
+  Vec<Halfedge>& halfedgeR = outR.halfedge_;
+  Vec<vec3>& vertPosR = outR.vertPos_;
 
-  for (auto &value : edgesNew) {
+  for (auto& value : edgesNew) {
     const int faceP = value.first.first;
     const int faceQ = value.first.second;
-    std::vector<EdgePos> &edgePos = value.second;
+    std::vector<EdgePos>& edgePos = value.second;
 
     Box bbox;
     for (auto edge : edgePos) {
@@ -401,7 +407,7 @@ void AppendNewEdges(
     const int i = (size.x > size.y && size.x > size.z) ? 0
                   : size.y > size.z                    ? 1
                                                        : 2;
-    for (auto &edge : edgePos) {
+    for (auto& edge : edgePos) {
       edge.edgePos = vertPosR[edge.vert][i];
     }
 
@@ -411,8 +417,8 @@ void AppendNewEdges(
     // add halfedges to result
     const int faceLeft = facePQ2R[faceP];
     const int faceRight = facePQ2R[numFaceP + faceQ];
-    const TriRef forwardRef = {0, -1, faceP};
-    const TriRef backwardRef = {1, -1, faceQ};
+    const TriRef forwardRef = {0, -1, faceP, -1};
+    const TriRef backwardRef = {1, -1, faceQ, -1};
     for (Halfedge e : edges) {
       const int forwardEdge = facePtrR[faceLeft]++;
       const int backwardEdge = facePtrR[faceRight]++;
@@ -459,8 +465,8 @@ struct DuplicateHalfedges {
     // Negative inclusion means the halfedges are reversed, which means our
     // reference is now to the endVert instead of the startVert, which is one
     // position advanced CCW.
-    const TriRef forwardRef = {forward ? 0 : 1, -1, faceLeftP};
-    const TriRef backwardRef = {forward ? 0 : 1, -1, faceRightP};
+    const TriRef forwardRef = {forward ? 0 : 1, -1, faceLeftP, -1};
+    const TriRef backwardRef = {forward ? 0 : 1, -1, faceRightP, -1};
 
     for (int i = 0; i < std::abs(inclusion); ++i) {
       int forwardEdge = AtomicAdd(facePtr[newFace], 1);
@@ -479,10 +485,10 @@ struct DuplicateHalfedges {
   }
 };
 
-void AppendWholeEdges(Manifold::Impl &outR, Vec<int> &facePtrR,
-                      Vec<TriRef> &halfedgeRef, const Manifold::Impl &inP,
-                      const Vec<char> wholeHalfedgeP, const Vec<int> &i03,
-                      const Vec<int> &vP2R, VecView<const int> faceP2R,
+void AppendWholeEdges(Manifold::Impl& outR, Vec<int>& facePtrR,
+                      Vec<TriRef>& halfedgeRef, const Manifold::Impl& inP,
+                      const Vec<char> wholeHalfedgeP, const Vec<int>& i03,
+                      const Vec<int>& vP2R, VecView<const int> faceP2R,
                       bool forward) {
   ZoneScoped;
   for_each_n(
@@ -496,26 +502,26 @@ struct MapTriRef {
   VecView<const TriRef> triRefQ;
   const int offsetQ;
 
-  void operator()(TriRef &triRef) {
-    const int tri = triRef.tri;
+  void operator()(TriRef& triRef) {
+    const int tri = triRef.faceID;
     const bool PQ = triRef.meshID == 0;
     triRef = PQ ? triRefP[tri] : triRefQ[tri];
     if (!PQ) triRef.meshID += offsetQ;
   }
 };
 
-void UpdateReference(Manifold::Impl &outR, const Manifold::Impl &inP,
-                     const Manifold::Impl &inQ, bool invertQ) {
+void UpdateReference(Manifold::Impl& outR, const Manifold::Impl& inP,
+                     const Manifold::Impl& inQ, bool invertQ) {
   const int offsetQ = Manifold::Impl::meshIDCounter_;
   for_each_n(
       autoPolicy(outR.NumTri(), 1e5), outR.meshRelation_.triRef.begin(),
       outR.NumTri(),
       MapTriRef({inP.meshRelation_.triRef, inQ.meshRelation_.triRef, offsetQ}));
 
-  for (const auto &pair : inP.meshRelation_.meshIDtransform) {
+  for (const auto& pair : inP.meshRelation_.meshIDtransform) {
     outR.meshRelation_.meshIDtransform[pair.first] = pair.second;
   }
-  for (const auto &pair : inQ.meshRelation_.meshIDtransform) {
+  for (const auto& pair : inQ.meshRelation_.meshIDtransform) {
     outR.meshRelation_.meshIDtransform[pair.first + offsetQ] = pair.second;
     outR.meshRelation_.meshIDtransform[pair.first + offsetQ].backSide ^=
         invertQ;
@@ -537,10 +543,10 @@ struct Barycentric {
     const TriRef refPQ = ref[tri];
     if (halfedgeR[3 * tri].startVert < 0) return;
 
-    const int triPQ = refPQ.tri;
+    const int triPQ = refPQ.faceID;
     const bool PQ = refPQ.meshID == 0;
-    const auto &vertPos = PQ ? vertPosP : vertPosQ;
-    const auto &halfedge = PQ ? halfedgeP : halfedgeQ;
+    const auto& vertPos = PQ ? vertPosP : vertPosQ;
+    const auto& halfedge = PQ ? halfedgeP : halfedgeQ;
 
     mat3 triPos;
     for (const int j : {0, 1, 2})
@@ -553,18 +559,16 @@ struct Barycentric {
   }
 };
 
-void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
-                      const Manifold::Impl &inQ) {
+void CreateProperties(Manifold::Impl& outR, const Manifold::Impl& inP,
+                      const Manifold::Impl& inQ) {
   ZoneScoped;
   const int numPropP = inP.NumProp();
   const int numPropQ = inQ.NumProp();
   const int numProp = std::max(numPropP, numPropQ);
-  outR.meshRelation_.numProp = numProp;
+  outR.numProp_ = numProp;
   if (numProp == 0) return;
 
   const int numTri = outR.NumTri();
-  outR.meshRelation_.triProperties.resize(numTri);
-
   Vec<vec3> bary(outR.halfedge_.size());
   for_each_n(autoPolicy(numTri, 1e4), countAt(0), numTri,
              Barycentric({bary, outR.meshRelation_.triRef, inP.vertPos_,
@@ -578,7 +582,7 @@ void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
   propMissIdx[0].resize(inQ.NumPropVert(), -1);
   propMissIdx[1].resize(inP.NumPropVert(), -1);
 
-  outR.meshRelation_.properties.reserve(outR.NumVert() * numProp);
+  outR.properties_.reserve(outR.NumVert() * numProp);
   int idx = 0;
 
   for (int tri = 0; tri < numTri; ++tri) {
@@ -588,15 +592,12 @@ void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
     const TriRef ref = outR.meshRelation_.triRef[tri];
     const bool PQ = ref.meshID == 0;
     const int oldNumProp = PQ ? numPropP : numPropQ;
-    const auto &properties =
-        PQ ? inP.meshRelation_.properties : inQ.meshRelation_.properties;
-    const ivec3 &triProp = oldNumProp == 0 ? ivec3(-1)
-                           : PQ ? inP.meshRelation_.triProperties[ref.tri]
-                                : inQ.meshRelation_.triProperties[ref.tri];
+    const auto& properties = PQ ? inP.properties_ : inQ.properties_;
+    const auto& halfedge = PQ ? inP.halfedge_ : inQ.halfedge_;
 
     for (const int i : {0, 1, 2}) {
       const int vert = outR.halfedge_[3 * tri + i].startVert;
-      const vec3 &uvw = bary[3 * tri + i];
+      const vec3& uvw = bary[3 * tri + i];
 
       ivec4 key(PQ, idMissProp, -1, -1);
       if (oldNumProp > 0) {
@@ -604,7 +605,7 @@ void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
         for (const int j : {0, 1, 2}) {
           if (uvw[j] == 1) {
             // On a retained vert, the propVert must also match
-            key[2] = triProp[j];
+            key[2] = halfedge[3 * ref.faceID + j].propVert;
             edge = -1;
             break;
           }
@@ -612,8 +613,8 @@ void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
         }
         if (edge >= 0) {
           // On an edge, both propVerts must match
-          const int p0 = triProp[Next3(edge)];
-          const int p1 = triProp[Prev3(edge)];
+          const int p0 = halfedge[3 * ref.faceID + Next3(edge)].propVert;
+          const int p1 = halfedge[3 * ref.faceID + Prev3(edge)].propVert;
           key[1] = vert;
           key[2] = std::min(p0, p1);
           key[3] = std::max(p0, p1);
@@ -624,19 +625,19 @@ void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
 
       if (key.y == idMissProp && key.z >= 0) {
         // only key.x/key.z matters
-        auto &entry = propMissIdx[key.x][key.z];
+        auto& entry = propMissIdx[key.x][key.z];
         if (entry >= 0) {
-          outR.meshRelation_.triProperties[tri][i] = entry;
+          outR.halfedge_[3 * tri + i].propVert = entry;
           continue;
         }
         entry = idx;
       } else {
-        auto &bin = propIdx[key.y];
+        auto& bin = propIdx[key.y];
         bool bFound = false;
-        for (const auto &b : bin) {
+        for (const auto& b : bin) {
           if (b.first == ivec3(key.x, key.z, key.w)) {
             bFound = true;
-            outR.meshRelation_.triProperties[tri][i] = b.second;
+            outR.halfedge_[3 * tri + i].propVert = b.second;
             break;
           }
         }
@@ -644,20 +645,55 @@ void CreateProperties(Manifold::Impl &outR, const Manifold::Impl &inP,
         bin.push_back(std::make_pair(ivec3(key.x, key.z, key.w), idx));
       }
 
-      outR.meshRelation_.triProperties[tri][i] = idx++;
+      outR.halfedge_[3 * tri + i].propVert = idx++;
       for (int p = 0; p < numProp; ++p) {
         if (p < oldNumProp) {
           vec3 oldProps;
           for (const int j : {0, 1, 2})
-            oldProps[j] = properties[oldNumProp * triProp[j] + p];
-          outR.meshRelation_.properties.push_back(la::dot(uvw, oldProps));
+            oldProps[j] =
+                properties[oldNumProp * halfedge[3 * ref.faceID + j].propVert +
+                           p];
+          outR.properties_.push_back(la::dot(uvw, oldProps));
         } else {
-          outR.meshRelation_.properties.push_back(0);
+          outR.properties_.push_back(0);
         }
       }
     }
   }
 }
+
+void ReorderHalfedges(VecView<Halfedge>& halfedges) {
+  // halfedges in the same face are added in non-deterministic order, so we have
+  // to reorder them for determinism
+
+  // step 1: reorder within the same face, such that the halfedge with the
+  // smallest starting vertex is placed first
+  for_each(autoPolicy(halfedges.size() / 3), countAt(0),
+           countAt(halfedges.size() / 3), [&halfedges](size_t tri) {
+             std::array<Halfedge, 3> face = {halfedges[tri * 3],
+                                             halfedges[tri * 3 + 1],
+                                             halfedges[tri * 3 + 2]};
+             int index = 0;
+             for (int i : {1, 2})
+               if (face[i].startVert < face[index].startVert) index = i;
+             for (int i : {0, 1, 2})
+               halfedges[tri * 3 + i] = face[(index + i) % 3];
+           });
+  // step 2: fix paired halfedge
+  for_each(autoPolicy(halfedges.size() / 3), countAt(0),
+           countAt(halfedges.size() / 3), [&halfedges](size_t tri) {
+             for (int i : {0, 1, 2}) {
+               Halfedge& curr = halfedges[tri * 3 + i];
+               int oppositeFace = curr.pairedHalfedge / 3;
+               int index = -1;
+               for (int j : {0, 1, 2})
+                 if (curr.startVert == halfedges[oppositeFace * 3 + j].endVert)
+                   index = j;
+               curr.pairedHalfedge = oppositeFace * 3 + index;
+             }
+           });
+}
+
 }  // namespace
 
 namespace manifold {
@@ -697,6 +733,12 @@ Manifold::Impl Boolean3::Result(OpType op) const {
     return inP_;
   }
 
+  if (!valid) {
+    auto impl = Manifold::Impl();
+    impl.status_ = Manifold::Error::ResultTooLarge;
+    return impl;
+  }
+
   const bool invertQ = op == OpType::Subtract;
 
   // Convert winding numbers to inclusion values based on operation type.
@@ -746,7 +788,7 @@ Manifold::Impl Boolean3::Result(OpType op) const {
   outR.epsilon_ = std::max(inP_.epsilon_, inQ_.epsilon_);
   outR.tolerance_ = std::max(inP_.tolerance_, inQ_.tolerance_);
 
-  outR.vertPos_.resize(numVertR);
+  outR.vertPos_.resize_nofill(numVertR);
   // Add vertices, duplicating for inclusion numbers not in [-1, 1].
   // Retained vertices from P and Q:
   for_each_n(autoPolicy(inP_.NumVert(), 1e4), countAt(0), inP_.NumVert(),
@@ -775,8 +817,9 @@ Manifold::Impl Boolean3::Result(OpType op) const {
   // This key is the face index of <P, Q>
   concurrent_map<std::pair<int, int>, std::vector<EdgePos>> edgesNew;
 
-  AddNewEdgeVerts(edgesP, edgesNew, p1q2_, i12, v12R, inP_.halfedge_, true);
-  AddNewEdgeVerts(edgesQ, edgesNew, p2q1_, i21, v21R, inQ_.halfedge_, false);
+  AddNewEdgeVerts(edgesP, edgesNew, p1q2_, i12, v12R, inP_.halfedge_, true, 0);
+  AddNewEdgeVerts(edgesQ, edgesNew, p2q1_, i21, v21R, inQ_.halfedge_, false,
+                  p1q2_.size());
 
   v12R.clear();
   v21R.clear();
@@ -842,6 +885,8 @@ Manifold::Impl Boolean3::Result(OpType op) const {
   halfedgeRef.clear();
   faceEdge.clear();
 
+  ReorderHalfedges(outR.halfedge_);
+
 #ifdef MANIFOLD_DEBUG
   triangulate.Stop();
   Timer simplify;
@@ -856,7 +901,7 @@ Manifold::Impl Boolean3::Result(OpType op) const {
 
   UpdateReference(outR, inP_, inQ_, invertQ);
 
-  outR.SimplifyTopology();
+  outR.SimplifyTopology(nPv + nQv);
   outR.RemoveUnreferencedVerts();
 
   if (ManifoldParams().intermediateChecks)
diff --git a/thirdparty/manifold/src/collider.h b/thirdparty/manifold/src/collider.h
index 80de94b7c2..d266669905 100644
--- a/thirdparty/manifold/src/collider.h
+++ b/thirdparty/manifold/src/collider.h
@@ -13,11 +13,10 @@
 // limitations under the License.
 
 #pragma once
-#include "./parallel.h"
-#include "./sparse.h"
-#include "./utils.h"
-#include "./vec.h"
 #include "manifold/common.h"
+#include "parallel.h"
+#include "utils.h"
+#include "vec.h"
 
 #ifdef _MSC_VER
 #include <intrin.h>
@@ -40,7 +39,7 @@ constexpr int kRoot = 1;
 #ifdef _MSC_VER
 
 #ifndef _WINDEF_
-typedef unsigned long DWORD;
+using DWORD = unsigned long;
 #endif
 
 uint32_t inline ctz(uint32_t value) {
@@ -163,14 +162,16 @@ struct FindCollision {
   VecView<const T> queries;
   VecView<const Box> nodeBBox_;
   VecView<const std::pair<int, int>> internalChildren_;
-  Recorder recorder;
+  Recorder& recorder;
 
-  inline int RecordCollision(int node, const int queryIdx, SparseIndices& ind) {
+  using Local = typename Recorder::Local;
+
+  inline int RecordCollision(int node, const int queryIdx, Local& local) {
     bool overlaps = nodeBBox_[node].DoesOverlap(queries[queryIdx]);
     if (overlaps && IsLeaf(node)) {
       int leafIdx = Node2Leaf(node);
       if (!selfCollision || leafIdx != queryIdx) {
-        recorder.record(queryIdx, leafIdx, ind);
+        recorder.record(queryIdx, leafIdx, local);
       }
     }
     return overlaps && IsInternal(node);  // Should traverse into node
@@ -183,14 +184,14 @@ struct FindCollision {
     int top = -1;
     // Depth-first search
     int node = kRoot;
-    SparseIndices& ind = recorder.local();
+    Local& local = recorder.local();
     while (1) {
       int internal = Node2Internal(node);
       int child1 = internalChildren_[internal].first;
       int child2 = internalChildren_[internal].second;
 
-      int traverse1 = RecordCollision(child1, queryIdx, ind);
-      int traverse2 = RecordCollision(child2, queryIdx, ind);
+      int traverse1 = RecordCollision(child1, queryIdx, local);
+      int traverse2 = RecordCollision(child2, queryIdx, local);
 
       if (!traverse1 && !traverse2) {
         if (top < 0) break;   // done
@@ -205,35 +206,6 @@ struct FindCollision {
   }
 };
 
-template <const bool inverted>
-struct SeqCollisionRecorder {
-  SparseIndices& queryTri_;
-  inline void record(int queryIdx, int leafIdx, SparseIndices& ind) const {
-    if (inverted)
-      ind.Add(leafIdx, queryIdx);
-    else
-      ind.Add(queryIdx, leafIdx);
-  }
-  SparseIndices& local() { return queryTri_; }
-};
-
-#if (MANIFOLD_PAR == 1)
-template <const bool inverted>
-struct ParCollisionRecorder {
-  tbb::combinable<SparseIndices>& store;
-  inline void record(int queryIdx, int leafIdx, SparseIndices& ind) const {
-    // Add may invoke something in parallel, and it may return in
-    // another thread, making thread local unsafe
-    // we need to explicitly forbid parallelization by passing a flag
-    if (inverted)
-      ind.Add(leafIdx, queryIdx, true);
-    else
-      ind.Add(queryIdx, leafIdx, true);
-  }
-  SparseIndices& local() { return store.local(); }
-};
-#endif
-
 struct BuildInternalBoxes {
   VecView<Box> nodeBBox_;
   VecView<int> counter_;
@@ -266,6 +238,22 @@ constexpr inline uint32_t SpreadBits3(uint32_t v) {
 }
 }  // namespace collider_internal
 
+template <typename F>
+struct SimpleRecorder {
+  using Local = F;
+  F& f;
+
+  inline void record(int queryIdx, int leafIdx, F& f) const {
+    f(queryIdx, leafIdx);
+  }
+  Local& local() { return f; }
+};
+
+template <typename F>
+inline SimpleRecorder<F> MakeSimpleRecorder(F& f) {
+  return SimpleRecorder<F>{f};
+}
+
 /** @ingroup Private */
 class Collider {
  public:
@@ -278,7 +266,7 @@ class Collider {
                  "vectors must be the same length");
     int num_nodes = 2 * leafBB.size() - 1;
     // assign and allocate members
-    nodeBBox_.resize(num_nodes);
+    nodeBBox_.resize_nofill(num_nodes);
     nodeParent_.resize(num_nodes, -1);
     internalChildren_.resize(leafBB.size() - 1, std::make_pair(-1, -1));
     // organize tree
@@ -321,40 +309,27 @@ class Collider {
                    {nodeBBox_, counter, nodeParent_, internalChildren_}));
   }
 
-  template <const bool selfCollision = false, const bool inverted = false,
-            typename T>
-  void Collisions(const VecView<const T>& queriesIn,
-                  SparseIndices& queryTri) const {
+  // This function iterates over queriesIn and calls recorder.record(queryIdx,
+  // leafIdx, local) for each collision it found.
+  // If selfCollisionl is true, it will skip the case where queryIdx == leafIdx.
+  // The recorder should provide a local() method that returns a Recorder::Local
+  // type, representing thread local storage. By default, recorder.record can
+  // run in parallel and the thread local storage can be combined at the end.
+  // If parallel is false, the function will run in sequential mode.
+  //
+  // If thread local storage is not needed, use SimpleRecorder.
+  template <const bool selfCollision = false, typename T, typename Recorder>
+  void Collisions(const VecView<const T>& queriesIn, Recorder& recorder,
+                  bool parallel = true) const {
     ZoneScoped;
     using collider_internal::FindCollision;
-#if (MANIFOLD_PAR == 1)
-    if (queriesIn.size() > collider_internal::kSequentialThreshold) {
-      tbb::combinable<SparseIndices> store;
-      for_each_n(
-          ExecutionPolicy::Par, countAt(0), queriesIn.size(),
-          FindCollision<T, selfCollision,
-                        collider_internal::ParCollisionRecorder<inverted>>{
-              queriesIn, nodeBBox_, internalChildren_, {store}});
-
-      std::vector<SparseIndices> tmp;
-      store.combine_each(
-          [&](SparseIndices& ind) { tmp.emplace_back(std::move(ind)); });
-      queryTri.FromIndices(tmp);
-      return;
-    }
-#endif
-    for_each_n(ExecutionPolicy::Seq, countAt(0), queriesIn.size(),
-               FindCollision<T, selfCollision,
-                             collider_internal::SeqCollisionRecorder<inverted>>{
-                   queriesIn, nodeBBox_, internalChildren_, {queryTri}});
-  }
-
-  template <const bool selfCollision = false, const bool inverted = false,
-            typename T>
-  SparseIndices Collisions(const VecView<const T>& queriesIn) const {
-    SparseIndices result;
-    Collisions<selfCollision, inverted, T>(queriesIn, result);
-    return result;
+    if (internalChildren_.empty()) return;
+    for_each_n(parallel ? autoPolicy(queriesIn.size(),
+                                     collider_internal::kSequentialThreshold)
+                        : ExecutionPolicy::Seq,
+               countAt(0), queriesIn.size(),
+               FindCollision<T, selfCollision, Recorder>{
+                   queriesIn, nodeBBox_, internalChildren_, recorder});
   }
 
   static uint32_t MortonCode(vec3 position, Box bBox) {
diff --git a/thirdparty/manifold/src/constructors.cpp b/thirdparty/manifold/src/constructors.cpp
index 2b3e528c6b..86acc2d1ab 100644
--- a/thirdparty/manifold/src/constructors.cpp
+++ b/thirdparty/manifold/src/constructors.cpp
@@ -12,10 +12,43 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "./csg_tree.h"
-#include "./impl.h"
-#include "./parallel.h"
+#include "csg_tree.h"
+#include "impl.h"
+#include "manifold/manifold.h"
 #include "manifold/polygon.h"
+#include "parallel.h"
+
+namespace {
+using namespace manifold;
+
+template <typename P, typename I>
+std::shared_ptr<Manifold::Impl> SmoothImpl(
+    const MeshGLP<P, I>& meshGL,
+    const std::vector<Smoothness>& sharpenedEdges) {
+  DEBUG_ASSERT(meshGL.halfedgeTangent.empty(), std::runtime_error,
+               "when supplying tangents, the normal constructor should be used "
+               "rather than Smooth().");
+
+  MeshGLP<P, I> meshTmp = meshGL;
+  meshTmp.faceID.resize(meshGL.NumTri());
+  std::iota(meshTmp.faceID.begin(), meshTmp.faceID.end(), 0);
+
+  std::shared_ptr<Manifold::Impl> impl =
+      std::make_shared<Manifold::Impl>(meshTmp);
+  impl->CreateTangents(impl->UpdateSharpenedEdges(sharpenedEdges));
+  // Restore the original faceID
+  const size_t numTri = impl->NumTri();
+  for (size_t i = 0; i < numTri; ++i) {
+    if (meshGL.faceID.size() == numTri) {
+      impl->meshRelation_.triRef[i].faceID =
+          meshGL.faceID[impl->meshRelation_.triRef[i].faceID];
+    } else {
+      impl->meshRelation_.triRef[i].faceID = -1;
+    }
+  }
+  return impl;
+}
+}  // namespace
 
 namespace manifold {
 /**
@@ -48,13 +81,7 @@ namespace manifold {
  */
 Manifold Manifold::Smooth(const MeshGL& meshGL,
                           const std::vector<Smoothness>& sharpenedEdges) {
-  DEBUG_ASSERT(meshGL.halfedgeTangent.empty(), std::runtime_error,
-               "when supplying tangents, the normal constructor should be used "
-               "rather than Smooth().");
-
-  std::shared_ptr<Impl> impl = std::make_shared<Impl>(meshGL);
-  impl->CreateTangents(impl->UpdateSharpenedEdges(sharpenedEdges));
-  return Manifold(impl);
+  return Manifold(SmoothImpl(meshGL, sharpenedEdges));
 }
 
 /**
@@ -87,13 +114,7 @@ Manifold Manifold::Smooth(const MeshGL& meshGL,
  */
 Manifold Manifold::Smooth(const MeshGL64& meshGL64,
                           const std::vector<Smoothness>& sharpenedEdges) {
-  DEBUG_ASSERT(meshGL64.halfedgeTangent.empty(), std::runtime_error,
-               "when supplying tangents, the normal constructor should be used "
-               "rather than Smooth().");
-
-  std::shared_ptr<Impl> impl = std::make_shared<Impl>(meshGL64);
-  impl->CreateTangents(impl->UpdateSharpenedEdges(sharpenedEdges));
-  return Manifold(impl);
+  return Manifold(SmoothImpl(meshGL64, sharpenedEdges));
 }
 
 /**
@@ -173,8 +194,7 @@ Manifold Manifold::Sphere(double radius, int circularSegments) {
   int n = circularSegments > 0 ? (circularSegments + 3) / 4
                                : Quality::GetCircularSegments(radius) / 4;
   auto pImpl_ = std::make_shared<Impl>(Impl::Shape::Octahedron);
-  pImpl_->Subdivide(
-      [n](vec3 edge, vec4 tangentStart, vec4 tangentEnd) { return n - 1; });
+  pImpl_->Subdivide([n](vec3, vec4, vec4) { return n - 1; });
   for_each_n(autoPolicy(pImpl_->NumVert(), 1e5), pImpl_->vertPos_.begin(),
              pImpl_->NumVert(), [radius](vec3& v) {
                v = la::cos(kHalfPi * (1.0 - v));
@@ -277,7 +297,7 @@ Manifold Manifold::Extrude(const Polygons& crossSection, double height,
   pImpl_->CreateHalfedges(triVertsDH);
   pImpl_->Finish();
   pImpl_->InitializeOriginal();
-  pImpl_->CreateFaces();
+  pImpl_->MarkCoplanar();
   return Manifold(pImpl_);
 }
 
@@ -316,7 +336,7 @@ Manifold Manifold::Revolve(const Polygons& crossSection, int circularSegments,
       }
       const size_t next = i + 1 == poly.size() ? 0 : i + 1;
       if ((poly[next].x < 0) != (poly[i].x < 0)) {
-        const double y = poly[next].y + poly[next].x *
+        const double y = poly[next].y - poly[next].x *
                                             (poly[i].y - poly[next].y) /
                                             (poly[i].x - poly[next].x);
         polygons.back().push_back({0, y});
@@ -352,8 +372,8 @@ Manifold Manifold::Revolve(const Polygons& crossSection, int circularSegments,
   const int nSlices = isFullRevolution ? nDivisions : nDivisions + 1;
 
   for (const auto& poly : polygons) {
-    std::size_t nPosVerts = 0;
-    std::size_t nRevolveAxisVerts = 0;
+    size_t nPosVerts = 0;
+    size_t nRevolveAxisVerts = 0;
     for (auto& pt : poly) {
       if (pt.x > 0) {
         nPosVerts++;
@@ -420,7 +440,7 @@ Manifold Manifold::Revolve(const Polygons& crossSection, int circularSegments,
   pImpl_->CreateHalfedges(triVertsDH);
   pImpl_->Finish();
   pImpl_->InitializeOriginal();
-  pImpl_->CreateFaces();
+  pImpl_->MarkCoplanar();
   return Manifold(pImpl_);
 }
 
diff --git a/thirdparty/manifold/src/cross_section/cross_section.cpp b/thirdparty/manifold/src/cross_section/cross_section.cpp
index bacdfd10e6..84d285cca7 100644
--- a/thirdparty/manifold/src/cross_section/cross_section.cpp
+++ b/thirdparty/manifold/src/cross_section/cross_section.cpp
@@ -376,6 +376,16 @@ CrossSection CrossSection::BatchBoolean(
     return crossSections[0];
 
   auto subjs = crossSections[0].GetPaths();
+
+  if (op == OpType::Intersect) {
+    auto res = subjs->paths_;
+    for (size_t i = 1; i < crossSections.size(); ++i) {
+      res = C2::BooleanOp(C2::ClipType::Intersection, C2::FillRule::Positive,
+                          res, crossSections[i].GetPaths()->paths_, precision_);
+    }
+    return CrossSection(shared_paths(res));
+  }
+
   int n_clips = 0;
   for (size_t i = 1; i < crossSections.size(); ++i) {
     n_clips += crossSections[i].GetPaths()->paths_.size();
@@ -446,7 +456,8 @@ CrossSection& CrossSection::operator^=(const CrossSection& Q) {
  * Construct a CrossSection from a vector of other CrossSections (batch
  * boolean union).
  */
-CrossSection CrossSection::Compose(std::vector<CrossSection>& crossSections) {
+CrossSection CrossSection::Compose(
+    const std::vector<CrossSection>& crossSections) {
   return BatchBoolean(crossSections, OpType::Add);
 }
 
@@ -518,9 +529,9 @@ CrossSection CrossSection::Scale(const vec2 scale) const {
 }
 
 /**
- * Mirror this CrossSection over the arbitrary axis described by the unit form
- * of the given vector. If the length of the vector is zero, an empty
- * CrossSection is returned. This operation can be chained. Transforms are
+ * Mirror this CrossSection over the arbitrary axis whose normal is described by
+ * the unit form of the given vector. If the length of the vector is zero, an
+ * empty CrossSection is returned. This operation can be chained. Transforms are
  * combined and applied lazily.
  *
  * @param ax the axis to be mirrored over
@@ -529,7 +540,7 @@ CrossSection CrossSection::Mirror(const vec2 ax) const {
   if (la::length(ax) == 0.) {
     return CrossSection();
   }
-  auto n = la::normalize(la::abs(ax));
+  auto n = la::normalize(ax);
   auto m = mat2x3(mat2(la::identity) - 2.0 * la::outerprod(n, n), vec2(0.0));
   return Transform(m);
 }
@@ -641,7 +652,7 @@ CrossSection CrossSection::Simplify(double epsilon) const {
  * to expand, and retraction of inner (hole) contours. Negative deltas will
  * have the opposite effect.
  * @param jointype The join type specifying the treatment of contour joins
- * (corners).
+ * (corners). Defaults to Round.
  * @param miter_limit The maximum distance in multiples of delta that vertices
  * can be offset from their original positions with before squaring is
  * applied, <B>when the join type is Miter</B> (default is 2, which is the
diff --git a/thirdparty/manifold/src/csg_tree.cpp b/thirdparty/manifold/src/csg_tree.cpp
index e126485ece..c41cb8f0c5 100644
--- a/thirdparty/manifold/src/csg_tree.cpp
+++ b/thirdparty/manifold/src/csg_tree.cpp
@@ -12,27 +12,23 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#if (MANIFOLD_PAR == 1) && __has_include(<tbb/concurrent_priority_queue.h>)
+#if MANIFOLD_PAR == 1
 #include <tbb/tbb.h>
-#define TBB_PREVIEW_CONCURRENT_ORDERED_CONTAINERS 1
-#include <tbb/concurrent_priority_queue.h>
 #endif
 
 #include <algorithm>
 
-#include "./boolean3.h"
-#include "./csg_tree.h"
-#include "./impl.h"
-#include "./mesh_fixes.h"
-#include "./parallel.h"
-
-constexpr int kParallelThreshold = 4096;
+#include "boolean3.h"
+#include "csg_tree.h"
+#include "impl.h"
+#include "mesh_fixes.h"
+#include "parallel.h"
 
 namespace {
 using namespace manifold;
 struct MeshCompare {
-  bool operator()(const std::shared_ptr<CsgLeafNode> &a,
-                  const std::shared_ptr<CsgLeafNode> &b) {
+  bool operator()(const std::shared_ptr<CsgLeafNode>& a,
+                  const std::shared_ptr<CsgLeafNode>& b) {
     return a->GetImpl()->NumVert() < b->GetImpl()->NumVert();
   }
 };
@@ -41,7 +37,7 @@ struct MeshCompare {
 namespace manifold {
 
 std::shared_ptr<CsgNode> CsgNode::Boolean(
-    const std::shared_ptr<CsgNode> &second, OpType op) {
+    const std::shared_ptr<CsgNode>& second, OpType op) {
   if (second->GetNodeType() != CsgNodeType::Leaf) {
     // "this" is not a CsgOpNode (which overrides Boolean), but if "second" is
     // and the operation is commutative, we let it built the tree.
@@ -54,13 +50,13 @@ std::shared_ptr<CsgNode> CsgNode::Boolean(
   return std::make_shared<CsgOpNode>(children, op);
 }
 
-std::shared_ptr<CsgNode> CsgNode::Translate(const vec3 &t) const {
+std::shared_ptr<CsgNode> CsgNode::Translate(const vec3& t) const {
   mat3x4 transform = la::identity;
   transform[3] += t;
   return Transform(transform);
 }
 
-std::shared_ptr<CsgNode> CsgNode::Scale(const vec3 &v) const {
+std::shared_ptr<CsgNode> CsgNode::Scale(const vec3& v) const {
   mat3x4 transform;
   for (int i : {0, 1, 2}) transform[i][i] = v[i];
   return Transform(transform);
@@ -102,18 +98,18 @@ std::shared_ptr<CsgLeafNode> CsgLeafNode::ToLeafNode() const {
   return std::make_shared<CsgLeafNode>(*this);
 }
 
-std::shared_ptr<CsgNode> CsgLeafNode::Transform(const mat3x4 &m) const {
+std::shared_ptr<CsgNode> CsgLeafNode::Transform(const mat3x4& m) const {
   return std::make_shared<CsgLeafNode>(pImpl_, m * Mat4(transform_));
 }
 
 CsgNodeType CsgLeafNode::GetNodeType() const { return CsgNodeType::Leaf; }
 
-std::shared_ptr<CsgLeafNode> ImplToLeaf(Manifold::Impl &&impl) {
+std::shared_ptr<CsgLeafNode> ImplToLeaf(Manifold::Impl&& impl) {
   return std::make_shared<CsgLeafNode>(std::make_shared<Manifold::Impl>(impl));
 }
 
-std::shared_ptr<CsgLeafNode> SimpleBoolean(const Manifold::Impl &a,
-                                           const Manifold::Impl &b, OpType op) {
+std::shared_ptr<CsgLeafNode> SimpleBoolean(const Manifold::Impl& a,
+                                           const Manifold::Impl& b, OpType op) {
 #ifdef MANIFOLD_DEBUG
   auto dump = [&]() {
     dump_lock.lock();
@@ -121,6 +117,7 @@ std::shared_ptr<CsgLeafNode> SimpleBoolean(const Manifold::Impl &a,
               << std::endl;
     std::cout << "RHS self-intersecting: " << b.IsSelfIntersecting()
               << std::endl;
+#ifdef MANIFOLD_EXPORT
     if (ManifoldParams().verbose) {
       if (op == OpType::Add)
         std::cout << "Add";
@@ -132,22 +129,23 @@ std::shared_ptr<CsgLeafNode> SimpleBoolean(const Manifold::Impl &a,
       std::cout << a;
       std::cout << b;
     }
+#endif
     dump_lock.unlock();
   };
   try {
     Boolean3 boolean(a, b, op);
     auto impl = boolean.Result(op);
-    if (ManifoldParams().intermediateChecks && impl.IsSelfIntersecting()) {
+    if (ManifoldParams().selfIntersectionChecks && impl.IsSelfIntersecting()) {
       dump_lock.lock();
       std::cout << "self intersections detected" << std::endl;
       dump_lock.unlock();
       throw logicErr("self intersection detected");
     }
     return ImplToLeaf(std::move(impl));
-  } catch (logicErr &err) {
+  } catch (logicErr& err) {
     dump();
     throw err;
-  } catch (geometryErr &err) {
+  } catch (geometryErr& err) {
     dump();
     throw err;
   }
@@ -160,7 +158,7 @@ std::shared_ptr<CsgLeafNode> SimpleBoolean(const Manifold::Impl &a,
  * Efficient union of a set of pairwise disjoint meshes.
  */
 std::shared_ptr<CsgLeafNode> CsgLeafNode::Compose(
-    const std::vector<std::shared_ptr<CsgLeafNode>> &nodes) {
+    const std::vector<std::shared_ptr<CsgLeafNode>>& nodes) {
   ZoneScoped;
   double epsilon = -1;
   double tolerance = -1;
@@ -173,7 +171,7 @@ std::shared_ptr<CsgLeafNode> CsgLeafNode::Compose(
   std::vector<int> triIndices;
   std::vector<int> propVertIndices;
   int numPropOut = 0;
-  for (auto &node : nodes) {
+  for (auto& node : nodes) {
     if (node->pImpl_->status_ != Manifold::Error::NoError) {
       Manifold::Impl impl;
       impl.status_ = node->pImpl_->status_;
@@ -199,22 +197,20 @@ std::shared_ptr<CsgLeafNode> CsgLeafNode::Compose(
     const int numProp = node->pImpl_->NumProp();
     numPropOut = std::max(numPropOut, numProp);
     numPropVert +=
-        numProp == 0 ? 1
-                     : node->pImpl_->meshRelation_.properties.size() / numProp;
+        numProp == 0 ? 1 : node->pImpl_->properties_.size() / numProp;
   }
 
   Manifold::Impl combined;
   combined.epsilon_ = epsilon;
   combined.tolerance_ = tolerance;
-  combined.vertPos_.resize(numVert);
-  combined.halfedge_.resize(2 * numEdge);
-  combined.faceNormal_.resize(numTri);
+  combined.vertPos_.resize_nofill(numVert);
+  combined.halfedge_.resize_nofill(2 * numEdge);
+  combined.faceNormal_.resize_nofill(numTri);
   combined.halfedgeTangent_.resize(2 * numEdge);
-  combined.meshRelation_.triRef.resize(numTri);
+  combined.meshRelation_.triRef.resize_nofill(numTri);
   if (numPropOut > 0) {
-    combined.meshRelation_.numProp = numPropOut;
-    combined.meshRelation_.properties.resize(numPropOut * numPropVert, 0);
-    combined.meshRelation_.triProperties.resize(numTri);
+    combined.numProp_ = numPropOut;
+    combined.properties_.resize(numPropOut * numPropVert, 0);
   }
   auto policy = autoPolicy(numTri);
 
@@ -228,50 +224,35 @@ std::shared_ptr<CsgLeafNode> CsgLeafNode::Compose(
       countAt(0), nodes.size(),
       [&nodes, &vertIndices, &edgeIndices, &triIndices, &propVertIndices,
        numPropOut, &combined, policy](int i) {
-        auto &node = nodes[i];
+        auto& node = nodes[i];
         copy(node->pImpl_->halfedgeTangent_.begin(),
              node->pImpl_->halfedgeTangent_.end(),
              combined.halfedgeTangent_.begin() + edgeIndices[i]);
         const int nextVert = vertIndices[i];
         const int nextEdge = edgeIndices[i];
-        const int nextFace = triIndices[i];
+        const int nextProp = propVertIndices[i];
         transform(node->pImpl_->halfedge_.begin(),
                   node->pImpl_->halfedge_.end(),
                   combined.halfedge_.begin() + edgeIndices[i],
-                  [nextVert, nextEdge, nextFace](Halfedge edge) {
+                  [nextVert, nextEdge, nextProp](Halfedge edge) {
                     edge.startVert += nextVert;
                     edge.endVert += nextVert;
                     edge.pairedHalfedge += nextEdge;
+                    edge.propVert += nextProp;
                     return edge;
                   });
 
-        if (numPropOut > 0) {
-          auto start =
-              combined.meshRelation_.triProperties.begin() + triIndices[i];
-          if (node->pImpl_->NumProp() > 0) {
-            auto &triProp = node->pImpl_->meshRelation_.triProperties;
-            const int nextProp = propVertIndices[i];
-            transform(triProp.begin(), triProp.end(), start,
-                      [nextProp](ivec3 tri) {
-                        tri += nextProp;
-                        return tri;
-                      });
-
-            const int numProp = node->pImpl_->NumProp();
-            auto &oldProp = node->pImpl_->meshRelation_.properties;
-            auto &newProp = combined.meshRelation_.properties;
-            for (int p = 0; p < numProp; ++p) {
-              auto oldRange =
-                  StridedRange(oldProp.cbegin() + p, oldProp.cend(), numProp);
-              auto newRange = StridedRange(
-                  newProp.begin() + numPropOut * propVertIndices[i] + p,
-                  newProp.end(), numPropOut);
-              copy(oldRange.begin(), oldRange.end(), newRange.begin());
-            }
-          } else {
-            // point all triangles at single new property of zeros.
-            fill(start, start + node->pImpl_->NumTri(),
-                 ivec3(propVertIndices[i]));
+        if (node->pImpl_->NumProp() > 0) {
+          const int numProp = node->pImpl_->NumProp();
+          auto& oldProp = node->pImpl_->properties_;
+          auto& newProp = combined.properties_;
+          for (int p = 0; p < numProp; ++p) {
+            auto oldRange =
+                StridedRange(oldProp.cbegin() + p, oldProp.cend(), numProp);
+            auto newRange = StridedRange(
+                newProp.begin() + numPropOut * propVertIndices[i] + p,
+                newProp.end(), numPropOut);
+            copy(oldRange.begin(), oldRange.end(), newRange.begin());
           }
         }
 
@@ -323,16 +304,16 @@ std::shared_ptr<CsgLeafNode> CsgLeafNode::Compose(
       });
 
   for (size_t i = 0; i < nodes.size(); i++) {
-    auto &node = nodes[i];
+    auto& node = nodes[i];
     const int offset = i * Manifold::Impl::meshIDCounter_;
 
-    for (const auto &pair : node->pImpl_->meshRelation_.meshIDtransform) {
+    for (const auto& pair : node->pImpl_->meshRelation_.meshIDtransform) {
       combined.meshRelation_.meshIDtransform[pair.first + offset] = pair.second;
     }
   }
 
   // required to remove parts that are smaller than the tolerance
-  combined.SimplifyTopology();
+  combined.RemoveDegenerates();
   combined.Finish();
   combined.IncrementMeshIDs();
   return ImplToLeaf(std::move(combined));
@@ -343,7 +324,7 @@ std::shared_ptr<CsgLeafNode> CsgLeafNode::Compose(
  * operation. Only supports union and intersection.
  */
 std::shared_ptr<CsgLeafNode> BatchBoolean(
-    OpType operation, std::vector<std::shared_ptr<CsgLeafNode>> &results) {
+    OpType operation, std::vector<std::shared_ptr<CsgLeafNode>>& results) {
   ZoneScoped;
   DEBUG_ASSERT(operation != OpType::Subtract, logicErr,
                "BatchBoolean doesn't support Difference.");
@@ -353,50 +334,44 @@ std::shared_ptr<CsgLeafNode> BatchBoolean(
   if (results.size() == 2)
     return SimpleBoolean(*results[0]->GetImpl(), *results[1]->GetImpl(),
                          operation);
-#if (MANIFOLD_PAR == 1) && __has_include(<tbb/tbb.h>)
-  tbb::task_group group;
-  tbb::concurrent_priority_queue<std::shared_ptr<CsgLeafNode>, MeshCompare>
-      queue(results.size());
-  for (auto result : results) {
-    queue.emplace(result);
-  }
-  results.clear();
-  std::function<void()> process = [&]() {
-    while (queue.size() > 1) {
-      std::shared_ptr<CsgLeafNode> a, b;
-      if (!queue.try_pop(a)) continue;
-      if (!queue.try_pop(b)) {
-        queue.push(a);
-        continue;
-      }
-      group.run([&, a, b]() {
-        queue.emplace(SimpleBoolean(*a->GetImpl(), *b->GetImpl(), operation));
-        return group.run(process);
-      });
-    }
-  };
-  group.run_and_wait(process);
-  std::shared_ptr<CsgLeafNode> r;
-  queue.try_pop(r);
-  return r;
-#endif
   // apply boolean operations starting from smaller meshes
   // the assumption is that boolean operations on smaller meshes is faster,
   // due to less data being copied and processed
   auto cmpFn = MeshCompare();
   std::make_heap(results.begin(), results.end(), cmpFn);
+  std::vector<std::shared_ptr<CsgLeafNode>> tmp;
+#if MANIFOLD_PAR == 1
+  tbb::task_group group;
+  std::mutex mutex;
+#endif
   while (results.size() > 1) {
-    std::pop_heap(results.begin(), results.end(), cmpFn);
-    auto a = std::move(results.back());
-    results.pop_back();
-    std::pop_heap(results.begin(), results.end(), cmpFn);
-    auto b = std::move(results.back());
-    results.pop_back();
-    // boolean operation
-    auto result = SimpleBoolean(*a->GetImpl(), *b->GetImpl(), operation);
-    if (results.size() == 0) return result;
-    results.push_back(result);
-    std::push_heap(results.begin(), results.end(), cmpFn);
+    for (size_t i = 0; i < 4 && results.size() > 1; i++) {
+      std::pop_heap(results.begin(), results.end(), cmpFn);
+      auto a = std::move(results.back());
+      results.pop_back();
+      std::pop_heap(results.begin(), results.end(), cmpFn);
+      auto b = std::move(results.back());
+      results.pop_back();
+#if MANIFOLD_PAR == 1
+      group.run([&, a, b]() {
+        auto result = SimpleBoolean(*a->GetImpl(), *b->GetImpl(), operation);
+        mutex.lock();
+        tmp.push_back(result);
+        mutex.unlock();
+      });
+#else
+      auto result = SimpleBoolean(*a->GetImpl(), *b->GetImpl(), operation);
+      tmp.push_back(result);
+#endif
+    }
+#if MANIFOLD_PAR == 1
+    group.wait();
+#endif
+    for (auto result : tmp) {
+      results.push_back(result);
+      std::push_heap(results.begin(), results.end(), cmpFn);
+    }
+    tmp.clear();
   }
   return results.front();
 }
@@ -406,7 +381,7 @@ std::shared_ptr<CsgLeafNode> BatchBoolean(
  * possible.
  */
 std::shared_ptr<CsgLeafNode> BatchUnion(
-    std::vector<std::shared_ptr<CsgLeafNode>> &children) {
+    std::vector<std::shared_ptr<CsgLeafNode>>& children) {
   ZoneScoped;
   // INVARIANT: children_ is a vector of leaf nodes
   // this kMaxUnionSize is a heuristic to avoid the pairwise disjoint check
@@ -429,7 +404,7 @@ std::shared_ptr<CsgLeafNode> BatchUnion(
     // each set contains a set of children that are pairwise disjoint
     std::vector<Vec<size_t>> disjointSets;
     for (size_t i = 0; i < boxes.size(); i++) {
-      auto lambda = [&boxes, i](const Vec<size_t> &set) {
+      auto lambda = [&boxes, i](const Vec<size_t>& set) {
         return std::find_if(set.begin(), set.end(), [&boxes, i](size_t j) {
                  return boxes[i].DoesOverlap(boxes[j]);
                }) == set.end();
@@ -443,7 +418,7 @@ std::shared_ptr<CsgLeafNode> BatchUnion(
     }
     // compose each set of disjoint children
     std::vector<std::shared_ptr<CsgLeafNode>> impls;
-    for (auto &set : disjointSets) {
+    for (auto& set : disjointSets) {
       if (set.size() == 1) {
         impls.push_back(children[start + set[0]]);
       } else {
@@ -466,7 +441,7 @@ std::shared_ptr<CsgLeafNode> BatchUnion(
 
 CsgOpNode::CsgOpNode() {}
 
-CsgOpNode::CsgOpNode(const std::vector<std::shared_ptr<CsgNode>> &children,
+CsgOpNode::CsgOpNode(const std::vector<std::shared_ptr<CsgNode>>& children,
                      OpType op)
     : impl_(children), op_(op) {}
 
@@ -475,7 +450,7 @@ CsgOpNode::~CsgOpNode() {
     auto impl = impl_.GetGuard();
     std::vector<std::shared_ptr<CsgOpNode>> toProcess;
     auto handleChildren =
-        [&toProcess](std::vector<std::shared_ptr<CsgNode>> &children) {
+        [&toProcess](std::vector<std::shared_ptr<CsgNode>>& children) {
           while (!children.empty()) {
             // move out so shrinking the vector will not trigger recursive drop
             auto movedChild = std::move(children.back());
@@ -498,7 +473,7 @@ CsgOpNode::~CsgOpNode() {
 }
 
 std::shared_ptr<CsgNode> CsgOpNode::Boolean(
-    const std::shared_ptr<CsgNode> &second, OpType op) {
+    const std::shared_ptr<CsgNode>& second, OpType op) {
   std::vector<std::shared_ptr<CsgNode>> children;
   children.push_back(shared_from_this());
   children.push_back(second);
@@ -506,7 +481,7 @@ std::shared_ptr<CsgNode> CsgOpNode::Boolean(
   return std::make_shared<CsgOpNode>(children, op);
 }
 
-std::shared_ptr<CsgNode> CsgOpNode::Transform(const mat3x4 &m) const {
+std::shared_ptr<CsgNode> CsgOpNode::Transform(const mat3x4& m) const {
   auto node = std::make_shared<CsgOpNode>();
   node->impl_ = impl_;
   node->transform_ = m * Mat4(transform_);
@@ -520,14 +495,14 @@ struct CsgStackFrame {
   bool finalize;
   OpType parent_op;
   mat3x4 transform;
-  Nodes *positive_dest;
-  Nodes *negative_dest;
+  Nodes* positive_dest;
+  Nodes* negative_dest;
   std::shared_ptr<const CsgOpNode> op_node;
   Nodes positive_children;
   Nodes negative_children;
 
   CsgStackFrame(bool finalize, OpType parent_op, mat3x4 transform,
-                Nodes *positive_dest, Nodes *negative_dest,
+                Nodes* positive_dest, Nodes* negative_dest,
                 std::shared_ptr<const CsgOpNode> op_node)
       : finalize(finalize),
         parent_op(parent_op),
@@ -675,8 +650,8 @@ std::shared_ptr<CsgLeafNode> CsgOpNode::ToLeafNode() const {
       stack.pop_back();
     } else {
       auto add_children =
-          [&stack](std::shared_ptr<CsgNode> &node, OpType op, mat3x4 transform,
-                   CsgStackFrame::Nodes *dest1, CsgStackFrame::Nodes *dest2) {
+          [&stack](std::shared_ptr<CsgNode>& node, OpType op, mat3x4 transform,
+                   CsgStackFrame::Nodes* dest1, CsgStackFrame::Nodes* dest2) {
             if (node->GetNodeType() == CsgNodeType::Leaf)
               dest1->push_back(std::static_pointer_cast<CsgLeafNode>(
                   node->Transform(transform)));
@@ -702,14 +677,14 @@ std::shared_ptr<CsgLeafNode> CsgOpNode::ToLeafNode() const {
       const mat3x4 transform =
           canCollapse ? (frame->transform * Mat4(frame->op_node->transform_))
                       : la::identity;
-      CsgStackFrame::Nodes *pos_dest =
+      CsgStackFrame::Nodes* pos_dest =
           canCollapse ? frame->positive_dest : &frame->positive_children;
-      CsgStackFrame::Nodes *neg_dest =
+      CsgStackFrame::Nodes* neg_dest =
           canCollapse ? frame->negative_dest : &frame->negative_children;
       for (size_t i = 0; i < impl->size(); i++) {
         const bool negative = op == OpType::Subtract && i != 0;
-        CsgStackFrame::Nodes *dest1 = negative ? neg_dest : pos_dest;
-        CsgStackFrame::Nodes *dest2 =
+        CsgStackFrame::Nodes* dest1 = negative ? neg_dest : pos_dest;
+        CsgStackFrame::Nodes* dest2 =
             (op == OpType::Subtract && i == 0) ? neg_dest : nullptr;
         add_children((*impl)[i], negative ? OpType::Add : op, transform, dest1,
                      dest2);
diff --git a/thirdparty/manifold/src/csg_tree.h b/thirdparty/manifold/src/csg_tree.h
index fb664df00c..fa5d22382d 100644
--- a/thirdparty/manifold/src/csg_tree.h
+++ b/thirdparty/manifold/src/csg_tree.h
@@ -13,8 +13,8 @@
 // limitations under the License.
 
 #pragma once
-#include "./utils.h"
 #include "manifold/manifold.h"
+#include "utils.h"
 
 namespace manifold {
 
@@ -25,14 +25,14 @@ class CsgLeafNode;
 class CsgNode : public std::enable_shared_from_this<CsgNode> {
  public:
   virtual std::shared_ptr<CsgLeafNode> ToLeafNode() const = 0;
-  virtual std::shared_ptr<CsgNode> Transform(const mat3x4 &m) const = 0;
+  virtual std::shared_ptr<CsgNode> Transform(const mat3x4& m) const = 0;
   virtual CsgNodeType GetNodeType() const = 0;
 
   virtual std::shared_ptr<CsgNode> Boolean(
-      const std::shared_ptr<CsgNode> &second, OpType op);
+      const std::shared_ptr<CsgNode>& second, OpType op);
 
-  std::shared_ptr<CsgNode> Translate(const vec3 &t) const;
-  std::shared_ptr<CsgNode> Scale(const vec3 &s) const;
+  std::shared_ptr<CsgNode> Translate(const vec3& t) const;
+  std::shared_ptr<CsgNode> Scale(const vec3& s) const;
   std::shared_ptr<CsgNode> Rotate(double xDegrees = 0, double yDegrees = 0,
                                   double zDegrees = 0) const;
 };
@@ -47,12 +47,12 @@ class CsgLeafNode final : public CsgNode {
 
   std::shared_ptr<CsgLeafNode> ToLeafNode() const override;
 
-  std::shared_ptr<CsgNode> Transform(const mat3x4 &m) const override;
+  std::shared_ptr<CsgNode> Transform(const mat3x4& m) const override;
 
   CsgNodeType GetNodeType() const override;
 
   static std::shared_ptr<CsgLeafNode> Compose(
-      const std::vector<std::shared_ptr<CsgLeafNode>> &nodes);
+      const std::vector<std::shared_ptr<CsgLeafNode>>& nodes);
 
  private:
   mutable std::shared_ptr<const Manifold::Impl> pImpl_;
@@ -63,12 +63,12 @@ class CsgOpNode final : public CsgNode {
  public:
   CsgOpNode();
 
-  CsgOpNode(const std::vector<std::shared_ptr<CsgNode>> &children, OpType op);
+  CsgOpNode(const std::vector<std::shared_ptr<CsgNode>>& children, OpType op);
 
-  std::shared_ptr<CsgNode> Boolean(const std::shared_ptr<CsgNode> &second,
+  std::shared_ptr<CsgNode> Boolean(const std::shared_ptr<CsgNode>& second,
                                    OpType op) override;
 
-  std::shared_ptr<CsgNode> Transform(const mat3x4 &m) const override;
+  std::shared_ptr<CsgNode> Transform(const mat3x4& m) const override;
 
   std::shared_ptr<CsgLeafNode> ToLeafNode() const override;
 
diff --git a/thirdparty/manifold/src/edge_op.cpp b/thirdparty/manifold/src/edge_op.cpp
index d22577a2a2..81567ffeba 100644
--- a/thirdparty/manifold/src/edge_op.cpp
+++ b/thirdparty/manifold/src/edge_op.cpp
@@ -12,8 +12,11 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "./impl.h"
-#include "./parallel.h"
+#include <unordered_map>
+
+#include "impl.h"
+#include "parallel.h"
+#include "shared.h"
 
 namespace {
 using namespace manifold;
@@ -47,33 +50,46 @@ struct DuplicateEdge {
 struct ShortEdge {
   VecView<const Halfedge> halfedge;
   VecView<const vec3> vertPos;
-  const double tolerance;
+  const double epsilon;
+  const int firstNewVert;
 
   bool operator()(int edge) const {
-    if (halfedge[edge].pairedHalfedge < 0) return false;
+    const Halfedge& half = halfedge[edge];
+    if (half.pairedHalfedge < 0 ||
+        (half.startVert < firstNewVert && half.endVert < firstNewVert))
+      return false;
     // Flag short edges
-    const vec3 delta =
-        vertPos[halfedge[edge].endVert] - vertPos[halfedge[edge].startVert];
-    return la::dot(delta, delta) < tolerance * tolerance;
+    const vec3 delta = vertPos[half.endVert] - vertPos[half.startVert];
+    return la::dot(delta, delta) < epsilon * epsilon;
   }
 };
 
 struct FlagEdge {
   VecView<const Halfedge> halfedge;
   VecView<const TriRef> triRef;
+  const int firstNewVert;
 
   bool operator()(int edge) const {
-    if (halfedge[edge].pairedHalfedge < 0) return false;
+    const Halfedge& half = halfedge[edge];
+    if (half.pairedHalfedge < 0 || half.startVert < firstNewVert) return false;
     // Flag redundant edges - those where the startVert is surrounded by only
     // two original triangles.
     const TriRef ref0 = triRef[edge / 3];
-    int current = NextHalfedge(halfedge[edge].pairedHalfedge);
-    const TriRef ref1 = triRef[current / 3];
+    int current = NextHalfedge(half.pairedHalfedge);
+    TriRef ref1 = triRef[current / 3];
+    bool ref1Updated = !ref0.SameFace(ref1);
     while (current != edge) {
       current = NextHalfedge(halfedge[current].pairedHalfedge);
       int tri = current / 3;
       const TriRef ref = triRef[tri];
-      if (!ref.SameFace(ref0) && !ref.SameFace(ref1)) return false;
+      if (!ref.SameFace(ref0) && !ref.SameFace(ref1)) {
+        if (!ref1Updated) {
+          ref1 = ref;
+          ref1Updated = true;
+        } else {
+          return false;
+        }
+      }
     }
     return true;
   }
@@ -84,9 +100,15 @@ struct SwappableEdge {
   VecView<const vec3> vertPos;
   VecView<const vec3> triNormal;
   const double tolerance;
+  const int firstNewVert;
 
   bool operator()(int edge) const {
-    if (halfedge[edge].pairedHalfedge < 0) return false;
+    const Halfedge& half = halfedge[edge];
+    if (half.pairedHalfedge < 0) return false;
+    if (half.startVert < firstNewVert && half.endVert < firstNewVert &&
+        halfedge[NextHalfedge(edge)].endVert < firstNewVert &&
+        halfedge[NextHalfedge(half.pairedHalfedge)].endVert < firstNewVert)
+      return false;
 
     int tri = edge / 3;
     ivec3 triEdge = TriOf(edge);
@@ -98,7 +120,7 @@ struct SwappableEdge {
       return false;
 
     // Switch to neighbor's projection.
-    edge = halfedge[edge].pairedHalfedge;
+    edge = half.pairedHalfedge;
     tri = edge / 3;
     triEdge = TriOf(edge);
     projection = GetAxisAlignedProjection(triNormal[tri]);
@@ -109,14 +131,67 @@ struct SwappableEdge {
   }
 };
 
-struct SortEntry {
-  int start;
-  int end;
-  size_t index;
-  inline bool operator<(const SortEntry& other) const {
-    return start == other.start ? end < other.end : start < other.start;
+struct FlagStore {
+#if MANIFOLD_PAR == 1
+  tbb::combinable<std::vector<size_t>> store;
+#endif
+  std::vector<size_t> s;
+
+  template <typename Pred, typename F>
+  void run_seq(size_t n, Pred pred, F f) {
+    for (size_t i = 0; i < n; ++i)
+      if (pred(i)) s.push_back(i);
+    for (size_t i : s) f(i);
+    s.clear();
+  }
+
+#if MANIFOLD_PAR == 1
+  template <typename Pred, typename F>
+  void run_par(size_t n, Pred pred, F f) {
+    // Test pred in parallel, store i into thread-local vectors when pred(i) is
+    // true. After testing pred, iterate and call f over the indices in
+    // ascending order by using a heap in a single thread
+    auto& store = this->store;
+    tbb::parallel_for(tbb::blocked_range<size_t>(0, n),
+                      [&store, &pred](const auto& r) {
+                        auto& local = store.local();
+                        for (auto i = r.begin(); i < r.end(); ++i) {
+                          if (pred(i)) local.push_back(i);
+                        }
+                      });
+
+    std::vector<std::vector<size_t>> stores;
+    std::vector<size_t> result;
+    store.combine_each(
+        [&](auto& data) { stores.emplace_back(std::move(data)); });
+    std::vector<size_t> sizes;
+    size_t total_size = 0;
+    for (const auto& tmp : stores) {
+      sizes.push_back(total_size);
+      total_size += tmp.size();
+    }
+    result.resize(total_size);
+    for_each_n(ExecutionPolicy::Seq, countAt(0), stores.size(), [&](size_t i) {
+      std::copy(stores[i].begin(), stores[i].end(), result.begin() + sizes[i]);
+    });
+    stable_sort(autoPolicy(result.size()), result.begin(), result.end());
+    for (size_t x : result) f(x);
+  }
+#endif
+
+  template <typename Pred, typename F>
+  void run(size_t n, Pred pred, F f) {
+#if MANIFOLD_PAR == 1
+    if (n > 1e5) {
+      run_par(n, pred, f);
+    } else
+#endif
+    {
+      run_seq(n, pred, f);
+    }
   }
 };
+
 }  // namespace
 
 namespace manifold {
@@ -131,41 +206,7 @@ void Manifold::Impl::CleanupTopology() {
   // In the case of a very bad triangulation, it is possible to create pinched
   // verts. They must be removed before edge collapse.
   SplitPinchedVerts();
-
-  while (1) {
-    ZoneScopedN("DedupeEdge");
-
-    const size_t nbEdges = halfedge_.size();
-    size_t numFlagged = 0;
-
-    Vec<SortEntry> entries;
-    entries.reserve(nbEdges / 2);
-    for (size_t i = 0; i < nbEdges; ++i) {
-      if (halfedge_[i].IsForward()) {
-        entries.push_back({halfedge_[i].startVert, halfedge_[i].endVert, i});
-      }
-    }
-
-    stable_sort(entries.begin(), entries.end());
-    for (size_t i = 0; i < entries.size() - 1; ++i) {
-      const int h0 = entries[i].index;
-      const int h1 = entries[i + 1].index;
-      if (halfedge_[h0].startVert == halfedge_[h1].startVert &&
-          halfedge_[h0].endVert == halfedge_[h1].endVert) {
-        DedupeEdge(entries[i].index);
-        numFlagged++;
-      }
-    }
-
-    if (numFlagged == 0) break;
-
-#ifdef MANIFOLD_DEBUG
-    if (ManifoldParams().verbose) {
-      std::cout << "found " << numFlagged << " duplicate edges to split"
-                << std::endl;
-    }
-#endif
-  }
+  DedupeEdges();
 }
 
 /**
@@ -184,95 +225,112 @@ void Manifold::Impl::CleanupTopology() {
  * meshes, thus decreasing the Genus(). It only increases when meshes that have
  * collapsed to just a pair of triangles are removed entirely.
  *
+ * Verts with index less than firstNewVert will be left uncollapsed. This is
+ * zero by default so that everything can be collapsed.
+ *
  * Rather than actually removing the edges, this step merely marks them for
  * removal, by setting vertPos to NaN and halfedge to {-1, -1, -1, -1}.
  */
-void Manifold::Impl::SimplifyTopology() {
+void Manifold::Impl::SimplifyTopology(int firstNewVert) {
   if (!halfedge_.size()) return;
 
   CleanupTopology();
+  CollapseShortEdges(firstNewVert);
+  CollapseColinearEdges(firstNewVert);
+  SwapDegenerates(firstNewVert);
+}
 
-  if (!ManifoldParams().cleanupTriangles) {
-    return;
-  }
+void Manifold::Impl::RemoveDegenerates(int firstNewVert) {
+  if (!halfedge_.size()) return;
 
-  const size_t nbEdges = halfedge_.size();
-  auto policy = autoPolicy(nbEdges, 1e5);
+  CleanupTopology();
+  CollapseShortEdges(firstNewVert);
+  SwapDegenerates(firstNewVert);
+}
+
+void Manifold::Impl::CollapseShortEdges(int firstNewVert) {
+  ZoneScopedN("CollapseShortEdge");
+  FlagStore s;
   size_t numFlagged = 0;
-  Vec<uint8_t> bFlags(nbEdges);
+  const size_t nbEdges = halfedge_.size();
 
   std::vector<int> scratchBuffer;
   scratchBuffer.reserve(10);
-  {
-    ZoneScopedN("CollapseShortEdge");
-    numFlagged = 0;
-    ShortEdge se{halfedge_, vertPos_, epsilon_};
-    for_each_n(policy, countAt(0_uz), nbEdges,
-               [&](size_t i) { bFlags[i] = se(i); });
-    for (size_t i = 0; i < nbEdges; ++i) {
-      if (bFlags[i]) {
-        CollapseEdge(i, scratchBuffer);
-        scratchBuffer.resize(0);
-        numFlagged++;
-      }
-    }
-  }
+  // Short edges get to skip several checks and hence remove more classes of
+  // degenerate triangles than flagged edges do, but this could in theory lead
+  // to error stacking where a vertex moves too far. For this reason this is
+  // restricted to epsilon, rather than tolerance.
+  ShortEdge se{halfedge_, vertPos_, epsilon_, firstNewVert};
+  s.run(nbEdges, se, [&](size_t i) {
+    const bool didCollapse = CollapseEdge(i, scratchBuffer);
+    if (didCollapse) numFlagged++;
+    scratchBuffer.resize(0);
+  });
 
 #ifdef MANIFOLD_DEBUG
-  if (ManifoldParams().verbose && numFlagged > 0) {
-    std::cout << "found " << numFlagged << " short edges to collapse"
-              << std::endl;
+  if (ManifoldParams().verbose > 0 && numFlagged > 0) {
+    std::cout << "collapsed " << numFlagged << " short edges" << std::endl;
   }
 #endif
+}
 
-  {
+void Manifold::Impl::CollapseColinearEdges(int firstNewVert) {
+  FlagStore s;
+  size_t numFlagged = 0;
+  const size_t nbEdges = halfedge_.size();
+  std::vector<int> scratchBuffer;
+  scratchBuffer.reserve(10);
+  while (1) {
     ZoneScopedN("CollapseFlaggedEdge");
     numFlagged = 0;
-    FlagEdge se{halfedge_, meshRelation_.triRef};
-    for_each_n(policy, countAt(0_uz), nbEdges,
-               [&](size_t i) { bFlags[i] = se(i); });
-    for (size_t i = 0; i < nbEdges; ++i) {
-      if (bFlags[i]) {
-        CollapseEdge(i, scratchBuffer);
-        scratchBuffer.resize(0);
-        numFlagged++;
-      }
-    }
-  }
+    // Collapse colinear edges, but only remove new verts, i.e. verts with
+    // index
+    // >= firstNewVert. This is used to keep the Boolean from changing the
+    // non-intersecting parts of the input meshes. Colinear is defined not by a
+    // local check, but by the global MarkCoplanar function, which keeps this
+    // from being vulnerable to error stacking.
+    FlagEdge se{halfedge_, meshRelation_.triRef, firstNewVert};
+    s.run(nbEdges, se, [&](size_t i) {
+      const bool didCollapse = CollapseEdge(i, scratchBuffer);
+      if (didCollapse) numFlagged++;
+      scratchBuffer.resize(0);
+    });
+    if (numFlagged == 0) break;
 
 #ifdef MANIFOLD_DEBUG
-  if (ManifoldParams().verbose && numFlagged > 0) {
-    std::cout << "found " << numFlagged << " colinear edges to collapse"
-              << std::endl;
-  }
+    if (ManifoldParams().verbose > 0 && numFlagged > 0) {
+      std::cout << "collapsed " << numFlagged << " colinear edges" << std::endl;
+    }
 #endif
-
-  {
-    ZoneScopedN("RecursiveEdgeSwap");
-    numFlagged = 0;
-    SwappableEdge se{halfedge_, vertPos_, faceNormal_, tolerance_};
-    for_each_n(policy, countAt(0_uz), nbEdges,
-               [&](size_t i) { bFlags[i] = se(i); });
-    std::vector<int> edgeSwapStack;
-    std::vector<int> visited(halfedge_.size(), -1);
-    int tag = 0;
-    for (size_t i = 0; i < nbEdges; ++i) {
-      if (bFlags[i]) {
-        numFlagged++;
-        tag++;
-        RecursiveEdgeSwap(i, tag, visited, edgeSwapStack, scratchBuffer);
-        while (!edgeSwapStack.empty()) {
-          int last = edgeSwapStack.back();
-          edgeSwapStack.pop_back();
-          RecursiveEdgeSwap(last, tag, visited, edgeSwapStack, scratchBuffer);
-        }
-      }
-    }
   }
+}
+
+void Manifold::Impl::SwapDegenerates(int firstNewVert) {
+  ZoneScopedN("RecursiveEdgeSwap");
+  FlagStore s;
+  size_t numFlagged = 0;
+  const size_t nbEdges = halfedge_.size();
+  std::vector<int> scratchBuffer;
+  scratchBuffer.reserve(10);
+
+  SwappableEdge se{halfedge_, vertPos_, faceNormal_, tolerance_, firstNewVert};
+  std::vector<int> edgeSwapStack;
+  std::vector<int> visited(halfedge_.size(), -1);
+  int tag = 0;
+  s.run(nbEdges, se, [&](size_t i) {
+    numFlagged++;
+    tag++;
+    RecursiveEdgeSwap(i, tag, visited, edgeSwapStack, scratchBuffer);
+    while (!edgeSwapStack.empty()) {
+      int last = edgeSwapStack.back();
+      edgeSwapStack.pop_back();
+      RecursiveEdgeSwap(last, tag, visited, edgeSwapStack, scratchBuffer);
+    }
+  });
 
 #ifdef MANIFOLD_DEBUG
-  if (ManifoldParams().verbose && numFlagged > 0) {
-    std::cout << "found " << numFlagged << " edges to swap" << std::endl;
+  if (ManifoldParams().verbose > 0 && numFlagged > 0) {
+    std::cout << "swapped " << numFlagged << " edges" << std::endl;
   }
 #endif
 }
@@ -283,6 +341,7 @@ void Manifold::Impl::DedupeEdge(const int edge) {
   // Orbit endVert
   const int startVert = halfedge_[edge].startVert;
   const int endVert = halfedge_[edge].endVert;
+  const int endProp = halfedge_[NextHalfedge(edge)].propVert;
   int current = halfedge_[NextHalfedge(edge)].pairedHalfedge;
   while (current != edge) {
     const int vert = halfedge_[current].startVert;
@@ -297,36 +356,30 @@ void Manifold::Impl::DedupeEdge(const int edge) {
       UpdateVert(newVert, current, opposite);
 
       int newHalfedge = halfedge_.size();
-      int newFace = newHalfedge / 3;
       int oldFace = current / 3;
       int outsideVert = halfedge_[current].startVert;
-      halfedge_.push_back({endVert, newVert, -1});
-      halfedge_.push_back({newVert, outsideVert, -1});
-      halfedge_.push_back({outsideVert, endVert, -1});
+      halfedge_.push_back({endVert, newVert, -1, endProp});
+      halfedge_.push_back({newVert, outsideVert, -1, endProp});
+      halfedge_.push_back(
+          {outsideVert, endVert, -1, halfedge_[current].propVert});
       PairUp(newHalfedge + 2, halfedge_[current].pairedHalfedge);
       PairUp(newHalfedge + 1, current);
       if (meshRelation_.triRef.size() > 0)
         meshRelation_.triRef.push_back(meshRelation_.triRef[oldFace]);
-      if (meshRelation_.triProperties.size() > 0)
-        meshRelation_.triProperties.push_back(
-            meshRelation_.triProperties[oldFace]);
       if (faceNormal_.size() > 0) faceNormal_.push_back(faceNormal_[oldFace]);
 
       newHalfedge += 3;
-      ++newFace;
       oldFace = opposite / 3;
       outsideVert = halfedge_[opposite].startVert;
-      halfedge_.push_back({newVert, endVert, -1});
-      halfedge_.push_back({endVert, outsideVert, -1});
-      halfedge_.push_back({outsideVert, newVert, -1});
+      halfedge_.push_back({newVert, endVert, -1, endProp});  // fix prop
+      halfedge_.push_back({endVert, outsideVert, -1, endProp});
+      halfedge_.push_back(
+          {outsideVert, newVert, -1, halfedge_[opposite].propVert});
       PairUp(newHalfedge + 2, halfedge_[opposite].pairedHalfedge);
       PairUp(newHalfedge + 1, opposite);
       PairUp(newHalfedge, newHalfedge - 3);
       if (meshRelation_.triRef.size() > 0)
         meshRelation_.triRef.push_back(meshRelation_.triRef[oldFace]);
-      if (meshRelation_.triProperties.size() > 0)
-        meshRelation_.triProperties.push_back(
-            meshRelation_.triProperties[oldFace]);
       if (faceNormal_.size() > 0) faceNormal_.push_back(faceNormal_[oldFace]);
 
       break;
@@ -420,7 +473,7 @@ void Manifold::Impl::CollapseTri(const ivec3& triEdge) {
   halfedge_[pair1].pairedHalfedge = pair2;
   halfedge_[pair2].pairedHalfedge = pair1;
   for (int i : {0, 1, 2}) {
-    halfedge_[triEdge[i]] = {-1, -1, -1};
+    halfedge_[triEdge[i]] = {-1, -1, -1, halfedge_[triEdge[i]].propVert};
   }
 }
 
@@ -452,16 +505,16 @@ void Manifold::Impl::RemoveIfFolded(int edge) {
   }
 }
 
-// Collapses the given edge by removing startVert. May split the mesh
-// topologically if the collapse would have resulted in a 4-manifold edge. Do
-// not collapse an edge if startVert is pinched - the vert will be marked NaN,
-// but other edges may still be pointing to it.
-void Manifold::Impl::CollapseEdge(const int edge, std::vector<int>& edges) {
+// Collapses the given edge by removing startVert - returns false if the edge
+// cannot be collapsed. May split the mesh topologically if the collapse would
+// have resulted in a 4-manifold edge. Do not collapse an edge if startVert is
+// pinched - the vert would be marked NaN, but other edges could still be
+// pointing to it.
+bool Manifold::Impl::CollapseEdge(const int edge, std::vector<int>& edges) {
   Vec<TriRef>& triRef = meshRelation_.triRef;
-  Vec<ivec3>& triProp = meshRelation_.triProperties;
 
   const Halfedge toRemove = halfedge_[edge];
-  if (toRemove.pairedHalfedge < 0) return;
+  if (toRemove.pairedHalfedge < 0) return false;
 
   const int endVert = toRemove.endVert;
   const ivec3 tri0edge = TriOf(edge);
@@ -470,23 +523,16 @@ void Manifold::Impl::CollapseEdge(const int edge, std::vector<int>& edges) {
   const vec3 pNew = vertPos_[endVert];
   const vec3 pOld = vertPos_[toRemove.startVert];
   const vec3 delta = pNew - pOld;
-  const bool shortEdge = la::dot(delta, delta) < tolerance_ * tolerance_;
-
-  // Orbit endVert
-  int current = halfedge_[tri0edge[1]].pairedHalfedge;
-  while (current != tri1edge[2]) {
-    current = NextHalfedge(current);
-    edges.push_back(current);
-    current = halfedge_[current].pairedHalfedge;
-  }
+  const bool shortEdge = la::dot(delta, delta) < epsilon_ * epsilon_;
 
   // Orbit startVert
   int start = halfedge_[tri1edge[1]].pairedHalfedge;
+  int current = tri1edge[2];
   if (!shortEdge) {
     current = start;
     TriRef refCheck = triRef[toRemove.pairedHalfedge / 3];
     vec3 pLast = vertPos_[halfedge_[tri1edge[1]].endVert];
-    while (current != tri0edge[2]) {
+    while (current != tri1edge[0]) {
       current = NextHalfedge(current);
       vec3 pNext = vertPos_[halfedge_[current].endVert];
       const int tri = current / 3;
@@ -495,28 +541,43 @@ void Manifold::Impl::CollapseEdge(const int edge, std::vector<int>& edges) {
       // Don't collapse if the edge is not redundant (this may have changed due
       // to the collapse of neighbors).
       if (!ref.SameFace(refCheck)) {
+        const TriRef oldRef = refCheck;
         refCheck = triRef[edge / 3];
         if (!ref.SameFace(refCheck)) {
-          return;
-        } else {
-          // Don't collapse if the edges separating the faces are not colinear
-          // (can happen when the two faces are coplanar).
-          if (CCW(projection * pOld, projection * pLast, projection * pNew,
+          return false;
+        }
+        if (ref.meshID != oldRef.meshID || ref.faceID != oldRef.faceID ||
+            la::dot(faceNormal_[toRemove.pairedHalfedge / 3],
+                    faceNormal_[tri]) < -0.5) {
+          // Restrict collapse to colinear edges when the edge separates faces
+          // or the edge is sharp. This ensures large shifts are not introduced
+          // parallel to the tangent plane.
+          if (CCW(projection * pLast, projection * pOld, projection * pNew,
                   epsilon_) != 0)
-            return;
+            return false;
         }
       }
 
       // Don't collapse edge if it would cause a triangle to invert.
       if (CCW(projection * pNext, projection * pLast, projection * pNew,
               epsilon_) < 0)
-        return;
+        return false;
 
       pLast = pNext;
       current = halfedge_[current].pairedHalfedge;
     }
   }
 
+  // Orbit endVert
+  {
+    int current = halfedge_[tri0edge[1]].pairedHalfedge;
+    while (current != tri1edge[2]) {
+      current = NextHalfedge(current);
+      edges.push_back(current);
+      current = halfedge_[current].pairedHalfedge;
+    }
+  }
+
   // Remove toRemove.startVert and replace with endVert.
   vertPos_[toRemove.startVert] = vec3(NAN);
   CollapseTri(tri1edge);
@@ -524,20 +585,18 @@ void Manifold::Impl::CollapseEdge(const int edge, std::vector<int>& edges) {
   // Orbit startVert
   const int tri0 = edge / 3;
   const int tri1 = toRemove.pairedHalfedge / 3;
-  const int triVert0 = (edge + 1) % 3;
-  const int triVert1 = toRemove.pairedHalfedge % 3;
   current = start;
   while (current != tri0edge[2]) {
     current = NextHalfedge(current);
 
-    if (triProp.size() > 0) {
+    if (NumProp() > 0) {
       // Update the shifted triangles to the vertBary of endVert
       const int tri = current / 3;
-      const int vIdx = current - 3 * tri;
       if (triRef[tri].SameFace(triRef[tri0])) {
-        triProp[tri][vIdx] = triProp[tri0][triVert0];
+        halfedge_[current].propVert = halfedge_[NextHalfedge(edge)].propVert;
       } else if (triRef[tri].SameFace(triRef[tri1])) {
-        triProp[tri][vIdx] = triProp[tri1][triVert1];
+        halfedge_[current].propVert =
+            halfedge_[toRemove.pairedHalfedge].propVert;
       }
     }
 
@@ -557,6 +616,7 @@ void Manifold::Impl::CollapseEdge(const int edge, std::vector<int>& edges) {
   UpdateVert(endVert, start, tri0edge[2]);
   CollapseTri(tri0edge);
   RemoveIfFolded(start);
+  return true;
 }
 
 void Manifold::Impl::RecursiveEdgeSwap(const int edge, int& tag,
@@ -574,8 +634,6 @@ void Manifold::Impl::RecursiveEdgeSwap(const int edge, int& tag,
 
   const ivec3 tri0edge = TriOf(edge);
   const ivec3 tri1edge = TriOf(pair);
-  const ivec3 perm0 = TriOf(edge % 3);
-  const ivec3 perm1 = TriOf(pair % 3);
 
   mat2x3 projection = GetAxisAlignedProjection(faceNormal_[edge / 3]);
   vec2 v[4];
@@ -611,22 +669,21 @@ void Manifold::Impl::RecursiveEdgeSwap(const int edge, int& tag,
     const double l02 = la::length(v[2] - v[0]);
     const double a = std::max(0.0, std::min(1.0, l02 / l01));
     // Update properties if applicable
-    if (meshRelation_.properties.size() > 0) {
-      Vec<ivec3>& triProp = meshRelation_.triProperties;
-      Vec<double>& prop = meshRelation_.properties;
-      triProp[tri0] = triProp[tri1];
-      triProp[tri0][perm0[1]] = triProp[tri1][perm1[0]];
-      triProp[tri0][perm0[0]] = triProp[tri1][perm1[2]];
+    if (properties_.size() > 0) {
+      Vec<double>& prop = properties_;
+      halfedge_[tri0edge[1]].propVert = halfedge_[tri1edge[0]].propVert;
+      halfedge_[tri0edge[0]].propVert = halfedge_[tri1edge[2]].propVert;
+      halfedge_[tri0edge[2]].propVert = halfedge_[tri1edge[2]].propVert;
       const int numProp = NumProp();
       const int newProp = prop.size() / numProp;
-      const int propIdx0 = triProp[tri1][perm1[0]];
-      const int propIdx1 = triProp[tri1][perm1[1]];
+      const int propIdx0 = halfedge_[tri1edge[0]].propVert;
+      const int propIdx1 = halfedge_[tri1edge[1]].propVert;
       for (int p = 0; p < numProp; ++p) {
         prop.push_back(a * prop[numProp * propIdx0 + p] +
                        (1 - a) * prop[numProp * propIdx1 + p]);
       }
-      triProp[tri1][perm1[0]] = newProp;
-      triProp[tri0][perm0[2]] = newProp;
+      halfedge_[tri1edge[0]].propVert = newProp;
+      halfedge_[tri0edge[2]].propVert = newProp;
     }
 
     // if the new edge already exists, duplicate the verts and split the mesh.
@@ -675,22 +732,224 @@ void Manifold::Impl::RecursiveEdgeSwap(const int edge, int& tag,
 
 void Manifold::Impl::SplitPinchedVerts() {
   ZoneScoped;
-  std::vector<bool> vertProcessed(NumVert(), false);
-  std::vector<bool> halfedgeProcessed(halfedge_.size(), false);
-  for (size_t i = 0; i < halfedge_.size(); ++i) {
-    if (halfedgeProcessed[i]) continue;
-    int vert = halfedge_[i].startVert;
-    if (vertProcessed[vert]) {
-      vertPos_.push_back(vertPos_[vert]);
-      vert = NumVert() - 1;
-    } else {
-      vertProcessed[vert] = true;
+
+  auto nbEdges = halfedge_.size();
+#if MANIFOLD_PAR == 1
+  if (nbEdges > 1e4) {
+    std::mutex mutex;
+    std::vector<size_t> pinched;
+    // This parallelized version is non-trivial so we can't reuse the code
+    //
+    // The idea here is to identify cycles of halfedges that can be iterated
+    // through using ForVert. Pinched verts are vertices where there are
+    // multiple cycles associated with the vertex. Each cycle is identified with
+    // the largest halfedge index within the cycle, and when there are multiple
+    // cycles associated with the same starting vertex but with different ids,
+    // it means we have a pinched vertex. This check is done by using a single
+    // atomic cas operation, the expected case is either invalid id (the vertex
+    // was not processed) or with the same id.
+    //
+    // The local store is to store the processed halfedges, so to avoid
+    // repetitive processing. Note that it only approximates the processed
+    // halfedges because it is thread local. This is why we need a vector to
+    // deduplicate the probematic halfedges we found.
+    std::vector<std::atomic<size_t>> largestEdge(NumVert());
+    for_each(ExecutionPolicy::Par, countAt(0), countAt(NumVert()),
+             [&largestEdge](size_t i) {
+               largestEdge[i].store(std::numeric_limits<size_t>::max());
+             });
+    tbb::combinable<std::vector<bool>> store(
+        [nbEdges]() { return std::vector<bool>(nbEdges, false); });
+    tbb::parallel_for(
+        tbb::blocked_range<size_t>(0, nbEdges),
+        [&store, &mutex, &pinched, &largestEdge, this](const auto& r) {
+          auto& local = store.local();
+          std::vector<size_t> pinchedLocal;
+          for (auto i = r.begin(); i < r.end(); ++i) {
+            if (local[i]) continue;
+            local[i] = true;
+            const int vert = halfedge_[i].startVert;
+            if (vert == -1) continue;
+            size_t largest = i;
+            ForVert(i, [&local, &largest](int current) {
+              local[current] = true;
+              largest = std::max(largest, static_cast<size_t>(current));
+            });
+            size_t expected = std::numeric_limits<size_t>::max();
+            if (!largestEdge[vert].compare_exchange_strong(expected, largest) &&
+                expected != largest) {
+              // we know that there is another loop...
+              pinchedLocal.push_back(largest);
+            }
+          }
+          if (!pinchedLocal.empty()) {
+            std::lock_guard<std::mutex> lock(mutex);
+            pinched.insert(pinched.end(), pinchedLocal.begin(),
+                           pinchedLocal.end());
+          }
+        });
+
+    manifold::stable_sort(pinched.begin(), pinched.end());
+    std::vector<bool> halfedgeProcessed(nbEdges, false);
+    for (size_t i : pinched) {
+      if (halfedgeProcessed[i]) continue;
+      vertPos_.push_back(vertPos_[halfedge_[i].startVert]);
+      const int vert = NumVert() - 1;
+      ForVert(i, [this, vert, &halfedgeProcessed](int current) {
+        halfedgeProcessed[current] = true;
+        halfedge_[current].startVert = vert;
+        halfedge_[halfedge_[current].pairedHalfedge].endVert = vert;
+      });
     }
-    ForVert(i, [this, &halfedgeProcessed, vert](int current) {
-      halfedgeProcessed[current] = true;
-      halfedge_[current].startVert = vert;
-      halfedge_[halfedge_[current].pairedHalfedge].endVert = vert;
-    });
+  } else
+#endif
+  {
+    std::vector<bool> vertProcessed(NumVert(), false);
+    std::vector<bool> halfedgeProcessed(nbEdges, false);
+    for (size_t i = 0; i < nbEdges; ++i) {
+      if (halfedgeProcessed[i]) continue;
+      int vert = halfedge_[i].startVert;
+      if (vert == -1) continue;
+      if (vertProcessed[vert]) {
+        vertPos_.push_back(vertPos_[vert]);
+        vert = NumVert() - 1;
+      } else {
+        vertProcessed[vert] = true;
+      }
+      ForVert(i, [this, &halfedgeProcessed, vert](int current) {
+        halfedgeProcessed[current] = true;
+        halfedge_[current].startVert = vert;
+        halfedge_[halfedge_[current].pairedHalfedge].endVert = vert;
+      });
+    }
+  }
+}
+
+void Manifold::Impl::DedupeEdges() {
+  while (1) {
+    ZoneScopedN("DedupeEdge");
+
+    const size_t nbEdges = halfedge_.size();
+    std::vector<size_t> duplicates;
+    auto localLoop = [&](size_t start, size_t end, std::vector<bool>& local,
+                         std::vector<size_t>& results) {
+      // Iterate over all halfedges that start with the same vertex, and check
+      // for halfedges with the same ending vertex.
+      // Note: we use Vec and linear search when the number of neighbor is
+      // small because unordered_set requires allocations and is expensive.
+      // We switch to unordered_set when the number of neighbor is
+      // larger to avoid making things quadratic.
+      // We do it in two pass, the first pass to find the minimal halfedges with
+      // the target start and end verts, the second pass flag all the duplicated
+      // halfedges that are not having the minimal index as duplicates.
+      // This ensures deterministic result.
+      //
+      // The local store is to store the processed halfedges, so to avoid
+      // repetitive processing. Note that it only approximates the processed
+      // halfedges because it is thread local.
+      Vec<std::pair<int, int>> endVerts;
+      std::unordered_map<int, int> endVertSet;
+      for (auto i = start; i < end; ++i) {
+        if (local[i] || halfedge_[i].startVert == -1 ||
+            halfedge_[i].endVert == -1)
+          continue;
+        // we want to keep the allocation
+        endVerts.clear(false);
+        endVertSet.clear();
+
+        // first iteration, populate entries
+        // this makes sure we always report the same set of entries
+        ForVert(i, [&local, &endVerts, &endVertSet, this](int current) {
+          local[current] = true;
+          if (halfedge_[current].startVert == -1 ||
+              halfedge_[current].endVert == -1) {
+            return;
+          }
+          int endV = halfedge_[current].endVert;
+          if (endVertSet.empty()) {
+            auto iter = std::find_if(endVerts.begin(), endVerts.end(),
+                                     [endV](const std::pair<int, int>& pair) {
+                                       return pair.first == endV;
+                                     });
+            if (iter != endVerts.end()) {
+              iter->second = std::min(iter->second, current);
+            } else {
+              endVerts.push_back({endV, current});
+              if (endVerts.size() > 32) {
+                endVertSet.insert(endVerts.begin(), endVerts.end());
+                endVerts.clear(false);
+              }
+            }
+          } else {
+            auto pair = endVertSet.insert({endV, current});
+            if (!pair.second)
+              pair.first->second = std::min(pair.first->second, current);
+          }
+        });
+        // second iteration, actually check for duplicates
+        // we always report the same set of duplicates, excluding the smallest
+        // halfedge in the set of duplicates
+        ForVert(i, [&endVerts, &endVertSet, &results, this](int current) {
+          if (halfedge_[current].startVert == -1 ||
+              halfedge_[current].endVert == -1) {
+            return;
+          }
+          int endV = halfedge_[current].endVert;
+          if (endVertSet.empty()) {
+            auto iter = std::find_if(endVerts.begin(), endVerts.end(),
+                                     [endV](const std::pair<int, int>& pair) {
+                                       return pair.first == endV;
+                                     });
+            if (iter->second != current) results.push_back(current);
+          } else {
+            auto iter = endVertSet.find(endV);
+            if (iter->second != current) results.push_back(current);
+          }
+        });
+      }
+    };
+#if MANIFOLD_PAR == 1
+    if (nbEdges > 1e4) {
+      std::mutex mutex;
+      tbb::combinable<std::vector<bool>> store(
+          [nbEdges]() { return std::vector<bool>(nbEdges, false); });
+      tbb::parallel_for(
+          tbb::blocked_range<size_t>(0, nbEdges),
+          [&store, &mutex, &duplicates, &localLoop](const auto& r) {
+            auto& local = store.local();
+            std::vector<size_t> duplicatesLocal;
+            localLoop(r.begin(), r.end(), local, duplicatesLocal);
+            if (!duplicatesLocal.empty()) {
+              std::lock_guard<std::mutex> lock(mutex);
+              duplicates.insert(duplicates.end(), duplicatesLocal.begin(),
+                                duplicatesLocal.end());
+            }
+          });
+      manifold::stable_sort(duplicates.begin(), duplicates.end());
+      duplicates.resize(
+          std::distance(duplicates.begin(),
+                        std::unique(duplicates.begin(), duplicates.end())));
+    } else
+#endif
+    {
+      std::vector<bool> local(nbEdges, false);
+      localLoop(0, nbEdges, local, duplicates);
+    }
+
+    size_t numFlagged = 0;
+    for (size_t i : duplicates) {
+      DedupeEdge(i);
+      numFlagged++;
+    }
+
+    if (numFlagged == 0) break;
+
+#ifdef MANIFOLD_DEBUG
+    if (ManifoldParams().verbose > 0) {
+      std::cout << "found " << numFlagged << " duplicate edges to split"
+                << std::endl;
+    }
+#endif
   }
 }
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/face_op.cpp b/thirdparty/manifold/src/face_op.cpp
index b1a6b16c73..5e826dd73b 100644
--- a/thirdparty/manifold/src/face_op.cpp
+++ b/thirdparty/manifold/src/face_op.cpp
@@ -12,16 +12,75 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+#include <unordered_set>
+
+#include "impl.h"
+#include "manifold/common.h"
+#include "manifold/polygon.h"
+#include "parallel.h"
+#include "shared.h"
+
 #if (MANIFOLD_PAR == 1) && __has_include(<tbb/concurrent_map.h>)
 #include <tbb/tbb.h>
 #define TBB_PREVIEW_CONCURRENT_ORDERED_CONTAINERS 1
 #include <tbb/concurrent_map.h>
 #endif
-#include <unordered_set>
 
-#include "./impl.h"
-#include "./parallel.h"
-#include "manifold/polygon.h"
+namespace {
+using namespace manifold;
+
+/**
+ * Returns an assembled set of vertex index loops of the input list of
+ * Halfedges, where each vert must be referenced the same number of times as a
+ * startVert and endVert. If startHalfedgeIdx is given, instead of putting
+ * vertex indices into the returned polygons structure, it will use the halfedge
+ * indices instead.
+ */
+std::vector<std::vector<int>> AssembleHalfedges(VecView<Halfedge>::IterC start,
+                                                VecView<Halfedge>::IterC end,
+                                                const int startHalfedgeIdx) {
+  std::multimap<int, int> vert_edge;
+  for (auto edge = start; edge != end; ++edge) {
+    vert_edge.emplace(
+        std::make_pair(edge->startVert, static_cast<int>(edge - start)));
+  }
+
+  std::vector<std::vector<int>> polys;
+  int startEdge = 0;
+  int thisEdge = startEdge;
+  while (1) {
+    if (thisEdge == startEdge) {
+      if (vert_edge.empty()) break;
+      startEdge = vert_edge.begin()->second;
+      thisEdge = startEdge;
+      polys.push_back({});
+    }
+    polys.back().push_back(startHalfedgeIdx + thisEdge);
+    const auto result = vert_edge.find((start + thisEdge)->endVert);
+    DEBUG_ASSERT(result != vert_edge.end(), topologyErr, "non-manifold edge");
+    thisEdge = result->second;
+    vert_edge.erase(result);
+  }
+  return polys;
+}
+
+/**
+ * Add the vertex position projection to the indexed polygons.
+ */
+PolygonsIdx ProjectPolygons(const std::vector<std::vector<int>>& polys,
+                            const Vec<Halfedge>& halfedge,
+                            const Vec<vec3>& vertPos, mat2x3 projection) {
+  PolygonsIdx polygons;
+  for (const auto& poly : polys) {
+    polygons.push_back({});
+    for (const auto& edge : poly) {
+      polygons.back().push_back(
+          {projection * vertPos[halfedge[edge].startVert], edge});
+    }  // for vert
+  }  // for poly
+  return polygons;
+}
+}  // namespace
 
 namespace manifold {
 
@@ -39,83 +98,71 @@ using AddTriangle = std::function<void(int, ivec3, vec3, TriRef)>;
  * faceNormal_ values are retained, repeated as necessary.
  */
 void Manifold::Impl::Face2Tri(const Vec<int>& faceEdge,
-                              const Vec<TriRef>& halfedgeRef) {
+                              const Vec<TriRef>& halfedgeRef,
+                              bool allowConvex) {
   ZoneScoped;
   Vec<ivec3> triVerts;
   Vec<vec3> triNormal;
+  Vec<ivec3> triProp;
   Vec<TriRef>& triRef = meshRelation_.triRef;
-  triRef.resize(0);
+  triRef.clear();
   auto processFace = [&](GeneralTriangulation general, AddTriangle addTri,
                          int face) {
     const int firstEdge = faceEdge[face];
     const int lastEdge = faceEdge[face + 1];
     const int numEdge = lastEdge - firstEdge;
+    if (numEdge == 0) return;
     DEBUG_ASSERT(numEdge >= 3, topologyErr, "face has less than three edges.");
     const vec3 normal = faceNormal_[face];
 
     if (numEdge == 3) {  // Single triangle
-      int mapping[3] = {halfedge_[firstEdge].startVert,
-                        halfedge_[firstEdge + 1].startVert,
-                        halfedge_[firstEdge + 2].startVert};
+      ivec3 triEdge(firstEdge, firstEdge + 1, firstEdge + 2);
       ivec3 tri(halfedge_[firstEdge].startVert,
                 halfedge_[firstEdge + 1].startVert,
                 halfedge_[firstEdge + 2].startVert);
       ivec3 ends(halfedge_[firstEdge].endVert, halfedge_[firstEdge + 1].endVert,
                  halfedge_[firstEdge + 2].endVert);
       if (ends[0] == tri[2]) {
+        std::swap(triEdge[1], triEdge[2]);
         std::swap(tri[1], tri[2]);
         std::swap(ends[1], ends[2]);
       }
       DEBUG_ASSERT(ends[0] == tri[1] && ends[1] == tri[2] && ends[2] == tri[0],
                    topologyErr, "These 3 edges do not form a triangle!");
 
-      addTri(face, tri, normal, halfedgeRef[firstEdge]);
+      addTri(face, triEdge, normal, halfedgeRef[firstEdge]);
     } else if (numEdge == 4) {  // Pair of triangles
-      int mapping[4] = {halfedge_[firstEdge].startVert,
-                        halfedge_[firstEdge + 1].startVert,
-                        halfedge_[firstEdge + 2].startVert,
-                        halfedge_[firstEdge + 3].startVert};
       const mat2x3 projection = GetAxisAlignedProjection(normal);
       auto triCCW = [&projection, this](const ivec3 tri) {
-        return CCW(projection * this->vertPos_[tri[0]],
-                   projection * this->vertPos_[tri[1]],
-                   projection * this->vertPos_[tri[2]], epsilon_) >= 0;
+        return CCW(projection * this->vertPos_[halfedge_[tri[0]].startVert],
+                   projection * this->vertPos_[halfedge_[tri[1]].startVert],
+                   projection * this->vertPos_[halfedge_[tri[2]].startVert],
+                   epsilon_) >= 0;
       };
 
-      ivec3 tri0(halfedge_[firstEdge].startVert, halfedge_[firstEdge].endVert,
-                 -1);
-      ivec3 tri1(-1, -1, tri0[0]);
-      for (const int i : {1, 2, 3}) {
-        if (halfedge_[firstEdge + i].startVert == tri0[1]) {
-          tri0[2] = halfedge_[firstEdge + i].endVert;
-          tri1[0] = tri0[2];
-        }
-        if (halfedge_[firstEdge + i].endVert == tri0[0]) {
-          tri1[1] = halfedge_[firstEdge + i].startVert;
-        }
-      }
-      DEBUG_ASSERT(la::all(la::gequal(tri0, ivec3(0))) &&
-                       la::all(la::gequal(tri1, ivec3(0))),
-                   topologyErr, "non-manifold quad!");
-      bool firstValid = triCCW(tri0) && triCCW(tri1);
-      tri0[2] = tri1[1];
-      tri1[2] = tri0[1];
-      bool secondValid = triCCW(tri0) && triCCW(tri1);
+      std::vector<int> quad = AssembleHalfedges(
+          halfedge_.cbegin() + faceEdge[face],
+          halfedge_.cbegin() + faceEdge[face + 1], faceEdge[face])[0];
 
-      if (!secondValid) {
-        tri0[2] = tri1[0];
-        tri1[2] = tri0[0];
-      } else if (firstValid) {
-        vec3 firstCross = vertPos_[tri0[0]] - vertPos_[tri1[0]];
-        vec3 secondCross = vertPos_[tri0[1]] - vertPos_[tri1[1]];
-        if (la::dot(firstCross, firstCross) <
-            la::dot(secondCross, secondCross)) {
-          tri0[2] = tri1[0];
-          tri1[2] = tri0[0];
+      const la::mat<int, 3, 2> tris[2] = {
+          {{quad[0], quad[1], quad[2]}, {quad[0], quad[2], quad[3]}},
+          {{quad[1], quad[2], quad[3]}, {quad[0], quad[1], quad[3]}}};
+
+      int choice = 0;
+
+      if (!(triCCW(tris[0][0]) && triCCW(tris[0][1]))) {
+        choice = 1;
+      } else if (triCCW(tris[1][0]) && triCCW(tris[1][1])) {
+        vec3 diag0 = vertPos_[halfedge_[quad[0]].startVert] -
+                     vertPos_[halfedge_[quad[2]].startVert];
+        vec3 diag1 = vertPos_[halfedge_[quad[1]].startVert] -
+                     vertPos_[halfedge_[quad[3]].startVert];
+        if (la::length2(diag0) > la::length2(diag1)) {
+          choice = 1;
         }
       }
 
-      for (const auto& tri : {tri0, tri1}) {
+      for (const auto& tri : tris[choice]) {
         addTri(face, tri, normal, halfedgeRef[firstEdge]);
       }
     } else {  // General triangulation
@@ -127,10 +174,12 @@ void Manifold::Impl::Face2Tri(const Vec<int>& faceEdge,
   auto generalTriangulation = [&](int face) {
     const vec3 normal = faceNormal_[face];
     const mat2x3 projection = GetAxisAlignedProjection(normal);
-    const PolygonsIdx polys =
-        Face2Polygons(halfedge_.cbegin() + faceEdge[face],
-                      halfedge_.cbegin() + faceEdge[face + 1], projection);
-    return TriangulateIdx(polys, epsilon_);
+    const PolygonsIdx polys = ProjectPolygons(
+        AssembleHalfedges(halfedge_.cbegin() + faceEdge[face],
+                          halfedge_.cbegin() + faceEdge[face + 1],
+                          faceEdge[face]),
+        halfedge_, vertPos_, projection);
+    return TriangulateIdx(polys, epsilon_, allowConvex);
   };
 #if (MANIFOLD_PAR == 1) && __has_include(<tbb/tbb.h>)
   tbb::task_group group;
@@ -156,13 +205,17 @@ void Manifold::Impl::Face2Tri(const Vec<int>& faceEdge,
   // prefix sum computation (assign unique index to each face) and preallocation
   exclusive_scan(triCount.begin(), triCount.end(), triCount.begin(), 0_uz);
   triVerts.resize(triCount.back());
+  triProp.resize(triCount.back());
   triNormal.resize(triCount.back());
   triRef.resize(triCount.back());
 
   auto processFace2 = std::bind(
       processFace, [&](size_t face) { return std::move(results[face]); },
       [&](size_t face, ivec3 tri, vec3 normal, TriRef r) {
-        triVerts[triCount[face]] = tri;
+        for (const int i : {0, 1, 2}) {
+          triVerts[triCount[face]][i] = halfedge_[tri[i]].startVert;
+          triProp[triCount[face]][i] = halfedge_[tri[i]].propVert;
+        }
         triNormal[triCount[face]] = normal;
         triRef[triCount[face]] = r;
         triCount[face]++;
@@ -177,8 +230,15 @@ void Manifold::Impl::Face2Tri(const Vec<int>& faceEdge,
   triRef.reserve(faceEdge.size());
   auto processFace2 = std::bind(
       processFace, generalTriangulation,
-      [&](size_t _face, ivec3 tri, vec3 normal, TriRef r) {
-        triVerts.push_back(tri);
+      [&](size_t, ivec3 tri, vec3 normal, TriRef r) {
+        ivec3 verts;
+        ivec3 props;
+        for (const int i : {0, 1, 2}) {
+          verts[i] = halfedge_[tri[i]].startVert;
+          props[i] = halfedge_[tri[i]].propVert;
+        }
+        triVerts.push_back(verts);
+        triProp.push_back(props);
         triNormal.push_back(normal);
         triRef.push_back(r);
       },
@@ -189,41 +249,7 @@ void Manifold::Impl::Face2Tri(const Vec<int>& faceEdge,
 #endif
 
   faceNormal_ = std::move(triNormal);
-  CreateHalfedges(triVerts);
-}
-
-/**
- * Returns a set of 2D polygons formed by the input projection of the vertices
- * of the list of Halfedges, which must be an even-manifold, meaning each vert
- * must be referenced the same number of times as a startVert and endVert.
- */
-PolygonsIdx Manifold::Impl::Face2Polygons(VecView<Halfedge>::IterC start,
-                                          VecView<Halfedge>::IterC end,
-                                          mat2x3 projection) const {
-  std::multimap<int, int> vert_edge;
-  for (auto edge = start; edge != end; ++edge) {
-    vert_edge.emplace(
-        std::make_pair(edge->startVert, static_cast<int>(edge - start)));
-  }
-
-  PolygonsIdx polys;
-  int startEdge = 0;
-  int thisEdge = startEdge;
-  while (1) {
-    if (thisEdge == startEdge) {
-      if (vert_edge.empty()) break;
-      startEdge = vert_edge.begin()->second;
-      thisEdge = startEdge;
-      polys.push_back({});
-    }
-    int vert = (start + thisEdge)->startVert;
-    polys.back().push_back({projection * vertPos_[vert], vert});
-    const auto result = vert_edge.find((start + thisEdge)->endVert);
-    DEBUG_ASSERT(result != vert_edge.end(), topologyErr, "non-manifold edge");
-    thisEdge = result->second;
-    vert_edge.erase(result);
-  }
-  return polys;
+  CreateHalfedges(triProp, triVerts);
 }
 
 Polygons Manifold::Impl::Slice(double height) const {
@@ -231,12 +257,9 @@ Polygons Manifold::Impl::Slice(double height) const {
   plane.min.z = plane.max.z = height;
   Vec<Box> query;
   query.push_back(plane);
-  const SparseIndices collisions =
-      collider_.Collisions<false, false>(query.cview());
 
   std::unordered_set<int> tris;
-  for (size_t i = 0; i < collisions.size(); ++i) {
-    const int tri = collisions.Get(i, 1);
+  auto recordCollision = [&](int, int tri) {
     double min = std::numeric_limits<double>::infinity();
     double max = -std::numeric_limits<double>::infinity();
     for (const int j : {0, 1, 2}) {
@@ -248,7 +271,10 @@ Polygons Manifold::Impl::Slice(double height) const {
     if (min <= height && max > height) {
       tris.insert(tri);
     }
-  }
+  };
+
+  auto recorder = MakeSimpleRecorder(recordCollision);
+  collider_.Collisions<false>(query.cview(), recorder, false);
 
   Polygons polys;
   while (!tris.empty()) {
@@ -303,7 +329,8 @@ Polygons Manifold::Impl::Project() const {
       cusps.begin());
 
   PolygonsIdx polysIndexed =
-      Face2Polygons(cusps.cbegin(), cusps.cend(), projection);
+      ProjectPolygons(AssembleHalfedges(cusps.cbegin(), cusps.cend(), 0), cusps,
+                      vertPos_, projection);
 
   Polygons polys;
   for (const auto& poly : polysIndexed) {
diff --git a/thirdparty/manifold/src/hashtable.h b/thirdparty/manifold/src/hashtable.h
index 052c34e09c..96107c357f 100644
--- a/thirdparty/manifold/src/hashtable.h
+++ b/thirdparty/manifold/src/hashtable.h
@@ -16,13 +16,12 @@
 
 #include <atomic>
 
-#include "./utils.h"
-#include "./vec.h"
+#include "utils.h"
+#include "vec.h"
 
 namespace {
-typedef unsigned long long int Uint64;
-typedef Uint64 (*hash_fun_t)(Uint64);
-inline constexpr Uint64 kOpen = std::numeric_limits<Uint64>::max();
+using hash_fun_t = uint64_t(uint64_t);
+inline constexpr uint64_t kOpen = std::numeric_limits<uint64_t>::max();
 
 template <typename T>
 T AtomicCAS(T& target, T compare, T val) {
@@ -45,13 +44,6 @@ T AtomicLoad(const T& target) {
   return tar.load(std::memory_order_acquire);
 }
 
-// https://stackoverflow.com/questions/664014/what-integer-hash-function-are-good-that-accepts-an-integer-hash-key
-inline Uint64 hash64bit(Uint64 x) {
-  x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9ull;
-  x = (x ^ (x >> 27)) * 0x94d049bb133111ebull;
-  x = x ^ (x >> 31);
-  return x;
-}
 }  // namespace
 
 namespace manifold {
@@ -59,7 +51,7 @@ namespace manifold {
 template <typename V, hash_fun_t H = hash64bit>
 class HashTableD {
  public:
-  HashTableD(Vec<Uint64>& keys, Vec<V>& values, std::atomic<size_t>& used,
+  HashTableD(Vec<uint64_t>& keys, Vec<V>& values, std::atomic<size_t>& used,
              uint32_t step = 1)
       : step_{step}, keys_{keys}, values_{values}, used_{used} {}
 
@@ -70,12 +62,12 @@ class HashTableD {
            static_cast<size_t>(Size());
   }
 
-  void Insert(Uint64 key, const V& val) {
+  void Insert(uint64_t key, const V& val) {
     uint32_t idx = H(key) & (Size() - 1);
     while (1) {
       if (Full()) return;
-      Uint64& k = keys_[idx];
-      const Uint64 found = AtomicCAS(k, kOpen, key);
+      uint64_t& k = keys_[idx];
+      const uint64_t found = AtomicCAS(k, kOpen, key);
       if (found == kOpen) {
         used_.fetch_add(1, std::memory_order_relaxed);
         values_[idx] = val;
@@ -86,10 +78,10 @@ class HashTableD {
     }
   }
 
-  V& operator[](Uint64 key) {
+  V& operator[](uint64_t key) {
     uint32_t idx = H(key) & (Size() - 1);
     while (1) {
-      const Uint64 k = AtomicLoad(keys_[idx]);
+      const uint64_t k = AtomicLoad(keys_[idx]);
       if (k == key || k == kOpen) {
         return values_[idx];
       }
@@ -97,10 +89,10 @@ class HashTableD {
     }
   }
 
-  const V& operator[](Uint64 key) const {
+  const V& operator[](uint64_t key) const {
     uint32_t idx = H(key) & (Size() - 1);
     while (1) {
-      const Uint64 k = AtomicLoad(keys_[idx]);
+      const uint64_t k = AtomicLoad(keys_[idx]);
       if (k == key || k == kOpen) {
         return values_[idx];
       }
@@ -108,13 +100,13 @@ class HashTableD {
     }
   }
 
-  Uint64 KeyAt(int idx) const { return AtomicLoad(keys_[idx]); }
+  uint64_t KeyAt(int idx) const { return AtomicLoad(keys_[idx]); }
   V& At(int idx) { return values_[idx]; }
   const V& At(int idx) const { return values_[idx]; }
 
  private:
   uint32_t step_;
-  VecView<Uint64> keys_;
+  VecView<uint64_t> keys_;
   VecView<V> values_;
   std::atomic<size_t>& used_;
 };
@@ -157,10 +149,10 @@ class HashTable {
 
   Vec<V>& GetValueStore() { return values_; }
 
-  static Uint64 Open() { return kOpen; }
+  static uint64_t Open() { return kOpen; }
 
  private:
-  Vec<Uint64> keys_;
+  Vec<uint64_t> keys_;
   Vec<V> values_;
   std::atomic<size_t> used_ = 0;
   uint32_t step_;
diff --git a/thirdparty/manifold/src/impl.cpp b/thirdparty/manifold/src/impl.cpp
index afa45dff30..ba9a5f71f3 100644
--- a/thirdparty/manifold/src/impl.cpp
+++ b/thirdparty/manifold/src/impl.cpp
@@ -12,38 +12,113 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "./impl.h"
+#include "impl.h"
 
 #include <algorithm>
 #include <atomic>
+#include <cstring>
 #include <map>
 #include <optional>
 
-#include "./hashtable.h"
-#include "./mesh_fixes.h"
-#include "./parallel.h"
-#include "./svd.h"
-
-#ifdef MANIFOLD_EXPORT
-#include <string.h>
-
-#include <iostream>
-#endif
+#include "csg_tree.h"
+#include "hashtable.h"
+#include "manifold/optional_assert.h"
+#include "mesh_fixes.h"
+#include "parallel.h"
+#include "shared.h"
+#include "svd.h"
 
 namespace {
 using namespace manifold;
 
-constexpr uint64_t kRemove = std::numeric_limits<uint64_t>::max();
-
-void AtomicAddVec3(vec3& target, const vec3& add) {
-  for (int i : {0, 1, 2}) {
-    std::atomic<double>& tar =
-        reinterpret_cast<std::atomic<double>&>(target[i]);
-    double old_val = tar.load(std::memory_order_relaxed);
-    while (!tar.compare_exchange_weak(old_val, old_val + add[i],
-                                      std::memory_order_relaxed)) {
+/**
+ * Returns arc cosine of 𝑥.
+ *
+ * @return value in range [0,M_PI]
+ * @return NAN if 𝑥 ∈ {NAN,+INFINITY,-INFINITY}
+ * @return NAN if 𝑥 ∉ [-1,1]
+ */
+double sun_acos(double x) {
+  /*
+   * Origin of acos function: FreeBSD /usr/src/lib/msun/src/e_acos.c
+   * Changed the use of union to memcpy to avoid undefined behavior.
+   * ====================================================
+   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+   *
+   * Developed at SunSoft, a Sun Microsystems, Inc. business.
+   * Permission to use, copy, modify, and distribute this
+   * software is freely granted, provided that this notice
+   * is preserved.
+   * ====================================================
+   */
+  constexpr double pio2_hi =
+      1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
+  constexpr double pio2_lo =
+      6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
+  constexpr double pS0 =
+      1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
+  constexpr double pS1 =
+      -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
+  constexpr double pS2 =
+      2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
+  constexpr double pS3 =
+      -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
+  constexpr double pS4 =
+      7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
+  constexpr double pS5 =
+      3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
+  constexpr double qS1 =
+      -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
+  constexpr double qS2 =
+      2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
+  constexpr double qS3 =
+      -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
+  constexpr double qS4 =
+      7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+  auto R = [=](double z) {
+    double p, q;
+    p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
+    q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
+    return p / q;
+  };
+  double z, w, s, c, df;
+  uint64_t xx;
+  uint32_t hx, lx, ix;
+  memcpy(&xx, &x, sizeof(xx));
+  hx = xx >> 32;
+  ix = hx & 0x7fffffff;
+  /* |x| >= 1 or nan */
+  if (ix >= 0x3ff00000) {
+    lx = xx;
+    if (((ix - 0x3ff00000) | lx) == 0) {
+      /* acos(1)=0, acos(-1)=pi */
+      if (hx >> 31) return 2 * pio2_hi + 0x1p-120f;
+      return 0;
     }
+    return 0 / (x - x);
   }
+  /* |x| < 0.5 */
+  if (ix < 0x3fe00000) {
+    if (ix <= 0x3c600000) /* |x| < 2**-57 */
+      return pio2_hi + 0x1p-120f;
+    return pio2_hi - (x - (pio2_lo - x * R(x * x)));
+  }
+  /* x < -0.5 */
+  if (hx >> 31) {
+    z = (1.0 + x) * 0.5;
+    s = sqrt(z);
+    w = R(z) * s - pio2_lo;
+    return 2 * (pio2_hi - (s + w));
+  }
+  /* x > 0.5 */
+  z = (1.0 - x) * 0.5;
+  s = sqrt(z);
+  memcpy(&xx, &s, sizeof(xx));
+  xx &= 0xffffffff00000000;
+  memcpy(&df, &xx, sizeof(xx));
+  c = (z - df * df) / (s + df);
+  w = R(z) * s + c;
+  return 2 * (df + w);
 }
 
 struct Transform4x3 {
@@ -52,143 +127,12 @@ struct Transform4x3 {
   vec3 operator()(vec3 position) { return transform * vec4(position, 1.0); }
 };
 
-template <bool calculateTriNormal>
-struct AssignNormals {
-  VecView<vec3> faceNormal;
-  VecView<vec3> vertNormal;
-  VecView<const vec3> vertPos;
-  VecView<const Halfedge> halfedges;
-
-  void operator()(const int face) {
-    vec3& triNormal = faceNormal[face];
-
-    ivec3 triVerts;
-    for (int i : {0, 1, 2}) triVerts[i] = halfedges[3 * face + i].startVert;
-
-    vec3 edge[3];
-    for (int i : {0, 1, 2}) {
-      const int j = (i + 1) % 3;
-      edge[i] = la::normalize(vertPos[triVerts[j]] - vertPos[triVerts[i]]);
-    }
-
-    if (calculateTriNormal) {
-      triNormal = la::normalize(la::cross(edge[0], edge[1]));
-      if (std::isnan(triNormal.x)) triNormal = vec3(0, 0, 1);
-    }
-
-    // corner angles
-    vec3 phi;
-    double dot = -la::dot(edge[2], edge[0]);
-    phi[0] = dot >= 1 ? 0 : (dot <= -1 ? kPi : std::acos(dot));
-    dot = -la::dot(edge[0], edge[1]);
-    phi[1] = dot >= 1 ? 0 : (dot <= -1 ? kPi : std::acos(dot));
-    phi[2] = kPi - phi[0] - phi[1];
-
-    // assign weighted sum
-    for (int i : {0, 1, 2}) {
-      AtomicAddVec3(vertNormal[triVerts[i]], phi[i] * triNormal);
-    }
-  }
-};
-
 struct UpdateMeshID {
   const HashTableD<uint32_t> meshIDold2new;
 
   void operator()(TriRef& ref) { ref.meshID = meshIDold2new[ref.meshID]; }
 };
 
-struct CoplanarEdge {
-  VecView<std::pair<int, int>> face2face;
-  VecView<double> triArea;
-  VecView<const Halfedge> halfedge;
-  VecView<const vec3> vertPos;
-  VecView<const TriRef> triRef;
-  VecView<const ivec3> triProp;
-  const int numProp;
-  const double epsilon;
-  const double tolerance;
-
-  void operator()(const int edgeIdx) {
-    const Halfedge edge = halfedge[edgeIdx];
-    const Halfedge pair = halfedge[edge.pairedHalfedge];
-    const int edgeFace = edgeIdx / 3;
-    const int pairFace = edge.pairedHalfedge / 3;
-
-    if (triRef[edgeFace].meshID != triRef[pairFace].meshID) return;
-
-    const vec3 base = vertPos[edge.startVert];
-    const int baseNum = edgeIdx - 3 * edgeFace;
-    const int jointNum = edge.pairedHalfedge - 3 * pairFace;
-
-    if (numProp > 0) {
-      if (triProp[edgeFace][baseNum] != triProp[pairFace][Next3(jointNum)] ||
-          triProp[edgeFace][Next3(baseNum)] != triProp[pairFace][jointNum])
-        return;
-    }
-
-    if (!edge.IsForward()) return;
-
-    const int edgeNum = baseNum == 0 ? 2 : baseNum - 1;
-    const int pairNum = jointNum == 0 ? 2 : jointNum - 1;
-    const vec3 jointVec = vertPos[pair.startVert] - base;
-    const vec3 edgeVec =
-        vertPos[halfedge[3 * edgeFace + edgeNum].startVert] - base;
-    const vec3 pairVec =
-        vertPos[halfedge[3 * pairFace + pairNum].startVert] - base;
-
-    const double length = std::max(la::length(jointVec), la::length(edgeVec));
-    const double lengthPair =
-        std::max(la::length(jointVec), la::length(pairVec));
-    vec3 normal = la::cross(jointVec, edgeVec);
-    const double area = la::length(normal);
-    const double areaPair = la::length(la::cross(pairVec, jointVec));
-
-    // make sure we only write this once
-    if (edgeIdx % 3 == 0) triArea[edgeFace] = area;
-    // Don't link degenerate triangles
-    if (area < length * epsilon || areaPair < lengthPair * epsilon) return;
-
-    const double volume = std::abs(la::dot(normal, pairVec));
-    // Only operate on coplanar triangles
-    if (volume > std::max(area, areaPair) * tolerance) return;
-
-    face2face[edgeIdx] = std::make_pair(edgeFace, pairFace);
-  }
-};
-
-struct CheckCoplanarity {
-  VecView<int> comp2tri;
-  VecView<const Halfedge> halfedge;
-  VecView<const vec3> vertPos;
-  std::vector<int>* components;
-  const double tolerance;
-
-  void operator()(int tri) {
-    const int component = (*components)[tri];
-    const int referenceTri =
-        reinterpret_cast<std::atomic<int>*>(&comp2tri[component])
-            ->load(std::memory_order_relaxed);
-    if (referenceTri < 0 || referenceTri == tri) return;
-
-    const vec3 origin = vertPos[halfedge[3 * referenceTri].startVert];
-    const vec3 normal = la::normalize(
-        la::cross(vertPos[halfedge[3 * referenceTri + 1].startVert] - origin,
-                  vertPos[halfedge[3 * referenceTri + 2].startVert] - origin));
-
-    for (const int i : {0, 1, 2}) {
-      const vec3 vert = vertPos[halfedge[3 * tri + i].startVert];
-      // If any component vertex is not coplanar with the component's reference
-      // triangle, unmark the entire component so that none of its triangles are
-      // marked coplanar.
-      if (std::abs(la::dot(normal, vert - origin)) > tolerance) {
-        reinterpret_cast<std::atomic<int>*>(&comp2tri[component])
-            ->store(-1, std::memory_order_relaxed);
-        break;
-      }
-    }
-  }
-};
-
 int GetLabels(std::vector<int>& components,
               const Vec<std::pair<int, int>>& edges, int numNodes) {
   UnionFind<> uf(numNodes);
@@ -199,19 +143,6 @@ int GetLabels(std::vector<int>& components,
 
   return uf.connectedComponents(components);
 }
-
-void DedupePropVerts(manifold::Vec<ivec3>& triProp,
-                     const Vec<std::pair<int, int>>& vert2vert,
-                     size_t numPropVert) {
-  ZoneScoped;
-  std::vector<int> vertLabels;
-  const int numLabels = GetLabels(vertLabels, vert2vert, numPropVert);
-
-  std::vector<int> label2vert(numLabels);
-  for (size_t v = 0; v < numPropVert; ++v) label2vert[vertLabels[v]] = v;
-  for (auto& prop : triProp)
-    for (int i : {0, 1, 2}) prop[i] = label2vert[vertLabels[prop[i]]];
-}
 }  // namespace
 
 namespace manifold {
@@ -271,7 +202,7 @@ Manifold::Impl::Impl(Shape shape, const mat3x4 m) {
   CreateHalfedges(triVerts);
   Finish();
   InitializeOriginal();
-  CreateFaces();
+  MarkCoplanar();
 }
 
 void Manifold::Impl::RemoveUnreferencedVerts() {
@@ -297,124 +228,165 @@ void Manifold::Impl::InitializeOriginal(bool keepFaceID) {
   const int meshID = ReserveIDs(1);
   meshRelation_.originalID = meshID;
   auto& triRef = meshRelation_.triRef;
-  triRef.resize(NumTri());
+  triRef.resize_nofill(NumTri());
   for_each_n(autoPolicy(NumTri(), 1e5), countAt(0), NumTri(),
              [meshID, keepFaceID, &triRef](const int tri) {
-               triRef[tri] = {meshID, meshID, tri,
-                              keepFaceID ? triRef[tri].faceID : tri};
+               triRef[tri] = {meshID, meshID, -1,
+                              keepFaceID ? triRef[tri].coplanarID : tri};
              });
   meshRelation_.meshIDtransform.clear();
   meshRelation_.meshIDtransform[meshID] = {meshID};
 }
 
-void Manifold::Impl::CreateFaces() {
+void Manifold::Impl::MarkCoplanar() {
   ZoneScoped;
-  Vec<std::pair<int, int>> face2face(halfedge_.size(), {-1, -1});
-  Vec<std::pair<int, int>> vert2vert(halfedge_.size(), {-1, -1});
-  Vec<double> triArea(NumTri());
+  const int numTri = NumTri();
+  struct TriPriority {
+    double area2;
+    int tri;
+  };
+  Vec<TriPriority> triPriority(numTri);
+  for_each_n(autoPolicy(numTri), countAt(0), numTri,
+             [&triPriority, this](int tri) {
+               meshRelation_.triRef[tri].coplanarID = -1;
+               if (halfedge_[3 * tri].startVert < 0) {
+                 triPriority[tri] = {0, tri};
+                 return;
+               }
+               const vec3 v = vertPos_[halfedge_[3 * tri].startVert];
+               triPriority[tri] = {
+                   length2(cross(vertPos_[halfedge_[3 * tri].endVert] - v,
+                                 vertPos_[halfedge_[3 * tri + 1].endVert] - v)),
+                   tri};
+             });
 
-  const size_t numProp = NumProp();
-  if (numProp > 0) {
-    for_each_n(
-        autoPolicy(halfedge_.size(), 1e4), countAt(0), halfedge_.size(),
-        [&vert2vert, numProp, this](const int edgeIdx) {
-          const Halfedge edge = halfedge_[edgeIdx];
-          const Halfedge pair = halfedge_[edge.pairedHalfedge];
-          const int edgeFace = edgeIdx / 3;
-          const int pairFace = edge.pairedHalfedge / 3;
+  stable_sort(triPriority.begin(), triPriority.end(),
+              [](auto a, auto b) { return a.area2 > b.area2; });
 
-          if (meshRelation_.triRef[edgeFace].meshID !=
-              meshRelation_.triRef[pairFace].meshID)
-            return;
+  Vec<int> interiorHalfedges;
+  for (const auto tp : triPriority) {
+    if (meshRelation_.triRef[tp.tri].coplanarID >= 0) continue;
 
-          const int baseNum = edgeIdx - 3 * edgeFace;
-          const int jointNum = edge.pairedHalfedge - 3 * pairFace;
+    meshRelation_.triRef[tp.tri].coplanarID = tp.tri;
+    if (halfedge_[3 * tp.tri].startVert < 0) continue;
+    const vec3 base = vertPos_[halfedge_[3 * tp.tri].startVert];
+    const vec3 normal = faceNormal_[tp.tri];
+    interiorHalfedges.resize(3);
+    interiorHalfedges[0] = 3 * tp.tri;
+    interiorHalfedges[1] = 3 * tp.tri + 1;
+    interiorHalfedges[2] = 3 * tp.tri + 2;
+    while (!interiorHalfedges.empty()) {
+      const int h =
+          NextHalfedge(halfedge_[interiorHalfedges.back()].pairedHalfedge);
+      interiorHalfedges.pop_back();
+      if (meshRelation_.triRef[h / 3].coplanarID >= 0) continue;
 
-          const int prop0 = meshRelation_.triProperties[edgeFace][baseNum];
-          const int prop1 =
-              meshRelation_
-                  .triProperties[pairFace][jointNum == 2 ? 0 : jointNum + 1];
-          if (prop0 == prop1) return;
+      const vec3 v = vertPos_[halfedge_[h].endVert];
+      if (std::abs(dot(v - base, normal)) < tolerance_) {
+        meshRelation_.triRef[h / 3].coplanarID = tp.tri;
 
-          bool propEqual = true;
-          for (size_t p = 0; p < numProp; ++p) {
-            if (meshRelation_.properties[numProp * prop0 + p] !=
-                meshRelation_.properties[numProp * prop1 + p]) {
-              propEqual = false;
-              break;
-            }
-          }
-          if (propEqual) {
-            vert2vert[edgeIdx] = std::make_pair(prop0, prop1);
-          }
-        });
-    DedupePropVerts(meshRelation_.triProperties, vert2vert, NumPropVert());
-  }
-
-  for_each_n(autoPolicy(halfedge_.size(), 1e4), countAt(0), halfedge_.size(),
-             CoplanarEdge({face2face, triArea, halfedge_, vertPos_,
-                           meshRelation_.triRef, meshRelation_.triProperties,
-                           meshRelation_.numProp, epsilon_, tolerance_}));
-
-  std::vector<int> components;
-  const int numComponent = GetLabels(components, face2face, NumTri());
-
-  Vec<int> comp2tri(numComponent, -1);
-  for (size_t tri = 0; tri < NumTri(); ++tri) {
-    const int comp = components[tri];
-    const int current = comp2tri[comp];
-    if (current < 0 || triArea[tri] > triArea[current]) {
-      comp2tri[comp] = tri;
-      triArea[comp] = triArea[tri];
-    }
-  }
-
-  for_each_n(autoPolicy(halfedge_.size(), 1e4), countAt(0), NumTri(),
-             CheckCoplanarity(
-                 {comp2tri, halfedge_, vertPos_, &components, tolerance_}));
-
-  Vec<TriRef>& triRef = meshRelation_.triRef;
-  for (size_t tri = 0; tri < NumTri(); ++tri) {
-    const int referenceTri = comp2tri[components[tri]];
-    if (referenceTri >= 0) {
-      triRef[tri].faceID = referenceTri;
+        if (interiorHalfedges.empty() ||
+            h != halfedge_[interiorHalfedges.back()].pairedHalfedge) {
+          interiorHalfedges.push_back(h);
+        } else {
+          interiorHalfedges.pop_back();
+        }
+        const int hNext = NextHalfedge(h);
+        interiorHalfedges.push_back(hNext);
+      }
     }
   }
 }
 
 /**
- * Create the halfedge_ data structure from an input triVerts array like Mesh.
+ * Dereference duplicate property vertices if they are exactly floating-point
+ * equal. These unreferenced properties are then removed by CompactProps.
  */
-void Manifold::Impl::CreateHalfedges(const Vec<ivec3>& triVerts) {
+void Manifold::Impl::DedupePropVerts() {
   ZoneScoped;
-  const size_t numTri = triVerts.size();
+  const size_t numProp = NumProp();
+  if (numProp == 0) return;
+
+  Vec<std::pair<int, int>> vert2vert(halfedge_.size(), {-1, -1});
+  for_each_n(autoPolicy(halfedge_.size(), 1e4), countAt(0), halfedge_.size(),
+             [&vert2vert, numProp, this](const int edgeIdx) {
+               const Halfedge edge = halfedge_[edgeIdx];
+               const int edgeFace = edgeIdx / 3;
+               const int pairFace = edge.pairedHalfedge / 3;
+
+               if (meshRelation_.triRef[edgeFace].meshID !=
+                   meshRelation_.triRef[pairFace].meshID)
+                 return;
+
+               const int prop0 = halfedge_[edgeIdx].propVert;
+               const int prop1 =
+                   halfedge_[NextHalfedge(edge.pairedHalfedge)].propVert;
+               bool propEqual = true;
+               for (size_t p = 0; p < numProp; ++p) {
+                 if (properties_[numProp * prop0 + p] !=
+                     properties_[numProp * prop1 + p]) {
+                   propEqual = false;
+                   break;
+                 }
+               }
+               if (propEqual) {
+                 vert2vert[edgeIdx] = std::make_pair(prop0, prop1);
+               }
+             });
+
+  std::vector<int> vertLabels;
+  const size_t numPropVert = NumPropVert();
+  const int numLabels = GetLabels(vertLabels, vert2vert, numPropVert);
+
+  std::vector<int> label2vert(numLabels);
+  for (size_t v = 0; v < numPropVert; ++v) label2vert[vertLabels[v]] = v;
+  for (Halfedge& edge : halfedge_)
+    edge.propVert = label2vert[vertLabels[edge.propVert]];
+}
+
+constexpr int kRemovedHalfedge = -2;
+
+/**
+ * Create the halfedge_ data structure from a list of triangles. If the optional
+ * prop2vert array is missing, it's assumed these triangles are are pointing to
+ * both vert and propVert indices. If prop2vert is present, the triangles are
+ * assumed to be pointing to propVert indices only. The prop2vert array is used
+ * to map the propVert indices to vert indices.
+ */
+void Manifold::Impl::CreateHalfedges(const Vec<ivec3>& triProp,
+                                     const Vec<ivec3>& triVert) {
+  ZoneScoped;
+  const size_t numTri = triProp.size();
   const int numHalfedge = 3 * numTri;
   // drop the old value first to avoid copy
-  halfedge_.resize(0);
-  halfedge_.resize(numHalfedge);
+  halfedge_.clear(true);
+  halfedge_.resize_nofill(numHalfedge);
   Vec<uint64_t> edge(numHalfedge);
   Vec<int> ids(numHalfedge);
   auto policy = autoPolicy(numTri, 1e5);
   sequence(ids.begin(), ids.end());
   for_each_n(policy, countAt(0), numTri,
-             [this, &edge, &triVerts](const int tri) {
-               const ivec3& verts = triVerts[tri];
+             [this, &edge, &triProp, &triVert](const int tri) {
+               const ivec3& props = triProp[tri];
                for (const int i : {0, 1, 2}) {
                  const int j = (i + 1) % 3;
                  const int e = 3 * tri + i;
-                 halfedge_[e] = {verts[i], verts[j], -1};
+                 const int v0 = triVert.empty() ? props[i] : triVert[tri][i];
+                 const int v1 = triVert.empty() ? props[j] : triVert[tri][j];
+                 DEBUG_ASSERT(v0 != v1, logicErr, "topological degeneracy");
+                 halfedge_[e] = {v0, v1, -1, props[i]};
                  // Sort the forward halfedges in front of the backward ones
                  // by setting the highest-order bit.
-                 edge[e] = uint64_t(verts[i] < verts[j] ? 1 : 0) << 63 |
-                           ((uint64_t)std::min(verts[i], verts[j])) << 32 |
-                           std::max(verts[i], verts[j]);
+                 edge[e] = uint64_t(v0 < v1 ? 1 : 0) << 63 |
+                           ((uint64_t)std::min(v0, v1)) << 32 |
+                           std::max(v0, v1);
                }
              });
   // Stable sort is required here so that halfedges from the same face are
   // paired together (the triangles were created in face order). In some
   // degenerate situations the triangulator can add the same internal edge in
   // two different faces, causing this edge to not be 2-manifold. These are
-  // fixed by duplicating verts in SimplifyTopology.
+  // fixed by duplicating verts in CleanupTopology.
   stable_sort(ids.begin(), ids.end(), [&edge](const int& a, const int& b) {
     return edge[a] < edge[b];
   });
@@ -422,26 +394,62 @@ void Manifold::Impl::CreateHalfedges(const Vec<ivec3>& triVerts) {
   // Mark opposed triangles for removal - this may strand unreferenced verts
   // which are removed later by RemoveUnreferencedVerts() and Finish().
   const int numEdge = numHalfedge / 2;
-  for (int i = 0; i < numEdge; ++i) {
+
+  const auto body = [&](int i, int consecutiveStart, int segmentEnd) {
     const int pair0 = ids[i];
-    Halfedge h0 = halfedge_[pair0];
-    int k = i + numEdge;
+    Halfedge& h0 = halfedge_[pair0];
+    int k = consecutiveStart + numEdge;
     while (1) {
       const int pair1 = ids[k];
-      Halfedge h1 = halfedge_[pair1];
+      Halfedge& h1 = halfedge_[pair1];
       if (h0.startVert != h1.endVert || h0.endVert != h1.startVert) break;
       if (halfedge_[NextHalfedge(pair0)].endVert ==
           halfedge_[NextHalfedge(pair1)].endVert) {
-        h0 = {-1, -1, -1};
-        h1 = {-1, -1, -1};
+        h0.pairedHalfedge = h1.pairedHalfedge = kRemovedHalfedge;
         // Reorder so that remaining edges pair up
         if (k != i + numEdge) std::swap(ids[i + numEdge], ids[k]);
         break;
       }
       ++k;
-      if (k >= numHalfedge) break;
+      if (k >= segmentEnd + numEdge) break;
     }
+    if (i + 1 == segmentEnd) return consecutiveStart;
+    Halfedge& h1 = halfedge_[ids[i + 1]];
+    if (h0.startVert == h1.startVert && h0.endVert == h1.endVert)
+      return consecutiveStart;
+    return i + 1;
+  };
+
+#if MANIFOLD_PAR == 1
+  Vec<std::pair<int, int>> ranges;
+  const int increment = std::min(
+      std::max(numEdge / tbb::this_task_arena::max_concurrency() / 2, 1024),
+      numEdge);
+  const auto duplicated = [&](int a, int b) {
+    const Halfedge& h0 = halfedge_[ids[a]];
+    const Halfedge& h1 = halfedge_[ids[b]];
+    return h0.startVert == h1.startVert && h0.endVert == h1.endVert;
+  };
+  int end = 0;
+  while (end < numEdge) {
+    const int start = end;
+    end = std::min(end + increment, numEdge);
+    // make sure duplicated halfedges are in the same partition
+    while (end < numEdge && duplicated(end - 1, end)) end++;
+    ranges.push_back(std::make_pair(start, end));
   }
+  for_each(ExecutionPolicy::Par, ranges.begin(), ranges.end(),
+           [&](const std::pair<int, int>& range) {
+             const auto [start, end] = range;
+             int consecutiveStart = start;
+             for (int i = start; i < end; ++i)
+               consecutiveStart = body(i, consecutiveStart, end);
+           });
+#else
+  int consecutiveStart = 0;
+  for (int i = 0; i < numEdge; ++i)
+    consecutiveStart = body(i, consecutiveStart, numEdge);
+#endif
 
   // Once sorted, the first half of the range is the forward halfedges, which
   // correspond to their backward pair at the same offset in the second half
@@ -449,9 +457,11 @@ void Manifold::Impl::CreateHalfedges(const Vec<ivec3>& triVerts) {
   for_each_n(policy, countAt(0), numEdge, [this, &ids, numEdge](int i) {
     const int pair0 = ids[i];
     const int pair1 = ids[i + numEdge];
-    if (halfedge_[pair0].startVert >= 0) {
+    if (halfedge_[pair0].pairedHalfedge != kRemovedHalfedge) {
       halfedge_[pair0].pairedHalfedge = pair1;
       halfedge_[pair1].pairedHalfedge = pair0;
+    } else {
+      halfedge_[pair0] = halfedge_[pair1] = {-1, -1, -1};
     }
   });
 }
@@ -468,13 +478,13 @@ void Manifold::Impl::Update() {
   collider_.UpdateBoxes(faceBox);
 }
 
-void Manifold::Impl::MarkFailure(Error status) {
+void Manifold::Impl::MakeEmpty(Error status) {
   bBox_ = Box();
-  vertPos_.resize(0);
-  halfedge_.resize(0);
-  vertNormal_.resize(0);
-  faceNormal_.resize(0);
-  halfedgeTangent_.resize(0);
+  vertPos_.clear();
+  halfedge_.clear();
+  vertNormal_.clear();
+  faceNormal_.clear();
+  halfedgeTangent_.clear();
   meshRelation_ = MeshRelationD();
   status_ = status;
 }
@@ -489,15 +499,14 @@ void Manifold::Impl::WarpBatch(std::function<void(VecView<vec3>)> warpFunc) {
   warpFunc(vertPos_.view());
   CalculateBBox();
   if (!IsFinite()) {
-    MarkFailure(Error::NonFiniteVertex);
+    MakeEmpty(Error::NonFiniteVertex);
     return;
   }
   Update();
-  faceNormal_.resize(0);  // force recalculation of triNormal
-  CalculateNormals();
+  faceNormal_.clear();  // force recalculation of triNormal
   SetEpsilon();
   Finish();
-  CreateFaces();
+  MarkCoplanar();
   meshRelation_.originalID = -1;
 }
 
@@ -511,13 +520,15 @@ Manifold::Impl Manifold::Impl::Transform(const mat3x4& transform_) const {
     return result;
   }
   if (!all(la::isfinite(transform_))) {
-    result.MarkFailure(Error::NonFiniteVertex);
+    result.MakeEmpty(Error::NonFiniteVertex);
     return result;
   }
   result.collider_ = collider_;
   result.meshRelation_ = meshRelation_;
   result.epsilon_ = epsilon_;
   result.tolerance_ = tolerance_;
+  result.numProp_ = numProp_;
+  result.properties_ = properties_;
   result.bBox_ = bBox_;
   result.halfedge_ = halfedge_;
   result.halfedgeTangent_.resize(halfedgeTangent_.size());
@@ -592,23 +603,73 @@ void Manifold::Impl::SetEpsilon(double minEpsilon, bool useSingle) {
 void Manifold::Impl::CalculateNormals() {
   ZoneScoped;
   vertNormal_.resize(NumVert());
-  auto policy = autoPolicy(NumTri(), 1e4);
-  fill(vertNormal_.begin(), vertNormal_.end(), vec3(0.0));
-  bool calculateTriNormal = false;
+  auto policy = autoPolicy(NumTri());
+
+  std::vector<std::atomic<int>> vertHalfedgeMap(NumVert());
+  for_each_n(policy, countAt(0), NumVert(), [&](const size_t vert) {
+    vertHalfedgeMap[vert] = std::numeric_limits<int>::max();
+  });
+
+  auto atomicMin = [&vertHalfedgeMap](int value, int vert) {
+    if (vert < 0) return;
+    int old = std::numeric_limits<int>::max();
+    while (!vertHalfedgeMap[vert].compare_exchange_strong(old, value))
+      if (old < value) break;
+  };
   if (faceNormal_.size() != NumTri()) {
     faceNormal_.resize(NumTri());
-    calculateTriNormal = true;
+    for_each_n(policy, countAt(0), NumTri(), [&](const int face) {
+      vec3& triNormal = faceNormal_[face];
+      if (halfedge_[3 * face].startVert < 0) {
+        triNormal = vec3(0, 0, 1);
+        return;
+      }
+
+      ivec3 triVerts;
+      for (int i : {0, 1, 2}) {
+        int v = halfedge_[3 * face + i].startVert;
+        triVerts[i] = v;
+        atomicMin(3 * face + i, v);
+      }
+
+      vec3 edge[3];
+      for (int i : {0, 1, 2}) {
+        const int j = (i + 1) % 3;
+        edge[i] = la::normalize(vertPos_[triVerts[j]] - vertPos_[triVerts[i]]);
+      }
+      triNormal = la::normalize(la::cross(edge[0], edge[1]));
+      if (std::isnan(triNormal.x)) triNormal = vec3(0, 0, 1);
+    });
+  } else {
+    for_each_n(policy, countAt(0), halfedge_.size(),
+               [&](const int i) { atomicMin(i, halfedge_[i].startVert); });
   }
-  if (calculateTriNormal)
-    for_each_n(
-        policy, countAt(0), NumTri(),
-        AssignNormals<true>({faceNormal_, vertNormal_, vertPos_, halfedge_}));
-  else
-    for_each_n(
-        policy, countAt(0), NumTri(),
-        AssignNormals<false>({faceNormal_, vertNormal_, vertPos_, halfedge_}));
-  for_each(policy, vertNormal_.begin(), vertNormal_.end(),
-           [](vec3& v) { v = SafeNormalize(v); });
+
+  for_each_n(policy, countAt(0), NumVert(), [&](const size_t vert) {
+    int firstEdge = vertHalfedgeMap[vert].load();
+    // not referenced
+    if (firstEdge == std::numeric_limits<int>::max()) {
+      vertNormal_[vert] = vec3(0.0);
+      return;
+    }
+    vec3 normal = vec3(0.0);
+    ForVert(firstEdge, [&](int edge) {
+      ivec3 triVerts = {halfedge_[edge].startVert, halfedge_[edge].endVert,
+                        halfedge_[NextHalfedge(edge)].endVert};
+      vec3 currEdge =
+          la::normalize(vertPos_[triVerts[1]] - vertPos_[triVerts[0]]);
+      vec3 prevEdge =
+          la::normalize(vertPos_[triVerts[0]] - vertPos_[triVerts[2]]);
+
+      // if it is not finite, this means that the triangle is degenerate, and we
+      // should just exclude it from the normal calculation...
+      if (!la::isfinite(currEdge[0]) || !la::isfinite(prevEdge[0])) return;
+      double dot = -la::dot(prevEdge, currEdge);
+      double phi = dot >= 1 ? 0 : (dot <= -1 ? kPi : sun_acos(dot));
+      normal += phi * faceNormal_[edge / 3];
+    });
+    vertNormal_[vert] = SafeNormalize(normal);
+  });
 }
 
 /**
@@ -632,55 +693,13 @@ void Manifold::Impl::IncrementMeshIDs() {
              UpdateMeshID({meshIDold2new.D()}));
 }
 
-/**
- * Returns a sparse array of the bounding box overlaps between the edges of
- * the input manifold, Q and the faces of this manifold. Returned indices only
- * point to forward halfedges.
- */
-SparseIndices Manifold::Impl::EdgeCollisions(const Impl& Q,
-                                             bool inverted) const {
-  ZoneScoped;
-  Vec<TmpEdge> edges = CreateTmpEdges(Q.halfedge_);
-  const size_t numEdge = edges.size();
-  Vec<Box> QedgeBB(numEdge);
-  const auto& vertPos = Q.vertPos_;
-  auto policy = autoPolicy(numEdge, 1e5);
-  for_each_n(
-      policy, countAt(0), numEdge, [&QedgeBB, &edges, &vertPos](const int e) {
-        QedgeBB[e] = Box(vertPos[edges[e].first], vertPos[edges[e].second]);
-      });
-
-  SparseIndices q1p2(0);
-  if (inverted)
-    q1p2 = collider_.Collisions<false, true>(QedgeBB.cview());
-  else
-    q1p2 = collider_.Collisions<false, false>(QedgeBB.cview());
-
-  if (inverted)
-    for_each(policy, countAt(0_uz), countAt(q1p2.size()),
-             ReindexEdge<true>({edges, q1p2}));
-  else
-    for_each(policy, countAt(0_uz), countAt(q1p2.size()),
-             ReindexEdge<false>({edges, q1p2}));
-  return q1p2;
-}
-
-/**
- * Returns a sparse array of the input vertices that project inside the XY
- * bounding boxes of the faces of this manifold.
- */
-SparseIndices Manifold::Impl::VertexCollisionsZ(VecView<const vec3> vertsIn,
-                                                bool inverted) const {
-  ZoneScoped;
-  if (inverted)
-    return collider_.Collisions<false, true>(vertsIn);
-  else
-    return collider_.Collisions<false, false>(vertsIn);
-}
-
 #ifdef MANIFOLD_DEBUG
+/**
+ * Debugging output using high precision OBJ files with specialized comments
+ */
 std::ostream& operator<<(std::ostream& stream, const Manifold::Impl& impl) {
-  stream << std::setprecision(17);  // for double precision
+  stream << std::setprecision(19);  // for double precision
+  stream << std::fixed;             // for uniformity in output numbers
   stream << "# ======= begin mesh ======" << std::endl;
   stream << "# tolerance = " << impl.tolerance_ << std::endl;
   stream << "# epsilon = " << impl.epsilon_ << std::endl;
@@ -699,13 +718,19 @@ std::ostream& operator<<(std::ostream& stream, const Manifold::Impl& impl) {
   stream << "# ======== end mesh =======" << std::endl;
   return stream;
 }
-#endif
 
-#ifdef MANIFOLD_EXPORT
-Manifold Manifold::ImportMeshGL64(std::istream& stream) {
+/**
+ * Import a mesh from a Wavefront OBJ file that was exported with Write.  This
+ * function is the counterpart to Write and should be used with it.  This
+ * function is not guaranteed to be able to import OBJ files not written by the
+ * Write function.
+ */
+Manifold Manifold::ReadOBJ(std::istream& stream) {
+  if (!stream.good()) return Invalid();
+
   MeshGL64 mesh;
   std::optional<double> epsilon;
-  stream.precision(17);
+  stream >> std::setprecision(19);
   while (true) {
     char c = stream.get();
     if (stream.eof()) break;
@@ -718,7 +743,7 @@ Manifold Manifold::ImportMeshGL64(std::istream& stream) {
           stream.get(tmp.data(), SIZE, '\n');
           if (strncmp(tmp.data(), "tolerance", SIZE) == 0) {
             // skip 3 letters
-            for (int i : {0, 1, 2}) stream.get();
+            for (int _ : {0, 1, 2}) stream.get();
             stream >> mesh.tolerance;
           } else if (strncmp(tmp.data(), "epsilon =", SIZE) == 0) {
             double tmp;
@@ -727,7 +752,7 @@ Manifold Manifold::ImportMeshGL64(std::istream& stream) {
           } else {
             // add it back because it is not what we want
             int end = 0;
-            while (tmp[end] != 0 && end < SIZE) end++;
+            while (end < SIZE && tmp[end] != 0) end++;
             while (--end > -1) stream.putback(tmp[end]);
           }
           c = stream.get();
@@ -739,29 +764,42 @@ Manifold Manifold::ImportMeshGL64(std::istream& stream) {
         break;
       }
       case 'v':
-        for (int i : {0, 1, 2}) {
+        for (int _ : {0, 1, 2}) {
           double x;
           stream >> x;
           mesh.vertProperties.push_back(x);
         }
         break;
       case 'f':
-        for (int i : {0, 1, 2}) {
+        for (int _ : {0, 1, 2}) {
           uint64_t x;
           stream >> x;
           mesh.triVerts.push_back(x - 1);
         }
         break;
+      case '\r':
       case '\n':
         break;
       default:
-        DEBUG_ASSERT(false, userErr, "unexpected character in MeshGL64 import");
+        DEBUG_ASSERT(false, userErr, "unexpected character in Manifold import");
     }
   }
   auto m = std::make_shared<Manifold::Impl>(mesh);
   if (epsilon) m->SetEpsilon(*epsilon);
   return Manifold(m);
 }
+
+/**
+ * Export the mesh to a Wavefront OBJ file in a way that preserves the full
+ * 64-bit precision of the vertex positions, as well as storing metadata such as
+ * the tolerance and epsilon. Useful for debugging and testing.  Files written
+ * by WriteOBJ should be read back in with ReadOBJ.
+ */
+bool Manifold::WriteOBJ(std::ostream& stream) const {
+  if (!stream.good()) return false;
+  stream << *this->GetCsgLeafNode().GetImpl();
+  return true;
+}
 #endif
 
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/impl.h b/thirdparty/manifold/src/impl.h
index d37a9a7d27..7af45bb257 100644
--- a/thirdparty/manifold/src/impl.h
+++ b/thirdparty/manifold/src/impl.h
@@ -15,12 +15,11 @@
 #pragma once
 #include <map>
 
-#include "./collider.h"
-#include "./shared.h"
-#include "./sparse.h"
-#include "./vec.h"
+#include "collider.h"
+#include "manifold/common.h"
 #include "manifold/manifold.h"
-#include "manifold/polygon.h"
+#include "shared.h"
+#include "vec.h"
 
 namespace manifold {
 
@@ -34,11 +33,8 @@ struct Manifold::Impl {
   struct MeshRelationD {
     /// The originalID of this Manifold if it is an original; -1 otherwise.
     int originalID = -1;
-    int numProp = 0;
-    Vec<double> properties;
     std::map<int, Relation> meshIDtransform;
     Vec<TriRef> triRef;
-    Vec<ivec3> triProperties;
   };
   struct BaryIndices {
     int tri, start4, end4;
@@ -47,9 +43,13 @@ struct Manifold::Impl {
   Box bBox_;
   double epsilon_ = -1;
   double tolerance_ = -1;
+  int numProp_ = 0;
   Error status_ = Error::NoError;
   Vec<vec3> vertPos_;
   Vec<Halfedge> halfedge_;
+  Vec<double> properties_;
+  // Note that vertNormal_ is not precise due to the use of an approximated acos
+  // function
   Vec<vec3> vertNormal_;
   Vec<vec3> faceNormal_;
   Vec<vec4> halfedgeTangent_;
@@ -69,153 +69,185 @@ struct Manifold::Impl {
     const uint32_t numTri = meshGL.NumTri();
 
     if (meshGL.numProp < 3) {
-      MarkFailure(Error::MissingPositionProperties);
+      MakeEmpty(Error::MissingPositionProperties);
       return;
     }
 
     if (meshGL.mergeFromVert.size() != meshGL.mergeToVert.size()) {
-      MarkFailure(Error::MergeVectorsDifferentLengths);
+      MakeEmpty(Error::MergeVectorsDifferentLengths);
       return;
     }
 
     if (!meshGL.runTransform.empty() &&
         12 * meshGL.runOriginalID.size() != meshGL.runTransform.size()) {
-      MarkFailure(Error::TransformWrongLength);
+      MakeEmpty(Error::TransformWrongLength);
       return;
     }
 
     if (!meshGL.runOriginalID.empty() && !meshGL.runIndex.empty() &&
         meshGL.runOriginalID.size() + 1 != meshGL.runIndex.size() &&
         meshGL.runOriginalID.size() != meshGL.runIndex.size()) {
-      MarkFailure(Error::RunIndexWrongLength);
+      MakeEmpty(Error::RunIndexWrongLength);
       return;
     }
 
     if (!meshGL.faceID.empty() && meshGL.faceID.size() != meshGL.NumTri()) {
-      MarkFailure(Error::FaceIDWrongLength);
+      MakeEmpty(Error::FaceIDWrongLength);
       return;
     }
 
-    std::vector<int> prop2vert(numVert);
-    std::iota(prop2vert.begin(), prop2vert.end(), 0);
-    for (size_t i = 0; i < meshGL.mergeFromVert.size(); ++i) {
-      const uint32_t from = meshGL.mergeFromVert[i];
-      const uint32_t to = meshGL.mergeToVert[i];
-      if (from >= numVert || to >= numVert) {
-        MarkFailure(Error::MergeIndexOutOfBounds);
-        return;
+    if (!manifold::all_of(meshGL.vertProperties.begin(),
+                          meshGL.vertProperties.end(),
+                          [](Precision x) { return std::isfinite(x); })) {
+      MakeEmpty(Error::NonFiniteVertex);
+      return;
+    }
+
+    if (!manifold::all_of(meshGL.runTransform.begin(),
+                          meshGL.runTransform.end(),
+                          [](Precision x) { return std::isfinite(x); })) {
+      MakeEmpty(Error::InvalidConstruction);
+      return;
+    }
+
+    if (!manifold::all_of(meshGL.halfedgeTangent.begin(),
+                          meshGL.halfedgeTangent.end(),
+                          [](Precision x) { return std::isfinite(x); })) {
+      MakeEmpty(Error::InvalidConstruction);
+      return;
+    }
+
+    std::vector<int> prop2vert;
+    if (!meshGL.mergeFromVert.empty()) {
+      prop2vert.resize(numVert);
+      std::iota(prop2vert.begin(), prop2vert.end(), 0);
+      for (size_t i = 0; i < meshGL.mergeFromVert.size(); ++i) {
+        const uint32_t from = meshGL.mergeFromVert[i];
+        const uint32_t to = meshGL.mergeToVert[i];
+        if (from >= numVert || to >= numVert) {
+          MakeEmpty(Error::MergeIndexOutOfBounds);
+          return;
+        }
+        prop2vert[from] = to;
       }
-      prop2vert[from] = to;
     }
 
     const auto numProp = meshGL.numProp - 3;
-    meshRelation_.numProp = numProp;
-    meshRelation_.properties.resize(meshGL.NumVert() * numProp);
+    numProp_ = numProp;
+    properties_.resize_nofill(meshGL.NumVert() * numProp);
     tolerance_ = meshGL.tolerance;
     // This will have unreferenced duplicate positions that will be removed by
     // Impl::RemoveUnreferencedVerts().
-    vertPos_.resize(meshGL.NumVert());
+    vertPos_.resize_nofill(meshGL.NumVert());
 
     for (size_t i = 0; i < meshGL.NumVert(); ++i) {
       for (const int j : {0, 1, 2})
         vertPos_[i][j] = meshGL.vertProperties[meshGL.numProp * i + j];
       for (size_t j = 0; j < numProp; ++j)
-        meshRelation_.properties[i * numProp + j] =
+        properties_[i * numProp + j] =
             meshGL.vertProperties[meshGL.numProp * i + 3 + j];
     }
 
-    halfedgeTangent_.resize(meshGL.halfedgeTangent.size() / 4);
+    halfedgeTangent_.resize_nofill(meshGL.halfedgeTangent.size() / 4);
     for (size_t i = 0; i < halfedgeTangent_.size(); ++i) {
       for (const int j : {0, 1, 2, 3})
         halfedgeTangent_[i][j] = meshGL.halfedgeTangent[4 * i + j];
     }
 
     Vec<TriRef> triRef;
-    if (!meshGL.runOriginalID.empty()) {
-      auto runIndex = meshGL.runIndex;
-      const auto runEnd = meshGL.triVerts.size();
-      if (runIndex.empty()) {
-        runIndex = {0, static_cast<I>(runEnd)};
-      } else if (runIndex.size() == meshGL.runOriginalID.size()) {
-        runIndex.push_back(runEnd);
-      }
-      triRef.resize(meshGL.NumTri());
-      const auto startID = Impl::ReserveIDs(meshGL.runOriginalID.size());
-      for (size_t i = 0; i < meshGL.runOriginalID.size(); ++i) {
-        const int meshID = startID + i;
-        const int originalID = meshGL.runOriginalID[i];
-        for (size_t tri = runIndex[i] / 3; tri < runIndex[i + 1] / 3; ++tri) {
-          TriRef& ref = triRef[tri];
-          ref.meshID = meshID;
-          ref.originalID = originalID;
-          ref.tri = meshGL.faceID.empty() ? tri : meshGL.faceID[tri];
-          ref.faceID = tri;
-        }
+    triRef.resize_nofill(meshGL.NumTri());
 
-        if (meshGL.runTransform.empty()) {
-          meshRelation_.meshIDtransform[meshID] = {originalID};
-        } else {
-          const Precision* m = meshGL.runTransform.data() + 12 * i;
-          meshRelation_.meshIDtransform[meshID] = {originalID,
-                                                   {{m[0], m[1], m[2]},
-                                                    {m[3], m[4], m[5]},
-                                                    {m[6], m[7], m[8]},
-                                                    {m[9], m[10], m[11]}}};
-        }
+    auto runIndex = meshGL.runIndex;
+    const auto runEnd = meshGL.triVerts.size();
+    if (runIndex.empty()) {
+      runIndex = {0, static_cast<I>(runEnd)};
+    } else if (runIndex.size() == meshGL.runOriginalID.size()) {
+      runIndex.push_back(runEnd);
+    } else if (runIndex.size() == 1) {
+      runIndex.push_back(runEnd);
+    }
+
+    const auto startID = Impl::ReserveIDs(meshGL.runOriginalID.size());
+    auto runOriginalID = meshGL.runOriginalID;
+    if (runOriginalID.empty()) {
+      runOriginalID.push_back(startID);
+    }
+    for (size_t i = 0; i < runOriginalID.size(); ++i) {
+      const int meshID = startID + i;
+      const int originalID = runOriginalID[i];
+      for (size_t tri = runIndex[i] / 3; tri < runIndex[i + 1] / 3; ++tri) {
+        TriRef& ref = triRef[tri];
+        ref.meshID = meshID;
+        ref.originalID = originalID;
+        ref.faceID = meshGL.faceID.empty() ? -1 : meshGL.faceID[tri];
+        ref.coplanarID = tri;
+      }
+
+      if (meshGL.runTransform.empty()) {
+        meshRelation_.meshIDtransform[meshID] = {originalID};
+      } else {
+        const Precision* m = meshGL.runTransform.data() + 12 * i;
+        meshRelation_.meshIDtransform[meshID] = {originalID,
+                                                 {{m[0], m[1], m[2]},
+                                                  {m[3], m[4], m[5]},
+                                                  {m[6], m[7], m[8]},
+                                                  {m[9], m[10], m[11]}}};
       }
     }
 
-    Vec<ivec3> triVerts;
-    triVerts.reserve(numTri);
+    Vec<ivec3> triProp;
+    triProp.reserve(numTri);
+    Vec<ivec3> triVert;
+    const bool needsPropMap = numProp > 0 && !prop2vert.empty();
+    if (needsPropMap) triVert.reserve(numTri);
+    if (triRef.size() > 0) meshRelation_.triRef.reserve(numTri);
     for (size_t i = 0; i < numTri; ++i) {
-      ivec3 tri;
+      ivec3 triP, triV;
       for (const size_t j : {0, 1, 2}) {
         uint32_t vert = (uint32_t)meshGL.triVerts[3 * i + j];
         if (vert >= numVert) {
-          MarkFailure(Error::VertexOutOfBounds);
+          MakeEmpty(Error::VertexOutOfBounds);
           return;
         }
-        tri[j] = prop2vert[vert];
+        triP[j] = vert;
+        triV[j] = prop2vert.empty() ? vert : prop2vert[vert];
       }
-      if (tri[0] != tri[1] && tri[1] != tri[2] && tri[2] != tri[0]) {
-        triVerts.push_back(tri);
+      if (triV[0] != triV[1] && triV[1] != triV[2] && triV[2] != triV[0]) {
+        if (needsPropMap) {
+          triProp.push_back(triP);
+          triVert.push_back(triV);
+        } else {
+          triProp.push_back(triV);
+        }
         if (triRef.size() > 0) {
           meshRelation_.triRef.push_back(triRef[i]);
         }
-        if (numProp > 0) {
-          meshRelation_.triProperties.push_back(
-              ivec3(static_cast<uint32_t>(meshGL.triVerts[3 * i]),
-                    static_cast<uint32_t>(meshGL.triVerts[3 * i + 1]),
-                    static_cast<uint32_t>(meshGL.triVerts[3 * i + 2])));
-        }
       }
     }
 
-    CreateHalfedges(triVerts);
+    CreateHalfedges(triProp, triVert);
     if (!IsManifold()) {
-      MarkFailure(Error::NotManifold);
+      MakeEmpty(Error::NotManifold);
       return;
     }
 
     CalculateBBox();
     SetEpsilon(-1, std::is_same<Precision, float>::value);
 
-    SplitPinchedVerts();
-
+    // we need to split pinched verts before calculating vertex normals, because
+    // the algorithm doesn't work with pinched verts
+    CleanupTopology();
     CalculateNormals();
 
-    if (meshGL.runOriginalID.empty()) {
-      InitializeOriginal();
-    }
+    DedupePropVerts();
+    MarkCoplanar();
 
-    CreateFaces();
-
-    SimplifyTopology();
+    RemoveDegenerates();
     RemoveUnreferencedVerts();
     Finish();
 
     if (!IsFinite()) {
-      MarkFailure(Error::NonFiniteVertex);
+      MakeEmpty(Error::NonFiniteVertex);
       return;
     }
 
@@ -224,7 +256,8 @@ struct Manifold::Impl {
     meshRelation_.originalID = -1;
   }
 
-  inline void ForVert(int halfedge, std::function<void(int halfedge)> func) {
+  template <typename F>
+  inline void ForVert(int halfedge, F func) {
     int current = halfedge;
     do {
       current = NextHalfedge(halfedge_[current].pairedHalfedge);
@@ -247,30 +280,28 @@ struct Manifold::Impl {
     } while (current != halfedge);
   }
 
-  void CreateFaces();
+  void MarkCoplanar();
+  void DedupePropVerts();
   void RemoveUnreferencedVerts();
   void InitializeOriginal(bool keepFaceID = false);
-  void CreateHalfedges(const Vec<ivec3>& triVerts);
+  void CreateHalfedges(const Vec<ivec3>& triProp,
+                       const Vec<ivec3>& triVert = {});
   void CalculateNormals();
   void IncrementMeshIDs();
 
   void Update();
-  void MarkFailure(Error status);
+  void MakeEmpty(Error status);
   void Warp(std::function<void(vec3&)> warpFunc);
   void WarpBatch(std::function<void(VecView<vec3>)> warpFunc);
   Impl Transform(const mat3x4& transform) const;
-  SparseIndices EdgeCollisions(const Impl& B, bool inverted = false) const;
-  SparseIndices VertexCollisionsZ(VecView<const vec3> vertsIn,
-                                  bool inverted = false) const;
 
   bool IsEmpty() const { return NumTri() == 0; }
   size_t NumVert() const { return vertPos_.size(); }
   size_t NumEdge() const { return halfedge_.size() / 2; }
   size_t NumTri() const { return halfedge_.size() / 3; }
-  size_t NumProp() const { return meshRelation_.numProp; }
+  size_t NumProp() const { return numProp_; }
   size_t NumPropVert() const {
-    return NumProp() == 0 ? NumVert()
-                          : meshRelation_.properties.size() / NumProp();
+    return NumProp() == 0 ? NumVert() : properties_.size() / NumProp();
   }
 
   // properties.cpp
@@ -299,18 +330,20 @@ struct Manifold::Impl {
   void GatherFaces(const Impl& old, const Vec<int>& faceNew2Old);
 
   // face_op.cpp
-  void Face2Tri(const Vec<int>& faceEdge, const Vec<TriRef>& halfedgeRef);
-  PolygonsIdx Face2Polygons(VecView<Halfedge>::IterC start,
-                            VecView<Halfedge>::IterC end,
-                            mat2x3 projection) const;
+  void Face2Tri(const Vec<int>& faceEdge, const Vec<TriRef>& halfedgeRef,
+                bool allowConvex = false);
   Polygons Slice(double height) const;
   Polygons Project() const;
 
   // edge_op.cpp
   void CleanupTopology();
-  void SimplifyTopology();
+  void SimplifyTopology(int firstNewVert = 0);
+  void RemoveDegenerates(int firstNewVert = 0);
+  void CollapseShortEdges(int firstNewVert = 0);
+  void CollapseColinearEdges(int firstNewVert = 0);
+  void SwapDegenerates(int firstNewVert = 0);
   void DedupeEdge(int edge);
-  void CollapseEdge(int edge, std::vector<int>& edges);
+  bool CollapseEdge(int edge, std::vector<int>& edges);
   void RecursiveEdgeSwap(int edge, int& tag, std::vector<int>& visited,
                          std::vector<int>& edgeSwapStack,
                          std::vector<int>& edges);
@@ -320,6 +353,7 @@ struct Manifold::Impl {
   void FormLoop(int current, int end);
   void CollapseTri(const ivec3& triEdge);
   void SplitPinchedVerts();
+  void DedupeEdges();
 
   // subdivision.cpp
   int GetNeighbor(int tri) const;
@@ -353,8 +387,6 @@ struct Manifold::Impl {
   void Hull(VecView<vec3> vertPos);
 };
 
-#ifdef MANIFOLD_DEBUG
 extern std::mutex dump_lock;
 std::ostream& operator<<(std::ostream& stream, const Manifold::Impl& impl);
-#endif
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/iters.h b/thirdparty/manifold/src/iters.h
index 8b5110ae14..65a1000ffc 100644
--- a/thirdparty/manifold/src/iters.h
+++ b/thirdparty/manifold/src/iters.h
@@ -14,6 +14,7 @@
 #pragma once
 
 #include <iterator>
+#include <optional>
 #include <type_traits>
 
 namespace manifold {
@@ -22,7 +23,7 @@ template <typename F, typename Iter>
 struct TransformIterator {
  private:
   Iter iter;
-  F f;
+  std::optional<F> f;
 
  public:
   using pointer = void;
@@ -36,16 +37,28 @@ struct TransformIterator {
 
   constexpr TransformIterator(Iter iter, F f) : iter(iter), f(f) {}
 
+  TransformIterator(const TransformIterator& other)
+      : iter(other.iter), f(other.f) {}
+
+  TransformIterator(TransformIterator&& other) : iter(other.iter), f(other.f) {}
+
   TransformIterator& operator=(const TransformIterator& other) {
     if (this == &other) return *this;
-    // don't copy function, should be the same
     iter = other.iter;
+    f.emplace(*other.f);
     return *this;
   }
 
-  constexpr reference operator*() const { return f(*iter); }
+  TransformIterator& operator=(TransformIterator&& other) {
+    if (this == &other) return *this;
+    iter = other.iter;
+    f.emplace(*other.f);
+    return *this;
+  }
 
-  constexpr reference operator[](size_t i) const { return f(iter[i]); }
+  constexpr reference operator*() const { return (*f)(*iter); }
+
+  constexpr reference operator[](size_t i) const { return (*f)(iter[i]); }
 
   // prefix increment
   TransformIterator& operator++() {
@@ -74,7 +87,7 @@ struct TransformIterator {
   }
 
   constexpr TransformIterator operator+(size_t n) const {
-    return TransformIterator(iter + n, f);
+    return TransformIterator(iter + n, *f);
   }
 
   TransformIterator& operator+=(size_t n) {
@@ -83,7 +96,7 @@ struct TransformIterator {
   }
 
   constexpr TransformIterator operator-(size_t n) const {
-    return TransformIterator(iter - n, f);
+    return TransformIterator(iter - n, *f);
   }
 
   TransformIterator& operator-=(size_t n) {
@@ -108,7 +121,7 @@ struct TransformIterator {
   }
 
   constexpr operator TransformIterator<F, const Iter>() const {
-    return TransformIterator(f, iter);
+    return TransformIterator(*f, iter);
   }
 };
 
diff --git a/thirdparty/manifold/src/manifold.cpp b/thirdparty/manifold/src/manifold.cpp
index a36dd460b9..627ef5ea38 100644
--- a/thirdparty/manifold/src/manifold.cpp
+++ b/thirdparty/manifold/src/manifold.cpp
@@ -16,36 +16,17 @@
 #include <map>
 #include <numeric>
 
-#include "./boolean3.h"
-#include "./csg_tree.h"
-#include "./impl.h"
-#include "./parallel.h"
+#include "boolean3.h"
+#include "csg_tree.h"
+#include "impl.h"
+#include "parallel.h"
+#include "shared.h"
 
 namespace {
 using namespace manifold;
 
 ExecutionParams manifoldParams;
 
-struct UpdateProperties {
-  double* properties;
-  const int numProp;
-  const double* oldProperties;
-  const int numOldProp;
-  const vec3* vertPos;
-  const ivec3* triProperties;
-  const Halfedge* halfedges;
-  std::function<void(double*, vec3, const double*)> propFunc;
-
-  void operator()(int tri) {
-    for (int i : {0, 1, 2}) {
-      const int vert = halfedges[3 * tri + i].startVert;
-      const int propVert = triProperties[tri][i];
-      propFunc(properties + numProp * propVert, vertPos[vert],
-               oldProperties + numOldProp * propVert);
-    }
-  }
-};
-
 Manifold Halfspace(Box bBox, vec3 normal, double originOffset) {
   normal = la::normalize(normal);
   Manifold cutter = Manifold::Cube(vec3(2.0), true).Translate({1.0, 0.0, 0.0});
@@ -94,11 +75,12 @@ MeshGLP<Precision, I> GetMeshGLImpl(const manifold::Manifold::Impl& impl,
   VecView<const TriRef> triRef = impl.meshRelation_.triRef;
   // Don't sort originals - keep them in order
   if (!isOriginal) {
-    std::sort(triNew2Old.begin(), triNew2Old.end(), [triRef](int a, int b) {
-      return triRef[a].originalID == triRef[b].originalID
-                 ? triRef[a].meshID < triRef[b].meshID
-                 : triRef[a].originalID < triRef[b].originalID;
-    });
+    std::stable_sort(triNew2Old.begin(), triNew2Old.end(),
+                     [triRef](int a, int b) {
+                       return triRef[a].originalID == triRef[b].originalID
+                                  ? triRef[a].meshID < triRef[b].meshID
+                                  : triRef[a].originalID < triRef[b].originalID;
+                     });
   }
 
   std::vector<mat3> runNormalTransform;
@@ -128,7 +110,7 @@ MeshGLP<Precision, I> GetMeshGLImpl(const manifold::Manifold::Impl& impl,
     const auto ref = triRef[oldTri];
     const int meshID = ref.meshID;
 
-    out.faceID[tri] = ref.tri;
+    out.faceID[tri] = ref.faceID >= 0 ? ref.faceID : ref.coplanarID;
     for (const int i : {0, 1, 2})
       out.triVerts[3 * tri + i] = impl.halfedge_[3 * oldTri + i].startVert;
 
@@ -166,9 +148,8 @@ MeshGLP<Precision, I> GetMeshGLImpl(const manifold::Manifold::Impl& impl,
   for (size_t run = 0; run < out.runOriginalID.size(); ++run) {
     for (size_t tri = out.runIndex[run] / 3; tri < out.runIndex[run + 1] / 3;
          ++tri) {
-      const ivec3 triProp = impl.meshRelation_.triProperties[triNew2Old[tri]];
       for (const int i : {0, 1, 2}) {
-        const int prop = triProp[i];
+        const int prop = impl.halfedge_[3 * triNew2Old[tri] + i].propVert;
         const int vert = out.triVerts[3 * tri + i];
 
         auto& bin = vertPropPair[vert];
@@ -189,8 +170,7 @@ MeshGLP<Precision, I> GetMeshGLImpl(const manifold::Manifold::Impl& impl,
           out.vertProperties.push_back(impl.vertPos_[vert][p]);
         }
         for (int p = 0; p < numProp; ++p) {
-          out.vertProperties.push_back(
-              impl.meshRelation_.properties[prop * numProp + p]);
+          out.vertProperties.push_back(impl.properties_[prop * numProp + p]);
         }
 
         if (updateNormals) {
@@ -332,11 +312,9 @@ MeshGL64 Manifold::GetMeshGL64(int normalIdx) const {
 bool Manifold::IsEmpty() const { return GetCsgLeafNode().GetImpl()->IsEmpty(); }
 /**
  * Returns the reason for an input Mesh producing an empty Manifold. This Status
- * only applies to Manifolds newly-created from an input Mesh - once they are
- * combined into a new Manifold via operations, the status reverts to NoError,
- * simply processing the problem mesh as empty. Likewise, empty meshes may still
- * show NoError, for instance if they are small enough relative to their
- * tolerance to be collapsed to nothing.
+ * will carry on through operations like NaN propogation, ensuring an errored
+ * mesh doesn't get mysteriously lost. Empty meshes may still show
+ * NoError, for instance the intersection of non-overlapping meshes.
  */
 Manifold::Error Manifold::Status() const {
   return GetCsgLeafNode().GetImpl()->status_;
@@ -404,7 +382,7 @@ Manifold Manifold::SetTolerance(double tolerance) const {
   auto impl = std::make_shared<Impl>(*GetCsgLeafNode().GetImpl());
   if (tolerance > impl->tolerance_) {
     impl->tolerance_ = tolerance;
-    impl->CreateFaces();
+    impl->MarkCoplanar();
     impl->SimplifyTopology();
     impl->Finish();
   } else {
@@ -415,6 +393,27 @@ Manifold Manifold::SetTolerance(double tolerance) const {
   return Manifold(impl);
 }
 
+/**
+ * Return a copy of the manifold simplified to the given tolerance, but with its
+ * actual tolerance value unchanged. If the tolerance is not given or is less
+ * than the current tolerance, the current tolerance is used for simplification.
+ * The result will contain a subset of the original verts and all surfaces will
+ * have moved by less than tolerance.
+ */
+Manifold Manifold::Simplify(double tolerance) const {
+  auto impl = std::make_shared<Impl>(*GetCsgLeafNode().GetImpl());
+  const double oldTolerance = impl->tolerance_;
+  if (tolerance == 0) tolerance = oldTolerance;
+  if (tolerance > oldTolerance) {
+    impl->tolerance_ = tolerance;
+    impl->MarkCoplanar();
+  }
+  impl->SimplifyTopology();
+  impl->Finish();
+  impl->tolerance_ = oldTolerance;
+  return Manifold(impl);
+}
+
 /**
  * The genus is a topological property of the manifold, representing the number
  * of "handles". A sphere is 0, torus 1, etc. It is only meaningful for a single
@@ -450,9 +449,10 @@ int Manifold::OriginalID() const {
 
 /**
  * This removes all relations (originalID, faceID, transform) to ancestor meshes
- * and this new Manifold is marked an original. It also collapses colinear edges
- * - these don't get collapsed at boundaries where originalID changes, so the
- * reset may allow flat faces to be further simplified.
+ * and this new Manifold is marked an original. It also recreates faces
+ * - these don't get joined at boundaries where originalID changes, so the
+ * reset may allow triangles of flat faces to be further collapsed with
+ * Simplify().
  */
 Manifold Manifold::AsOriginal() const {
   auto oldImpl = GetCsgLeafNode().GetImpl();
@@ -463,9 +463,7 @@ Manifold Manifold::AsOriginal() const {
   }
   auto newImpl = std::make_shared<Impl>(*oldImpl);
   newImpl->InitializeOriginal();
-  newImpl->CreateFaces();
-  newImpl->SimplifyTopology();
-  newImpl->Finish();
+  newImpl->MarkCoplanar();
   newImpl->InitializeOriginal(true);
   return Manifold(std::make_shared<CsgLeafNode>(newImpl));
 }
@@ -497,22 +495,6 @@ size_t Manifold::NumDegenerateTris() const {
   return GetCsgLeafNode().GetImpl()->NumDegenerateTris();
 }
 
-/**
- * This is a checksum-style verification of the collider, simply returning the
- * total number of edge-face bounding box overlaps between this and other.
- *
- * @param other A Manifold to overlap with.
- */
-size_t Manifold::NumOverlaps(const Manifold& other) const {
-  SparseIndices overlaps = GetCsgLeafNode().GetImpl()->EdgeCollisions(
-      *other.GetCsgLeafNode().GetImpl());
-  int num_overlaps = overlaps.size();
-
-  overlaps = other.GetCsgLeafNode().GetImpl()->EdgeCollisions(
-      *GetCsgLeafNode().GetImpl());
-  return num_overlaps + overlaps.size();
-}
-
 /**
  * Move this Manifold in space. This operation can be chained. Transforms are
  * combined and applied lazily.
@@ -635,38 +617,33 @@ Manifold Manifold::SetProperties(
         propFunc) const {
   auto pImpl = std::make_shared<Impl>(*GetCsgLeafNode().GetImpl());
   const int oldNumProp = NumProp();
-  const Vec<double> oldProperties = pImpl->meshRelation_.properties;
+  const Vec<double> oldProperties = pImpl->properties_;
 
-  auto& triProperties = pImpl->meshRelation_.triProperties;
   if (numProp == 0) {
-    triProperties.resize(0);
-    pImpl->meshRelation_.properties.resize(0);
+    pImpl->properties_.clear();
   } else {
-    if (triProperties.size() == 0) {
-      const int numTri = NumTri();
-      triProperties.resize(numTri);
-      for (int i = 0; i < numTri; ++i) {
-        for (const int j : {0, 1, 2}) {
-          triProperties[i][j] = pImpl->halfedge_[3 * i + j].startVert;
-        }
-      }
-      pImpl->meshRelation_.properties = Vec<double>(numProp * NumVert(), 0);
-    } else {
-      pImpl->meshRelation_.properties = Vec<double>(numProp * NumPropVert(), 0);
-    }
+    pImpl->properties_ = Vec<double>(numProp * NumPropVert(), 0);
     for_each_n(
         propFunc == nullptr ? ExecutionPolicy::Par : ExecutionPolicy::Seq,
-        countAt(0), NumTri(),
-        UpdateProperties(
-            {pImpl->meshRelation_.properties.data(), numProp,
-             oldProperties.data(), oldNumProp, pImpl->vertPos_.data(),
-             triProperties.data(), pImpl->halfedge_.data(),
-             propFunc == nullptr ? [](double* newProp, vec3 position,
-                                      const double* oldProp) { *newProp = 0; }
-                                 : propFunc}));
+        countAt(0), NumTri(), [&](int tri) {
+          for (int i : {0, 1, 2}) {
+            const Halfedge& edge = pImpl->halfedge_[3 * tri + i];
+            const int vert = edge.startVert;
+            const int propVert = edge.propVert;
+            if (propFunc == nullptr) {
+              for (int p = 0; p < numProp; ++p) {
+                pImpl->properties_[numProp * propVert + p] = 0;
+              }
+            } else {
+              propFunc(&pImpl->properties_[numProp * propVert],
+                       pImpl->vertPos_[vert],
+                       oldProperties.data() + oldNumProp * propVert);
+            }
+          }
+        });
   }
 
-  pImpl->meshRelation_.numProp = numProp;
+  pImpl->numProp_ = numProp;
   return Manifold(std::make_shared<CsgLeafNode>(pImpl));
 }
 
@@ -754,14 +731,15 @@ Manifold Manifold::SmoothOut(double minSharpAngle, double minSmoothness) const {
   auto pImpl = std::make_shared<Impl>(*GetCsgLeafNode().GetImpl());
   if (!IsEmpty()) {
     if (minSmoothness == 0) {
-      const int numProp = pImpl->meshRelation_.numProp;
-      Vec<double> properties = pImpl->meshRelation_.properties;
-      Vec<ivec3> triProperties = pImpl->meshRelation_.triProperties;
+      const int numProp = pImpl->numProp_;
+      Vec<double> properties = pImpl->properties_;
+      Vec<Halfedge> halfedge = pImpl->halfedge_;
       pImpl->SetNormals(0, minSharpAngle);
       pImpl->CreateTangents(0);
-      pImpl->meshRelation_.numProp = numProp;
-      pImpl->meshRelation_.properties.swap(properties);
-      pImpl->meshRelation_.triProperties.swap(triProperties);
+      // Reset the properties to the original values, removing temporary normals
+      pImpl->numProp_ = numProp;
+      pImpl->properties_.swap(properties);
+      pImpl->halfedge_.swap(halfedge);
     } else {
       pImpl->CreateTangents(pImpl->SharpenEdges(minSharpAngle, minSmoothness));
     }
@@ -783,8 +761,7 @@ Manifold Manifold::SmoothOut(double minSharpAngle, double minSmoothness) const {
 Manifold Manifold::Refine(int n) const {
   auto pImpl = std::make_shared<Impl>(*GetCsgLeafNode().GetImpl());
   if (n > 1) {
-    pImpl->Refine(
-        [n](vec3 edge, vec4 tangentStart, vec4 tangentEnd) { return n - 1; });
+    pImpl->Refine([n](vec3, vec4, vec4) { return n - 1; });
   }
   return Manifold(std::make_shared<CsgLeafNode>(pImpl));
 }
@@ -802,7 +779,7 @@ Manifold Manifold::Refine(int n) const {
 Manifold Manifold::RefineToLength(double length) const {
   length = std::abs(length);
   auto pImpl = std::make_shared<Impl>(*GetCsgLeafNode().GetImpl());
-  pImpl->Refine([length](vec3 edge, vec4 tangentStart, vec4 tangentEnd) {
+  pImpl->Refine([length](vec3 edge, vec4, vec4) {
     return static_cast<int>(la::length(edge) / length);
   });
   return Manifold(std::make_shared<CsgLeafNode>(pImpl));
diff --git a/thirdparty/manifold/src/mesh_fixes.h b/thirdparty/manifold/src/mesh_fixes.h
index d4aa800b4a..fc11486a6b 100644
--- a/thirdparty/manifold/src/mesh_fixes.h
+++ b/thirdparty/manifold/src/mesh_fixes.h
@@ -12,7 +12,7 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 #pragma once
-#include "./shared.h"
+#include "shared.h"
 
 namespace {
 using namespace manifold;
diff --git a/thirdparty/manifold/src/parallel.h b/thirdparty/manifold/src/parallel.h
index a434939494..05d75be959 100644
--- a/thirdparty/manifold/src/parallel.h
+++ b/thirdparty/manifold/src/parallel.h
@@ -17,7 +17,7 @@
 
 #pragma once
 
-#include "./iters.h"
+#include "iters.h"
 #if (MANIFOLD_PAR == 1)
 #include <tbb/combinable.h>
 #include <tbb/parallel_for.h>
@@ -114,20 +114,20 @@ template <typename T, typename InputIter, typename OutputIter, typename BinOp>
 struct ScanBody {
   T sum;
   T identity;
-  BinOp &f;
+  BinOp& f;
   InputIter input;
   OutputIter output;
 
-  ScanBody(T sum, T identity, BinOp &f, InputIter input, OutputIter output)
+  ScanBody(T sum, T identity, BinOp& f, InputIter input, OutputIter output)
       : sum(sum), identity(identity), f(f), input(input), output(output) {}
-  ScanBody(ScanBody &b, tbb::split)
+  ScanBody(ScanBody& b, tbb::split)
       : sum(b.identity),
         identity(b.identity),
         f(b.f),
         input(b.input),
         output(b.output) {}
   template <typename Tag>
-  void operator()(const tbb::blocked_range<size_t> &r, Tag) {
+  void operator()(const tbb::blocked_range<size_t>& r, Tag) {
     T temp = sum;
     for (size_t i = r.begin(); i < r.end(); ++i) {
       T inputTmp = input[i];
@@ -137,23 +137,23 @@ struct ScanBody {
     sum = temp;
   }
   T get_sum() const { return sum; }
-  void reverse_join(ScanBody &a) { sum = f(a.sum, sum); }
-  void assign(ScanBody &b) { sum = b.sum; }
+  void reverse_join(ScanBody& a) { sum = f(a.sum, sum); }
+  void assign(ScanBody& b) { sum = b.sum; }
 };
 
 template <typename InputIter, typename OutputIter, typename P>
 struct CopyIfScanBody {
   size_t sum;
-  P &pred;
+  P& pred;
   InputIter input;
   OutputIter output;
 
-  CopyIfScanBody(P &pred, InputIter input, OutputIter output)
+  CopyIfScanBody(P& pred, InputIter input, OutputIter output)
       : sum(0), pred(pred), input(input), output(output) {}
-  CopyIfScanBody(CopyIfScanBody &b, tbb::split)
+  CopyIfScanBody(CopyIfScanBody& b, tbb::split)
       : sum(0), pred(b.pred), input(b.input), output(b.output) {}
   template <typename Tag>
-  void operator()(const tbb::blocked_range<size_t> &r, Tag) {
+  void operator()(const tbb::blocked_range<size_t>& r, Tag) {
     size_t temp = sum;
     for (size_t i = r.begin(); i < r.end(); ++i) {
       if (pred(i)) {
@@ -164,8 +164,8 @@ struct CopyIfScanBody {
     sum = temp;
   }
   size_t get_sum() const { return sum; }
-  void reverse_join(CopyIfScanBody &a) { sum = a.sum + sum; }
-  void assign(CopyIfScanBody &b) { sum = b.sum; }
+  void reverse_join(CopyIfScanBody& a) { sum = a.sum + sum; }
+  void assign(CopyIfScanBody& b) { sum = b.sum; }
 };
 
 template <typename N, const int K>
@@ -173,11 +173,11 @@ struct Hist {
   using SizeType = N;
   static constexpr int k = K;
   N hist[k][256] = {{0}};
-  void merge(const Hist<N, K> &other) {
+  void merge(const Hist<N, K>& other) {
     for (int i = 0; i < k; ++i)
       for (int j = 0; j < 256; ++j) hist[i][j] += other.hist[i][j];
   }
-  void prefixSum(N total, bool *canSkip) {
+  void prefixSum(N total, bool* canSkip) {
     for (int i = 0; i < k; ++i) {
       size_t count = 0;
       for (int j = 0; j < 256; ++j) {
@@ -191,8 +191,8 @@ struct Hist {
 };
 
 template <typename T, typename H>
-void histogram(T *ptr, typename H::SizeType n, H &hist) {
-  auto worker = [](T *ptr, typename H::SizeType n, H &hist) {
+void histogram(T* ptr, typename H::SizeType n, H& hist) {
+  auto worker = [](T* ptr, typename H::SizeType n, H& hist) {
     for (typename H::SizeType i = 0; i < n; ++i)
       for (int k = 0; k < hist.k; ++k)
         ++hist.hist[k][(ptr[i] >> (8 * k)) & 0xFF];
@@ -203,21 +203,21 @@ void histogram(T *ptr, typename H::SizeType n, H &hist) {
     tbb::combinable<H> store;
     tbb::parallel_for(
         tbb::blocked_range<typename H::SizeType>(0, n, kSeqThreshold),
-        [&worker, &store, ptr](const auto &r) {
+        [&worker, &store, ptr](const auto& r) {
           worker(ptr + r.begin(), r.end() - r.begin(), store.local());
         });
-    store.combine_each([&hist](const H &h) { hist.merge(h); });
+    store.combine_each([&hist](const H& h) { hist.merge(h); });
   }
 }
 
 template <typename T, typename H>
-void shuffle(T *src, T *target, typename H::SizeType n, H &hist, int k) {
+void shuffle(T* src, T* target, typename H::SizeType n, H& hist, int k) {
   for (typename H::SizeType i = 0; i < n; ++i)
     target[hist.hist[k][(src[i] >> (8 * k)) & 0xFF]++] = src[i];
 }
 
 template <typename T, typename SizeType>
-bool LSB_radix_sort(T *input, T *tmp, SizeType n) {
+bool LSB_radix_sort(T* input, T* tmp, SizeType n) {
   Hist<SizeType, sizeof(T) / sizeof(char)> hist;
   if (std::is_sorted(input, input + n)) return false;
   histogram(input, n, hist);
@@ -240,9 +240,9 @@ struct SortedRange {
   SizeType offset = 0, length = 0;
   bool inTmp = false;
 
-  SortedRange(T *input, T *tmp, SizeType offset = 0, SizeType length = 0)
+  SortedRange(T* input, T* tmp, SizeType offset = 0, SizeType length = 0)
       : input(input), tmp(tmp), offset(offset), length(length) {}
-  SortedRange(SortedRange<T, SizeType> &r, tbb::split)
+  SortedRange(SortedRange<T, SizeType>& r, tbb::split)
       : input(r.input), tmp(r.tmp) {}
   // FIXME: no idea why thread sanitizer reports data race here
 #if defined(__has_feature)
@@ -251,7 +251,7 @@ struct SortedRange {
 #endif
 #endif
   void
-  operator()(const tbb::blocked_range<SizeType> &range) {
+  operator()(const tbb::blocked_range<SizeType>& range) {
     SortedRange<T, SizeType> rhs(input, tmp, range.begin(),
                                  range.end() - range.begin());
     rhs.inTmp =
@@ -267,7 +267,7 @@ struct SortedRange {
     copy(src + offset, src + offset + length, target + offset);
     return !inTmp;
   }
-  void join(const SortedRange<T, SizeType> &rhs) {
+  void join(const SortedRange<T, SizeType>& rhs) {
     if (inTmp != rhs.inTmp) {
       if (length < rhs.length)
         inTmp = swapBuffer();
@@ -286,8 +286,8 @@ struct SortedRange {
 };
 
 template <typename T, typename SizeTy>
-void radix_sort(T *input, SizeTy n) {
-  T *aux = new T[n];
+void radix_sort(T* input, SizeTy n) {
+  T* aux = new T[n];
   SizeTy blockSize = std::max(n / tbb::this_task_arena::max_concurrency() / 4,
                               static_cast<SizeTy>(kSeqThreshold / sizeof(T)));
   SortedRange<T, SizeTy> result(input, aux);
@@ -306,7 +306,7 @@ void mergeSort(ExecutionPolicy policy, Iterator first, Iterator last,
     // apparently this prioritizes threads inside here?
     tbb::this_task_arena::isolate([&] {
       size_t length = std::distance(first, last);
-      T *tmp = new T[length];
+      T* tmp = new T[length];
       copy(policy, first, last, tmp);
       details::mergeSortRec(tmp, first, 0, length, comp);
       delete[] tmp;
@@ -376,13 +376,16 @@ void for_each(ExecutionPolicy policy, Iter first, Iter last, F f) {
                     typename std::iterator_traits<Iter>::iterator_category,
                     std::random_access_iterator_tag>,
                 "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
-    tbb::parallel_for(tbb::blocked_range<Iter>(first, last),
-                      [&f](const tbb::blocked_range<Iter> &range) {
-                        for (Iter i = range.begin(); i != range.end(); i++)
-                          f(*i);
-                      });
+    tbb::this_task_arena::isolate([&]() {
+      tbb::parallel_for(tbb::blocked_range<Iter>(first, last),
+                        [&f](const tbb::blocked_range<Iter>& range) {
+                          for (Iter i = range.begin(); i != range.end(); i++)
+                            f(*i);
+                        });
+    });
     return;
   }
 #endif
@@ -412,16 +415,19 @@ T reduce(ExecutionPolicy policy, InputIter first, InputIter last, T init,
                     typename std::iterator_traits<InputIter>::iterator_category,
                     std::random_access_iterator_tag>,
                 "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
     // should we use deterministic reduce here?
-    return tbb::parallel_reduce(
-        tbb::blocked_range<InputIter>(first, last, details::kSeqThreshold),
-        init,
-        [&f](const tbb::blocked_range<InputIter> &range, T value) {
-          return std::reduce(range.begin(), range.end(), value, f);
-        },
-        f);
+    return tbb::this_task_arena::isolate([&]() {
+      return tbb::parallel_reduce(
+          tbb::blocked_range<InputIter>(first, last, details::kSeqThreshold),
+          init,
+          [&f](const tbb::blocked_range<InputIter>& range, T value) {
+            return std::reduce(range.begin(), range.end(), value, f);
+          },
+          f);
+    });
   }
 #endif
   return std::reduce(first, last, init, f);
@@ -488,21 +494,24 @@ void inclusive_scan(ExecutionPolicy policy, InputIter first, InputIter last,
           typename std::iterator_traits<OutputIter>::iterator_category,
           std::random_access_iterator_tag>,
       "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
-    tbb::parallel_scan(
-        tbb::blocked_range<size_t>(0, std::distance(first, last)),
-        static_cast<T>(0),
-        [&](const tbb::blocked_range<size_t> &range, T sum,
-            bool is_final_scan) {
-          T temp = sum;
-          for (size_t i = range.begin(); i < range.end(); ++i) {
-            temp = temp + first[i];
-            if (is_final_scan) d_first[i] = temp;
-          }
-          return temp;
-        },
-        std::plus<T>());
+    tbb::this_task_arena::isolate([&]() {
+      tbb::parallel_scan(
+          tbb::blocked_range<size_t>(0, std::distance(first, last)),
+          static_cast<T>(0),
+          [&](const tbb::blocked_range<size_t>& range, T sum,
+              bool is_final_scan) {
+            T temp = sum;
+            for (size_t i = range.begin(); i < range.end(); ++i) {
+              temp = temp + first[i];
+              if (is_final_scan) d_first[i] = temp;
+            }
+            return temp;
+          },
+          std::plus<T>());
+    });
     return;
   }
 #endif
@@ -550,12 +559,16 @@ void exclusive_scan(ExecutionPolicy policy, InputIter first, InputIter last,
           typename std::iterator_traits<OutputIter>::iterator_category,
           std::random_access_iterator_tag>,
       "You can only parallelize RandomAccessIterator.");
+  (void)policy;
+  (void)identity;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
     details::ScanBody<T, InputIter, OutputIter, BinOp> body(init, identity, f,
                                                             first, d_first);
-    tbb::parallel_scan(
-        tbb::blocked_range<size_t>(0, std::distance(first, last)), body);
+    tbb::this_task_arena::isolate([&]() {
+      tbb::parallel_scan(
+          tbb::blocked_range<size_t>(0, std::distance(first, last)), body);
+    });
     return;
   }
 #endif
@@ -603,15 +616,18 @@ void transform(ExecutionPolicy policy, InputIter first, InputIter last,
           typename std::iterator_traits<OutputIter>::iterator_category,
           std::random_access_iterator_tag>,
       "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
-    tbb::parallel_for(tbb::blocked_range<size_t>(
-                          0, static_cast<size_t>(std::distance(first, last))),
-                      [&](const tbb::blocked_range<size_t> &range) {
-                        std::transform(first + range.begin(),
-                                       first + range.end(),
-                                       d_first + range.begin(), f);
-                      });
+    tbb::this_task_arena::isolate([&]() {
+      tbb::parallel_for(tbb::blocked_range<size_t>(
+                            0, static_cast<size_t>(std::distance(first, last))),
+                        [&](const tbb::blocked_range<size_t>& range) {
+                          std::transform(first + range.begin(),
+                                         first + range.end(),
+                                         d_first + range.begin(), f);
+                        });
+    });
     return;
   }
 #endif
@@ -647,15 +663,18 @@ void copy(ExecutionPolicy policy, InputIter first, InputIter last,
           typename std::iterator_traits<OutputIter>::iterator_category,
           std::random_access_iterator_tag>,
       "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
-    tbb::parallel_for(tbb::blocked_range<size_t>(
-                          0, static_cast<size_t>(std::distance(first, last)),
-                          details::kSeqThreshold),
-                      [&](const tbb::blocked_range<size_t> &range) {
-                        std::copy(first + range.begin(), first + range.end(),
-                                  d_first + range.begin());
-                      });
+    tbb::this_task_arena::isolate([&]() {
+      tbb::parallel_for(tbb::blocked_range<size_t>(
+                            0, static_cast<size_t>(std::distance(first, last)),
+                            details::kSeqThreshold),
+                        [&](const tbb::blocked_range<size_t>& range) {
+                          std::copy(first + range.begin(), first + range.end(),
+                                    d_first + range.begin());
+                        });
+    });
     return;
   }
 #endif
@@ -704,12 +723,15 @@ void fill(ExecutionPolicy policy, OutputIter first, OutputIter last, T value) {
           typename std::iterator_traits<OutputIter>::iterator_category,
           std::random_access_iterator_tag>,
       "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
-    tbb::parallel_for(tbb::blocked_range<OutputIter>(first, last),
-                      [&](const tbb::blocked_range<OutputIter> &range) {
-                        std::fill(range.begin(), range.end(), value);
-                      });
+    tbb::this_task_arena::isolate([&]() {
+      tbb::parallel_for(tbb::blocked_range<OutputIter>(first, last),
+                        [&](const tbb::blocked_range<OutputIter>& range) {
+                          std::fill(range.begin(), range.end(), value);
+                        });
+    });
     return;
   }
 #endif
@@ -727,6 +749,7 @@ void fill(OutputIter first, OutputIter last, T value) {
 template <typename InputIter, typename P>
 size_t count_if(ExecutionPolicy policy, InputIter first, InputIter last,
                 P pred) {
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
     return reduce(policy, TransformIterator(first, pred),
@@ -751,18 +774,21 @@ bool all_of(ExecutionPolicy policy, InputIter first, InputIter last, P pred) {
                     typename std::iterator_traits<InputIter>::iterator_category,
                     std::random_access_iterator_tag>,
                 "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
     // should we use deterministic reduce here?
-    return tbb::parallel_reduce(
-        tbb::blocked_range<InputIter>(first, last), true,
-        [&](const tbb::blocked_range<InputIter> &range, bool value) {
-          if (!value) return false;
-          for (InputIter i = range.begin(); i != range.end(); i++)
-            if (!pred(*i)) return false;
-          return true;
-        },
-        [](bool a, bool b) { return a && b; });
+    return tbb::this_task_arena::isolate([&]() {
+      return tbb::parallel_reduce(
+          tbb::blocked_range<InputIter>(first, last), true,
+          [&](const tbb::blocked_range<InputIter>& range, bool value) {
+            if (!value) return false;
+            for (InputIter i = range.begin(); i != range.end(); i++)
+              if (!pred(*i)) return false;
+            return true;
+          },
+          [](bool a, bool b) { return a && b; });
+    });
   }
 #endif
   return std::all_of(first, last, pred);
@@ -798,13 +824,16 @@ OutputIter copy_if(ExecutionPolicy policy, InputIter first, InputIter last,
           typename std::iterator_traits<OutputIter>::iterator_category,
           std::random_access_iterator_tag>,
       "You can only parallelize RandomAccessIterator.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
     auto pred2 = [&](size_t i) { return pred(first[i]); };
     details::CopyIfScanBody body(pred2, first, d_first);
-    tbb::parallel_scan(
-        tbb::blocked_range<size_t>(0, std::distance(first, last)), body);
-    return d_first + body.get_sum();
+    tbb::this_task_arena::isolate([&]() {
+      tbb::parallel_scan(
+          tbb::blocked_range<size_t>(0, std::distance(first, last)), body);
+      return d_first + body.get_sum();
+    });
   }
 #endif
   return std::copy_if(first, last, d_first, pred);
@@ -845,9 +874,10 @@ Iter remove_if(ExecutionPolicy policy, Iter first, Iter last, P pred) {
   static_assert(std::is_trivially_destructible_v<T>,
                 "Our simple implementation does not support types that are "
                 "not trivially destructable.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
-    T *tmp = new T[std::distance(first, last)];
+    T* tmp = new T[std::distance(first, last)];
     auto back =
         copy_if(policy, first, last, tmp, [&](T v) { return !pred(v); });
     copy(policy, tmp, back, first);
@@ -892,9 +922,10 @@ Iter remove(ExecutionPolicy policy, Iter first, Iter last, T value) {
   static_assert(std::is_trivially_destructible_v<T>,
                 "Our simple implementation does not support types that are "
                 "not trivially destructable.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par) {
-    T *tmp = new T[std::distance(first, last)];
+    T* tmp = new T[std::distance(first, last)];
     auto back =
         copy_if(policy, first, last, tmp, [&](T v) { return v != value; });
     copy(policy, tmp, back, first);
@@ -939,13 +970,14 @@ Iter unique(ExecutionPolicy policy, Iter first, Iter last) {
   static_assert(std::is_trivially_destructible_v<T>,
                 "Our simple implementation does not support types that are "
                 "not trivially destructable.");
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   if (policy == ExecutionPolicy::Par && first != last) {
     Iter newSrcStart = first;
     // cap the maximum buffer size, proved to be beneficial for unique with huge
     // array size
     constexpr size_t MAX_BUFFER_SIZE = 1 << 16;
-    T *tmp = new T[std::min(MAX_BUFFER_SIZE,
+    T* tmp = new T[std::min(MAX_BUFFER_SIZE,
                             static_cast<size_t>(std::distance(first, last)))];
     auto pred = [&](size_t i) { return tmp[i] != tmp[i + 1]; };
     do {
@@ -957,7 +989,9 @@ Iter unique(ExecutionPolicy policy, Iter first, Iter last) {
       // this is not a typo, the index i is offset by 1, so to compare an
       // element with its predecessor we need to compare i and i + 1.
       details::CopyIfScanBody body(pred, tmp + 1, first + 1);
-      tbb::parallel_scan(tbb::blocked_range<size_t>(0, length - 1), body);
+      tbb::this_task_arena::isolate([&]() {
+        tbb::parallel_scan(tbb::blocked_range<size_t>(0, length - 1), body);
+      });
       first += body.get_sum() + 1;
       newSrcStart += length;
     } while (newSrcStart != last);
@@ -992,6 +1026,7 @@ Iter unique(Iter first, Iter last) {
 template <typename Iterator,
           typename T = typename std::iterator_traits<Iterator>::value_type>
 void stable_sort(ExecutionPolicy policy, Iterator first, Iterator last) {
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   details::SortFunctor<Iterator, T>()(policy, first, last);
 #else
@@ -1023,6 +1058,7 @@ template <typename Iterator,
           typename Comp = decltype(std::less<T>())>
 void stable_sort(ExecutionPolicy policy, Iterator first, Iterator last,
                  Comp comp) {
+  (void)policy;
 #if (MANIFOLD_PAR == 1)
   details::mergeSort(policy, first, last, comp);
 #else
diff --git a/thirdparty/manifold/src/polygon.cpp b/thirdparty/manifold/src/polygon.cpp
index 60f510a98b..db7c58e71a 100644
--- a/thirdparty/manifold/src/polygon.cpp
+++ b/thirdparty/manifold/src/polygon.cpp
@@ -18,15 +18,20 @@
 #include <map>
 #include <set>
 
-#include "./collider.h"
-#include "./parallel.h"
-#include "./utils.h"
+#include "manifold/manifold.h"
 #include "manifold/optional_assert.h"
+#include "parallel.h"
+#include "tree2d.h"
+#include "utils.h"
+
+#ifdef MANIFOLD_DEBUG
+#include <iomanip>
+#endif
 
 namespace {
 using namespace manifold;
 
-static ExecutionParams params;
+constexpr int TRIANGULATOR_VERBOSE_LEVEL = 2;
 
 constexpr double kBest = -std::numeric_limits<double>::infinity();
 
@@ -40,9 +45,9 @@ struct PolyEdge {
   int startVert, endVert;
 };
 
-std::vector<PolyEdge> Polygons2Edges(const PolygonsIdx &polys) {
+std::vector<PolyEdge> Polygons2Edges(const PolygonsIdx& polys) {
   std::vector<PolyEdge> halfedges;
-  for (const auto &poly : polys) {
+  for (const auto& poly : polys) {
     for (size_t i = 1; i < poly.size(); ++i) {
       halfedges.push_back({poly[i - 1].idx, poly[i].idx});
     }
@@ -51,10 +56,10 @@ std::vector<PolyEdge> Polygons2Edges(const PolygonsIdx &polys) {
   return halfedges;
 }
 
-std::vector<PolyEdge> Triangles2Edges(const std::vector<ivec3> &triangles) {
+std::vector<PolyEdge> Triangles2Edges(const std::vector<ivec3>& triangles) {
   std::vector<PolyEdge> halfedges;
   halfedges.reserve(triangles.size() * 3);
-  for (const ivec3 &tri : triangles) {
+  for (const ivec3& tri : triangles) {
     halfedges.push_back({tri[0], tri[1]});
     halfedges.push_back({tri[1], tri[2]});
     halfedges.push_back({tri[2], tri[0]});
@@ -62,7 +67,7 @@ std::vector<PolyEdge> Triangles2Edges(const std::vector<ivec3> &triangles) {
   return halfedges;
 }
 
-void CheckTopology(const std::vector<PolyEdge> &halfedges) {
+void CheckTopology(const std::vector<PolyEdge>& halfedges) {
   DEBUG_ASSERT(halfedges.size() % 2 == 0, topologyErr,
                "Odd number of halfedges.");
   size_t n_edges = halfedges.size() / 2;
@@ -83,8 +88,8 @@ void CheckTopology(const std::vector<PolyEdge> &halfedges) {
   backward.resize(n_edges);
 
   std::for_each(backward.begin(), backward.end(),
-                [](PolyEdge &e) { std::swap(e.startVert, e.endVert); });
-  auto cmp = [](const PolyEdge &a, const PolyEdge &b) {
+                [](PolyEdge& e) { std::swap(e.startVert, e.endVert); });
+  auto cmp = [](const PolyEdge& a, const PolyEdge& b) {
     return a.startVert < b.startVert ||
            (a.startVert == b.startVert && a.endVert < b.endVert);
   };
@@ -97,8 +102,8 @@ void CheckTopology(const std::vector<PolyEdge> &halfedges) {
   }
 }
 
-void CheckTopology(const std::vector<ivec3> &triangles,
-                   const PolygonsIdx &polys) {
+void CheckTopology(const std::vector<ivec3>& triangles,
+                   const PolygonsIdx& polys) {
   std::vector<PolyEdge> halfedges = Triangles2Edges(triangles);
   std::vector<PolyEdge> openEdges = Polygons2Edges(polys);
   for (PolyEdge e : openEdges) {
@@ -107,23 +112,24 @@ void CheckTopology(const std::vector<ivec3> &triangles,
   CheckTopology(halfedges);
 }
 
-void CheckGeometry(const std::vector<ivec3> &triangles,
-                   const PolygonsIdx &polys, double epsilon) {
+void CheckGeometry(const std::vector<ivec3>& triangles,
+                   const PolygonsIdx& polys, double epsilon) {
   std::unordered_map<int, vec2> vertPos;
-  for (const auto &poly : polys) {
+  for (const auto& poly : polys) {
     for (size_t i = 0; i < poly.size(); ++i) {
       vertPos[poly[i].idx] = poly[i].pos;
     }
   }
   DEBUG_ASSERT(std::all_of(triangles.begin(), triangles.end(),
-                           [&vertPos, epsilon](const ivec3 &tri) {
+                           [&vertPos, epsilon](const ivec3& tri) {
                              return CCW(vertPos[tri[0]], vertPos[tri[1]],
                                         vertPos[tri[2]], epsilon) >= 0;
                            }),
                geometryErr, "triangulation is not entirely CCW!");
 }
 
-void Dump(const PolygonsIdx &polys, double epsilon) {
+void Dump(const PolygonsIdx& polys, double epsilon) {
+  std::cout << std::setprecision(19);
   std::cout << "Polygon 0 " << epsilon << " " << polys.size() << std::endl;
   for (auto poly : polys) {
     std::cout << poly.size() << std::endl;
@@ -141,12 +147,18 @@ void Dump(const PolygonsIdx &polys, double epsilon) {
   }
 }
 
-void PrintFailure(const std::exception &e, const PolygonsIdx &polys,
-                  std::vector<ivec3> &triangles, double epsilon) {
+std::atomic<int> numFailures(0);
+
+void PrintFailure(const std::exception& e, const PolygonsIdx& polys,
+                  std::vector<ivec3>& triangles, double epsilon) {
+  // only print the first triangulation failure
+  if (numFailures.fetch_add(1) != 0) return;
+  std::cout << std::setprecision(19);
   std::cout << "-----------------------------------" << std::endl;
   std::cout << "Triangulation failed! Precision = " << epsilon << std::endl;
   std::cout << e.what() << std::endl;
-  if (triangles.size() > 1000 && !PolygonParams().verbose) {
+  if (triangles.size() > 1000 &&
+      ManifoldParams().verbose < TRIANGULATOR_VERBOSE_LEVEL) {
     std::cout << "Output truncated due to producing " << triangles.size()
               << " triangles." << std::endl;
     return;
@@ -159,8 +171,9 @@ void PrintFailure(const std::exception &e, const PolygonsIdx &polys,
   }
 }
 
-#define PRINT(msg) \
-  if (params.verbose) std::cout << msg << std::endl;
+#define PRINT(msg)                                            \
+  if (ManifoldParams().verbose >= TRIANGULATOR_VERBOSE_LEVEL) \
+    std::cout << msg << std::endl;
 #else
 #define PRINT(msg)
 #endif
@@ -170,8 +183,8 @@ void PrintFailure(const std::exception &e, const PolygonsIdx &polys,
  * Exactly colinear edges and zero-length edges are treated conservatively as
  * reflex. Does not check for overlaps.
  */
-bool IsConvex(const PolygonsIdx &polys, double epsilon) {
-  for (const SimplePolygonIdx &poly : polys) {
+bool IsConvex(const PolygonsIdx& polys, double epsilon) {
+  for (const SimplePolygonIdx& poly : polys) {
     const vec2 firstEdge = poly[0].pos - poly[poly.size() - 1].pos;
     // Zero-length edges comes out NaN, which won't trip the early return, but
     // it's okay because that zero-length edge will also get tested
@@ -193,14 +206,14 @@ bool IsConvex(const PolygonsIdx &polys, double epsilon) {
  * Triangulates a set of convex polygons by alternating instead of a fan, to
  * avoid creating high-degree vertices.
  */
-std::vector<ivec3> TriangulateConvex(const PolygonsIdx &polys) {
+std::vector<ivec3> TriangulateConvex(const PolygonsIdx& polys) {
   const size_t numTri = manifold::transform_reduce(
       polys.begin(), polys.end(), 0_uz,
       [](size_t a, size_t b) { return a + b; },
-      [](const SimplePolygonIdx &poly) { return poly.size() - 2; });
+      [](const SimplePolygonIdx& poly) { return poly.size() - 2; });
   std::vector<ivec3> triangles;
   triangles.reserve(numTri);
-  for (const SimplePolygonIdx &poly : polys) {
+  for (const SimplePolygonIdx& poly : polys) {
     size_t i = 0;
     size_t k = poly.size() - 1;
     bool right = true;
@@ -222,9 +235,7 @@ std::vector<ivec3> TriangulateConvex(const PolygonsIdx &polys) {
  * Ear-clipping triangulator based on David Eberly's approach from Geometric
  * Tools, but adjusted to handle epsilon-valid polygons, and including a
  * fallback that ensures a manifold triangulation even for overlapping polygons.
- * This is an O(n^2) algorithm, but hopefully this is not a big problem as the
- * number of edges in a given polygon is generally much less than the number of
- * triangles in a mesh, and relatively few faces even need triangulation.
+ * This is reduced from an O(n^2) algorithm by means of our BVH Collider.
  *
  * The main adjustments for robustness involve clipping the sharpest ears first
  * (a known technique to get higher triangle quality), and doing an exhaustive
@@ -234,11 +245,11 @@ std::vector<ivec3> TriangulateConvex(const PolygonsIdx &polys) {
 
 class EarClip {
  public:
-  EarClip(const PolygonsIdx &polys, double epsilon) : epsilon_(epsilon) {
+  EarClip(const PolygonsIdx& polys, double epsilon) : epsilon_(epsilon) {
     ZoneScoped;
 
     size_t numVert = 0;
-    for (const SimplePolygonIdx &poly : polys) {
+    for (const SimplePolygonIdx& poly : polys) {
       numVert += poly.size();
     }
     polygon_.reserve(numVert + 2 * polys.size());
@@ -272,19 +283,19 @@ class EarClip {
 
  private:
   struct Vert;
-  typedef std::vector<Vert>::iterator VertItr;
-  typedef std::vector<Vert>::const_iterator VertItrC;
+  using VertItr = std::vector<Vert>::iterator;
+  using VertItrC = std::vector<Vert>::const_iterator;
   struct MaxX {
-    bool operator()(const VertItr &a, const VertItr &b) const {
+    bool operator()(const VertItr& a, const VertItr& b) const {
       return a->pos.x > b->pos.x;
     }
   };
   struct MinCost {
-    bool operator()(const VertItr &a, const VertItr &b) const {
+    bool operator()(const VertItr& a, const VertItr& b) const {
       return a->cost < b->cost;
     }
   };
-  typedef std::set<VertItr, MinCost>::iterator qItr;
+  using qItr = std::set<VertItr, MinCost>::iterator;
 
   // The flat list where all the Verts are stored. Not used much for traversal.
   std::vector<Vert> polygon_;
@@ -306,9 +317,8 @@ class EarClip {
   double epsilon_;
 
   struct IdxCollider {
-    Collider collider;
+    Vec<PolyVert> points;
     std::vector<VertItr> itr;
-    SparseIndices ind;
   };
 
   // A circularly-linked list representing the polygon(s) that still need to be
@@ -399,20 +409,9 @@ class EarClip {
       return true;
     }
 
-    // A major key to robustness is to only clip convex ears, but this is
-    // difficult to determine when an edge is folded back on itself. This
-    // function walks down the kinks in a degenerate portion of a polygon until
-    // it finds a clear geometric result. In the vast majority of cases the loop
-    // will only need one or two iterations.
+    // Returns true for convex or colinear ears.
     bool IsConvex(double epsilon) const {
-      const int convexity = CCW(left->pos, pos, right->pos, epsilon);
-      if (convexity != 0) {
-        return convexity > 0;
-      }
-      if (la::dot(left->pos - pos, right->pos - pos) <= 0) {
-        return true;
-      }
-      return left->InsideEdge(left->right, epsilon, true);
+      return CCW(left->pos, pos, right->pos, epsilon) >= 0;
     }
 
     // Subtly different from !IsConvex because IsConvex will return true for
@@ -489,7 +488,7 @@ class EarClip {
     // values < -epsilon so they will never affect validity. The first
     // totalCost is designed to give priority to sharper angles. Any cost < (-1
     // - epsilon) has satisfied the Delaunay condition.
-    double EarCost(double epsilon, IdxCollider &collider) const {
+    double EarCost(double epsilon, IdxCollider& collider) const {
       vec2 openSide = left->pos - right->pos;
       const vec2 center = 0.5 * (left->pos + right->pos);
       const double scale = 4 / la::dot(openSide, openSide);
@@ -502,38 +501,32 @@ class EarClip {
         return totalCost;
       }
 
-      Box earBox = Box{vec3(center.x - radius, center.y - radius, 0),
-                       vec3(center.x + radius, center.y + radius, 0)};
-      earBox.Union(vec3(pos, 0));
-      collider.collider.Collisions(VecView<const Box>(&earBox, 1),
-                                   collider.ind);
+      Rect earBox = Rect(vec2(center.x - radius, center.y - radius),
+                         vec2(center.x + radius, center.y + radius));
+      earBox.Union(pos);
+      earBox.min -= epsilon;
+      earBox.max += epsilon;
 
       const int lid = left->mesh_idx;
       const int rid = right->mesh_idx;
-
-      totalCost = transform_reduce(
-          countAt(0), countAt(collider.ind.size()), totalCost,
-          [](double a, double b) { return std::max(a, b); },
-          [&](size_t i) {
-            const VertItr test = collider.itr[collider.ind.Get(i, true)];
-            if (!Clipped(test) && test->mesh_idx != mesh_idx &&
-                test->mesh_idx != lid &&
-                test->mesh_idx != rid) {  // Skip duplicated verts
-              double cost = Cost(test, openSide, epsilon);
-              if (cost < -epsilon) {
-                cost = DelaunayCost(test->pos - center, scale, epsilon);
-              }
-              return cost;
-            }
-            return std::numeric_limits<double>::lowest();
-          });
-      collider.ind.Clear();
+      QueryTwoDTree(collider.points, earBox, [&](PolyVert point) {
+        const VertItr test = collider.itr[point.idx];
+        if (!Clipped(test) && test->mesh_idx != mesh_idx &&
+            test->mesh_idx != lid &&
+            test->mesh_idx != rid) {  // Skip duplicated verts
+          double cost = Cost(test, openSide, epsilon);
+          if (cost < -epsilon) {
+            cost = DelaunayCost(test->pos - center, scale, epsilon);
+          }
+          if (cost > totalCost) totalCost = cost;
+        }
+      });
       return totalCost;
     }
 
     void PrintVert() const {
 #ifdef MANIFOLD_DEBUG
-      if (!params.verbose) return;
+      if (ManifoldParams().verbose < TRIANGULATOR_VERBOSE_LEVEL) return;
       std::cout << "vert: " << mesh_idx << ", left: " << left->mesh_idx
                 << ", right: " << right->mesh_idx << ", cost: " << cost
                 << std::endl;
@@ -603,8 +596,7 @@ class EarClip {
 
   // If an ear will make a degenerate triangle, clip it early to avoid
   // difficulty in key-holing. This function is recursive, as the process of
-  // clipping may cause the neighbors to degenerate. Reflex degenerates *must
-  // not* be clipped, unless they have a short edge.
+  // clipping may cause the neighbors to degenerate.
   void ClipIfDegenerate(VertItr ear) {
     if (Clipped(ear)) {
       return;
@@ -614,8 +606,7 @@ class EarClip {
     }
     if (ear->IsShort(epsilon_) ||
         (CCW(ear->left->pos, ear->pos, ear->right->pos, epsilon_) == 0 &&
-         la::dot(ear->left->pos - ear->pos, ear->right->pos - ear->pos) > 0 &&
-         ear->IsConvex(epsilon_))) {
+         la::dot(ear->left->pos - ear->pos, ear->right->pos - ear->pos) > 0)) {
       ClipEar(ear);
       ClipIfDegenerate(ear->left);
       ClipIfDegenerate(ear->right);
@@ -623,11 +614,18 @@ class EarClip {
   }
 
   // Build the circular list polygon structures.
-  std::vector<VertItr> Initialize(const PolygonsIdx &polys) {
+  std::vector<VertItr> Initialize(const PolygonsIdx& polys) {
     std::vector<VertItr> starts;
-    for (const SimplePolygonIdx &poly : polys) {
+    const auto invalidItr = polygon_.begin();
+    for (const SimplePolygonIdx& poly : polys) {
       auto vert = poly.begin();
-      polygon_.push_back({vert->idx, 0.0, earsQueue_.end(), vert->pos});
+      polygon_.push_back({vert->idx,
+                          0.0,
+                          earsQueue_.end(),
+                          vert->pos,
+                          {0, 0},
+                          invalidItr,
+                          invalidItr});
       const VertItr first = std::prev(polygon_.end());
 
       bBox_.Union(first->pos);
@@ -639,7 +637,13 @@ class EarClip {
       for (++vert; vert != poly.end(); ++vert) {
         bBox_.Union(vert->pos);
 
-        polygon_.push_back({vert->idx, 0.0, earsQueue_.end(), vert->pos});
+        polygon_.push_back({vert->idx,
+                            0.0,
+                            earsQueue_.end(),
+                            vert->pos,
+                            {0, 0},
+                            invalidItr,
+                            invalidItr});
         VertItr next = std::prev(polygon_.end());
 
         Link(last, next);
@@ -740,7 +744,7 @@ class EarClip {
     JoinPolygons(start, connector);
 
 #ifdef MANIFOLD_DEBUG
-    if (params.verbose) {
+    if (ManifoldParams().verbose >= TRIANGULATOR_VERBOSE_LEVEL) {
       std::cout << "connected " << start->mesh_idx << " to "
                 << connector->mesh_idx << std::endl;
     }
@@ -767,7 +771,8 @@ class EarClip {
           above * CCW(start->pos, vert->pos, connector->pos, epsilon_);
       if (vert->pos.x > start->pos.x - epsilon_ &&
           vert->pos.y * above > start->pos.y * above - epsilon_ &&
-          (inside > 0 || (inside == 0 && vert->pos.x < connector->pos.x)) &&
+          (inside > 0 || (inside == 0 && vert->pos.x < connector->pos.x &&
+                          vert->pos.y * above < connector->pos.y * above)) &&
           vert->InsideEdge(edge, epsilon_, true) && vert->IsReflex(epsilon_)) {
         connector = vert;
       }
@@ -803,7 +808,7 @@ class EarClip {
 
   // Recalculate the cost of the Vert v ear, updating it in the queue by
   // removing and reinserting it.
-  void ProcessEar(VertItr v, IdxCollider &collider) {
+  void ProcessEar(VertItr v, IdxCollider& collider) {
     if (v->ear != earsQueue_.end()) {
       earsQueue_.erase(v->ear);
       v->ear = earsQueue_.end();
@@ -823,35 +828,16 @@ class EarClip {
   // epsilon_. Each ear uses this BVH to quickly find a subset of vertices to
   // check for cost.
   IdxCollider VertCollider(VertItr start) const {
-    Vec<Box> vertBox;
-    Vec<uint32_t> vertMorton;
+    ZoneScoped;
     std::vector<VertItr> itr;
-    const Box box(vec3(bBox_.min, 0), vec3(bBox_.max, 0));
-
-    Loop(start, [&vertBox, &vertMorton, &itr, &box, this](VertItr v) {
+    Vec<PolyVert> points;
+    Loop(start, [&itr, &points](VertItr v) {
+      points.push_back({v->pos, static_cast<int>(itr.size())});
       itr.push_back(v);
-      const vec3 pos(v->pos, 0);
-      vertBox.push_back({pos - epsilon_, pos + epsilon_});
-      vertMorton.push_back(Collider::MortonCode(pos, box));
     });
 
-    if (itr.empty()) {
-      return {Collider(), itr};
-    }
-
-    const int numVert = itr.size();
-    Vec<int> vertNew2Old(numVert);
-    sequence(vertNew2Old.begin(), vertNew2Old.end());
-
-    stable_sort(vertNew2Old.begin(), vertNew2Old.end(),
-                [&vertMorton](const int a, const int b) {
-                  return vertMorton[a] < vertMorton[b];
-                });
-    Permute(vertMorton, vertNew2Old);
-    Permute(vertBox, vertNew2Old);
-    Permute(itr, vertNew2Old);
-
-    return {Collider(vertBox, vertMorton), itr};
+    BuildTwoDTree(points);
+    return {std::move(points), std::move(itr)};
   }
 
   // The main ear-clipping loop. This is called once for each simple polygon -
@@ -907,7 +893,7 @@ class EarClip {
 
   void Dump(VertItrC start) const {
 #ifdef MANIFOLD_DEBUG
-    if (!params.verbose) return;
+    if (ManifoldParams().verbose < TRIANGULATOR_VERBOSE_LEVEL) return;
     VertItrC v = start;
     std::cout << "show(array([" << std::setprecision(15) << std::endl;
     do {
@@ -944,16 +930,21 @@ namespace manifold {
  * references back to the original vertices.
  * @param epsilon The value of &epsilon;, bounding the uncertainty of the
  * input.
+ * @param allowConvex If true (default), the triangulator will use a fast
+ * triangulation if the input is convex, falling back to ear-clipping if not.
+ * The triangle quality may be lower, so set to false to disable this
+ * optimization.
  * @return std::vector<ivec3> The triangles, referencing the original
  * vertex indicies.
  */
-std::vector<ivec3> TriangulateIdx(const PolygonsIdx &polys, double epsilon) {
+std::vector<ivec3> TriangulateIdx(const PolygonsIdx& polys, double epsilon,
+                                  bool allowConvex) {
   std::vector<ivec3> triangles;
   double updatedEpsilon = epsilon;
 #ifdef MANIFOLD_DEBUG
   try {
 #endif
-    if (IsConvex(polys, epsilon)) {  // fast path
+    if (allowConvex && IsConvex(polys, epsilon)) {  // fast path
       triangles = TriangulateConvex(polys);
     } else {
       EarClip triangulator(polys, epsilon);
@@ -961,18 +952,18 @@ std::vector<ivec3> TriangulateIdx(const PolygonsIdx &polys, double epsilon) {
       updatedEpsilon = triangulator.GetPrecision();
     }
 #ifdef MANIFOLD_DEBUG
-    if (params.intermediateChecks) {
+    if (ManifoldParams().intermediateChecks) {
       CheckTopology(triangles, polys);
-      if (!params.processOverlaps) {
+      if (!ManifoldParams().processOverlaps) {
         CheckGeometry(triangles, polys, 2 * updatedEpsilon);
       }
     }
-  } catch (const geometryErr &e) {
-    if (!params.suppressErrors) {
+  } catch (const geometryErr& e) {
+    if (!ManifoldParams().suppressErrors) {
       PrintFailure(e, polys, triangles, updatedEpsilon);
     }
     throw;
-  } catch (const std::exception &e) {
+  } catch (const std::exception& e) {
     PrintFailure(e, polys, triangles, updatedEpsilon);
     throw;
   }
@@ -989,22 +980,25 @@ std::vector<ivec3> TriangulateIdx(const PolygonsIdx &polys, double epsilon) {
  * polygons and/or holes.
  * @param epsilon The value of &epsilon;, bounding the uncertainty of the
  * input.
+ * @param allowConvex If true (default), the triangulator will use a fast
+ * triangulation if the input is convex, falling back to ear-clipping if not.
+ * The triangle quality may be lower, so set to false to disable this
+ * optimization.
  * @return std::vector<ivec3> The triangles, referencing the original
  * polygon points in order.
  */
-std::vector<ivec3> Triangulate(const Polygons &polygons, double epsilon) {
+std::vector<ivec3> Triangulate(const Polygons& polygons, double epsilon,
+                               bool allowConvex) {
   int idx = 0;
   PolygonsIdx polygonsIndexed;
-  for (const auto &poly : polygons) {
+  for (const auto& poly : polygons) {
     SimplePolygonIdx simpleIndexed;
-    for (const vec2 &polyVert : poly) {
+    for (const vec2& polyVert : poly) {
       simpleIndexed.push_back({polyVert, idx++});
     }
     polygonsIndexed.push_back(simpleIndexed);
   }
-  return TriangulateIdx(polygonsIndexed, epsilon);
+  return TriangulateIdx(polygonsIndexed, epsilon, allowConvex);
 }
 
-ExecutionParams &PolygonParams() { return params; }
-
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/properties.cpp b/thirdparty/manifold/src/properties.cpp
index 5b6403a6c1..d66b05595d 100644
--- a/thirdparty/manifold/src/properties.cpp
+++ b/thirdparty/manifold/src/properties.cpp
@@ -14,9 +14,13 @@
 
 #include <limits>
 
-#include "./impl.h"
-#include "./parallel.h"
-#include "./tri_dist.h"
+#if MANIFOLD_PAR == 1
+#include <tbb/combinable.h>
+#endif
+
+#include "impl.h"
+#include "parallel.h"
+#include "tri_dist.h"
 
 namespace {
 using namespace manifold;
@@ -64,48 +68,6 @@ struct CurvatureAngles {
   }
 };
 
-struct UpdateProperties {
-  VecView<ivec3> triProp;
-  VecView<double> properties;
-  VecView<uint8_t> counters;
-
-  VecView<const double> oldProperties;
-  VecView<const Halfedge> halfedge;
-  VecView<const double> meanCurvature;
-  VecView<const double> gaussianCurvature;
-  const int oldNumProp;
-  const int numProp;
-  const int gaussianIdx;
-  const int meanIdx;
-
-  void operator()(const size_t tri) {
-    for (const int i : {0, 1, 2}) {
-      const int vert = halfedge[3 * tri + i].startVert;
-      if (oldNumProp == 0) {
-        triProp[tri][i] = vert;
-      }
-      const int propVert = triProp[tri][i];
-
-      auto old = std::atomic_exchange(
-          reinterpret_cast<std::atomic<uint8_t>*>(&counters[propVert]),
-          static_cast<uint8_t>(1));
-      if (old == 1) continue;
-
-      for (int p = 0; p < oldNumProp; ++p) {
-        properties[numProp * propVert + p] =
-            oldProperties[oldNumProp * propVert + p];
-      }
-
-      if (gaussianIdx >= 0) {
-        properties[numProp * propVert + gaussianIdx] = gaussianCurvature[vert];
-      }
-      if (meanIdx >= 0) {
-        properties[numProp * propVert + meanIdx] = meanCurvature[vert];
-      }
-    }
-  }
-};
-
 struct CheckHalfedges {
   VecView<const Halfedge> halfedges;
 
@@ -138,33 +100,8 @@ struct CheckCCW {
     for (int i : {0, 1, 2})
       v[i] = projection * vertPos[halfedges[3 * face + i].startVert];
 
-    int ccw = CCW(v[0], v[1], v[2], std::abs(tol));
-    bool check = tol > 0 ? ccw >= 0 : ccw == 0;
-
-#ifdef MANIFOLD_DEBUG
-    if (tol > 0 && !check) {
-      vec2 v1 = v[1] - v[0];
-      vec2 v2 = v[2] - v[0];
-      double area = v1.x * v2.y - v1.y * v2.x;
-      double base2 = std::max(la::dot(v1, v1), la::dot(v2, v2));
-      double base = std::sqrt(base2);
-      vec3 V0 = vertPos[halfedges[3 * face].startVert];
-      vec3 V1 = vertPos[halfedges[3 * face + 1].startVert];
-      vec3 V2 = vertPos[halfedges[3 * face + 2].startVert];
-      vec3 norm = la::cross(V1 - V0, V2 - V0);
-      printf(
-          "Tri %ld does not match normal, approx height = %g, base = %g\n"
-          "tol = %g, area2 = %g, base2*tol2 = %g\n"
-          "normal = %g, %g, %g\n"
-          "norm = %g, %g, %g\nverts: %d, %d, %d\n",
-          static_cast<long>(face), area / base, base, tol, area * area,
-          base2 * tol * tol, triNormal[face].x, triNormal[face].y,
-          triNormal[face].z, norm.x, norm.y, norm.z,
-          halfedges[3 * face].startVert, halfedges[3 * face + 1].startVert,
-          halfedges[3 * face + 2].startVert);
-    }
-#endif
-    return check;
+    const int ccw = CCW(v[0], v[1], v[2], std::abs(tol));
+    return tol > 0 ? ccw >= 0 : ccw == 0;
   }
 };
 }  // namespace
@@ -211,55 +148,58 @@ std::mutex dump_lock;
  * Note that this is not checking for epsilon-validity.
  */
 bool Manifold::Impl::IsSelfIntersecting() const {
-  const double epsilonSq = epsilon_ * epsilon_;
+  const double ep = 2 * epsilon_;
+  const double epsilonSq = ep * ep;
   Vec<Box> faceBox;
   Vec<uint32_t> faceMorton;
   GetFaceBoxMorton(faceBox, faceMorton);
-  SparseIndices collisions = collider_.Collisions<true>(faceBox.cview());
 
-  const bool verbose = ManifoldParams().verbose;
-  return !all_of(countAt(0), countAt(collisions.size()), [&](size_t i) {
-    size_t x = collisions.Get(i, false);
-    size_t y = collisions.Get(i, true);
-    std::array<vec3, 3> tri_x, tri_y;
+  std::atomic<bool> intersecting(false);
+
+  auto f = [&](int tri0, int tri1) {
+    std::array<vec3, 3> triVerts0, triVerts1;
     for (int i : {0, 1, 2}) {
-      tri_x[i] = vertPos_[halfedge_[3 * x + i].startVert];
-      tri_y[i] = vertPos_[halfedge_[3 * y + i].startVert];
+      triVerts0[i] = vertPos_[halfedge_[3 * tri0 + i].startVert];
+      triVerts1[i] = vertPos_[halfedge_[3 * tri1 + i].startVert];
     }
-    // if triangles x and y share a vertex, return true to skip the
+    // if triangles tri0 and tri1 share a vertex, return true to skip the
     // check. we relax the sharing criteria a bit to allow for at most
     // distance epsilon squared
     for (int i : {0, 1, 2})
       for (int j : {0, 1, 2})
-        if (distance2(tri_x[i], tri_y[j]) <= epsilonSq) return true;
+        if (distance2(triVerts0[i], triVerts1[j]) <= epsilonSq) return;
 
-    if (DistanceTriangleTriangleSquared(tri_x, tri_y) == 0.0) {
+    if (DistanceTriangleTriangleSquared(triVerts0, triVerts1) == 0.0) {
       // try to move the triangles around the normal of the other face
-      std::array<vec3, 3> tmp_x, tmp_y;
-      for (int i : {0, 1, 2}) tmp_x[i] = tri_x[i] + epsilon_ * faceNormal_[y];
-      if (DistanceTriangleTriangleSquared(tmp_x, tri_y) > 0.0) return true;
-      for (int i : {0, 1, 2}) tmp_x[i] = tri_x[i] - epsilon_ * faceNormal_[y];
-      if (DistanceTriangleTriangleSquared(tmp_x, tri_y) > 0.0) return true;
-      for (int i : {0, 1, 2}) tmp_y[i] = tri_y[i] + epsilon_ * faceNormal_[x];
-      if (DistanceTriangleTriangleSquared(tri_x, tmp_y) > 0.0) return true;
-      for (int i : {0, 1, 2}) tmp_y[i] = tri_y[i] - epsilon_ * faceNormal_[x];
-      if (DistanceTriangleTriangleSquared(tri_x, tmp_y) > 0.0) return true;
+      std::array<vec3, 3> tmp0, tmp1;
+      for (int i : {0, 1, 2}) tmp0[i] = triVerts0[i] + ep * faceNormal_[tri1];
+      if (DistanceTriangleTriangleSquared(tmp0, triVerts1) > 0.0) return;
+      for (int i : {0, 1, 2}) tmp0[i] = triVerts0[i] - ep * faceNormal_[tri1];
+      if (DistanceTriangleTriangleSquared(tmp0, triVerts1) > 0.0) return;
+      for (int i : {0, 1, 2}) tmp1[i] = triVerts1[i] + ep * faceNormal_[tri0];
+      if (DistanceTriangleTriangleSquared(triVerts0, tmp1) > 0.0) return;
+      for (int i : {0, 1, 2}) tmp1[i] = triVerts1[i] - ep * faceNormal_[tri0];
+      if (DistanceTriangleTriangleSquared(triVerts0, tmp1) > 0.0) return;
 
 #ifdef MANIFOLD_DEBUG
-      if (verbose) {
+      if (ManifoldParams().verbose > 0) {
         dump_lock.lock();
         std::cout << "intersecting:" << std::endl;
-        for (int i : {0, 1, 2}) std::cout << tri_x[i] << " ";
+        for (int i : {0, 1, 2}) std::cout << triVerts0[i] << " ";
         std::cout << std::endl;
-        for (int i : {0, 1, 2}) std::cout << tri_y[i] << " ";
+        for (int i : {0, 1, 2}) std::cout << triVerts1[i] << " ";
         std::cout << std::endl;
         dump_lock.unlock();
       }
 #endif
-      return false;
+      intersecting.store(true);
     }
-    return true;
-  });
+  };
+
+  auto recorder = MakeSimpleRecorder(f);
+  collider_.Collisions<true>(faceBox.cview(), recorder);
+
+  return intersecting.load();
 }
 
 /**
@@ -335,20 +275,36 @@ void Manifold::Impl::CalculateCurvature(int gaussianIdx, int meanIdx) {
 
   const int oldNumProp = NumProp();
   const int numProp = std::max(oldNumProp, std::max(gaussianIdx, meanIdx) + 1);
-  const Vec<double> oldProperties = meshRelation_.properties;
-  meshRelation_.properties = Vec<double>(numProp * NumPropVert(), 0);
-  meshRelation_.numProp = numProp;
-  if (meshRelation_.triProperties.size() == 0) {
-    meshRelation_.triProperties.resize(NumTri());
-  }
+  const Vec<double> oldProperties = properties_;
+  properties_ = Vec<double>(numProp * NumPropVert(), 0);
+  numProp_ = numProp;
 
-  const Vec<uint8_t> counters(NumPropVert(), 0);
-  for_each_n(
-      policy, countAt(0_uz), NumTri(),
-      UpdateProperties({meshRelation_.triProperties, meshRelation_.properties,
-                        counters, oldProperties, halfedge_, vertMeanCurvature,
-                        vertGaussianCurvature, oldNumProp, numProp, gaussianIdx,
-                        meanIdx}));
+  Vec<uint8_t> counters(NumPropVert(), 0);
+  for_each_n(policy, countAt(0_uz), NumTri(), [&](const size_t tri) {
+    for (const int i : {0, 1, 2}) {
+      const Halfedge& edge = halfedge_[3 * tri + i];
+      const int vert = edge.startVert;
+      const int propVert = edge.propVert;
+
+      auto old = std::atomic_exchange(
+          reinterpret_cast<std::atomic<uint8_t>*>(&counters[propVert]),
+          static_cast<uint8_t>(1));
+      if (old == 1) continue;
+
+      for (int p = 0; p < oldNumProp; ++p) {
+        properties_[numProp * propVert + p] =
+            oldProperties[oldNumProp * propVert + p];
+      }
+
+      if (gaussianIdx >= 0) {
+        properties_[numProp * propVert + gaussianIdx] =
+            vertGaussianCurvature[vert];
+      }
+      if (meanIdx >= 0) {
+        properties_[numProp * propVert + meanIdx] = vertMeanCurvature[vert];
+      }
+    }
+  });
 }
 
 /**
@@ -404,6 +360,36 @@ bool Manifold::Impl::IsIndexInBounds(VecView<const ivec3> triVerts) const {
   return minmax[0] >= 0 && minmax[1] < static_cast<int>(NumVert());
 }
 
+struct MinDistanceRecorder {
+  using Local = double;
+  const Manifold::Impl &self, &other;
+#if MANIFOLD_PAR == 1
+  tbb::combinable<double> store = tbb::combinable<double>(
+      []() { return std::numeric_limits<double>::infinity(); });
+  Local& local() { return store.local(); }
+  double get() {
+    double result = std::numeric_limits<double>::infinity();
+    store.combine_each([&](double& val) { result = std::min(result, val); });
+    return result;
+  }
+#else
+  double result = std::numeric_limits<double>::infinity();
+  Local& local() { return result; }
+  double get() { return result; }
+#endif
+
+  void record(int triOther, int tri, double& minDistance) {
+    std::array<vec3, 3> p;
+    std::array<vec3, 3> q;
+
+    for (const int j : {0, 1, 2}) {
+      p[j] = self.vertPos_[self.halfedge_[3 * tri + j].startVert];
+      q[j] = other.vertPos_[other.halfedge_[3 * triOther + j].startVert];
+    }
+    minDistance = std::min(minDistance, DistanceTriangleTriangleSquared(p, q));
+  }
+};
+
 /*
  * Returns the minimum gap between two manifolds. Returns a double between
  * 0 and searchLength.
@@ -422,26 +408,11 @@ double Manifold::Impl::MinGap(const Manifold::Impl& other,
                          box.max + vec3(searchLength));
             });
 
-  SparseIndices collisions = collider_.Collisions(faceBoxOther.cview());
-
-  double minDistanceSquared = transform_reduce(
-      countAt(0_uz), countAt(collisions.size()), searchLength * searchLength,
-      [](double a, double b) { return std::min(a, b); },
-      [&collisions, this, &other](int i) {
-        const int tri = collisions.Get(i, 1);
-        const int triOther = collisions.Get(i, 0);
-
-        std::array<vec3, 3> p;
-        std::array<vec3, 3> q;
-
-        for (const int j : {0, 1, 2}) {
-          p[j] = vertPos_[halfedge_[3 * tri + j].startVert];
-          q[j] = other.vertPos_[other.halfedge_[3 * triOther + j].startVert];
-        }
-
-        return DistanceTriangleTriangleSquared(p, q);
-      });
-
+  MinDistanceRecorder recorder{*this, other};
+  collider_.Collisions<false, Box, MinDistanceRecorder>(faceBoxOther.cview(),
+                                                        recorder, false);
+  double minDistanceSquared =
+      std::min(recorder.get(), searchLength * searchLength);
   return sqrt(minDistanceSquared);
 };
 
diff --git a/thirdparty/manifold/src/quickhull.cpp b/thirdparty/manifold/src/quickhull.cpp
index be2b89e1ca..54733d6807 100644
--- a/thirdparty/manifold/src/quickhull.cpp
+++ b/thirdparty/manifold/src/quickhull.cpp
@@ -20,7 +20,7 @@
 #include <algorithm>
 #include <limits>
 
-#include "./impl.h"
+#include "impl.h"
 
 namespace manifold {
 
@@ -289,7 +289,7 @@ std::pair<Vec<Halfedge>, Vec<vec3>> QuickHull::buildMesh(double epsilon) {
   for_each(
       autoPolicy(halfedges.size()), halfedges.begin(), halfedges.end(),
       [&](Halfedge& he) { he.pairedHalfedge = mapping[he.pairedHalfedge]; });
-  counts.resize(originalVertexData.size() + 1);
+  counts.resize_nofill(originalVertexData.size() + 1);
   fill(counts.begin(), counts.end(), 0);
 
   // remove unused vertices
@@ -804,7 +804,7 @@ void QuickHull::setupInitialTetrahedron() {
 
 std::unique_ptr<Vec<size_t>> QuickHull::getIndexVectorFromPool() {
   auto r = indexVectorPool.get();
-  r->resize(0);
+  r->clear();
   return r;
 }
 
@@ -851,10 +851,9 @@ void Manifold::Impl::Hull(VecView<vec3> vertPos) {
   std::tie(halfedge_, vertPos_) = qh.buildMesh();
   CalculateBBox();
   SetEpsilon();
-  CalculateNormals();
   InitializeOriginal();
   Finish();
-  CreateFaces();
+  MarkCoplanar();
 }
 
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/quickhull.h b/thirdparty/manifold/src/quickhull.h
index 3f90575097..1167143c6a 100644
--- a/thirdparty/manifold/src/quickhull.h
+++ b/thirdparty/manifold/src/quickhull.h
@@ -58,8 +58,8 @@
 #include <deque>
 #include <vector>
 
-#include "./shared.h"
-#include "./vec.h"
+#include "shared.h"
+#include "vec.h"
 
 namespace manifold {
 
diff --git a/thirdparty/manifold/src/sdf.cpp b/thirdparty/manifold/src/sdf.cpp
index ad95b9b6fe..00bd40f81c 100644
--- a/thirdparty/manifold/src/sdf.cpp
+++ b/thirdparty/manifold/src/sdf.cpp
@@ -12,12 +12,12 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "./hashtable.h"
-#include "./impl.h"
-#include "./parallel.h"
-#include "./utils.h"
-#include "./vec.h"
+#include "hashtable.h"
+#include "impl.h"
 #include "manifold/manifold.h"
+#include "parallel.h"
+#include "utils.h"
+#include "vec.h"
 
 namespace {
 using namespace manifold;
@@ -95,13 +95,14 @@ ivec4 Neighbor(ivec4 base, int i) {
   return neighborIndex;
 }
 
-Uint64 EncodeIndex(ivec4 gridPos, ivec3 gridPow) {
-  return static_cast<Uint64>(gridPos.w) | static_cast<Uint64>(gridPos.z) << 1 |
-         static_cast<Uint64>(gridPos.y) << (1 + gridPow.z) |
-         static_cast<Uint64>(gridPos.x) << (1 + gridPow.z + gridPow.y);
+uint64_t EncodeIndex(ivec4 gridPos, ivec3 gridPow) {
+  return static_cast<uint64_t>(gridPos.w) |
+         static_cast<uint64_t>(gridPos.z) << 1 |
+         static_cast<uint64_t>(gridPos.y) << (1 + gridPow.z) |
+         static_cast<uint64_t>(gridPos.x) << (1 + gridPow.z + gridPow.y);
 }
 
-ivec4 DecodeIndex(Uint64 idx, ivec3 gridPow) {
+ivec4 DecodeIndex(uint64_t idx, ivec3 gridPow) {
   ivec4 gridPos;
   gridPos.w = idx & 1;
   idx = idx >> 1;
@@ -211,7 +212,7 @@ struct NearSurface {
   const double level;
   const double tol;
 
-  inline void operator()(Uint64 index) {
+  inline void operator()(uint64_t index) {
     ZoneScoped;
     if (gridVerts.Full()) return;
 
@@ -296,7 +297,7 @@ struct ComputeVerts {
 
   void operator()(int idx) {
     ZoneScoped;
-    Uint64 baseKey = gridVerts.KeyAt(idx);
+    uint64_t baseKey = gridVerts.KeyAt(idx);
     if (baseKey == kOpen) return;
 
     GridVert& gridVert = gridVerts.At(idx);
@@ -358,7 +359,7 @@ struct BuildTris {
 
   void operator()(int idx) {
     ZoneScoped;
-    Uint64 baseKey = gridVerts.KeyAt(idx);
+    uint64_t baseKey = gridVerts.KeyAt(idx);
     if (baseKey == kOpen) return;
 
     const GridVert& base = gridVerts.At(idx);
@@ -467,7 +468,7 @@ Manifold Manifold::LevelSet(std::function<double(vec3)> sdf, Box bounds,
   const vec3 spacing = dim / (vec3(gridSize - 1));
 
   const ivec3 gridPow(la::log2(gridSize + 2) + 1);
-  const Uint64 maxIndex = EncodeIndex(ivec4(gridSize + 2, 1), gridPow);
+  const uint64_t maxIndex = EncodeIndex(ivec4(gridSize + 2, 1), gridPow);
 
   // Parallel policies violate will crash language runtimes with runtime locks
   // that expect to not be called back by unregistered threads. This allows
@@ -479,15 +480,15 @@ Manifold Manifold::LevelSet(std::function<double(vec3)> sdf, Box bounds,
   Vec<double> voxels(maxIndex);
   for_each_n(
       pol, countAt(0_uz), maxIndex,
-      [&voxels, sdf, level, origin, spacing, gridSize, gridPow](Uint64 idx) {
+      [&voxels, sdf, level, origin, spacing, gridSize, gridPow](uint64_t idx) {
         voxels[idx] = BoundedSDF(DecodeIndex(idx, gridPow) - kVoxelOffset,
                                  origin, spacing, gridSize, level, sdf);
       });
 
   size_t tableSize = std::min(
-      2 * maxIndex, static_cast<Uint64>(10 * la::pow(maxIndex, 0.667)));
+      2 * maxIndex, static_cast<uint64_t>(10 * la::pow(maxIndex, 0.667)));
   HashTable<GridVert> gridVerts(tableSize);
-  vertPos.resize(gridVerts.Size() * 7);
+  vertPos.resize_nofill(gridVerts.Size() * 7);
 
   while (1) {
     Vec<int> index(1, 0);
@@ -497,7 +498,7 @@ Manifold Manifold::LevelSet(std::function<double(vec3)> sdf, Box bounds,
 
     if (gridVerts.Full()) {  // Resize HashTable
       const vec3 lastVert = vertPos[index[0] - 1];
-      const Uint64 lastIndex =
+      const uint64_t lastIndex =
           EncodeIndex(ivec4(ivec3((lastVert - origin) / spacing), 1), gridPow);
       const double ratio = static_cast<double>(maxIndex) / lastIndex;
 
@@ -529,6 +530,7 @@ Manifold Manifold::LevelSet(std::function<double(vec3)> sdf, Box bounds,
   pImpl_->RemoveUnreferencedVerts();
   pImpl_->Finish();
   pImpl_->InitializeOriginal();
+  pImpl_->MarkCoplanar();
   return Manifold(pImpl_);
 }
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/shared.h b/thirdparty/manifold/src/shared.h
index 3f3336141d..7a28c41421 100644
--- a/thirdparty/manifold/src/shared.h
+++ b/thirdparty/manifold/src/shared.h
@@ -14,10 +14,9 @@
 
 #pragma once
 
-#include "./parallel.h"
-#include "./sparse.h"
-#include "./utils.h"
-#include "./vec.h"
+#include "parallel.h"
+#include "utils.h"
+#include "vec.h"
 
 namespace manifold {
 
@@ -120,6 +119,7 @@ inline vec3 GetBarycentric(const vec3& v, const mat3& triPos,
 struct Halfedge {
   int startVert, endVert;
   int pairedHalfedge;
+  int propVert;
   bool IsForward() const { return startVert < endVert; }
   bool operator<(const Halfedge& other) const {
     return startVert == other.startVert ? endVert < other.endVert
@@ -142,12 +142,13 @@ struct TriRef {
   int originalID;
   /// Probably the triangle index of the original triangle this was part of:
   /// Mesh.triVerts[tri], but it's an input, so just pass it along unchanged.
-  int tri;
-  /// Triangles with the same face ID are coplanar.
   int faceID;
+  /// Triangles with the same coplanar ID are coplanar.
+  int coplanarID;
 
   bool SameFace(const TriRef& other) const {
-    return meshID == other.meshID && faceID == other.faceID;
+    return meshID == other.meshID && coplanarID == other.coplanarID &&
+           faceID == other.faceID;
   }
 };
 
@@ -188,22 +189,12 @@ Vec<TmpEdge> inline CreateTmpEdges(const Vec<Halfedge>& halfedge) {
   return edges;
 }
 
-template <const bool inverted>
-struct ReindexEdge {
-  VecView<const TmpEdge> edges;
-  SparseIndices& indices;
-
-  void operator()(size_t i) {
-    int& edge = indices.Get(i, inverted);
-    edge = edges[edge].halfedgeIdx;
-  }
-};
-
 #ifdef MANIFOLD_DEBUG
 inline std::ostream& operator<<(std::ostream& stream, const Halfedge& edge) {
   return stream << "startVert = " << edge.startVert
                 << ", endVert = " << edge.endVert
-                << ", pairedHalfedge = " << edge.pairedHalfedge;
+                << ", pairedHalfedge = " << edge.pairedHalfedge
+                << ", propVert = " << edge.propVert;
 }
 
 inline std::ostream& operator<<(std::ostream& stream, const Barycentric& bary) {
@@ -212,8 +203,9 @@ inline std::ostream& operator<<(std::ostream& stream, const Barycentric& bary) {
 
 inline std::ostream& operator<<(std::ostream& stream, const TriRef& ref) {
   return stream << "meshID: " << ref.meshID
-                << ", originalID: " << ref.originalID << ", tri: " << ref.tri
-                << ", faceID: " << ref.faceID;
+                << ", originalID: " << ref.originalID
+                << ", faceID: " << ref.faceID
+                << ", coplanarID: " << ref.coplanarID;
 }
 #endif
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/smoothing.cpp b/thirdparty/manifold/src/smoothing.cpp
index 57d81b4623..bf8903dfb3 100644
--- a/thirdparty/manifold/src/smoothing.cpp
+++ b/thirdparty/manifold/src/smoothing.cpp
@@ -12,8 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "./impl.h"
-#include "./parallel.h"
+#include "impl.h"
+#include "parallel.h"
 
 namespace {
 using namespace manifold;
@@ -254,13 +254,10 @@ namespace manifold {
  * normalIdx shows the beginning of where normals are stored in the properties.
  */
 vec3 Manifold::Impl::GetNormal(int halfedge, int normalIdx) const {
-  const int tri = halfedge / 3;
-  const int j = halfedge % 3;
-  const int prop = meshRelation_.triProperties[tri][j];
+  const int prop = halfedge_[halfedge].propVert;
   vec3 normal;
   for (const int i : {0, 1, 2}) {
-    normal[i] =
-        meshRelation_.properties[prop * meshRelation_.numProp + normalIdx + i];
+    normal[i] = properties_[prop * numProp_ + normalIdx + i];
   }
   return normal;
 }
@@ -320,12 +317,12 @@ bool Manifold::Impl::IsMarkedInsideQuad(int halfedge) const {
 
 // sharpenedEdges are referenced to the input Mesh, but the triangles have
 // been sorted in creating the Manifold, so the indices are converted using
-// meshRelation_.
+// meshRelation_.faceID, which temporarily holds the mapping.
 std::vector<Smoothness> Manifold::Impl::UpdateSharpenedEdges(
     const std::vector<Smoothness>& sharpenedEdges) const {
   std::unordered_map<int, int> oldHalfedge2New;
   for (size_t tri = 0; tri < NumTri(); ++tri) {
-    int oldTri = meshRelation_.triRef[tri].tri;
+    int oldTri = meshRelation_.triRef[tri].faceID;
     for (int i : {0, 1, 2}) oldHalfedge2New[3 * oldTri + i] = 3 * tri + i;
   }
   std::vector<Smoothness> newSharp = sharpenedEdges;
@@ -371,7 +368,7 @@ Vec<bool> Manifold::Impl::FlatFaces() const {
 // gets -1, and if there are more than one it gets -2.
 Vec<int> Manifold::Impl::VertFlatFace(const Vec<bool>& flatFaces) const {
   Vec<int> vertFlatFace(NumVert(), -1);
-  Vec<TriRef> vertRef(NumVert(), {-1, -1, -1});
+  Vec<TriRef> vertRef(NumVert(), {-1, -1, -1, -1});
   for (size_t tri = 0; tri < NumTri(); ++tri) {
     if (flatFaces[tri]) {
       for (const int j : {0, 1, 2}) {
@@ -439,7 +436,6 @@ void Manifold::Impl::SetNormals(int normalIdx, double minSharpAngle) {
   if (normalIdx < 0) return;
 
   const int oldNumProp = NumProp();
-  const int numTri = NumTri();
 
   Vec<bool> triIsFlatFace = FlatFaces();
   Vec<int> vertFlatFace = VertFlatFace(triIsFlatFace);
@@ -470,164 +466,153 @@ void Manifold::Impl::SetNormals(int normalIdx, double minSharpAngle) {
 
   const int numProp = std::max(oldNumProp, normalIdx + 3);
   Vec<double> oldProperties(numProp * NumPropVert(), 0);
-  meshRelation_.properties.swap(oldProperties);
-  meshRelation_.numProp = numProp;
-  if (meshRelation_.triProperties.size() == 0) {
-    meshRelation_.triProperties.resize(numTri);
-    for_each_n(autoPolicy(numTri, 1e5), countAt(0), numTri, [this](int tri) {
-      for (const int j : {0, 1, 2})
-        meshRelation_.triProperties[tri][j] = halfedge_[3 * tri + j].startVert;
-    });
-  }
-  Vec<ivec3> oldTriProp(numTri, {-1, -1, -1});
-  meshRelation_.triProperties.swap(oldTriProp);
+  properties_.swap(oldProperties);
+  numProp_ = numProp;
 
-  for (int tri = 0; tri < numTri; ++tri) {
-    for (const int i : {0, 1, 2}) {
-      if (meshRelation_.triProperties[tri][i] >= 0) continue;
-      int startEdge = 3 * tri + i;
-      const int vert = halfedge_[startEdge].startVert;
+  Vec<int> oldHalfedgeProp(halfedge_.size());
+  for_each_n(autoPolicy(halfedge_.size(), 1e5), countAt(0), halfedge_.size(),
+             [this, &oldHalfedgeProp](int i) {
+               oldHalfedgeProp[i] = halfedge_[i].propVert;
+               halfedge_[i].propVert = -1;
+             });
 
-      if (vertNumSharp[vert] < 2) {  // vertex has single normal
-        const vec3 normal = vertFlatFace[vert] >= 0
-                                ? faceNormal_[vertFlatFace[vert]]
-                                : vertNormal_[vert];
-        int lastProp = -1;
-        ForVert(startEdge, [&](int current) {
-          const int thisTri = current / 3;
-          const int j = current - 3 * thisTri;
-          const int prop = oldTriProp[thisTri][j];
-          meshRelation_.triProperties[thisTri][j] = prop;
-          if (prop == lastProp) return;
-          lastProp = prop;
-          // update property vertex
-          auto start = oldProperties.begin() + prop * oldNumProp;
+  const int numEdge = halfedge_.size();
+  for (int startEdge = 0; startEdge < numEdge; ++startEdge) {
+    if (halfedge_[startEdge].propVert >= 0) continue;
+    const int vert = halfedge_[startEdge].startVert;
+
+    if (vertNumSharp[vert] < 2) {  // vertex has single normal
+      const vec3 normal = vertFlatFace[vert] >= 0
+                              ? faceNormal_[vertFlatFace[vert]]
+                              : vertNormal_[vert];
+      int lastProp = -1;
+      ForVert(startEdge, [&](int current) {
+        const int prop = oldHalfedgeProp[current];
+        halfedge_[current].propVert = prop;
+        if (prop == lastProp) return;
+        lastProp = prop;
+        // update property vertex
+        auto start = oldProperties.begin() + prop * oldNumProp;
+        std::copy(start, start + oldNumProp,
+                  properties_.begin() + prop * numProp);
+        for (const int i : {0, 1, 2})
+          properties_[prop * numProp + normalIdx + i] = normal[i];
+      });
+    } else {  // vertex has multiple normals
+      const vec3 centerPos = vertPos_[vert];
+      // Length degree
+      std::vector<int> group;
+      // Length number of normals
+      std::vector<vec3> normals;
+      int current = startEdge;
+      int prevFace = current / 3;
+
+      do {  // find a sharp edge to start on
+        int next = NextHalfedge(halfedge_[current].pairedHalfedge);
+        const int face = next / 3;
+
+        const double dihedral = degrees(
+            std::acos(la::dot(faceNormal_[face], faceNormal_[prevFace])));
+        if (dihedral > minSharpAngle ||
+            triIsFlatFace[face] != triIsFlatFace[prevFace] ||
+            (triIsFlatFace[face] && triIsFlatFace[prevFace] &&
+             !meshRelation_.triRef[face].SameFace(
+                 meshRelation_.triRef[prevFace]))) {
+          break;
+        }
+        current = next;
+        prevFace = face;
+      } while (current != startEdge);
+
+      const int endEdge = current;
+
+      struct FaceEdge {
+        int face;
+        vec3 edgeVec;
+      };
+
+      // calculate pseudo-normals between each sharp edge
+      ForVert<FaceEdge>(
+          endEdge,
+          [this, centerPos, &vertNumSharp, &vertFlatFace](int current) {
+            if (IsInsideQuad(current)) {
+              return FaceEdge({current / 3, vec3(NAN)});
+            }
+            const int vert = halfedge_[current].endVert;
+            vec3 pos = vertPos_[vert];
+            if (vertNumSharp[vert] < 2) {
+              // opposite vert has fixed normal
+              const vec3 normal = vertFlatFace[vert] >= 0
+                                      ? faceNormal_[vertFlatFace[vert]]
+                                      : vertNormal_[vert];
+              // Flair out the normal we're calculating to give the edge a
+              // more constant curvature to meet the opposite normal. Achieve
+              // this by pointing the tangent toward the opposite bezier
+              // control point instead of the vert itself.
+              pos += vec3(
+                  TangentFromNormal(normal, halfedge_[current].pairedHalfedge));
+            }
+            return FaceEdge({current / 3, SafeNormalize(pos - centerPos)});
+          },
+          [this, &triIsFlatFace, &normals, &group, minSharpAngle](
+              int, const FaceEdge& here, FaceEdge& next) {
+            const double dihedral = degrees(std::acos(
+                la::dot(faceNormal_[here.face], faceNormal_[next.face])));
+            if (dihedral > minSharpAngle ||
+                triIsFlatFace[here.face] != triIsFlatFace[next.face] ||
+                (triIsFlatFace[here.face] && triIsFlatFace[next.face] &&
+                 !meshRelation_.triRef[here.face].SameFace(
+                     meshRelation_.triRef[next.face]))) {
+              normals.push_back(vec3(0.0));
+            }
+            group.push_back(normals.size() - 1);
+            if (std::isfinite(next.edgeVec.x)) {
+              normals.back() +=
+                  SafeNormalize(la::cross(next.edgeVec, here.edgeVec)) *
+                  AngleBetween(here.edgeVec, next.edgeVec);
+            } else {
+              next.edgeVec = here.edgeVec;
+            }
+          });
+
+      for (auto& normal : normals) {
+        normal = SafeNormalize(normal);
+      }
+
+      int lastGroup = 0;
+      int lastProp = -1;
+      int newProp = -1;
+      int idx = 0;
+      ForVert(endEdge, [&](int current1) {
+        const int prop = oldHalfedgeProp[current1];
+        auto start = oldProperties.begin() + prop * oldNumProp;
+
+        if (group[idx] != lastGroup && group[idx] != 0 && prop == lastProp) {
+          // split property vertex, duplicating but with an updated normal
+          lastGroup = group[idx];
+          newProp = NumPropVert();
+          properties_.resize(properties_.size() + numProp);
           std::copy(start, start + oldNumProp,
-                    meshRelation_.properties.begin() + prop * numProp);
-          for (const int i : {0, 1, 2})
-            meshRelation_.properties[prop * numProp + normalIdx + i] =
-                normal[i];
-        });
-      } else {  // vertex has multiple normals
-        const vec3 centerPos = vertPos_[vert];
-        // Length degree
-        std::vector<int> group;
-        // Length number of normals
-        std::vector<vec3> normals;
-        int current = startEdge;
-        int prevFace = current / 3;
-
-        do {  // find a sharp edge to start on
-          int next = NextHalfedge(halfedge_[current].pairedHalfedge);
-          const int face = next / 3;
-
-          const double dihedral = degrees(
-              std::acos(la::dot(faceNormal_[face], faceNormal_[prevFace])));
-          if (dihedral > minSharpAngle ||
-              triIsFlatFace[face] != triIsFlatFace[prevFace] ||
-              (triIsFlatFace[face] && triIsFlatFace[prevFace] &&
-               !meshRelation_.triRef[face].SameFace(
-                   meshRelation_.triRef[prevFace]))) {
-            break;
+                    properties_.begin() + newProp * numProp);
+          for (const int i : {0, 1, 2}) {
+            properties_[newProp * numProp + normalIdx + i] =
+                normals[group[idx]][i];
           }
-          current = next;
-          prevFace = face;
-        } while (current != startEdge);
-
-        const int endEdge = current;
-
-        struct FaceEdge {
-          int face;
-          vec3 edgeVec;
-        };
-
-        // calculate pseudo-normals between each sharp edge
-        ForVert<FaceEdge>(
-            endEdge,
-            [this, centerPos, &vertNumSharp, &vertFlatFace](int current) {
-              if (IsInsideQuad(current)) {
-                return FaceEdge({current / 3, vec3(NAN)});
-              }
-              const int vert = halfedge_[current].endVert;
-              vec3 pos = vertPos_[vert];
-              const vec3 edgeVec = centerPos - pos;
-              if (vertNumSharp[vert] < 2) {
-                // opposite vert has fixed normal
-                const vec3 normal = vertFlatFace[vert] >= 0
-                                        ? faceNormal_[vertFlatFace[vert]]
-                                        : vertNormal_[vert];
-                // Flair out the normal we're calculating to give the edge a
-                // more constant curvature to meet the opposite normal. Achieve
-                // this by pointing the tangent toward the opposite bezier
-                // control point instead of the vert itself.
-                pos += vec3(TangentFromNormal(
-                    normal, halfedge_[current].pairedHalfedge));
-              }
-              return FaceEdge({current / 3, SafeNormalize(pos - centerPos)});
-            },
-            [this, &triIsFlatFace, &normals, &group, minSharpAngle](
-                int current, const FaceEdge& here, FaceEdge& next) {
-              const double dihedral = degrees(std::acos(
-                  la::dot(faceNormal_[here.face], faceNormal_[next.face])));
-              if (dihedral > minSharpAngle ||
-                  triIsFlatFace[here.face] != triIsFlatFace[next.face] ||
-                  (triIsFlatFace[here.face] && triIsFlatFace[next.face] &&
-                   !meshRelation_.triRef[here.face].SameFace(
-                       meshRelation_.triRef[next.face]))) {
-                normals.push_back(vec3(0.0));
-              }
-              group.push_back(normals.size() - 1);
-              if (std::isfinite(next.edgeVec.x)) {
-                normals.back() +=
-                    SafeNormalize(la::cross(next.edgeVec, here.edgeVec)) *
-                    AngleBetween(here.edgeVec, next.edgeVec);
-              } else {
-                next.edgeVec = here.edgeVec;
-              }
-            });
-
-        for (auto& normal : normals) {
-          normal = SafeNormalize(normal);
+        } else if (prop != lastProp) {
+          // update property vertex
+          lastProp = prop;
+          newProp = prop;
+          std::copy(start, start + oldNumProp,
+                    properties_.begin() + prop * numProp);
+          for (const int i : {0, 1, 2})
+            properties_[prop * numProp + normalIdx + i] =
+                normals[group[idx]][i];
         }
 
-        int lastGroup = 0;
-        int lastProp = -1;
-        int newProp = -1;
-        int idx = 0;
-        ForVert(endEdge, [&](int current1) {
-          const int thisTri = current1 / 3;
-          const int j = current1 - 3 * thisTri;
-          const int prop = oldTriProp[thisTri][j];
-          auto start = oldProperties.begin() + prop * oldNumProp;
-
-          if (group[idx] != lastGroup && group[idx] != 0 && prop == lastProp) {
-            // split property vertex, duplicating but with an updated normal
-            lastGroup = group[idx];
-            newProp = NumPropVert();
-            meshRelation_.properties.resize(meshRelation_.properties.size() +
-                                            numProp);
-            std::copy(start, start + oldNumProp,
-                      meshRelation_.properties.begin() + newProp * numProp);
-            for (const int i : {0, 1, 2}) {
-              meshRelation_.properties[newProp * numProp + normalIdx + i] =
-                  normals[group[idx]][i];
-            }
-          } else if (prop != lastProp) {
-            // update property vertex
-            lastProp = prop;
-            newProp = prop;
-            std::copy(start, start + oldNumProp,
-                      meshRelation_.properties.begin() + prop * numProp);
-            for (const int i : {0, 1, 2})
-              meshRelation_.properties[prop * numProp + normalIdx + i] =
-                  normals[group[idx]][i];
-          }
-
-          // point to updated property vertex
-          meshRelation_.triProperties[thisTri][j] = newProp;
-          ++idx;
-        });
-      }
+        // point to updated property vertex
+        halfedge_[current1].propVert = newProp;
+        ++idx;
+      });
     }
   }
 }
@@ -770,7 +755,7 @@ void Manifold::Impl::CreateTangents(int normalIdx) {
   ZoneScoped;
   const int numVert = NumVert();
   const int numHalfedge = halfedge_.size();
-  halfedgeTangent_.resize(0);
+  halfedgeTangent_.clear();
   Vec<vec4> tangent(numHalfedge);
   Vec<bool> fixedHalfedge(numHalfedge, false);
 
@@ -854,7 +839,7 @@ void Manifold::Impl::CreateTangents(int normalIdx) {
 void Manifold::Impl::CreateTangents(std::vector<Smoothness> sharpenedEdges) {
   ZoneScoped;
   const int numHalfedge = halfedge_.size();
-  halfedgeTangent_.resize(0);
+  halfedgeTangent_.clear();
   Vec<vec4> tangent(numHalfedge);
   Vec<bool> fixedHalfedge(numHalfedge, false);
 
@@ -994,9 +979,11 @@ void Manifold::Impl::Refine(std::function<int(vec3, vec4, vec4)> edgeDivisions,
                InterpTri({vertPos_, vertBary, &old}));
   }
 
-  halfedgeTangent_.resize(0);
+  halfedgeTangent_.clear();
   Finish();
-  CreateFaces();
+  if (old.halfedgeTangent_.size() == old.halfedge_.size()) {
+    MarkCoplanar();
+  }
   meshRelation_.originalID = -1;
 }
 
diff --git a/thirdparty/manifold/src/sort.cpp b/thirdparty/manifold/src/sort.cpp
index f394aa5266..691e21cc9e 100644
--- a/thirdparty/manifold/src/sort.cpp
+++ b/thirdparty/manifold/src/sort.cpp
@@ -15,8 +15,9 @@
 #include <atomic>
 #include <set>
 
-#include "./impl.h"
-#include "./parallel.h"
+#include "impl.h"
+#include "parallel.h"
+#include "shared.h"
 
 namespace {
 using namespace manifold;
@@ -31,37 +32,6 @@ uint32_t MortonCode(vec3 position, Box bBox) {
   return Collider::MortonCode(position, bBox);
 }
 
-struct Reindex {
-  VecView<const int> indexInv;
-
-  void operator()(Halfedge& edge) {
-    if (edge.startVert < 0) return;
-    edge.startVert = indexInv[edge.startVert];
-    edge.endVert = indexInv[edge.endVert];
-  }
-};
-
-struct MarkProp {
-  VecView<int> keep;
-
-  void operator()(ivec3 triProp) {
-    for (const int i : {0, 1, 2}) {
-      reinterpret_cast<std::atomic<int>*>(&keep[triProp[i]])
-          ->store(1, std::memory_order_relaxed);
-    }
-  }
-};
-
-struct ReindexProps {
-  VecView<const int> old2new;
-
-  void operator()(ivec3& triProp) {
-    for (const int i : {0, 1, 2}) {
-      triProp[i] = old2new[triProp[i]];
-    }
-  }
-};
-
 struct ReindexFace {
   VecView<Halfedge> halfedge;
   VecView<vec4> halfedgeTangent;
@@ -180,18 +150,20 @@ bool MergeMeshGLP(MeshGLP<Precision, I>& mesh) {
   Permute(vertMorton, vertNew2Old);
   Permute(vertBox, vertNew2Old);
   Permute(openVerts, vertNew2Old);
-  Collider collider(vertBox, vertMorton);
-  SparseIndices toMerge = collider.Collisions<true>(vertBox.cview());
 
+  Collider collider(vertBox, vertMorton);
   UnionFind<> uf(numVert);
+
+  auto f = [&uf, &openVerts](int a, int b) {
+    return uf.unionXY(openVerts[a], openVerts[b]);
+  };
+  auto recorder = MakeSimpleRecorder(f);
+  collider.Collisions<true>(vertBox.cview(), recorder, false);
+
   for (size_t i = 0; i < mesh.mergeFromVert.size(); ++i) {
     uf.unionXY(static_cast<int>(mesh.mergeFromVert[i]),
                static_cast<int>(mesh.mergeToVert[i]));
   }
-  for (size_t i = 0; i < toMerge.size(); ++i) {
-    uf.unionXY(openVerts[toMerge.Get(i, false)],
-               openVerts[toMerge.Get(i, true)]);
-  }
 
   mesh.mergeToVert.clear();
   mesh.mergeFromVert.clear();
@@ -221,7 +193,7 @@ void Manifold::Impl::Finish() {
   SetEpsilon(epsilon_);
   if (!bBox_.IsFinite()) {
     // Decimated out of existence - early out.
-    MarkFailure(Error::NoError);
+    MakeEmpty(Error::NoError);
     return;
   }
 
@@ -237,31 +209,33 @@ void Manifold::Impl::Finish() {
                "Not an even number of faces after sorting faces!");
 
 #ifdef MANIFOLD_DEBUG
-  auto MaxOrMinus = [](int a, int b) {
-    return std::min(a, b) < 0 ? -1 : std::max(a, b);
-  };
-  int face = 0;
-  Halfedge extrema = {0, 0, 0};
-  for (size_t i = 0; i < halfedge_.size(); i++) {
-    Halfedge e = halfedge_[i];
-    if (!e.IsForward()) std::swap(e.startVert, e.endVert);
-    extrema.startVert = std::min(extrema.startVert, e.startVert);
-    extrema.endVert = std::min(extrema.endVert, e.endVert);
-    extrema.pairedHalfedge =
-        MaxOrMinus(extrema.pairedHalfedge, e.pairedHalfedge);
-    face = MaxOrMinus(face, i / 3);
+  if (ManifoldParams().intermediateChecks) {
+    auto MaxOrMinus = [](int a, int b) {
+      return std::min(a, b) < 0 ? -1 : std::max(a, b);
+    };
+    int face = 0;
+    Halfedge extrema = {0, 0, 0};
+    for (size_t i = 0; i < halfedge_.size(); i++) {
+      Halfedge e = halfedge_[i];
+      if (!e.IsForward()) std::swap(e.startVert, e.endVert);
+      extrema.startVert = std::min(extrema.startVert, e.startVert);
+      extrema.endVert = std::min(extrema.endVert, e.endVert);
+      extrema.pairedHalfedge =
+          MaxOrMinus(extrema.pairedHalfedge, e.pairedHalfedge);
+      face = MaxOrMinus(face, i / 3);
+    }
+    DEBUG_ASSERT(extrema.startVert >= 0, topologyErr,
+                 "Vertex index is negative!");
+    DEBUG_ASSERT(extrema.endVert < static_cast<int>(NumVert()), topologyErr,
+                 "Vertex index exceeds number of verts!");
+    DEBUG_ASSERT(extrema.pairedHalfedge >= 0, topologyErr,
+                 "Halfedge index is negative!");
+    DEBUG_ASSERT(extrema.pairedHalfedge < 2 * static_cast<int>(NumEdge()),
+                 topologyErr, "Halfedge index exceeds number of halfedges!");
+    DEBUG_ASSERT(face >= 0, topologyErr, "Face index is negative!");
+    DEBUG_ASSERT(face < static_cast<int>(NumTri()), topologyErr,
+                 "Face index exceeds number of faces!");
   }
-  DEBUG_ASSERT(extrema.startVert >= 0, topologyErr,
-               "Vertex index is negative!");
-  DEBUG_ASSERT(extrema.endVert < static_cast<int>(NumVert()), topologyErr,
-               "Vertex index exceeds number of verts!");
-  DEBUG_ASSERT(extrema.pairedHalfedge >= 0, topologyErr,
-               "Halfedge index is negative!");
-  DEBUG_ASSERT(extrema.pairedHalfedge < 2 * static_cast<int>(NumEdge()),
-               topologyErr, "Halfedge index exceeds number of halfedges!");
-  DEBUG_ASSERT(face >= 0, topologyErr, "Face index is negative!");
-  DEBUG_ASSERT(face < static_cast<int>(NumTri()), topologyErr,
-               "Face index exceeds number of faces!");
 #endif
 
   DEBUG_ASSERT(meshRelation_.triRef.size() == NumTri() ||
@@ -301,11 +275,12 @@ void Manifold::Impl::SortVerts() {
 
   // Verts were flagged for removal with NaNs and assigned kNoCode to sort
   // them to the end, which allows them to be removed.
-  const auto newNumVert = std::find_if(vertNew2Old.begin(), vertNew2Old.end(),
-                                       [&vertMorton](const int vert) {
-                                         return vertMorton[vert] == kNoCode;
-                                       }) -
-                          vertNew2Old.begin();
+  const auto newNumVert =
+      std::lower_bound(vertNew2Old.begin(), vertNew2Old.end(), kNoCode,
+                       [&vertMorton](const int vert, const uint32_t val) {
+                         return vertMorton[vert] < val;
+                       }) -
+      vertNew2Old.begin();
 
   vertNew2Old.resize(newNumVert);
   Permute(vertPos_, vertNew2Old);
@@ -326,31 +301,41 @@ void Manifold::Impl::ReindexVerts(const Vec<int>& vertNew2Old,
   Vec<int> vertOld2New(oldNumVert);
   scatter(countAt(0), countAt(static_cast<int>(NumVert())), vertNew2Old.begin(),
           vertOld2New.begin());
+  const bool hasProp = NumProp() > 0;
   for_each(autoPolicy(oldNumVert, 1e5), halfedge_.begin(), halfedge_.end(),
-           Reindex({vertOld2New}));
+           [&vertOld2New, hasProp](Halfedge& edge) {
+             if (edge.startVert < 0) return;
+             edge.startVert = vertOld2New[edge.startVert];
+             edge.endVert = vertOld2New[edge.endVert];
+             if (!hasProp) {
+               edge.propVert = edge.startVert;
+             }
+           });
 }
 
 /**
- * Removes unreferenced property verts and reindexes triProperties.
+ * Removes unreferenced property verts and reindexes propVerts.
  */
 void Manifold::Impl::CompactProps() {
   ZoneScoped;
-  if (meshRelation_.numProp == 0) return;
+  if (numProp_ == 0) return;
 
-  const auto numVerts = meshRelation_.properties.size() / meshRelation_.numProp;
+  const int numProp = NumProp();
+  const auto numVerts = properties_.size() / numProp;
   Vec<int> keep(numVerts, 0);
   auto policy = autoPolicy(numVerts, 1e5);
 
-  for_each(policy, meshRelation_.triProperties.cbegin(),
-           meshRelation_.triProperties.cend(), MarkProp({keep}));
+  for_each(policy, halfedge_.cbegin(), halfedge_.cend(), [&keep](Halfedge h) {
+    reinterpret_cast<std::atomic<int>*>(&keep[h.propVert])
+        ->store(1, std::memory_order_relaxed);
+  });
   Vec<int> propOld2New(numVerts + 1, 0);
   inclusive_scan(keep.begin(), keep.end(), propOld2New.begin() + 1);
 
-  Vec<double> oldProp = meshRelation_.properties;
+  Vec<double> oldProp = properties_;
   const int numVertsNew = propOld2New[numVerts];
-  const int numProp = meshRelation_.numProp;
-  auto& properties = meshRelation_.properties;
-  properties.resize(numProp * numVertsNew);
+  auto& properties = properties_;
+  properties.resize_nofill(numProp * numVertsNew);
   for_each_n(
       policy, countAt(0), numVerts,
       [&properties, &oldProp, &propOld2New, &keep, &numProp](const int oldIdx) {
@@ -360,8 +345,10 @@ void Manifold::Impl::CompactProps() {
               oldProp[oldIdx * numProp + p];
         }
       });
-  for_each_n(policy, meshRelation_.triProperties.begin(), NumTri(),
-             ReindexProps({propOld2New}));
+  for_each(policy, halfedge_.begin(), halfedge_.end(),
+           [&propOld2New](Halfedge& edge) {
+             edge.propVert = propOld2New[edge.propVert];
+           });
 }
 
 /**
@@ -372,8 +359,9 @@ void Manifold::Impl::CompactProps() {
 void Manifold::Impl::GetFaceBoxMorton(Vec<Box>& faceBox,
                                       Vec<uint32_t>& faceMorton) const {
   ZoneScoped;
-  faceBox.resize(NumTri());
-  faceMorton.resize(NumTri());
+  // faceBox should be initialized
+  faceBox.resize(NumTri(), Box());
+  faceMorton.resize_nofill(NumTri());
   for_each_n(autoPolicy(NumTri(), 1e5), countAt(0), NumTri(),
              [this, &faceBox, &faceMorton](const int face) {
                // Removed tris are marked by all halfedges having pairedHalfedge
@@ -413,11 +401,12 @@ void Manifold::Impl::SortFaces(Vec<Box>& faceBox, Vec<uint32_t>& faceMorton) {
 
   // Tris were flagged for removal with pairedHalfedge = -1 and assigned kNoCode
   // to sort them to the end, which allows them to be removed.
-  const int newNumTri = std::find_if(faceNew2Old.begin(), faceNew2Old.end(),
-                                     [&faceMorton](const int face) {
-                                       return faceMorton[face] == kNoCode;
-                                     }) -
-                        faceNew2Old.begin();
+  const int newNumTri =
+      std::lower_bound(faceNew2Old.begin(), faceNew2Old.end(), kNoCode,
+                       [&faceMorton](const int face, const uint32_t val) {
+                         return faceMorton[face] < val;
+                       }) -
+      faceNew2Old.begin();
   faceNew2Old.resize(newNumTri);
 
   Permute(faceMorton, faceNew2Old);
@@ -435,8 +424,6 @@ void Manifold::Impl::GatherFaces(const Vec<int>& faceNew2Old) {
   const auto numTri = faceNew2Old.size();
   if (meshRelation_.triRef.size() == NumTri())
     Permute(meshRelation_.triRef, faceNew2Old);
-  if (meshRelation_.triProperties.size() == NumTri())
-    Permute(meshRelation_.triProperties, faceNew2Old);
   if (faceNormal_.size() == NumTri()) Permute(faceNormal_, faceNew2Old);
 
   Vec<Halfedge> oldHalfedge(std::move(halfedge_));
@@ -446,8 +433,9 @@ void Manifold::Impl::GatherFaces(const Vec<int>& faceNew2Old) {
   scatter(countAt(0_uz), countAt(numTri), faceNew2Old.begin(),
           faceOld2New.begin());
 
-  halfedge_.resize(3 * numTri);
-  if (oldHalfedgeTangent.size() != 0) halfedgeTangent_.resize(3 * numTri);
+  halfedge_.resize_nofill(3 * numTri);
+  if (oldHalfedgeTangent.size() != 0)
+    halfedgeTangent_.resize_nofill(3 * numTri);
   for_each_n(policy, countAt(0), numTri,
              ReindexFace({halfedge_, halfedgeTangent_, oldHalfedge,
                           oldHalfedgeTangent, faceNew2Old, faceOld2New}));
@@ -457,7 +445,7 @@ void Manifold::Impl::GatherFaces(const Impl& old, const Vec<int>& faceNew2Old) {
   ZoneScoped;
   const auto numTri = faceNew2Old.size();
 
-  meshRelation_.triRef.resize(numTri);
+  meshRelation_.triRef.resize_nofill(numTri);
   gather(faceNew2Old.begin(), faceNew2Old.end(),
          old.meshRelation_.triRef.begin(), meshRelation_.triRef.begin());
 
@@ -465,17 +453,13 @@ void Manifold::Impl::GatherFaces(const Impl& old, const Vec<int>& faceNew2Old) {
     meshRelation_.meshIDtransform[pair.first] = pair.second;
   }
 
-  if (old.meshRelation_.triProperties.size() > 0) {
-    meshRelation_.triProperties.resize(numTri);
-    gather(faceNew2Old.begin(), faceNew2Old.end(),
-           old.meshRelation_.triProperties.begin(),
-           meshRelation_.triProperties.begin());
-    meshRelation_.numProp = old.meshRelation_.numProp;
-    meshRelation_.properties = old.meshRelation_.properties;
+  if (old.NumProp() > 0) {
+    numProp_ = old.numProp_;
+    properties_ = old.properties_;
   }
 
   if (old.faceNormal_.size() == old.NumTri()) {
-    faceNormal_.resize(numTri);
+    faceNormal_.resize_nofill(numTri);
     gather(faceNew2Old.begin(), faceNew2Old.end(), old.faceNormal_.begin(),
            faceNormal_.begin());
   }
@@ -484,8 +468,9 @@ void Manifold::Impl::GatherFaces(const Impl& old, const Vec<int>& faceNew2Old) {
   scatter(countAt(0_uz), countAt(numTri), faceNew2Old.begin(),
           faceOld2New.begin());
 
-  halfedge_.resize(3 * numTri);
-  if (old.halfedgeTangent_.size() != 0) halfedgeTangent_.resize(3 * numTri);
+  halfedge_.resize_nofill(3 * numTri);
+  if (old.halfedgeTangent_.size() != 0)
+    halfedgeTangent_.resize_nofill(3 * numTri);
   for_each_n(autoPolicy(numTri, 1e5), countAt(0), numTri,
              ReindexFace({halfedge_, halfedgeTangent_, old.halfedge_,
                           old.halfedgeTangent_, faceNew2Old, faceOld2New}));
diff --git a/thirdparty/manifold/src/subdivision.cpp b/thirdparty/manifold/src/subdivision.cpp
index c8631d79c8..71fbd36338 100644
--- a/thirdparty/manifold/src/subdivision.cpp
+++ b/thirdparty/manifold/src/subdivision.cpp
@@ -12,8 +12,8 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "./impl.h"
-#include "./parallel.h"
+#include "impl.h"
+#include "parallel.h"
 
 template <>
 struct std::hash<manifold::ivec4> {
@@ -113,7 +113,7 @@ class Partition {
     }
     const int offset = interiorOffset - newVerts.size();
     size_t old = newVerts.size();
-    newVerts.resize(vertBary.size());
+    newVerts.resize_nofill(vertBary.size());
     std::iota(newVerts.begin() + old, newVerts.end(), old + offset);
 
     const int numTri = triVert.size();
@@ -535,7 +535,7 @@ Vec<Barycentric> Manifold::Impl::Subdivide(
           auto Added = [&edgeAdded, &half2Edge, thisAdded, this](int hIdx) {
             int longest = 0;
             int total = 0;
-            for (int j : {0, 1, 2}) {
+            for (int _ : {0, 1, 2}) {
               const int added = edgeAdded[half2Edge[hIdx]];
               longest = la::max(longest, added);
               total += added;
@@ -586,7 +586,7 @@ Vec<Barycentric> Manifold::Impl::Subdivide(
 
   std::vector<Partition> subTris(numTri);
   for_each_n(policy, countAt(0), numTri,
-             [this, &subTris, &half2Edge, &edgeAdded, &faceHalfedges](int tri) {
+             [&subTris, &half2Edge, &edgeAdded, &faceHalfedges](int tri) {
                const ivec4 halfedges = faceHalfedges[tri];
                ivec4 divisions(0);
                for (const int i : {0, 1, 2, 3}) {
@@ -684,18 +684,19 @@ Vec<Barycentric> Manifold::Impl::Subdivide(
              });
   vertPos_ = newVertPos;
 
-  faceNormal_.resize(0);
+  faceNormal_.clear();
 
-  if (meshRelation_.numProp > 0) {
+  if (numProp_ > 0) {
     const int numPropVert = NumPropVert();
     const int addedVerts = NumVert() - numVert;
     const int propOffset = numPropVert - numVert;
-    Vec<double> prop(meshRelation_.numProp *
-                     (numPropVert + addedVerts + totalEdgeAdded));
+    // duplicate the prop verts along all new edges even though this is
+    // unnecessary for edges that share the same prop verts. The duplicates will
+    // be removed by CompactProps.
+    Vec<double> prop(numProp_ * (numPropVert + addedVerts + totalEdgeAdded));
 
     // copy retained prop verts
-    copy(meshRelation_.properties.begin(), meshRelation_.properties.end(),
-         prop.begin());
+    copy(properties_.begin(), properties_.end(), prop.begin());
 
     // copy interior prop verts and forward edge prop verts
     for_each_n(
@@ -705,104 +706,99 @@ Vec<Barycentric> Manifold::Impl::Subdivide(
           const int vert = numPropVert + i;
           const Barycentric bary = vertBary[numVert + i];
           const ivec4 halfedges = faceHalfedges[bary.tri];
-          auto& rel = meshRelation_;
+          const int numProp = NumProp();
 
-          for (int p = 0; p < rel.numProp; ++p) {
+          for (int p = 0; p < numProp; ++p) {
             if (halfedges[3] < 0) {
               vec3 triProp;
               for (const int i : {0, 1, 2}) {
-                triProp[i] = rel.properties[rel.triProperties[bary.tri][i] *
-                                                rel.numProp +
-                                            p];
+                triProp[i] =
+                    properties_[halfedge_[3 * bary.tri + i].propVert * numProp +
+                                p];
               }
-              prop[vert * rel.numProp + p] = la::dot(triProp, vec3(bary.uvw));
+              prop[vert * numProp + p] = la::dot(triProp, vec3(bary.uvw));
             } else {
               vec4 quadProp;
               for (const int i : {0, 1, 2, 3}) {
-                const int tri = halfedges[i] / 3;
-                const int j = halfedges[i] % 3;
                 quadProp[i] =
-                    rel.properties[rel.triProperties[tri][j] * rel.numProp + p];
+                    properties_[halfedge_[halfedges[i]].propVert * numProp + p];
               }
-              prop[vert * rel.numProp + p] = la::dot(quadProp, bary.uvw);
+              prop[vert * numProp + p] = la::dot(quadProp, bary.uvw);
             }
           }
         });
 
-    // copy backward edge prop verts
+    // copy backward edge prop verts, some of which will be unreferenced
+    // duplicates.
     for_each_n(policy, countAt(0), numEdge,
                [this, &prop, &edges, &edgeAdded, &edgeOffset, propOffset,
                 addedVerts](const int i) {
                  const int n = edgeAdded[i];
                  const int offset = edgeOffset[i] + propOffset + addedVerts;
-                 auto& rel = meshRelation_;
+                 const int numProp = NumProp();
 
                  const double frac = 1.0 / (n + 1);
                  const int halfedgeIdx =
                      halfedge_[edges[i].halfedgeIdx].pairedHalfedge;
-                 const int v0 = halfedgeIdx % 3;
-                 const int tri = halfedgeIdx / 3;
-                 const int prop0 = rel.triProperties[tri][v0];
-                 const int prop1 = rel.triProperties[tri][Next3(v0)];
+                 const int prop0 = halfedge_[halfedgeIdx].propVert;
+                 const int prop1 =
+                     halfedge_[NextHalfedge(halfedgeIdx)].propVert;
                  for (int i = 0; i < n; ++i) {
-                   for (int p = 0; p < rel.numProp; ++p) {
-                     prop[(offset + i) * rel.numProp + p] =
-                         la::lerp(rel.properties[prop0 * rel.numProp + p],
-                                  rel.properties[prop1 * rel.numProp + p],
-                                  (i + 1) * frac);
+                   for (int p = 0; p < numProp; ++p) {
+                     prop[(offset + i) * numProp + p] = la::lerp(
+                         properties_[prop0 * numProp + p],
+                         properties_[prop1 * numProp + p], (i + 1) * frac);
                    }
                  }
                });
 
     Vec<ivec3> triProp(triVerts.size());
-    for_each_n(policy, countAt(0), numTri,
-               [this, &triProp, &subTris, &edgeOffset, &half2Edge, &triOffset,
-                &interiorOffset, &faceHalfedges, propOffset,
-                addedVerts](const int tri) {
-                 const ivec4 halfedges = faceHalfedges[tri];
-                 if (halfedges[0] < 0) return;
+    for_each_n(
+        policy, countAt(0), numTri,
+        [this, &triProp, &subTris, &edgeOffset, &half2Edge, &triOffset,
+         &interiorOffset, &faceHalfedges, propOffset,
+         addedVerts](const int tri) {
+          const ivec4 halfedges = faceHalfedges[tri];
+          if (halfedges[0] < 0) return;
 
-                 auto& rel = meshRelation_;
-                 ivec4 tri3;
-                 ivec4 edgeOffsets;
-                 bvec4 edgeFwd(true);
-                 for (const int i : {0, 1, 2, 3}) {
-                   if (halfedges[i] < 0) {
-                     tri3[i] = -1;
-                     continue;
-                   }
-                   const int thisTri = halfedges[i] / 3;
-                   const int j = halfedges[i] % 3;
-                   const Halfedge& halfedge = halfedge_[halfedges[i]];
-                   tri3[i] = rel.triProperties[thisTri][j];
-                   edgeOffsets[i] = edgeOffset[half2Edge[halfedges[i]]];
-                   if (!halfedge.IsForward()) {
-                     const int pairTri = halfedge.pairedHalfedge / 3;
-                     const int k = halfedge.pairedHalfedge % 3;
-                     if (rel.triProperties[pairTri][k] !=
-                             rel.triProperties[thisTri][Next3(j)] ||
-                         rel.triProperties[pairTri][Next3(k)] !=
-                             rel.triProperties[thisTri][j]) {
-                       edgeOffsets[i] += addedVerts;
-                     } else {
-                       edgeFwd[i] = false;
-                     }
-                   }
-                 }
+          ivec4 tri3;
+          ivec4 edgeOffsets;
+          bvec4 edgeFwd(true);
+          for (const int i : {0, 1, 2, 3}) {
+            if (halfedges[i] < 0) {
+              tri3[i] = -1;
+              continue;
+            }
+            const Halfedge& halfedge = halfedge_[halfedges[i]];
+            tri3[i] = halfedge.propVert;
+            edgeOffsets[i] = edgeOffset[half2Edge[halfedges[i]]];
+            if (!halfedge.IsForward()) {
+              if (halfedge_[halfedge.pairedHalfedge].propVert !=
+                      halfedge_[NextHalfedge(halfedges[i])].propVert ||
+                  halfedge_[NextHalfedge(halfedge.pairedHalfedge)].propVert !=
+                      halfedge.propVert) {
+                // if the edge doesn't match, point to the backward edge
+                // propverts.
+                edgeOffsets[i] += addedVerts;
+              } else {
+                edgeFwd[i] = false;
+              }
+            }
+          }
 
-                 Vec<ivec3> newTris = subTris[tri].Reindex(
-                     tri3, edgeOffsets + propOffset, edgeFwd,
-                     interiorOffset[tri] + propOffset);
-                 copy(newTris.begin(), newTris.end(),
-                      triProp.begin() + triOffset[tri]);
-               });
+          Vec<ivec3> newTris =
+              subTris[tri].Reindex(tri3, edgeOffsets + propOffset, edgeFwd,
+                                   interiorOffset[tri] + propOffset);
+          copy(newTris.begin(), newTris.end(),
+               triProp.begin() + triOffset[tri]);
+        });
 
-    meshRelation_.properties = prop;
-    meshRelation_.triProperties = triProp;
+    properties_ = prop;
+    CreateHalfedges(triProp, triVerts);
+  } else {
+    CreateHalfedges(triVerts);
   }
 
-  CreateHalfedges(triVerts);
-
   return vertBary;
 }
 
diff --git a/thirdparty/manifold/src/svd.h b/thirdparty/manifold/src/svd.h
index cc1a82035f..3978a17415 100644
--- a/thirdparty/manifold/src/svd.h
+++ b/thirdparty/manifold/src/svd.h
@@ -82,7 +82,7 @@ struct QR {
   mat3 Q, R;
 };
 // Calculates the squared norm of the vector.
-inline double Dist2(vec3 v) { return la::dot(v, v); }
+inline double Dist2(vec3 v) { return manifold::la::dot(v, v); }
 // For an explanation of the math see
 // http://pages.cs.wisc.edu/~sifakis/papers/SVD_TR1690.pdf Computing the
 // Singular Value Decomposition of 3 x 3 matrices with minimal branching and
@@ -101,29 +101,26 @@ inline Givens ApproximateGivensQuaternion(Symmetric3x3& A) {
 inline void JacobiConjugation(const int32_t x, const int32_t y, const int32_t z,
                               Symmetric3x3& S, vec4& q) {
   auto g = ApproximateGivensQuaternion(S);
-  double scale = 1.0 / fma(g.ch, g.ch, g.sh * g.sh);
-  double a = fma(g.ch, g.ch, -g.sh * g.sh) * scale;
+  double scale = 1.0 / (g.ch * g.ch + g.sh * g.sh);
+  double a = (g.ch * g.ch - g.sh * g.sh) * scale;
   double b = 2.0 * g.sh * g.ch * scale;
   Symmetric3x3 _S = S;
   // perform conjugation S = Q'*S*Q
-  S.m_00 =
-      fma(a, fma(a, _S.m_00, b * _S.m_10), b * (fma(a, _S.m_10, b * _S.m_11)));
-  S.m_10 = fma(a, fma(-b, _S.m_00, a * _S.m_10),
-               b * (fma(-b, _S.m_10, a * _S.m_11)));
-  S.m_11 = fma(-b, fma(-b, _S.m_00, a * _S.m_10),
-               a * (fma(-b, _S.m_10, a * _S.m_11)));
-  S.m_20 = fma(a, _S.m_20, b * _S.m_21);
-  S.m_21 = fma(-b, _S.m_20, a * _S.m_21);
+  S.m_00 = a * (a * _S.m_00 + b * _S.m_10) + b * (a * _S.m_10 + b * _S.m_11);
+  S.m_10 = a * (-b * _S.m_00 + a * _S.m_10) + b * (-b * _S.m_10 + a * _S.m_11);
+  S.m_11 = -b * (-b * _S.m_00 + a * _S.m_10) + a * (-b * _S.m_10 + a * _S.m_11);
+  S.m_20 = a * _S.m_20 + b * _S.m_21;
+  S.m_21 = -b * _S.m_20 + a * _S.m_21;
   S.m_22 = _S.m_22;
   // update cumulative rotation qV
   vec3 tmp = g.sh * vec3(q);
   g.sh *= q[3];
   // (x,y,z) corresponds to ((0,1,2),(1,2,0),(2,0,1)) for (p,q) =
   // ((0,1),(1,2),(0,2))
-  q[z] = fma(q[z], g.ch, g.sh);
-  q[3] = fma(q[3], g.ch, -tmp[z]);  // w
-  q[x] = fma(q[x], g.ch, tmp[y]);
-  q[y] = fma(q[y], g.ch, -tmp[x]);
+  q[z] = q[z] * g.ch + g.sh;
+  q[3] = q[3] * g.ch + -tmp[z];  // w
+  q[x] = q[x] * g.ch + tmp[y];
+  q[y] = q[y] * g.ch + -tmp[x];
   // re-arrange matrix for next iteration
   _S.m_00 = S.m_11;
   _S.m_10 = S.m_21;
@@ -148,15 +145,15 @@ inline mat3 JacobiEigenAnalysis(Symmetric3x3 S) {
     JacobiConjugation(1, 2, 0, S, q);
     JacobiConjugation(2, 0, 1, S, q);
   }
-  return mat3({1.0 - 2.0 * (fma(q.y, q.y, q.z * q.z)),  //
-               2.0 * fma(q.x, q.y, +q.w * q.z),         //
-               2.0 * fma(q.x, q.z, -q.w * q.y)},        //
-              {2 * fma(q.x, q.y, -q.w * q.z),           //
-               1 - 2 * fma(q.x, q.x, q.z * q.z),        //
-               2 * fma(q.y, q.z, q.w * q.x)},           //
-              {2 * fma(q.x, q.z, q.w * q.y),            //
-               2 * fma(q.y, q.z, -q.w * q.x),           //
-               1 - 2 * fma(q.x, q.x, q.y * q.y)});
+  return mat3({1.0 - 2.0 * (q.y * q.y + q.z * q.z),  //
+               2.0 * (q.x * q.y + +q.w * q.z),       //
+               2.0 * (q.x * q.z + -q.w * q.y)},      //
+              {2 * (q.x * q.y + -q.w * q.z),         //
+               1 - 2 * (q.x * q.x + q.z * q.z),      //
+               2 * (q.y * q.z + q.w * q.x)},         //
+              {2 * (q.x * q.z + q.w * q.y),          //
+               2 * (q.y * q.z + -q.w * q.x),         //
+               1 - 2 * (q.x * q.x + q.y * q.y)});
 }
 // Implementation of Algorithm 3
 inline void SortSingularValues(mat3& B, mat3& V) {
@@ -207,65 +204,64 @@ inline QR QRDecomposition(mat3& B) {
   mat3 Q, R;
   // first Givens rotation (ch,0,0,sh)
   auto g1 = QRGivensQuaternion(B[0][0], B[0][1]);
-  auto a = fma(-2.0, g1.sh * g1.sh, 1.0);
+  auto a = -2.0 * g1.sh * g1.sh + 1.0;
   auto b = 2.0 * g1.ch * g1.sh;
   // apply B = Q' * B
-  R[0][0] = fma(a, B[0][0], b * B[0][1]);
-  R[1][0] = fma(a, B[1][0], b * B[1][1]);
-  R[2][0] = fma(a, B[2][0], b * B[2][1]);
-  R[0][1] = fma(-b, B[0][0], a * B[0][1]);
-  R[1][1] = fma(-b, B[1][0], a * B[1][1]);
-  R[2][1] = fma(-b, B[2][0], a * B[2][1]);
+  R[0][0] = a * B[0][0] + b * B[0][1];
+  R[1][0] = a * B[1][0] + b * B[1][1];
+  R[2][0] = a * B[2][0] + b * B[2][1];
+  R[0][1] = -b * B[0][0] + a * B[0][1];
+  R[1][1] = -b * B[1][0] + a * B[1][1];
+  R[2][1] = -b * B[2][0] + a * B[2][1];
   R[0][2] = B[0][2];
   R[1][2] = B[1][2];
   R[2][2] = B[2][2];
   // second Givens rotation (ch,0,-sh,0)
   auto g2 = QRGivensQuaternion(R[0][0], R[0][2]);
-  a = fma(-2.0, g2.sh * g2.sh, 1.0);
+  a = -2.0 * g2.sh * g2.sh + 1.0;
   b = 2.0 * g2.ch * g2.sh;
   // apply B = Q' * B;
-  B[0][0] = fma(a, R[0][0], b * R[0][2]);
-  B[1][0] = fma(a, R[1][0], b * R[1][2]);
-  B[2][0] = fma(a, R[2][0], b * R[2][2]);
+  B[0][0] = a * R[0][0] + b * R[0][2];
+  B[1][0] = a * R[1][0] + b * R[1][2];
+  B[2][0] = a * R[2][0] + b * R[2][2];
   B[0][1] = R[0][1];
   B[1][1] = R[1][1];
   B[2][1] = R[2][1];
-  B[0][2] = fma(-b, R[0][0], a * R[0][2]);
-  B[1][2] = fma(-b, R[1][0], a * R[1][2]);
-  B[2][2] = fma(-b, R[2][0], a * R[2][2]);
+  B[0][2] = -b * R[0][0] + a * R[0][2];
+  B[1][2] = -b * R[1][0] + a * R[1][2];
+  B[2][2] = -b * R[2][0] + a * R[2][2];
   // third Givens rotation (ch,sh,0,0)
   auto g3 = QRGivensQuaternion(B[1][1], B[1][2]);
-  a = fma(-2.0, g3.sh * g3.sh, 1.0);
+  a = -2.0 * g3.sh * g3.sh + 1.0;
   b = 2.0 * g3.ch * g3.sh;
   // R is now set to desired value
   R[0][0] = B[0][0];
   R[1][0] = B[1][0];
   R[2][0] = B[2][0];
-  R[0][1] = fma(a, B[0][1], b * B[0][2]);
-  R[1][1] = fma(a, B[1][1], b * B[1][2]);
-  R[2][1] = fma(a, B[2][1], b * B[2][2]);
-  R[0][2] = fma(-b, B[0][1], a * B[0][2]);
-  R[1][2] = fma(-b, B[1][1], a * B[1][2]);
-  R[2][2] = fma(-b, B[2][1], a * B[2][2]);
+  R[0][1] = a * B[0][1] + b * B[0][2];
+  R[1][1] = a * B[1][1] + b * B[1][2];
+  R[2][1] = a * B[2][1] + b * B[2][2];
+  R[0][2] = -b * B[0][1] + a * B[0][2];
+  R[1][2] = -b * B[1][1] + a * B[1][2];
+  R[2][2] = -b * B[2][1] + a * B[2][2];
   // construct the cumulative rotation Q=Q1 * Q2 * Q3
   // the number of floating point operations for three quaternion
   // multiplications is more or less comparable to the explicit form of the
   // joined matrix. certainly more memory-efficient!
-  auto sh12 = 2.0 * fma(g1.sh, g1.sh, -0.5);
-  auto sh22 = 2.0 * fma(g2.sh, g2.sh, -0.5);
-  auto sh32 = 2.0 * fma(g3.sh, g3.sh, -0.5);
+  auto sh12 = 2.0 * (g1.sh * g1.sh + -0.5);
+  auto sh22 = 2.0 * (g2.sh * g2.sh + -0.5);
+  auto sh32 = 2.0 * (g3.sh * g3.sh + -0.5);
   Q[0][0] = sh12 * sh22;
-  Q[1][0] = fma(4.0 * g2.ch * g3.ch, sh12 * g2.sh * g3.sh,
-                2.0 * g1.ch * g1.sh * sh32);
-  Q[2][0] = fma(4.0 * g1.ch * g3.ch, g1.sh * g3.sh,
-                -2.0 * g2.ch * sh12 * g2.sh * sh32);
+  Q[1][0] =
+      4.0 * g2.ch * g3.ch * sh12 * g2.sh * g3.sh + 2.0 * g1.ch * g1.sh * sh32;
+  Q[2][0] =
+      4.0 * g1.ch * g3.ch * g1.sh * g3.sh + -2.0 * g2.ch * sh12 * g2.sh * sh32;
 
   Q[0][1] = -2.0 * g1.ch * g1.sh * sh22;
-  Q[1][1] =
-      fma(-8.0 * g1.ch * g2.ch * g3.ch, g1.sh * g2.sh * g3.sh, sh12 * sh32);
-  Q[2][1] = fma(
-      -2.0 * g3.ch, g3.sh,
-      4.0 * g1.sh * fma(g3.ch * g1.sh, g3.sh, g1.ch * g2.ch * g2.sh * sh32));
+  Q[1][1] = -8.0 * g1.ch * g2.ch * g3.ch * g1.sh * g2.sh * g3.sh + sh12 * sh32;
+  Q[2][1] =
+      -2.0 * g3.ch * g3.sh +
+      4.0 * g1.sh * (g3.ch * g1.sh * g3.sh + g1.ch * g2.ch * g2.sh * sh32);
 
   Q[0][2] = 2.0 * g2.ch * g2.sh;
   Q[1][2] = -2.0 * g3.ch * sh22 * g3.sh;
diff --git a/thirdparty/manifold/src/tree2d.cpp b/thirdparty/manifold/src/tree2d.cpp
new file mode 100644
index 0000000000..b47c7a2f78
--- /dev/null
+++ b/thirdparty/manifold/src/tree2d.cpp
@@ -0,0 +1,59 @@
+// Copyright 2025 The Manifold Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "tree2d.h"
+
+#include "parallel.h"
+
+#ifndef ZoneScoped
+#if __has_include(<tracy/Tracy.hpp>)
+#include <tracy/Tracy.hpp>
+#else
+#define FrameMarkStart(x)
+#define FrameMarkEnd(x)
+// putting ZoneScoped in a function will instrument the function execution when
+// TRACY_ENABLE is set, which allows the profiler to record more accurate
+// timing.
+#define ZoneScoped
+#define ZoneScopedN(name)
+#endif
+#endif
+
+namespace manifold {
+
+// Not really a proper KD-tree, but a kd tree with k = 2 and alternating x/y
+// partition.
+// Recursive sorting is not the most efficient, but simple and guaranteed to
+// result in a balanced tree.
+void BuildTwoDTreeImpl(VecView<PolyVert> points, bool sortX) {
+  using CmpFn = std::function<bool(const PolyVert&, const PolyVert&)>;
+  CmpFn cmpx = [](const PolyVert& a, const PolyVert& b) {
+    return a.pos.x < b.pos.x;
+  };
+  CmpFn cmpy = [](const PolyVert& a, const PolyVert& b) {
+    return a.pos.y < b.pos.y;
+  };
+  manifold::stable_sort(points.begin(), points.end(), sortX ? cmpx : cmpy);
+  if (points.size() < 2) return;
+  BuildTwoDTreeImpl(points.view(0, points.size() / 2), !sortX);
+  BuildTwoDTreeImpl(points.view(points.size() / 2 + 1), !sortX);
+}
+
+void BuildTwoDTree(VecView<PolyVert> points) {
+  ZoneScoped;
+  // don't even bother...
+  if (points.size() <= 8) return;
+  BuildTwoDTreeImpl(points, true);
+}
+}  // namespace manifold
diff --git a/thirdparty/manifold/src/tree2d.h b/thirdparty/manifold/src/tree2d.h
new file mode 100644
index 0000000000..d16b2ab3e3
--- /dev/null
+++ b/thirdparty/manifold/src/tree2d.h
@@ -0,0 +1,85 @@
+// Copyright 2025 The Manifold Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include "manifold/common.h"
+#include "manifold/optional_assert.h"
+#include "manifold/polygon.h"
+#include "manifold/vec_view.h"
+
+namespace manifold {
+
+void BuildTwoDTreeImpl(VecView<PolyVert> points, bool sortX);
+
+void BuildTwoDTree(VecView<PolyVert> points);
+
+template <typename F>
+void QueryTwoDTree(VecView<PolyVert> points, Rect r, F f) {
+  if (points.size() <= 8) {
+    for (const auto& p : points)
+      if (r.Contains(p.pos)) f(p);
+    return;
+  }
+  Rect current;
+  current.min = vec2(-std::numeric_limits<double>::infinity());
+  current.max = vec2(std::numeric_limits<double>::infinity());
+
+  int level = 0;
+  VecView<PolyVert> currentView = points;
+  std::array<Rect, 64> rectStack;
+  std::array<VecView<PolyVert>, 64> viewStack;
+  std::array<int, 64> levelStack;
+  int stackPointer = 0;
+
+  while (1) {
+    if (currentView.size() <= 2) {
+      for (const auto& p : currentView)
+        if (r.Contains(p.pos)) f(p);
+      if (--stackPointer < 0) break;
+      level = levelStack[stackPointer];
+      currentView = viewStack[stackPointer];
+      current = rectStack[stackPointer];
+      continue;
+    }
+
+    // these are conceptual left/right trees
+    Rect left = current;
+    Rect right = current;
+    const PolyVert middle = currentView[currentView.size() / 2];
+    if (level % 2 == 0)
+      left.max.x = right.min.x = middle.pos.x;
+    else
+      left.max.y = right.min.y = middle.pos.y;
+
+    if (r.Contains(middle.pos)) f(middle);
+    if (left.DoesOverlap(r)) {
+      if (right.DoesOverlap(r)) {
+        DEBUG_ASSERT(stackPointer < 64, logicErr, "Stack overflow");
+        rectStack[stackPointer] = right;
+        viewStack[stackPointer] = currentView.view(currentView.size() / 2 + 1);
+        levelStack[stackPointer] = level + 1;
+        stackPointer++;
+      }
+      current = left;
+      currentView = currentView.view(0, currentView.size() / 2);
+      level++;
+    } else {
+      current = right;
+      currentView = currentView.view(currentView.size() / 2 + 1);
+      level++;
+    }
+  }
+}
+}  // namespace manifold
diff --git a/thirdparty/manifold/src/tri_dist.h b/thirdparty/manifold/src/tri_dist.h
index 4e83ca5253..123d71f805 100644
--- a/thirdparty/manifold/src/tri_dist.h
+++ b/thirdparty/manifold/src/tri_dist.h
@@ -15,6 +15,7 @@
 #pragma once
 
 #include <array>
+#include <cstdint>
 
 #include "manifold/common.h"
 
diff --git a/thirdparty/manifold/src/utils.h b/thirdparty/manifold/src/utils.h
index 12d6a58477..48e8218b85 100644
--- a/thirdparty/manifold/src/utils.h
+++ b/thirdparty/manifold/src/utils.h
@@ -19,8 +19,8 @@
 #include <mutex>
 #include <unordered_map>
 
-#include "./vec.h"
 #include "manifold/common.h"
+#include "vec.h"
 
 #ifndef MANIFOLD_PAR
 #error "MANIFOLD_PAR must be defined to either 1 (parallel) or -1 (series)"
@@ -33,7 +33,7 @@
 #endif
 #endif
 
-#include "./parallel.h"
+#include "parallel.h"
 
 #if __has_include(<tracy/Tracy.hpp>)
 #include <tracy/Tracy.hpp>
@@ -72,7 +72,7 @@ inline int Prev3(int i) {
 template <typename T, typename T1>
 void Permute(Vec<T>& inOut, const Vec<T1>& new2Old) {
   Vec<T> tmp(std::move(inOut));
-  inOut.resize(new2Old.size());
+  inOut.resize_nofill(new2Old.size());
   gather(new2Old.begin(), new2Old.end(), tmp.begin(), inOut.begin());
 }
 
@@ -106,6 +106,12 @@ class ConcurrentSharedPtr {
   ConcurrentSharedPtr(T value) : impl(std::make_shared<T>(value)) {}
   ConcurrentSharedPtr(const ConcurrentSharedPtr<T>& other)
       : impl(other.impl), mutex(other.mutex) {}
+  ConcurrentSharedPtr& operator=(const ConcurrentSharedPtr<T>& other) {
+    if (this == &other) return *this;
+    impl = other.impl;
+    mutex = other.mutex;
+    return *this;
+  }
   class SharedPtrGuard {
    public:
     SharedPtrGuard(std::recursive_mutex* mutex, T* content)
@@ -211,7 +217,7 @@ struct Negate {
 inline int CCW(vec2 p0, vec2 p1, vec2 p2, double tol) {
   vec2 v1 = p1 - p0;
   vec2 v2 = p2 - p0;
-  double area = fma(v1.x, v2.y, -v1.y * v2.x);
+  double area = v1.x * v2.y - v1.y * v2.x;
   double base2 = la::max(la::dot(v1, v1), la::dot(v2, v2));
   if (area * area * 4 <= base2 * tol * tol)
     return 0;
@@ -224,4 +230,11 @@ inline mat4 Mat4(mat3x4 a) {
 }
 inline mat3 Mat3(mat2x3 a) { return mat3({a[0], 0}, {a[1], 0}, {a[2], 1}); }
 
+// https://stackoverflow.com/questions/664014/what-integer-hash-function-are-good-that-accepts-an-integer-hash-key
+constexpr uint64_t hash64bit(uint64_t x) {
+  x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9ull;
+  x = (x ^ (x >> 27)) * 0x94d049bb133111ebull;
+  x = x ^ (x >> 31);
+  return x;
+}
 }  // namespace manifold
diff --git a/thirdparty/manifold/src/vec.h b/thirdparty/manifold/src/vec.h
index b59b4b6ad5..a37ad188be 100644
--- a/thirdparty/manifold/src/vec.h
+++ b/thirdparty/manifold/src/vec.h
@@ -21,8 +21,8 @@
 #endif
 #include <vector>
 
-#include "./parallel.h"
 #include "manifold/vec_view.h"
+#include "parallel.h"
 
 namespace manifold {
 
@@ -45,40 +45,40 @@ class Vec : public VecView<T> {
   // Note that the vector constructed with this constructor will contain
   // uninitialized memory. Please specify `val` if you need to make sure that
   // the data is initialized.
-  Vec(size_t size) {
+  Vec(size_t size) : VecView<T>() {
     reserve(size);
     this->size_ = size;
   }
 
-  Vec(size_t size, T val) { resize(size, val); }
+  Vec(size_t size, T val) : VecView<T>() { resize(size, val); }
 
-  Vec(const Vec<T> &vec) { *this = Vec(vec.view()); }
+  Vec(const Vec<T>& vec) : VecView<T>() { *this = Vec(vec.view()); }
 
-  Vec(const VecView<const T> &vec) {
+  Vec(const VecView<const T>& vec) : VecView<T>() {
     this->size_ = vec.size();
     this->capacity_ = this->size_;
     auto policy = autoPolicy(this->size_);
     if (this->size_ != 0) {
-      this->ptr_ = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
+      this->ptr_ = reinterpret_cast<T*>(malloc(this->size_ * sizeof(T)));
       ASSERT(this->ptr_ != nullptr, std::bad_alloc());
       TracyAllocS(this->ptr_, this->size_ * sizeof(T), 3);
       copy(policy, vec.begin(), vec.end(), this->ptr_);
     }
   }
 
-  Vec(const std::vector<T> &vec) {
+  Vec(const std::vector<T>& vec) : VecView<T>() {
     this->size_ = vec.size();
     this->capacity_ = this->size_;
     auto policy = autoPolicy(this->size_);
     if (this->size_ != 0) {
-      this->ptr_ = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
+      this->ptr_ = reinterpret_cast<T*>(malloc(this->size_ * sizeof(T)));
       ASSERT(this->ptr_ != nullptr, std::bad_alloc());
       TracyAllocS(this->ptr_, this->size_ * sizeof(T), 3);
       copy(policy, vec.begin(), vec.end(), this->ptr_);
     }
   }
 
-  Vec(Vec<T> &&vec) {
+  Vec(Vec<T>&& vec) : VecView<T>() {
     this->ptr_ = vec.ptr_;
     this->size_ = vec.size_;
     capacity_ = vec.capacity_;
@@ -100,7 +100,7 @@ class Vec : public VecView<T> {
     capacity_ = 0;
   }
 
-  Vec<T> &operator=(const Vec<T> &other) {
+  Vec<T>& operator=(const Vec<T>& other) {
     if (&other == this) return *this;
     if (this->ptr_ != nullptr) {
       TracyFreeS(this->ptr_, 3);
@@ -109,7 +109,7 @@ class Vec : public VecView<T> {
     this->size_ = other.size_;
     capacity_ = other.size_;
     if (this->size_ != 0) {
-      this->ptr_ = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
+      this->ptr_ = reinterpret_cast<T*>(malloc(this->size_ * sizeof(T)));
       ASSERT(this->ptr_ != nullptr, std::bad_alloc());
       TracyAllocS(this->ptr_, this->size_ * sizeof(T), 3);
       manifold::copy(other.begin(), other.end(), this->ptr_);
@@ -117,7 +117,7 @@ class Vec : public VecView<T> {
     return *this;
   }
 
-  Vec<T> &operator=(Vec<T> &&other) {
+  Vec<T>& operator=(Vec<T>&& other) {
     if (&other == this) return *this;
     if (this->ptr_ != nullptr) {
       TracyFreeS(this->ptr_, 3);
@@ -134,38 +134,37 @@ class Vec : public VecView<T> {
 
   operator VecView<T>() const { return {this->ptr_, this->size_}; }
 
-  void swap(Vec<T> &other) {
+  void swap(Vec<T>& other) {
     std::swap(this->ptr_, other.ptr_);
     std::swap(this->size_, other.size_);
     std::swap(capacity_, other.capacity_);
   }
 
-  inline void push_back(const T &val, bool seq = false) {
+  inline void push_back(const T& val) {
     if (this->size_ >= capacity_) {
       // avoid dangling pointer in case val is a reference of our array
       T val_copy = val;
-      reserve(capacity_ == 0 ? 128 : capacity_ * 2, seq);
+      reserve(capacity_ == 0 ? 128 : capacity_ * 2);
       this->ptr_[this->size_++] = val_copy;
       return;
     }
     this->ptr_[this->size_++] = val;
   }
 
-  inline void extend(size_t n, bool seq = false) {
+  inline void extend(size_t n) {
     if (this->size_ + n >= capacity_)
-      reserve(capacity_ == 0 ? 128 : std::max(capacity_ * 2, this->size_ + n),
-              seq);
+      reserve(capacity_ == 0 ? 128 : std::max(capacity_ * 2, this->size_ + n));
     this->size_ += n;
   }
 
-  void reserve(size_t n, bool seq = false) {
+  void reserve(size_t n) {
     if (n > capacity_) {
-      T *newBuffer = reinterpret_cast<T *>(malloc(n * sizeof(T)));
+      T* newBuffer = reinterpret_cast<T*>(malloc(n * sizeof(T)));
       ASSERT(newBuffer != nullptr, std::bad_alloc());
       TracyAllocS(newBuffer, n * sizeof(T), 3);
       if (this->size_ > 0)
-        manifold::copy(seq ? ExecutionPolicy::Seq : autoPolicy(this->size_),
-                       this->ptr_, this->ptr_ + this->size_, newBuffer);
+        manifold::copy(autoPolicy(this->size_), this->ptr_,
+                       this->ptr_ + this->size_, newBuffer);
       if (this->ptr_ != nullptr) {
         TracyFreeS(this->ptr_, 3);
         free(this->ptr_);
@@ -176,7 +175,7 @@ class Vec : public VecView<T> {
   }
 
   void resize(size_t newSize, T val = T()) {
-    bool shrink = this->size_ > 2 * newSize;
+    bool shrink = this->size_ > 2 * newSize && this->size_ > 16;
     reserve(newSize);
     if (this->size_ < newSize) {
       fill(autoPolicy(newSize - this->size_), this->ptr_ + this->size_,
@@ -186,7 +185,14 @@ class Vec : public VecView<T> {
     if (shrink) shrink_to_fit();
   }
 
-  void pop_back() { resize(this->size_ - 1); }
+  void resize_nofill(size_t newSize) {
+    bool shrink = this->size_ > 2 * newSize && this->size_ > 16;
+    reserve(newSize);
+    this->size_ = newSize;
+    if (shrink) shrink_to_fit();
+  }
+
+  void pop_back() { resize_nofill(this->size_ - 1); }
 
   void clear(bool shrink = true) {
     this->size_ = 0;
@@ -194,9 +200,9 @@ class Vec : public VecView<T> {
   }
 
   void shrink_to_fit() {
-    T *newBuffer = nullptr;
+    T* newBuffer = nullptr;
     if (this->size_ > 0) {
-      newBuffer = reinterpret_cast<T *>(malloc(this->size_ * sizeof(T)));
+      newBuffer = reinterpret_cast<T*>(malloc(this->size_ * sizeof(T)));
       ASSERT(newBuffer != nullptr, std::bad_alloc());
       TracyAllocS(newBuffer, this->size_ * sizeof(T), 3);
       manifold::copy(this->ptr_, this->ptr_ + this->size_, newBuffer);