Replace QuickHull with Bullet's convex hull computer.

The code is based on the current version of thirdparty/vhacd and modified to use Godot's types and code style.

Additional changes:
- backported and extended PagedAllocator to allow leaked objects
- applied patch from https://github.com/bulletphysics/bullet3/pull/3037

COPYRIGHT.txt

@@ -55,6 +55,14 @@ Comment: Godot Engine logo
 Copyright: 2017, Andrea Calabró
 License: CC-BY-4.0
 
+Files: ./core/math/convex_hull.cpp
+ ./core/math/convex_hull.h
+Comment: Bullet Continuous Collision Detection and Physics Library
+Copyright: 2011, Ole Kniemeyer, MAXON, www.maxon.net
+ 2007-2021, Juan Linietsky, Ariel Manzur.
+ 2014-2021, Godot Engine contributors.
+License: Expat and Zlib
+
 Files: ./modules/fbx/fbx_parser/
 Comment: Open Asset Import Library (FBX parser)
 Copyright: 2006-2020, assimp team

core/math/convex_hull.cpp

@@ -0,0 +1,2290 @@
+/*************************************************************************/
+/*  convex_hull.cpp                                                      */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+/*
+ * Based on Godot's patched VHACD-version of Bullet's btConvexHullComputer.
+ * See /thirdparty/vhacd/btConvexHullComputer.cpp at 64403ddcab9f1dca2408f0a412a22d899708bbb1
+ * In turn, based on /src/LinearMath/btConvexHullComputer.cpp in <https://github.com/bulletphysics/bullet3>
+ * at 73b217fb07e7e3ce126caeb28ab3c9ddd0718467
+ *
+ * Changes:
+ * - int32_t is consistently used instead of int in some cases
+ * - integrated patch db0d6c92927f5a1358b887f2645c11f3014f0e8a from Bullet (CWE-190 integer overflow in btConvexHullComputer)
+ * - adapted to Godot's code style
+ * - replaced Bullet's types (e.g. vectors) with Godot's
+ * - replaced custom Pool implementation with PagedAllocator
+ */
+
+/*
+Copyright (c) 2011 Ole Kniemeyer, MAXON, www.maxon.net
+
+This software is provided 'as-is', without any express or implied warranty.
+In no event will the authors be held liable for any damages arising from the use of this software.
+Permission is granted to anyone to use this software for any purpose,
+including commercial applications, and to alter it and redistribute it freely,
+subject to the following restrictions:
+
+1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
+2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
+3. This notice may not be removed or altered from any source distribution.
+*/
+
+#include "convex_hull.h"
+
+#include "core/error_macros.h"
+#include "core/math/aabb.h"
+#include "core/math/math_defs.h"
+#include "core/os/memory.h"
+#include "core/paged_allocator.h"
+
+#include <string.h>
+
+//#define DEBUG_CONVEX_HULL
+//#define SHOW_ITERATIONS
+
+// -- GODOT start --
+// Assembly optimizations are not used at the moment.
+//#define USE_X86_64_ASM
+// -- GODOT end --
+
+#ifdef DEBUG_ENABLED
+#define CHULL_ASSERT(m_cond)                                    \
+	do {                                                        \
+		if (unlikely(!(m_cond))) {                              \
+			ERR_PRINT("Assertion \"" _STR(m_cond) "\" failed.") \
+		}                                                       \
+	} while (0)
+#else
+#define CHULL_ASSERT(m_cond) \
+	do {                     \
+	} while (0)
+#endif
+
+#if defined(DEBUG_CONVEX_HULL) || defined(SHOW_ITERATIONS)
+#include <stdio.h>
+#endif
+
+// Convex hull implementation based on Preparata and Hong
+// Ole Kniemeyer, MAXON Computer GmbH
+class ConvexHullInternal {
+public:
+	class Point64 {
+	public:
+		int64_t x;
+		int64_t y;
+		int64_t z;
+
+		Point64(int64_t p_x, int64_t p_y, int64_t p_z) {
+			x = p_x;
+			y = p_y;
+			z = p_z;
+		}
+
+		bool is_zero() {
+			return (x == 0) && (y == 0) && (z == 0);
+		}
+
+		int64_t dot(const Point64 &b) const {
+			return x * b.x + y * b.y + z * b.z;
+		}
+	};
+
+	class Point32 {
+	public:
+		int32_t x = 0;
+		int32_t y = 0;
+		int32_t z = 0;
+		int32_t index = -1;
+
+		Point32() {
+		}
+
+		Point32(int32_t p_x, int32_t p_y, int32_t p_z) {
+			x = p_x;
+			y = p_y;
+			z = p_z;
+		}
+
+		bool operator==(const Point32 &b) const {
+			return (x == b.x) && (y == b.y) && (z == b.z);
+		}
+
+		bool operator!=(const Point32 &b) const {
+			return (x != b.x) || (y != b.y) || (z != b.z);
+		}
+
+		bool is_zero() {
+			return (x == 0) && (y == 0) && (z == 0);
+		}
+
+		Point64 cross(const Point32 &b) const {
+			return Point64((int64_t)y * b.z - (int64_t)z * b.y, (int64_t)z * b.x - (int64_t)x * b.z, (int64_t)x * b.y - (int64_t)y * b.x);
+		}
+
+		Point64 cross(const Point64 &b) const {
+			return Point64(y * b.z - z * b.y, z * b.x - x * b.z, x * b.y - y * b.x);
+		}
+
+		int64_t dot(const Point32 &b) const {
+			return (int64_t)x * b.x + (int64_t)y * b.y + (int64_t)z * b.z;
+		}
+
+		int64_t dot(const Point64 &b) const {
+			return x * b.x + y * b.y + z * b.z;
+		}
+
+		Point32 operator+(const Point32 &b) const {
+			return Point32(x + b.x, y + b.y, z + b.z);
+		}
+
+		Point32 operator-(const Point32 &b) const {
+			return Point32(x - b.x, y - b.y, z - b.z);
+		}
+	};
+
+	class Int128 {
+	public:
+		uint64_t low = 0;
+		uint64_t high = 0;
+
+		Int128() {
+		}
+
+		Int128(uint64_t p_low, uint64_t p_high) {
+			low = p_low;
+			high = p_high;
+		}
+
+		Int128(uint64_t p_low) {
+			low = p_low;
+			high = 0;
+		}
+
+		Int128(int64_t p_value) {
+			low = p_value;
+			if (p_value >= 0) {
+				high = 0;
+			} else {
+				high = (uint64_t)-1LL;
+			}
+		}
+
+		static Int128 mul(int64_t a, int64_t b);
+
+		static Int128 mul(uint64_t a, uint64_t b);
+
+		Int128 operator-() const {
+			return Int128((uint64_t) - (int64_t)low, ~high + (low == 0));
+		}
+
+		Int128 operator+(const Int128 &b) const {
+#ifdef USE_X86_64_ASM
+			Int128 result;
+			__asm__("addq %[bl], %[rl]\n\t"
+					"adcq %[bh], %[rh]\n\t"
+					: [rl] "=r"(result.low), [rh] "=r"(result.high)
+					: "0"(low), "1"(high), [bl] "g"(b.low), [bh] "g"(b.high)
+					: "cc");
+			return result;
+#else
+			uint64_t lo = low + b.low;
+			return Int128(lo, high + b.high + (lo < low));
+#endif
+		}
+
+		Int128 operator-(const Int128 &b) const {
+#ifdef USE_X86_64_ASM
+			Int128 result;
+			__asm__("subq %[bl], %[rl]\n\t"
+					"sbbq %[bh], %[rh]\n\t"
+					: [rl] "=r"(result.low), [rh] "=r"(result.high)
+					: "0"(low), "1"(high), [bl] "g"(b.low), [bh] "g"(b.high)
+					: "cc");
+			return result;
+#else
+			return *this + -b;
+#endif
+		}
+
+		Int128 &operator+=(const Int128 &b) {
+#ifdef USE_X86_64_ASM
+			__asm__("addq %[bl], %[rl]\n\t"
+					"adcq %[bh], %[rh]\n\t"
+					: [rl] "=r"(low), [rh] "=r"(high)
+					: "0"(low), "1"(high), [bl] "g"(b.low), [bh] "g"(b.high)
+					: "cc");
+#else
+			uint64_t lo = low + b.low;
+			if (lo < low) {
+				++high;
+			}
+			low = lo;
+			high += b.high;
+#endif
+			return *this;
+		}
+
+		Int128 &operator++() {
+			if (++low == 0) {
+				++high;
+			}
+			return *this;
+		}
+
+		Int128 operator*(int64_t b) const;
+
+		real_t to_scalar() const {
+			return ((int64_t)high >= 0) ? real_t(high) * (real_t(0x100000000LL) * real_t(0x100000000LL)) + real_t(low) : -(-*this).to_scalar();
+		}
+
+		int32_t get_sign() const {
+			return ((int64_t)high < 0) ? -1 : (high || low) ? 1 :
+																0;
+		}
+
+		bool operator<(const Int128 &b) const {
+			return (high < b.high) || ((high == b.high) && (low < b.low));
+		}
+
+		int32_t ucmp(const Int128 &b) const {
+			if (high < b.high) {
+				return -1;
+			}
+			if (high > b.high) {
+				return 1;
+			}
+			if (low < b.low) {
+				return -1;
+			}
+			if (low > b.low) {
+				return 1;
+			}
+			return 0;
+		}
+	};
+
+	class Rational64 {
+	private:
+		uint64_t numerator;
+		uint64_t denominator;
+		int32_t sign;
+
+	public:
+		Rational64(int64_t p_numerator, int64_t p_denominator) {
+			if (p_numerator > 0) {
+				sign = 1;
+				numerator = (uint64_t)p_numerator;
+			} else if (p_numerator < 0) {
+				sign = -1;
+				numerator = (uint64_t)-p_numerator;
+			} else {
+				sign = 0;
+				numerator = 0;
+			}
+			if (p_denominator > 0) {
+				denominator = (uint64_t)p_denominator;
+			} else if (p_denominator < 0) {
+				sign = -sign;
+				denominator = (uint64_t)-p_denominator;
+			} else {
+				denominator = 0;
+			}
+		}
+
+		bool is_negative_infinity() const {
+			return (sign < 0) && (denominator == 0);
+		}
+
+		bool is_nan() const {
+			return (sign == 0) && (denominator == 0);
+		}
+
+		int32_t compare(const Rational64 &b) const;
+
+		real_t to_scalar() const {
+			return sign * ((denominator == 0) ? FLT_MAX : (real_t)numerator / denominator);
+		}
+	};
+
+	class Rational128 {
+	private:
+		Int128 numerator;
+		Int128 denominator;
+		int32_t sign;
+		bool is_int_64;
+
+	public:
+		Rational128(int64_t p_value) {
+			if (p_value > 0) {
+				sign = 1;
+				this->numerator = p_value;
+			} else if (p_value < 0) {
+				sign = -1;
+				this->numerator = -p_value;
+			} else {
+				sign = 0;
+				this->numerator = (uint64_t)0;
+			}
+			this->denominator = (uint64_t)1;
+			is_int_64 = true;
+		}
+
+		Rational128(const Int128 &p_numerator, const Int128 &p_denominator) {
+			sign = p_numerator.get_sign();
+			if (sign >= 0) {
+				this->numerator = p_numerator;
+			} else {
+				this->numerator = -p_numerator;
+			}
+			int32_t dsign = p_denominator.get_sign();
+			if (dsign >= 0) {
+				this->denominator = p_denominator;
+			} else {
+				sign = -sign;
+				this->denominator = -p_denominator;
+			}
+			is_int_64 = false;
+		}
+
+		int32_t compare(const Rational128 &b) const;
+
+		int32_t compare(int64_t b) const;
+
+		real_t to_scalar() const {
+			return sign * ((denominator.get_sign() == 0) ? FLT_MAX : numerator.to_scalar() / denominator.to_scalar());
+		}
+	};
+
+	class PointR128 {
+	public:
+		Int128 x;
+		Int128 y;
+		Int128 z;
+		Int128 denominator;
+
+		PointR128() {
+		}
+
+		PointR128(Int128 p_x, Int128 p_y, Int128 p_z, Int128 p_denominator) {
+			x = p_x;
+			y = p_y;
+			z = p_z;
+			denominator = p_denominator;
+		}
+
+		real_t xvalue() const {
+			return x.to_scalar() / denominator.to_scalar();
+		}
+
+		real_t yvalue() const {
+			return y.to_scalar() / denominator.to_scalar();
+		}
+
+		real_t zvalue() const {
+			return z.to_scalar() / denominator.to_scalar();
+		}
+	};
+
+	class Edge;
+	class Face;
+
+	class Vertex {
+	public:
+		Vertex *next = nullptr;
+		Vertex *prev = nullptr;
+		Edge *edges = nullptr;
+		Face *first_nearby_face = nullptr;
+		Face *last_nearby_face = nullptr;
+		PointR128 point128;
+		Point32 point;
+		int32_t copy = -1;
+
+		Vertex() {
+		}
+
+#ifdef DEBUG_CONVEX_HULL
+		void print() {
+			printf("V%d (%d, %d, %d)", point.index, point.x, point.y, point.z);
+		}
+
+		void print_graph();
+#endif
+
+		Point32 operator-(const Vertex &b) const {
+			return point - b.point;
+		}
+
+		Rational128 dot(const Point64 &b) const {
+			return (point.index >= 0) ? Rational128(point.dot(b)) : Rational128(point128.x * b.x + point128.y * b.y + point128.z * b.z, point128.denominator);
+		}
+
+		real_t xvalue() const {
+			return (point.index >= 0) ? real_t(point.x) : point128.xvalue();
+		}
+
+		real_t yvalue() const {
+			return (point.index >= 0) ? real_t(point.y) : point128.yvalue();
+		}
+
+		real_t zvalue() const {
+			return (point.index >= 0) ? real_t(point.z) : point128.zvalue();
+		}
+
+		void receive_nearby_faces(Vertex *p_src) {
+			if (last_nearby_face) {
+				last_nearby_face->next_with_same_nearby_vertex = p_src->first_nearby_face;
+			} else {
+				first_nearby_face = p_src->first_nearby_face;
+			}
+			if (p_src->last_nearby_face) {
+				last_nearby_face = p_src->last_nearby_face;
+			}
+			for (Face *f = p_src->first_nearby_face; f; f = f->next_with_same_nearby_vertex) {
+				CHULL_ASSERT(f->nearby_vertex == p_src);
+				f->nearby_vertex = this;
+			}
+			p_src->first_nearby_face = nullptr;
+			p_src->last_nearby_face = nullptr;
+		}
+	};
+
+	class Edge {
+	public:
+		Edge *next = nullptr;
+		Edge *prev = nullptr;
+		Edge *reverse = nullptr;
+		Vertex *target = nullptr;
+		Face *face = nullptr;
+		int32_t copy = -1;
+
+		void link(Edge *n) {
+			CHULL_ASSERT(reverse->target == n->reverse->target);
+			next = n;
+			n->prev = this;
+		}
+
+#ifdef DEBUG_CONVEX_HULL
+		void print() {
+			printf("E%p : %d -> %d,  n=%p p=%p   (0 %d\t%d\t%d) -> (%d %d %d)", this, reverse->target->point.index, target->point.index, next, prev,
+					reverse->target->point.x, reverse->target->point.y, reverse->target->point.z, target->point.x, target->point.y, target->point.z);
+		}
+#endif
+	};
+
+	class Face {
+	public:
+		Face *next = nullptr;
+		Vertex *nearby_vertex = nullptr;
+		Face *next_with_same_nearby_vertex = nullptr;
+		Point32 origin;
+		Point32 dir0;
+		Point32 dir1;
+
+		Face() {
+		}
+
+		void init(Vertex *p_a, Vertex *p_b, Vertex *p_c) {
+			nearby_vertex = p_a;
+			origin = p_a->point;
+			dir0 = *p_b - *p_a;
+			dir1 = *p_c - *p_a;
+			if (p_a->last_nearby_face) {
+				p_a->last_nearby_face->next_with_same_nearby_vertex = this;
+			} else {
+				p_a->first_nearby_face = this;
+			}
+			p_a->last_nearby_face = this;
+		}
+
+		Point64 get_normal() {
+			return dir0.cross(dir1);
+		}
+	};
+
+	template <typename UWord, typename UHWord>
+	class DMul {
+	private:
+		static uint32_t high(uint64_t p_value) {
+			return (uint32_t)(p_value >> 32);
+		}
+
+		static uint32_t low(uint64_t p_value) {
+			return (uint32_t)p_value;
+		}
+
+		static uint64_t mul(uint32_t a, uint32_t b) {
+			return (uint64_t)a * (uint64_t)b;
+		}
+
+		static void shl_half(uint64_t &p_value) {
+			p_value <<= 32;
+		}
+
+		static uint64_t high(Int128 p_value) {
+			return p_value.high;
+		}
+
+		static uint64_t low(Int128 p_value) {
+			return p_value.low;
+		}
+
+		static Int128 mul(uint64_t a, uint64_t b) {
+			return Int128::mul(a, b);
+		}
+
+		static void shl_half(Int128 &p_value) {
+			p_value.high = p_value.low;
+			p_value.low = 0;
+		}
+
+	public:
+		static void mul(UWord p_a, UWord p_b, UWord &r_low, UWord &r_high) {
+			UWord p00 = mul(low(p_a), low(p_b));
+			UWord p01 = mul(low(p_a), high(p_b));
+			UWord p10 = mul(high(p_a), low(p_b));
+			UWord p11 = mul(high(p_a), high(p_b));
+			UWord p0110 = UWord(low(p01)) + UWord(low(p10));
+			p11 += high(p01);
+			p11 += high(p10);
+			p11 += high(p0110);
+			shl_half(p0110);
+			p00 += p0110;
+			if (p00 < p0110) {
+				++p11;
+			}
+			r_low = p00;
+			r_high = p11;
+		}
+	};
+
+private:
+	class IntermediateHull {
+	public:
+		Vertex *min_xy = nullptr;
+		Vertex *max_xy = nullptr;
+		Vertex *min_yx = nullptr;
+		Vertex *max_yx = nullptr;
+
+		IntermediateHull() {
+		}
+
+		void print();
+	};
+
+	enum Orientation { NONE,
+		CLOCKWISE,
+		COUNTER_CLOCKWISE };
+
+	Vector3 scaling;
+	Vector3 center;
+	PagedAllocator<Vertex> vertex_pool;
+	PagedAllocator<Edge> edge_pool;
+	PagedAllocator<Face> face_pool;
+	LocalVector<Vertex *> original_vertices;
+	int32_t merge_stamp = 0;
+	int32_t min_axis = 0;
+	int32_t med_axis = 0;
+	int32_t max_axis = 0;
+	int32_t used_edge_pairs = 0;
+	int32_t max_used_edge_pairs = 0;
+
+	static Orientation get_orientation(const Edge *p_prev, const Edge *p_next, const Point32 &p_s, const Point32 &p_t);
+	Edge *find_max_angle(bool p_ccw, const Vertex *p_start, const Point32 &p_s, const Point64 &p_rxs, const Point64 &p_ssxrxs, Rational64 &p_min_cot);
+	void find_edge_for_coplanar_faces(Vertex *p_c0, Vertex *p_c1, Edge *&p_e0, Edge *&p_e1, Vertex *p_stop0, Vertex *p_stop1);
+
+	Edge *new_edge_pair(Vertex *p_from, Vertex *p_to);
+
+	void remove_edge_pair(Edge *p_edge) {
+		Edge *n = p_edge->next;
+		Edge *r = p_edge->reverse;
+
+		CHULL_ASSERT(p_edge->target && r->target);
+
+		if (n != p_edge) {
+			n->prev = p_edge->prev;
+			p_edge->prev->next = n;
+			r->target->edges = n;
+		} else {
+			r->target->edges = nullptr;
+		}
+
+		n = r->next;
+
+		if (n != r) {
+			n->prev = r->prev;
+			r->prev->next = n;
+			p_edge->target->edges = n;
+		} else {
+			p_edge->target->edges = nullptr;
+		}
+
+		edge_pool.free(p_edge);
+		edge_pool.free(r);
+		used_edge_pairs--;
+	}
+
+	void compute_internal(int32_t p_start, int32_t p_end, IntermediateHull &r_result);
+
+	bool merge_projection(IntermediateHull &p_h0, IntermediateHull &p_h1, Vertex *&r_c0, Vertex *&r_c1);
+
+	void merge(IntermediateHull &p_h0, IntermediateHull &p_h1);
+
+	Vector3 to_gd_vector(const Point32 &p_v);
+
+	Vector3 get_gd_normal(Face *p_face);
+
+	bool shift_face(Face *p_face, real_t p_amount, LocalVector<Vertex *> p_stack);
+
+public:
+	~ConvexHullInternal() {
+		vertex_pool.reset(true);
+		edge_pool.reset(true);
+		face_pool.reset(true);
+	}
+
+	Vertex *vertex_list;
+
+	void compute(const Vector3 *p_coords, int32_t p_count);
+
+	Vector3 get_coordinates(const Vertex *p_v);
+
+	real_t shrink(real_t amount, real_t p_clamp_amount);
+};
+
+ConvexHullInternal::Int128 ConvexHullInternal::Int128::operator*(int64_t b) const {
+	bool negative = (int64_t)high < 0;
+	Int128 a = negative ? -*this : *this;
+	if (b < 0) {
+		negative = !negative;
+		b = -b;
+	}
+	Int128 result = mul(a.low, (uint64_t)b);
+	result.high += a.high * (uint64_t)b;
+	return negative ? -result : result;
+}
+
+ConvexHullInternal::Int128 ConvexHullInternal::Int128::mul(int64_t a, int64_t b) {
+	Int128 result;
+
+#ifdef USE_X86_64_ASM
+	__asm__("imulq %[b]"
+			: "=a"(result.low), "=d"(result.high)
+			: "0"(a), [b] "r"(b)
+			: "cc");
+	return result;
+
+#else
+	bool negative = a < 0;
+	if (negative) {
+		a = -a;
+	}
+	if (b < 0) {
+		negative = !negative;
+		b = -b;
+	}
+	DMul<uint64_t, uint32_t>::mul((uint64_t)a, (uint64_t)b, result.low, result.high);
+	return negative ? -result : result;
+#endif
+}
+
+ConvexHullInternal::Int128 ConvexHullInternal::Int128::mul(uint64_t a, uint64_t b) {
+	Int128 result;
+
+#ifdef USE_X86_64_ASM
+	__asm__("mulq %[b]"
+			: "=a"(result.low), "=d"(result.high)
+			: "0"(a), [b] "r"(b)
+			: "cc");
+
+#else
+	DMul<uint64_t, uint32_t>::mul(a, b, result.low, result.high);
+#endif
+
+	return result;
+}
+
+int32_t ConvexHullInternal::Rational64::compare(const Rational64 &b) const {
+	if (sign != b.sign) {
+		return sign - b.sign;
+	} else if (sign == 0) {
+		return 0;
+	}
+
+	//	return (numerator * b.denominator > b.numerator * denominator) ? sign : (numerator * b.denominator < b.numerator * denominator) ? -sign : 0;
+
+#ifdef USE_X86_64_ASM
+
+	int32_t result;
+	int64_t tmp;
+	int64_t dummy;
+	__asm__("mulq %[bn]\n\t"
+			"movq %%rax, %[tmp]\n\t"
+			"movq %%rdx, %%rbx\n\t"
+			"movq %[tn], %%rax\n\t"
+			"mulq %[bd]\n\t"
+			"subq %[tmp], %%rax\n\t"
+			"sbbq %%rbx, %%rdx\n\t" // rdx:rax contains 128-bit-difference "numerator*b.denominator - b.numerator*denominator"
+			"setnsb %%bh\n\t" // bh=1 if difference is non-negative, bh=0 otherwise
+			"orq %%rdx, %%rax\n\t"
+			"setnzb %%bl\n\t" // bl=1 if difference if non-zero, bl=0 if it is zero
+			"decb %%bh\n\t" // now bx=0x0000 if difference is zero, 0xff01 if it is negative, 0x0001 if it is positive (i.e., same sign as difference)
+			"shll $16, %%ebx\n\t" // ebx has same sign as difference
+			: "=&b"(result), [tmp] "=&r"(tmp), "=a"(dummy)
+			: "a"(denominator), [bn] "g"(b.numerator), [tn] "g"(numerator), [bd] "g"(b.denominator)
+			: "%rdx", "cc");
+	return result ? result ^ sign // if sign is +1, only bit 0 of result is inverted, which does not change the sign of result (and cannot result in zero)
+					// if sign is -1, all bits of result are inverted, which changes the sign of result (and again cannot result in zero)
+					:
+					  0;
+
+#else
+
+	return sign * Int128::mul(numerator, b.denominator).ucmp(Int128::mul(denominator, b.numerator));
+
+#endif
+}
+
+int32_t ConvexHullInternal::Rational128::compare(const Rational128 &b) const {
+	if (sign != b.sign) {
+		return sign - b.sign;
+	} else if (sign == 0) {
+		return 0;
+	}
+	if (is_int_64) {
+		return -b.compare(sign * (int64_t)numerator.low);
+	}
+
+	Int128 nbd_low, nbd_high, dbn_low, dbn_high;
+	DMul<Int128, uint64_t>::mul(numerator, b.denominator, nbd_low, nbd_high);
+	DMul<Int128, uint64_t>::mul(denominator, b.numerator, dbn_low, dbn_high);
+
+	int32_t cmp = nbd_high.ucmp(dbn_high);
+	if (cmp) {
+		return cmp * sign;
+	}
+	return nbd_low.ucmp(dbn_low) * sign;
+}
+
+int32_t ConvexHullInternal::Rational128::compare(int64_t b) const {
+	if (is_int_64) {
+		int64_t a = sign * (int64_t)numerator.low;
+		return (a > b) ? 1 : (a < b) ? -1 :
+										 0;
+	}
+	if (b > 0) {
+		if (sign <= 0) {
+			return -1;
+		}
+	} else if (b < 0) {
+		if (sign >= 0) {
+			return 1;
+		}
+		b = -b;
+	} else {
+		return sign;
+	}
+
+	return numerator.ucmp(denominator * b) * sign;
+}
+
+ConvexHullInternal::Edge *ConvexHullInternal::new_edge_pair(Vertex *p_from, Vertex *p_to) {
+	CHULL_ASSERT(p_from && p_to);
+	Edge *e = edge_pool.alloc();
+	Edge *r = edge_pool.alloc();
+	e->reverse = r;
+	r->reverse = e;
+	e->copy = merge_stamp;
+	r->copy = merge_stamp;
+	e->target = p_to;
+	r->target = p_from;
+	e->face = nullptr;
+	r->face = nullptr;
+	used_edge_pairs++;
+	if (used_edge_pairs > max_used_edge_pairs) {
+		max_used_edge_pairs = used_edge_pairs;
+	}
+	return e;
+}
+
+bool ConvexHullInternal::merge_projection(IntermediateHull &r_h0, IntermediateHull &r_h1, Vertex *&r_c0, Vertex *&r_c1) {
+	Vertex *v0 = r_h0.max_yx;
+	Vertex *v1 = r_h1.min_yx;
+	if ((v0->point.x == v1->point.x) && (v0->point.y == v1->point.y)) {
+		CHULL_ASSERT(v0->point.z < v1->point.z);
+		Vertex *v1p = v1->prev;
+		if (v1p == v1) {
+			r_c0 = v0;
+			if (v1->edges) {
+				CHULL_ASSERT(v1->edges->next == v1->edges);
+				v1 = v1->edges->target;
+				CHULL_ASSERT(v1->edges->next == v1->edges);
+			}
+			r_c1 = v1;
+			return false;
+		}
+		Vertex *v1n = v1->next;
+		v1p->next = v1n;
+		v1n->prev = v1p;
+		if (v1 == r_h1.min_xy) {
+			if ((v1n->point.x < v1p->point.x) || ((v1n->point.x == v1p->point.x) && (v1n->point.y < v1p->point.y))) {
+				r_h1.min_xy = v1n;
+			} else {
+				r_h1.min_xy = v1p;
+			}
+		}
+		if (v1 == r_h1.max_xy) {
+			if ((v1n->point.x > v1p->point.x) || ((v1n->point.x == v1p->point.x) && (v1n->point.y > v1p->point.y))) {
+				r_h1.max_xy = v1n;
+			} else {
+				r_h1.max_xy = v1p;
+			}
+		}
+	}
+
+	v0 = r_h0.max_xy;
+	v1 = r_h1.max_xy;
+	Vertex *v00 = nullptr;
+	Vertex *v10 = nullptr;
+	int32_t sign = 1;
+
+	for (int32_t side = 0; side <= 1; side++) {
+		int32_t dx = (v1->point.x - v0->point.x) * sign;
+		if (dx > 0) {
+			while (true) {
+				int32_t dy = v1->point.y - v0->point.y;
+
+				Vertex *w0 = side ? v0->next : v0->prev;
+				if (w0 != v0) {
+					int32_t dx0 = (w0->point.x - v0->point.x) * sign;
+					int32_t dy0 = w0->point.y - v0->point.y;
+					if ((dy0 <= 0) && ((dx0 == 0) || ((dx0 < 0) && (dy0 * dx <= dy * dx0)))) {
+						v0 = w0;
+						dx = (v1->point.x - v0->point.x) * sign;
+						continue;
+					}
+				}
+
+				Vertex *w1 = side ? v1->next : v1->prev;
+				if (w1 != v1) {
+					int32_t dx1 = (w1->point.x - v1->point.x) * sign;
+					int32_t dy1 = w1->point.y - v1->point.y;
+					int32_t dxn = (w1->point.x - v0->point.x) * sign;
+					if ((dxn > 0) && (dy1 < 0) && ((dx1 == 0) || ((dx1 < 0) && (dy1 * dx < dy * dx1)))) {
+						v1 = w1;
+						dx = dxn;
+						continue;
+					}
+				}
+
+				break;
+			}
+		} else if (dx < 0) {
+			while (true) {
+				int32_t dy = v1->point.y - v0->point.y;
+
+				Vertex *w1 = side ? v1->prev : v1->next;
+				if (w1 != v1) {
+					int32_t dx1 = (w1->point.x - v1->point.x) * sign;
+					int32_t dy1 = w1->point.y - v1->point.y;
+					if ((dy1 >= 0) && ((dx1 == 0) || ((dx1 < 0) && (dy1 * dx <= dy * dx1)))) {
+						v1 = w1;
+						dx = (v1->point.x - v0->point.x) * sign;
+						continue;
+					}
+				}
+
+				Vertex *w0 = side ? v0->prev : v0->next;
+				if (w0 != v0) {
+					int32_t dx0 = (w0->point.x - v0->point.x) * sign;
+					int32_t dy0 = w0->point.y - v0->point.y;
+					int32_t dxn = (v1->point.x - w0->point.x) * sign;
+					if ((dxn < 0) && (dy0 > 0) && ((dx0 == 0) || ((dx0 < 0) && (dy0 * dx < dy * dx0)))) {
+						v0 = w0;
+						dx = dxn;
+						continue;
+					}
+				}
+
+				break;
+			}
+		} else {
+			int32_t x = v0->point.x;
+			int32_t y0 = v0->point.y;
+			Vertex *w0 = v0;
+			Vertex *t;
+			while (((t = side ? w0->next : w0->prev) != v0) && (t->point.x == x) && (t->point.y <= y0)) {
+				w0 = t;
+				y0 = t->point.y;
+			}
+			v0 = w0;
+
+			int32_t y1 = v1->point.y;
+			Vertex *w1 = v1;
+			while (((t = side ? w1->prev : w1->next) != v1) && (t->point.x == x) && (t->point.y >= y1)) {
+				w1 = t;
+				y1 = t->point.y;
+			}
+			v1 = w1;
+		}
+
+		if (side == 0) {
+			v00 = v0;
+			v10 = v1;
+
+			v0 = r_h0.min_xy;
+			v1 = r_h1.min_xy;
+			sign = -1;
+		}
+	}
+
+	v0->prev = v1;
+	v1->next = v0;
+
+	v00->next = v10;
+	v10->prev = v00;
+
+	if (r_h1.min_xy->point.x < r_h0.min_xy->point.x) {
+		r_h0.min_xy = r_h1.min_xy;
+	}
+	if (r_h1.max_xy->point.x >= r_h0.max_xy->point.x) {
+		r_h0.max_xy = r_h1.max_xy;
+	}
+
+	r_h0.max_yx = r_h1.max_yx;
+
+	r_c0 = v00;
+	r_c1 = v10;
+
+	return true;
+}
+
+void ConvexHullInternal::compute_internal(int32_t p_start, int32_t p_end, IntermediateHull &r_result) {
+	int32_t n = p_end - p_start;
+	switch (n) {
+		case 0:
+			r_result.min_xy = nullptr;
+			r_result.max_xy = nullptr;
+			r_result.min_yx = nullptr;
+			r_result.max_yx = nullptr;
+			return;
+		case 2: {
+			Vertex *v = original_vertices[p_start];
+			Vertex *w = original_vertices[p_start + 1];
+			if (v->point != w->point) {
+				int32_t dx = v->point.x - w->point.x;
+				int32_t dy = v->point.y - w->point.y;
+
+				if ((dx == 0) && (dy == 0)) {
+					if (v->point.z > w->point.z) {
+						Vertex *t = w;
+						w = v;
+						v = t;
+					}
+					CHULL_ASSERT(v->point.z < w->point.z);
+					v->next = v;
+					v->prev = v;
+					r_result.min_xy = v;
+					r_result.max_xy = v;
+					r_result.min_yx = v;
+					r_result.max_yx = v;
+				} else {
+					v->next = w;
+					v->prev = w;
+					w->next = v;
+					w->prev = v;
+
+					if ((dx < 0) || ((dx == 0) && (dy < 0))) {
+						r_result.min_xy = v;
+						r_result.max_xy = w;
+					} else {
+						r_result.min_xy = w;
+						r_result.max_xy = v;
+					}
+
+					if ((dy < 0) || ((dy == 0) && (dx < 0))) {
+						r_result.min_yx = v;
+						r_result.max_yx = w;
+					} else {
+						r_result.min_yx = w;
+						r_result.max_yx = v;
+					}
+				}
+
+				Edge *e = new_edge_pair(v, w);
+				e->link(e);
+				v->edges = e;
+
+				e = e->reverse;
+				e->link(e);
+				w->edges = e;
+
+				return;
+			}
+		}
+		// lint -fallthrough
+		case 1: {
+			Vertex *v = original_vertices[p_start];
+			v->edges = nullptr;
+			v->next = v;
+			v->prev = v;
+
+			r_result.min_xy = v;
+			r_result.max_xy = v;
+			r_result.min_yx = v;
+			r_result.max_yx = v;
+
+			return;
+		}
+	}
+
+	int32_t split0 = p_start + n / 2;
+	Point32 p = original_vertices[split0 - 1]->point;
+	int32_t split1 = split0;
+	while ((split1 < p_end) && (original_vertices[split1]->point == p)) {
+		split1++;
+	}
+	compute_internal(p_start, split0, r_result);
+	IntermediateHull hull1;
+	compute_internal(split1, p_end, hull1);
+#ifdef DEBUG_CONVEX_HULL
+	printf("\n\nMerge\n");
+	r_result.print();
+	hull1.print();
+#endif
+	merge(r_result, hull1);
+#ifdef DEBUG_CONVEX_HULL
+	printf("\n  Result\n");
+	r_result.print();
+#endif
+}
+
+#ifdef DEBUG_CONVEX_HULL
+void ConvexHullInternal::IntermediateHull::print() {
+	printf("    Hull\n");
+	for (Vertex *v = min_xy; v;) {
+		printf("      ");
+		v->print();
+		if (v == max_xy) {
+			printf(" max_xy");
+		}
+		if (v == min_yx) {
+			printf(" min_yx");
+		}
+		if (v == max_yx) {
+			printf(" max_yx");
+		}
+		if (v->next->prev != v) {
+			printf(" Inconsistency");
+		}
+		printf("\n");
+		v = v->next;
+		if (v == min_xy) {
+			break;
+		}
+	}
+	if (min_xy) {
+		min_xy->copy = (min_xy->copy == -1) ? -2 : -1;
+		min_xy->print_graph();
+	}
+}
+
+void ConvexHullInternal::Vertex::print_graph() {
+	print();
+	printf("\nEdges\n");
+	Edge *e = edges;
+	if (e) {
+		do {
+			e->print();
+			printf("\n");
+			e = e->next;
+		} while (e != edges);
+		do {
+			Vertex *v = e->target;
+			if (v->copy != copy) {
+				v->copy = copy;
+				v->print_graph();
+			}
+			e = e->next;
+		} while (e != edges);
+	}
+}
+#endif
+
+ConvexHullInternal::Orientation ConvexHullInternal::get_orientation(const Edge *p_prev, const Edge *p_next, const Point32 &p_s, const Point32 &p_t) {
+	CHULL_ASSERT(p_prev->reverse->target == p_next->reverse->target);
+	if (p_prev->next == p_next) {
+		if (p_prev->prev == p_next) {
+			Point64 n = p_t.cross(p_s);
+			Point64 m = (*p_prev->target - *p_next->reverse->target).cross(*p_next->target - *p_next->reverse->target);
+			CHULL_ASSERT(!m.is_zero());
+			int64_t dot = n.dot(m);
+			CHULL_ASSERT(dot != 0);
+			return (dot > 0) ? COUNTER_CLOCKWISE : CLOCKWISE;
+		}
+		return COUNTER_CLOCKWISE;
+	} else if (p_prev->prev == p_next) {
+		return CLOCKWISE;
+	} else {
+		return NONE;
+	}
+}
+
+ConvexHullInternal::Edge *ConvexHullInternal::find_max_angle(bool p_ccw, const Vertex *p_start, const Point32 &p_s, const Point64 &p_rxs, const Point64 &p_sxrxs, Rational64 &p_min_cot) {
+	Edge *min_edge = nullptr;
+
+#ifdef DEBUG_CONVEX_HULL
+	printf("find max edge for %d\n", p_start->point.index);
+#endif
+	Edge *e = p_start->edges;
+	if (e) {
+		do {
+			if (e->copy > merge_stamp) {
+				Point32 t = *e->target - *p_start;
+				Rational64 cot(t.dot(p_sxrxs), t.dot(p_rxs));
+#ifdef DEBUG_CONVEX_HULL
+				printf("      Angle is %f (%d) for ", Math::atan(cot.to_scalar()), (int32_t)cot.is_nan());
+				e->print();
+#endif
+				if (cot.is_nan()) {
+					CHULL_ASSERT(p_ccw ? (t.dot(p_s) < 0) : (t.dot(p_s) > 0));
+				} else {
+					int32_t cmp;
+					if (min_edge == nullptr) {
+						p_min_cot = cot;
+						min_edge = e;
+					} else if ((cmp = cot.compare(p_min_cot)) < 0) {
+						p_min_cot = cot;
+						min_edge = e;
+					} else if ((cmp == 0) && (p_ccw == (get_orientation(min_edge, e, p_s, t) == COUNTER_CLOCKWISE))) {
+						min_edge = e;
+					}
+				}
+#ifdef DEBUG_CONVEX_HULL
+				printf("\n");
+#endif
+			}
+			e = e->next;
+		} while (e != p_start->edges);
+	}
+	return min_edge;
+}
+
+void ConvexHullInternal::find_edge_for_coplanar_faces(Vertex *p_c0, Vertex *p_c1, Edge *&p_e0, Edge *&p_e1, Vertex *p_stop0, Vertex *p_stop1) {
+	Edge *start0 = p_e0;
+	Edge *start1 = p_e1;
+	Point32 et0 = start0 ? start0->target->point : p_c0->point;
+	Point32 et1 = start1 ? start1->target->point : p_c1->point;
+	Point32 s = p_c1->point - p_c0->point;
+	Point64 normal = ((start0 ? start0 : start1)->target->point - p_c0->point).cross(s);
+	int64_t dist = p_c0->point.dot(normal);
+	CHULL_ASSERT(!start1 || (start1->target->point.dot(normal) == dist));
+	Point64 perp = s.cross(normal);
+	CHULL_ASSERT(!perp.is_zero());
+
+#ifdef DEBUG_CONVEX_HULL
+	printf("   Advancing %d %d  (%p %p, %d %d)\n", p_c0->point.index, p_c1->point.index, start0, start1, start0 ? start0->target->point.index : -1, start1 ? start1->target->point.index : -1);
+#endif
+
+	int64_t max_dot0 = et0.dot(perp);
+	if (p_e0) {
+		while (p_e0->target != p_stop0) {
+			Edge *e = p_e0->reverse->prev;
+			if (e->target->point.dot(normal) < dist) {
+				break;
+			}
+			CHULL_ASSERT(e->target->point.dot(normal) == dist);
+			if (e->copy == merge_stamp) {
+				break;
+			}
+			int64_t dot = e->target->point.dot(perp);
+			if (dot <= max_dot0) {
+				break;
+			}
+			max_dot0 = dot;
+			p_e0 = e;
+			et0 = e->target->point;
+		}
+	}
+
+	int64_t max_dot1 = et1.dot(perp);
+	if (p_e1) {
+		while (p_e1->target != p_stop1) {
+			Edge *e = p_e1->reverse->next;
+			if (e->target->point.dot(normal) < dist) {
+				break;
+			}
+			CHULL_ASSERT(e->target->point.dot(normal) == dist);
+			if (e->copy == merge_stamp) {
+				break;
+			}
+			int64_t dot = e->target->point.dot(perp);
+			if (dot <= max_dot1) {
+				break;
+			}
+			max_dot1 = dot;
+			p_e1 = e;
+			et1 = e->target->point;
+		}
+	}
+
+#ifdef DEBUG_CONVEX_HULL
+	printf("   Starting at %d %d\n", et0.index, et1.index);
+#endif
+
+	int64_t dx = max_dot1 - max_dot0;
+	if (dx > 0) {
+		while (true) {
+			int64_t dy = (et1 - et0).dot(s);
+
+			if (p_e0 && (p_e0->target != p_stop0)) {
+				Edge *f0 = p_e0->next->reverse;
+				if (f0->copy > merge_stamp) {
+					int64_t dx0 = (f0->target->point - et0).dot(perp);
+					int64_t dy0 = (f0->target->point - et0).dot(s);
+					if ((dx0 == 0) ? (dy0 < 0) : ((dx0 < 0) && (Rational64(dy0, dx0).compare(Rational64(dy, dx)) >= 0))) {
+						et0 = f0->target->point;
+						dx = (et1 - et0).dot(perp);
+						p_e0 = (p_e0 == start0) ? nullptr : f0;
+						continue;
+					}
+				}
+			}
+
+			if (p_e1 && (p_e1->target != p_stop1)) {
+				Edge *f1 = p_e1->reverse->next;
+				if (f1->copy > merge_stamp) {
+					Point32 d1 = f1->target->point - et1;
+					if (d1.dot(normal) == 0) {
+						int64_t dx1 = d1.dot(perp);
+						int64_t dy1 = d1.dot(s);
+						int64_t dxn = (f1->target->point - et0).dot(perp);
+						if ((dxn > 0) && ((dx1 == 0) ? (dy1 < 0) : ((dx1 < 0) && (Rational64(dy1, dx1).compare(Rational64(dy, dx)) > 0)))) {
+							p_e1 = f1;
+							et1 = p_e1->target->point;
+							dx = dxn;
+							continue;
+						}
+					} else {
+						CHULL_ASSERT((p_e1 == start1) && (d1.dot(normal) < 0));
+					}
+				}
+			}
+
+			break;
+		}
+	} else if (dx < 0) {
+		while (true) {
+			int64_t dy = (et1 - et0).dot(s);
+
+			if (p_e1 && (p_e1->target != p_stop1)) {
+				Edge *f1 = p_e1->prev->reverse;
+				if (f1->copy > merge_stamp) {
+					int64_t dx1 = (f1->target->point - et1).dot(perp);
+					int64_t dy1 = (f1->target->point - et1).dot(s);
+					if ((dx1 == 0) ? (dy1 > 0) : ((dx1 < 0) && (Rational64(dy1, dx1).compare(Rational64(dy, dx)) <= 0))) {
+						et1 = f1->target->point;
+						dx = (et1 - et0).dot(perp);
+						p_e1 = (p_e1 == start1) ? nullptr : f1;
+						continue;
+					}
+				}
+			}
+
+			if (p_e0 && (p_e0->target != p_stop0)) {
+				Edge *f0 = p_e0->reverse->prev;
+				if (f0->copy > merge_stamp) {
+					Point32 d0 = f0->target->point - et0;
+					if (d0.dot(normal) == 0) {
+						int64_t dx0 = d0.dot(perp);
+						int64_t dy0 = d0.dot(s);
+						int64_t dxn = (et1 - f0->target->point).dot(perp);
+						if ((dxn < 0) && ((dx0 == 0) ? (dy0 > 0) : ((dx0 < 0) && (Rational64(dy0, dx0).compare(Rational64(dy, dx)) < 0)))) {
+							p_e0 = f0;
+							et0 = p_e0->target->point;
+							dx = dxn;
+							continue;
+						}
+					} else {
+						CHULL_ASSERT((p_e0 == start0) && (d0.dot(normal) < 0));
+					}
+				}
+			}
+
+			break;
+		}
+	}
+#ifdef DEBUG_CONVEX_HULL
+	printf("   Advanced edges to %d %d\n", et0.index, et1.index);
+#endif
+}
+
+void ConvexHullInternal::merge(IntermediateHull &p_h0, IntermediateHull &p_h1) {
+	if (!p_h1.max_xy) {
+		return;
+	}
+	if (!p_h0.max_xy) {
+		p_h0 = p_h1;
+		return;
+	}
+
+	merge_stamp--;
+
+	Vertex *c0 = nullptr;
+	Edge *to_prev0 = nullptr;
+	Edge *first_new0 = nullptr;
+	Edge *pending_head0 = nullptr;
+	Edge *pending_tail0 = nullptr;
+	Vertex *c1 = nullptr;
+	Edge *to_prev1 = nullptr;
+	Edge *first_new1 = nullptr;
+	Edge *pending_head1 = nullptr;
+	Edge *pending_tail1 = nullptr;
+	Point32 prev_point;
+
+	if (merge_projection(p_h0, p_h1, c0, c1)) {
+		Point32 s = *c1 - *c0;
+		Point64 normal = Point32(0, 0, -1).cross(s);
+		Point64 t = s.cross(normal);
+		CHULL_ASSERT(!t.is_zero());
+
+		Edge *e = c0->edges;
+		Edge *start0 = nullptr;
+		if (e) {
+			do {
+				int64_t dot = (*e->target - *c0).dot(normal);
+				CHULL_ASSERT(dot <= 0);
+				if ((dot == 0) && ((*e->target - *c0).dot(t) > 0)) {
+					if (!start0 || (get_orientation(start0, e, s, Point32(0, 0, -1)) == CLOCKWISE)) {
+						start0 = e;
+					}
+				}
+				e = e->next;
+			} while (e != c0->edges);
+		}
+
+		e = c1->edges;
+		Edge *start1 = nullptr;
+		if (e) {
+			do {
+				int64_t dot = (*e->target - *c1).dot(normal);
+				CHULL_ASSERT(dot <= 0);
+				if ((dot == 0) && ((*e->target - *c1).dot(t) > 0)) {
+					if (!start1 || (get_orientation(start1, e, s, Point32(0, 0, -1)) == COUNTER_CLOCKWISE)) {
+						start1 = e;
+					}
+				}
+				e = e->next;
+			} while (e != c1->edges);
+		}
+
+		if (start0 || start1) {
+			find_edge_for_coplanar_faces(c0, c1, start0, start1, nullptr, nullptr);
+			if (start0) {
+				c0 = start0->target;
+			}
+			if (start1) {
+				c1 = start1->target;
+			}
+		}
+
+		prev_point = c1->point;
+		prev_point.z++;
+	} else {
+		prev_point = c1->point;
+		prev_point.x++;
+	}
+
+	Vertex *first0 = c0;
+	Vertex *first1 = c1;
+	bool first_run = true;
+
+	while (true) {
+		Point32 s = *c1 - *c0;
+		Point32 r = prev_point - c0->point;
+		Point64 rxs = r.cross(s);
+		Point64 sxrxs = s.cross(rxs);
+
+#ifdef DEBUG_CONVEX_HULL
+		printf("\n  Checking %d %d\n", c0->point.index, c1->point.index);
+#endif
+		Rational64 min_cot0(0, 0);
+		Edge *min0 = find_max_angle(false, c0, s, rxs, sxrxs, min_cot0);
+		Rational64 min_cot1(0, 0);
+		Edge *min1 = find_max_angle(true, c1, s, rxs, sxrxs, min_cot1);
+		if (!min0 && !min1) {
+			Edge *e = new_edge_pair(c0, c1);
+			e->link(e);
+			c0->edges = e;
+
+			e = e->reverse;
+			e->link(e);
+			c1->edges = e;
+			return;
+		} else {
+			int32_t cmp = !min0 ? 1 : !min1 ? -1 :
+												min_cot0.compare(min_cot1);
+#ifdef DEBUG_CONVEX_HULL
+			printf("    -> Result %d\n", cmp);
+#endif
+			if (first_run || ((cmp >= 0) ? !min_cot1.is_negative_infinity() : !min_cot0.is_negative_infinity())) {
+				Edge *e = new_edge_pair(c0, c1);
+				if (pending_tail0) {
+					pending_tail0->prev = e;
+				} else {
+					pending_head0 = e;
+				}
+				e->next = pending_tail0;
+				pending_tail0 = e;
+
+				e = e->reverse;
+				if (pending_tail1) {
+					pending_tail1->next = e;
+				} else {
+					pending_head1 = e;
+				}
+				e->prev = pending_tail1;
+				pending_tail1 = e;
+			}
+
+			Edge *e0 = min0;
+			Edge *e1 = min1;
+
+#ifdef DEBUG_CONVEX_HULL
+			printf("   Found min edges to %d %d\n", e0 ? e0->target->point.index : -1, e1 ? e1->target->point.index : -1);
+#endif
+
+			if (cmp == 0) {
+				find_edge_for_coplanar_faces(c0, c1, e0, e1, nullptr, nullptr);
+			}
+
+			if ((cmp >= 0) && e1) {
+				if (to_prev1) {
+					for (Edge *e = to_prev1->next, *n = nullptr; e != min1; e = n) {
+						n = e->next;
+						remove_edge_pair(e);
+					}
+				}
+
+				if (pending_tail1) {
+					if (to_prev1) {
+						to_prev1->link(pending_head1);
+					} else {
+						min1->prev->link(pending_head1);
+						first_new1 = pending_head1;
+					}
+					pending_tail1->link(min1);
+					pending_head1 = nullptr;
+					pending_tail1 = nullptr;
+				} else if (!to_prev1) {
+					first_new1 = min1;
+				}
+
+				prev_point = c1->point;
+				c1 = e1->target;
+				to_prev1 = e1->reverse;
+			}
+
+			if ((cmp <= 0) && e0) {
+				if (to_prev0) {
+					for (Edge *e = to_prev0->prev, *n = nullptr; e != min0; e = n) {
+						n = e->prev;
+						remove_edge_pair(e);
+					}
+				}
+
+				if (pending_tail0) {
+					if (to_prev0) {
+						pending_head0->link(to_prev0);
+					} else {
+						pending_head0->link(min0->next);
+						first_new0 = pending_head0;
+					}
+					min0->link(pending_tail0);
+					pending_head0 = nullptr;
+					pending_tail0 = nullptr;
+				} else if (!to_prev0) {
+					first_new0 = min0;
+				}
+
+				prev_point = c0->point;
+				c0 = e0->target;
+				to_prev0 = e0->reverse;
+			}
+		}
+
+		if ((c0 == first0) && (c1 == first1)) {
+			if (to_prev0 == nullptr) {
+				pending_head0->link(pending_tail0);
+				c0->edges = pending_tail0;
+			} else {
+				for (Edge *e = to_prev0->prev, *n = nullptr; e != first_new0; e = n) {
+					n = e->prev;
+					remove_edge_pair(e);
+				}
+				if (pending_tail0) {
+					pending_head0->link(to_prev0);
+					first_new0->link(pending_tail0);
+				}
+			}
+
+			if (to_prev1 == nullptr) {
+				pending_tail1->link(pending_head1);
+				c1->edges = pending_tail1;
+			} else {
+				for (Edge *e = to_prev1->next, *n = nullptr; e != first_new1; e = n) {
+					n = e->next;
+					remove_edge_pair(e);
+				}
+				if (pending_tail1) {
+					to_prev1->link(pending_head1);
+					pending_tail1->link(first_new1);
+				}
+			}
+
+			return;
+		}
+
+		first_run = false;
+	}
+}
+
+struct PointComparator {
+	_FORCE_INLINE_ bool operator()(const ConvexHullInternal::Point32 &p, const ConvexHullInternal::Point32 &q) const {
+		return (p.y < q.y) || ((p.y == q.y) && ((p.x < q.x) || ((p.x == q.x) && (p.z < q.z))));
+	}
+};
+
+void ConvexHullInternal::compute(const Vector3 *p_coords, int32_t p_count) {
+	AABB aabb;
+	for (int32_t i = 0; i < p_count; i++) {
+		Vector3 p = p_coords[i];
+		if (i == 0) {
+			aabb.position = p;
+		} else {
+			aabb.expand_to(p);
+		}
+	}
+
+	Vector3 s = aabb.size;
+	max_axis = s.max_axis();
+	min_axis = s.min_axis();
+	if (min_axis == max_axis) {
+		min_axis = (max_axis + 1) % 3;
+	}
+	med_axis = 3 - max_axis - min_axis;
+
+	s /= real_t(10216);
+	if (((med_axis + 1) % 3) != max_axis) {
+		s *= -1;
+	}
+	scaling = s;
+
+	if (s[0] != 0) {
+		s[0] = real_t(1) / s[0];
+	}
+	if (s[1] != 0) {
+		s[1] = real_t(1) / s[1];
+	}
+	if (s[2] != 0) {
+		s[2] = real_t(1) / s[2];
+	}
+
+	center = aabb.position;
+
+	LocalVector<Point32> points;
+	points.resize(p_count);
+	for (int32_t i = 0; i < p_count; i++) {
+		Vector3 p = p_coords[i];
+		p = (p - center) * s;
+		points[i].x = (int32_t)p[med_axis];
+		points[i].y = (int32_t)p[max_axis];
+		points[i].z = (int32_t)p[min_axis];
+		points[i].index = i;
+	}
+
+	points.sort_custom<PointComparator>();
+
+	vertex_pool.reset(true);
+	original_vertices.resize(p_count);
+	for (int32_t i = 0; i < p_count; i++) {
+		Vertex *v = vertex_pool.alloc();
+		v->edges = nullptr;
+		v->point = points[i];
+		v->copy = -1;
+		original_vertices[i] = v;
+	}
+
+	points.clear();
+
+	edge_pool.reset(true);
+
+	used_edge_pairs = 0;
+	max_used_edge_pairs = 0;
+
+	merge_stamp = -3;
+
+	IntermediateHull hull;
+	compute_internal(0, p_count, hull);
+	vertex_list = hull.min_xy;
+#ifdef DEBUG_CONVEX_HULL
+	printf("max. edges %d (3v = %d)", max_used_edge_pairs, 3 * p_count);
+#endif
+}
+
+Vector3 ConvexHullInternal::to_gd_vector(const Point32 &p_v) {
+	Vector3 p;
+	p[med_axis] = real_t(p_v.x);
+	p[max_axis] = real_t(p_v.y);
+	p[min_axis] = real_t(p_v.z);
+	return p * scaling;
+}
+
+Vector3 ConvexHullInternal::get_gd_normal(Face *p_face) {
+	return to_gd_vector(p_face->dir0).cross(to_gd_vector(p_face->dir1)).normalized();
+}
+
+Vector3 ConvexHullInternal::get_coordinates(const Vertex *p_v) {
+	Vector3 p;
+	p[med_axis] = p_v->xvalue();
+	p[max_axis] = p_v->yvalue();
+	p[min_axis] = p_v->zvalue();
+	return p * scaling + center;
+}
+
+real_t ConvexHullInternal::shrink(real_t p_amount, real_t p_clamp_amount) {
+	if (!vertex_list) {
+		return 0;
+	}
+	int32_t stamp = --merge_stamp;
+	LocalVector<Vertex *> stack;
+	vertex_list->copy = stamp;
+	stack.push_back(vertex_list);
+	LocalVector<Face *> faces;
+
+	Point32 ref = vertex_list->point;
+	Int128 hull_center_x(0, 0);
+	Int128 hull_center_y(0, 0);
+	Int128 hull_center_z(0, 0);
+	Int128 volume(0, 0);
+
+	while (stack.size() > 0) {
+		Vertex *v = stack[stack.size() - 1];
+		stack.remove(stack.size() - 1);
+		Edge *e = v->edges;
+		if (e) {
+			do {
+				if (e->target->copy != stamp) {
+					e->target->copy = stamp;
+					stack.push_back(e->target);
+				}
+				if (e->copy != stamp) {
+					Face *face = face_pool.alloc();
+					face->init(e->target, e->reverse->prev->target, v);
+					faces.push_back(face);
+					Edge *f = e;
+
+					Vertex *a = nullptr;
+					Vertex *b = nullptr;
+					do {
+						if (a && b) {
+							int64_t vol = (v->point - ref).dot((a->point - ref).cross(b->point - ref));
+							CHULL_ASSERT(vol >= 0);
+							Point32 c = v->point + a->point + b->point + ref;
+							hull_center_x += vol * c.x;
+							hull_center_y += vol * c.y;
+							hull_center_z += vol * c.z;
+							volume += vol;
+						}
+
+						CHULL_ASSERT(f->copy != stamp);
+						f->copy = stamp;
+						f->face = face;
+
+						a = b;
+						b = f->target;
+
+						f = f->reverse->prev;
+					} while (f != e);
+				}
+				e = e->next;
+			} while (e != v->edges);
+		}
+	}
+
+	if (volume.get_sign() <= 0) {
+		return 0;
+	}
+
+	Vector3 hull_center;
+	hull_center[med_axis] = hull_center_x.to_scalar();
+	hull_center[max_axis] = hull_center_y.to_scalar();
+	hull_center[min_axis] = hull_center_z.to_scalar();
+	hull_center /= 4 * volume.to_scalar();
+	hull_center *= scaling;
+
+	int32_t face_count = faces.size();
+
+	if (p_clamp_amount > 0) {
+		real_t min_dist = FLT_MAX;
+		for (int32_t i = 0; i < face_count; i++) {
+			Vector3 normal = get_gd_normal(faces[i]);
+			real_t dist = normal.dot(to_gd_vector(faces[i]->origin) - hull_center);
+			if (dist < min_dist) {
+				min_dist = dist;
+			}
+		}
+
+		if (min_dist <= 0) {
+			return 0;
+		}
+
+		p_amount = MIN(p_amount, min_dist * p_clamp_amount);
+	}
+
+	uint32_t seed = 243703;
+	for (int32_t i = 0; i < face_count; i++, seed = 1664525 * seed + 1013904223) {
+		SWAP(faces[i], faces[seed % face_count]);
+	}
+
+	for (int32_t i = 0; i < face_count; i++) {
+		if (!shift_face(faces[i], p_amount, stack)) {
+			return -p_amount;
+		}
+	}
+
+	return p_amount;
+}
+
+bool ConvexHullInternal::shift_face(Face *p_face, real_t p_amount, LocalVector<Vertex *> p_stack) {
+	Vector3 orig_shift = get_gd_normal(p_face) * -p_amount;
+	if (scaling[0] != 0) {
+		orig_shift[0] /= scaling[0];
+	}
+	if (scaling[1] != 0) {
+		orig_shift[1] /= scaling[1];
+	}
+	if (scaling[2] != 0) {
+		orig_shift[2] /= scaling[2];
+	}
+	Point32 shift((int32_t)orig_shift[med_axis], (int32_t)orig_shift[max_axis], (int32_t)orig_shift[min_axis]);
+	if (shift.is_zero()) {
+		return true;
+	}
+	Point64 normal = p_face->get_normal();
+#ifdef DEBUG_CONVEX_HULL
+	printf("\nShrinking p_face (%d %d %d) (%d %d %d) (%d %d %d) by (%d %d %d)\n",
+			p_face->origin.x, p_face->origin.y, p_face->origin.z, p_face->dir0.x, p_face->dir0.y, p_face->dir0.z, p_face->dir1.x, p_face->dir1.y, p_face->dir1.z, shift.x, shift.y, shift.z);
+#endif
+	int64_t orig_dot = p_face->origin.dot(normal);
+	Point32 shifted_origin = p_face->origin + shift;
+	int64_t shifted_dot = shifted_origin.dot(normal);
+	CHULL_ASSERT(shifted_dot <= orig_dot);
+	if (shifted_dot >= orig_dot) {
+		return false;
+	}
+
+	Edge *intersection = nullptr;
+
+	Edge *start_edge = p_face->nearby_vertex->edges;
+#ifdef DEBUG_CONVEX_HULL
+	printf("Start edge is ");
+	start_edge->print();
+	printf(", normal is (%lld %lld %lld), shifted dot is %lld\n", normal.x, normal.y, normal.z, shifted_dot);
+#endif
+	Rational128 opt_dot = p_face->nearby_vertex->dot(normal);
+	int32_t cmp = opt_dot.compare(shifted_dot);
+#ifdef SHOW_ITERATIONS
+	int32_t n = 0;
+#endif
+	if (cmp >= 0) {
+		Edge *e = start_edge;
+		do {
+#ifdef SHOW_ITERATIONS
+			n++;
+#endif
+			Rational128 dot = e->target->dot(normal);
+			CHULL_ASSERT(dot.compare(orig_dot) <= 0);
+#ifdef DEBUG_CONVEX_HULL
+			printf("Moving downwards, edge is ");
+			e->print();
+			printf(", dot is %f (%f %lld)\n", (float)dot.to_scalar(), (float)opt_dot.to_scalar(), shifted_dot);
+#endif
+			if (dot.compare(opt_dot) < 0) {
+				int32_t c = dot.compare(shifted_dot);
+				opt_dot = dot;
+				e = e->reverse;
+				start_edge = e;
+				if (c < 0) {
+					intersection = e;
+					break;
+				}
+				cmp = c;
+			}
+			e = e->prev;
+		} while (e != start_edge);
+
+		if (!intersection) {
+			return false;
+		}
+	} else {
+		Edge *e = start_edge;
+		do {
+#ifdef SHOW_ITERATIONS
+			n++;
+#endif
+			Rational128 dot = e->target->dot(normal);
+			CHULL_ASSERT(dot.compare(orig_dot) <= 0);
+#ifdef DEBUG_CONVEX_HULL
+			printf("Moving upwards, edge is ");
+			e->print();
+			printf(", dot is %f (%f %lld)\n", (float)dot.to_scalar(), (float)opt_dot.to_scalar(), shifted_dot);
+#endif
+			if (dot.compare(opt_dot) > 0) {
+				cmp = dot.compare(shifted_dot);
+				if (cmp >= 0) {
+					intersection = e;
+					break;
+				}
+				opt_dot = dot;
+				e = e->reverse;
+				start_edge = e;
+			}
+			e = e->prev;
+		} while (e != start_edge);
+
+		if (!intersection) {
+			return true;
+		}
+	}
+
+#ifdef SHOW_ITERATIONS
+	printf("Needed %d iterations to find initial intersection\n", n);
+#endif
+
+	if (cmp == 0) {
+		Edge *e = intersection->reverse->next;
+#ifdef SHOW_ITERATIONS
+		n = 0;
+#endif
+		while (e->target->dot(normal).compare(shifted_dot) <= 0) {
+#ifdef SHOW_ITERATIONS
+			n++;
+#endif
+			e = e->next;
+			if (e == intersection->reverse) {
+				return true;
+			}
+#ifdef DEBUG_CONVEX_HULL
+			printf("Checking for outwards edge, current edge is ");
+			e->print();
+			printf("\n");
+#endif
+		}
+#ifdef SHOW_ITERATIONS
+		printf("Needed %d iterations to check for complete containment\n", n);
+#endif
+	}
+
+	Edge *first_intersection = nullptr;
+	Edge *face_edge = nullptr;
+	Edge *first_face_edge = nullptr;
+
+#ifdef SHOW_ITERATIONS
+	int32_t m = 0;
+#endif
+	while (true) {
+#ifdef SHOW_ITERATIONS
+		m++;
+#endif
+#ifdef DEBUG_CONVEX_HULL
+		printf("Intersecting edge is ");
+		intersection->print();
+		printf("\n");
+#endif
+		if (cmp == 0) {
+			Edge *e = intersection->reverse->next;
+			start_edge = e;
+#ifdef SHOW_ITERATIONS
+			n = 0;
+#endif
+			while (true) {
+#ifdef SHOW_ITERATIONS
+				n++;
+#endif
+				if (e->target->dot(normal).compare(shifted_dot) >= 0) {
+					break;
+				}
+				intersection = e->reverse;
+				e = e->next;
+				if (e == start_edge) {
+					return true;
+				}
+			}
+#ifdef SHOW_ITERATIONS
+			printf("Needed %d iterations to advance intersection\n", n);
+#endif
+		}
+
+#ifdef DEBUG_CONVEX_HULL
+		printf("Advanced intersecting edge to ");
+		intersection->print();
+		printf(", cmp = %d\n", cmp);
+#endif
+
+		if (!first_intersection) {
+			first_intersection = intersection;
+		} else if (intersection == first_intersection) {
+			break;
+		}
+
+		int32_t prev_cmp = cmp;
+		Edge *prev_intersection = intersection;
+		Edge *prev_face_edge = face_edge;
+
+		Edge *e = intersection->reverse;
+#ifdef SHOW_ITERATIONS
+		n = 0;
+#endif
+		while (true) {
+#ifdef SHOW_ITERATIONS
+			n++;
+#endif
+			e = e->reverse->prev;
+			CHULL_ASSERT(e != intersection->reverse);
+			cmp = e->target->dot(normal).compare(shifted_dot);
+#ifdef DEBUG_CONVEX_HULL
+			printf("Testing edge ");
+			e->print();
+			printf(" -> cmp = %d\n", cmp);
+#endif
+			if (cmp >= 0) {
+				intersection = e;
+				break;
+			}
+		}
+#ifdef SHOW_ITERATIONS
+		printf("Needed %d iterations to find other intersection of p_face\n", n);
+#endif
+
+		if (cmp > 0) {
+			Vertex *removed = intersection->target;
+			e = intersection->reverse;
+			if (e->prev == e) {
+				removed->edges = nullptr;
+			} else {
+				removed->edges = e->prev;
+				e->prev->link(e->next);
+				e->link(e);
+			}
+#ifdef DEBUG_CONVEX_HULL
+			printf("1: Removed part contains (%d %d %d)\n", removed->point.x, removed->point.y, removed->point.z);
+#endif
+
+			Point64 n0 = intersection->face->get_normal();
+			Point64 n1 = intersection->reverse->face->get_normal();
+			int64_t m00 = p_face->dir0.dot(n0);
+			int64_t m01 = p_face->dir1.dot(n0);
+			int64_t m10 = p_face->dir0.dot(n1);
+			int64_t m11 = p_face->dir1.dot(n1);
+			int64_t r0 = (intersection->face->origin - shifted_origin).dot(n0);
+			int64_t r1 = (intersection->reverse->face->origin - shifted_origin).dot(n1);
+			Int128 det = Int128::mul(m00, m11) - Int128::mul(m01, m10);
+			CHULL_ASSERT(det.get_sign() != 0);
+			Vertex *v = vertex_pool.alloc();
+			v->point.index = -1;
+			v->copy = -1;
+			v->point128 = PointR128(Int128::mul(p_face->dir0.x * r0, m11) - Int128::mul(p_face->dir0.x * r1, m01) + Int128::mul(p_face->dir1.x * r1, m00) - Int128::mul(p_face->dir1.x * r0, m10) + det * shifted_origin.x,
+					Int128::mul(p_face->dir0.y * r0, m11) - Int128::mul(p_face->dir0.y * r1, m01) + Int128::mul(p_face->dir1.y * r1, m00) - Int128::mul(p_face->dir1.y * r0, m10) + det * shifted_origin.y,
+					Int128::mul(p_face->dir0.z * r0, m11) - Int128::mul(p_face->dir0.z * r1, m01) + Int128::mul(p_face->dir1.z * r1, m00) - Int128::mul(p_face->dir1.z * r0, m10) + det * shifted_origin.z,
+					det);
+			v->point.x = (int32_t)v->point128.xvalue();
+			v->point.y = (int32_t)v->point128.yvalue();
+			v->point.z = (int32_t)v->point128.zvalue();
+			intersection->target = v;
+			v->edges = e;
+
+			p_stack.push_back(v);
+			p_stack.push_back(removed);
+			p_stack.push_back(nullptr);
+		}
+
+		if (cmp || prev_cmp || (prev_intersection->reverse->next->target != intersection->target)) {
+			face_edge = new_edge_pair(prev_intersection->target, intersection->target);
+			if (prev_cmp == 0) {
+				face_edge->link(prev_intersection->reverse->next);
+			}
+			if ((prev_cmp == 0) || prev_face_edge) {
+				prev_intersection->reverse->link(face_edge);
+			}
+			if (cmp == 0) {
+				intersection->reverse->prev->link(face_edge->reverse);
+			}
+			face_edge->reverse->link(intersection->reverse);
+		} else {
+			face_edge = prev_intersection->reverse->next;
+		}
+
+		if (prev_face_edge) {
+			if (prev_cmp > 0) {
+				face_edge->link(prev_face_edge->reverse);
+			} else if (face_edge != prev_face_edge->reverse) {
+				p_stack.push_back(prev_face_edge->target);
+				while (face_edge->next != prev_face_edge->reverse) {
+					Vertex *removed = face_edge->next->target;
+					remove_edge_pair(face_edge->next);
+					p_stack.push_back(removed);
+#ifdef DEBUG_CONVEX_HULL
+					printf("2: Removed part contains (%d %d %d)\n", removed->point.x, removed->point.y, removed->point.z);
+#endif
+				}
+				p_stack.push_back(nullptr);
+			}
+		}
+		face_edge->face = p_face;
+		face_edge->reverse->face = intersection->face;
+
+		if (!first_face_edge) {
+			first_face_edge = face_edge;
+		}
+	}
+#ifdef SHOW_ITERATIONS
+	printf("Needed %d iterations to process all intersections\n", m);
+#endif
+
+	if (cmp > 0) {
+		first_face_edge->reverse->target = face_edge->target;
+		first_intersection->reverse->link(first_face_edge);
+		first_face_edge->link(face_edge->reverse);
+	} else if (first_face_edge != face_edge->reverse) {
+		p_stack.push_back(face_edge->target);
+		while (first_face_edge->next != face_edge->reverse) {
+			Vertex *removed = first_face_edge->next->target;
+			remove_edge_pair(first_face_edge->next);
+			p_stack.push_back(removed);
+#ifdef DEBUG_CONVEX_HULL
+			printf("3: Removed part contains (%d %d %d)\n", removed->point.x, removed->point.y, removed->point.z);
+#endif
+		}
+		p_stack.push_back(nullptr);
+	}
+
+	CHULL_ASSERT(p_stack.size() > 0);
+	vertex_list = p_stack[0];
+
+#ifdef DEBUG_CONVEX_HULL
+	printf("Removing part\n");
+#endif
+#ifdef SHOW_ITERATIONS
+	n = 0;
+#endif
+	uint32_t pos = 0;
+	while (pos < p_stack.size()) {
+		uint32_t end = p_stack.size();
+		while (pos < end) {
+			Vertex *kept = p_stack[pos++];
+#ifdef DEBUG_CONVEX_HULL
+			kept->print();
+#endif
+			bool deeper = false;
+			Vertex *removed;
+			while ((removed = p_stack[pos++]) != nullptr) {
+#ifdef SHOW_ITERATIONS
+				n++;
+#endif
+				kept->receive_nearby_faces(removed);
+				while (removed->edges) {
+					if (!deeper) {
+						deeper = true;
+						p_stack.push_back(kept);
+					}
+					p_stack.push_back(removed->edges->target);
+					remove_edge_pair(removed->edges);
+				}
+			}
+			if (deeper) {
+				p_stack.push_back(nullptr);
+			}
+		}
+	}
+#ifdef SHOW_ITERATIONS
+	printf("Needed %d iterations to remove part\n", n);
+#endif
+
+	p_stack.resize(0);
+	p_face->origin = shifted_origin;
+
+	return true;
+}
+
+static int32_t get_vertex_copy(ConvexHullInternal::Vertex *p_vertex, LocalVector<ConvexHullInternal::Vertex *> &p_vertices) {
+	int32_t index = p_vertex->copy;
+	if (index < 0) {
+		index = p_vertices.size();
+		p_vertex->copy = index;
+		p_vertices.push_back(p_vertex);
+#ifdef DEBUG_CONVEX_HULL
+		printf("Vertex %d gets index *%d\n", p_vertex->point.index, index);
+#endif
+	}
+	return index;
+}
+
+real_t ConvexHullComputer::compute(const Vector3 *p_coords, int32_t p_count, real_t p_shrink, real_t p_shrink_clamp) {
+	if (p_count <= 0) {
+		vertices.clear();
+		edges.clear();
+		faces.clear();
+		return 0;
+	}
+
+	ConvexHullInternal hull;
+	hull.compute(p_coords, p_count);
+
+	real_t shift = 0;
+	if ((p_shrink > 0) && ((shift = hull.shrink(p_shrink, p_shrink_clamp)) < 0)) {
+		vertices.clear();
+		edges.clear();
+		faces.clear();
+		return shift;
+	}
+
+	vertices.resize(0);
+	edges.resize(0);
+	faces.resize(0);
+
+	LocalVector<ConvexHullInternal::Vertex *> old_vertices;
+	get_vertex_copy(hull.vertex_list, old_vertices);
+	int32_t copied = 0;
+	while (copied < (int32_t)old_vertices.size()) {
+		ConvexHullInternal::Vertex *v = old_vertices[copied];
+		vertices.push_back(hull.get_coordinates(v));
+		ConvexHullInternal::Edge *first_edge = v->edges;
+		if (first_edge) {
+			int32_t first_copy = -1;
+			int32_t prev_copy = -1;
+			ConvexHullInternal::Edge *e = first_edge;
+			do {
+				if (e->copy < 0) {
+					int32_t s = edges.size();
+					edges.push_back(Edge());
+					edges.push_back(Edge());
+					Edge *c = &edges[s];
+					Edge *r = &edges[s + 1];
+					e->copy = s;
+					e->reverse->copy = s + 1;
+					c->reverse = 1;
+					r->reverse = -1;
+					c->target_vertex = get_vertex_copy(e->target, old_vertices);
+					r->target_vertex = copied;
+#ifdef DEBUG_CONVEX_HULL
+					printf("      CREATE: Vertex *%d has edge to *%d\n", copied, c->get_target_vertex());
+#endif
+				}
+				if (prev_copy >= 0) {
+					edges[e->copy].next = prev_copy - e->copy;
+				} else {
+					first_copy = e->copy;
+				}
+				prev_copy = e->copy;
+				e = e->next;
+			} while (e != first_edge);
+			edges[first_copy].next = prev_copy - first_copy;
+		}
+		copied++;
+	}
+
+	for (int32_t i = 0; i < copied; i++) {
+		ConvexHullInternal::Vertex *v = old_vertices[i];
+		ConvexHullInternal::Edge *first_edge = v->edges;
+		if (first_edge) {
+			ConvexHullInternal::Edge *e = first_edge;
+			do {
+				if (e->copy >= 0) {
+#ifdef DEBUG_CONVEX_HULL
+					printf("Vertex *%d has edge to *%d\n", i, edges[e->copy].get_target_vertex());
+#endif
+					faces.push_back(e->copy);
+					ConvexHullInternal::Edge *f = e;
+					do {
+#ifdef DEBUG_CONVEX_HULL
+						printf("   Face *%d\n", edges[f->copy].get_target_vertex());
+#endif
+						f->copy = -1;
+						f = f->reverse->prev;
+					} while (f != e);
+				}
+				e = e->next;
+			} while (e != first_edge);
+		}
+	}
+
+	return shift;
+}
+
+Error ConvexHullComputer::convex_hull(const Vector<Vector3> &p_points, Geometry::MeshData &r_mesh) {
+	r_mesh = Geometry::MeshData(); // clear
+
+	if (p_points.size() == 0) {
+		return FAILED; // matches QuickHull
+	}
+
+	ConvexHullComputer ch;
+	ch.compute(p_points.ptr(), p_points.size(), -1.0, -1.0);
+
+	r_mesh.vertices = ch.vertices;
+
+	r_mesh.edges.resize(ch.edges.size());
+	for (uint32_t i = 0; i < ch.edges.size(); i++) {
+		r_mesh.edges.write[i].a = (&ch.edges[i])->get_source_vertex();
+		r_mesh.edges.write[i].b = (&ch.edges[i])->get_target_vertex();
+	}
+
+	r_mesh.faces.resize(ch.faces.size());
+	for (uint32_t i = 0; i < ch.faces.size(); i++) {
+		const Edge *e_start = &ch.edges[ch.faces[i]];
+		const Edge *e = e_start;
+		Geometry::MeshData::Face &face = r_mesh.faces.write[i];
+
+		do {
+			face.indices.push_back(e->get_target_vertex());
+
+			e = e->get_next_edge_of_face();
+		} while (e != e_start);
+
+		// compute normal
+		if (face.indices.size() >= 3) {
+			face.plane = Plane(r_mesh.vertices[face.indices[0]], r_mesh.vertices[face.indices[2]], r_mesh.vertices[face.indices[1]]);
+		} else {
+			WARN_PRINT("Too few vertices per face.");
+		}
+	}
+
+	return OK;
+}

core/math/convex_hull.h

@@ -0,0 +1,116 @@
+/*************************************************************************/
+/*  convex_hull.h                                                        */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+/*
+Copyright (c) 2011 Ole Kniemeyer, MAXON, www.maxon.net
+
+This software is provided 'as-is', without any express or implied warranty.
+In no event will the authors be held liable for any damages arising from the use of this software.
+Permission is granted to anyone to use this software for any purpose,
+including commercial applications, and to alter it and redistribute it freely,
+subject to the following restrictions:
+
+1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
+2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
+3. This notice may not be removed or altered from any source distribution.
+*/
+
+#ifndef CONVEX_HULL_H
+#define CONVEX_HULL_H
+
+#include "core/local_vector.h"
+#include "core/math/geometry.h"
+#include "core/math/vector3.h"
+#include "core/vector.h"
+
+/// Convex hull implementation based on Preparata and Hong
+/// See http://code.google.com/p/bullet/issues/detail?id=275
+/// Ole Kniemeyer, MAXON Computer GmbH
+class ConvexHullComputer {
+public:
+	class Edge {
+	private:
+		int32_t next = 0;
+		int32_t reverse = 0;
+		int32_t target_vertex = 0;
+
+		friend class ConvexHullComputer;
+
+	public:
+		int32_t get_source_vertex() const {
+			return (this + reverse)->target_vertex;
+		}
+
+		int32_t get_target_vertex() const {
+			return target_vertex;
+		}
+
+		const Edge *get_next_edge_of_vertex() const // clockwise list of all edges of a vertex
+		{
+			return this + next;
+		}
+
+		const Edge *get_next_edge_of_face() const // counter-clockwise list of all edges of a face
+		{
+			return (this + reverse)->get_next_edge_of_vertex();
+		}
+
+		const Edge *get_reverse_edge() const {
+			return this + reverse;
+		}
+	};
+
+	// Vertices of the output hull
+	Vector<Vector3> vertices;
+
+	// Edges of the output hull
+	LocalVector<Edge> edges;
+
+	// Faces of the convex hull. Each entry is an index into the "edges" array pointing to an edge of the face. Faces are planar n-gons
+	LocalVector<int32_t> faces;
+
+	/*
+		Compute convex hull of "count" vertices stored in "coords".
+		If "shrink" is positive, the convex hull is shrunken by that amount (each face is moved by "shrink" length units
+		towards the center along its normal).
+		If "shrinkClamp" is positive, "shrink" is clamped to not exceed "shrinkClamp * innerRadius", where "innerRadius"
+		is the minimum distance of a face to the center of the convex hull.
+
+		The returned value is the amount by which the hull has been shrunken. If it is negative, the amount was so large
+		that the resulting convex hull is empty.
+
+		The output convex hull can be found in the member variables "vertices", "edges", "faces".
+		*/
+	real_t compute(const Vector3 *p_coords, int32_t p_count, real_t p_shrink, real_t p_shrink_clamp);
+
+	static Error convex_hull(const Vector<Vector3> &p_points, Geometry::MeshData &r_mesh);
+};
+
+#endif // CONVEX_HULL_H

core/os/spin_lock.h

@@ -0,0 +1,51 @@
+/*************************************************************************/
+/*  spin_lock.h                                                          */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef SPIN_LOCK_H
+#define SPIN_LOCK_H
+
+#include "core/typedefs.h"
+
+#include <atomic>
+
+class SpinLock {
+	std::atomic_flag locked = ATOMIC_FLAG_INIT;
+
+public:
+	_ALWAYS_INLINE_ void lock() {
+		while (locked.test_and_set(std::memory_order_acquire)) {
+			;
+		}
+	}
+	_ALWAYS_INLINE_ void unlock() {
+		locked.clear(std::memory_order_release);
+	}
+};
+#endif // SPIN_LOCK_H

core/paged_allocator.h

@@ -0,0 +1,133 @@
+/*************************************************************************/
+/*  paged_allocator.h                                                    */
+/*************************************************************************/
+/*                       This file is part of:                           */
+/*                           GODOT ENGINE                                */
+/*                      https://godotengine.org                          */
+/*************************************************************************/
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur.                 */
+/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md).   */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef PAGED_ALLOCATOR_H
+#define PAGED_ALLOCATOR_H
+
+#include "core/os/memory.h"
+#include "core/os/spin_lock.h"
+#include "core/typedefs.h"
+
+#include <type_traits>
+
+template <class T, bool thread_safe = false>
+class PagedAllocator {
+	T **page_pool = nullptr;
+	T ***available_pool = nullptr;
+	uint32_t pages_allocated = 0;
+	uint32_t allocs_available = 0;
+
+	uint32_t page_shift = 0;
+	uint32_t page_mask = 0;
+	uint32_t page_size = 0;
+	SpinLock spin_lock;
+
+public:
+	T *alloc() {
+		if (thread_safe) {
+			spin_lock.lock();
+		}
+		if (unlikely(allocs_available == 0)) {
+			uint32_t pages_used = pages_allocated;
+
+			pages_allocated++;
+			page_pool = (T **)memrealloc(page_pool, sizeof(T *) * pages_allocated);
+			available_pool = (T ***)memrealloc(available_pool, sizeof(T **) * pages_allocated);
+
+			page_pool[pages_used] = (T *)memalloc(sizeof(T) * page_size);
+			available_pool[pages_used] = (T **)memalloc(sizeof(T *) * page_size);
+
+			for (uint32_t i = 0; i < page_size; i++) {
+				available_pool[0][i] = &page_pool[pages_used][i];
+			}
+			allocs_available += page_size;
+		}
+
+		allocs_available--;
+		T *alloc = available_pool[allocs_available >> page_shift][allocs_available & page_mask];
+		if (thread_safe) {
+			spin_lock.unlock();
+		}
+		memnew_placement(alloc, T);
+		return alloc;
+	}
+
+	void free(T *p_mem) {
+		if (thread_safe) {
+			spin_lock.lock();
+		}
+		p_mem->~T();
+		available_pool[allocs_available >> page_shift][allocs_available & page_mask] = p_mem;
+		if (thread_safe) {
+			spin_lock.unlock();
+		}
+		allocs_available++;
+	}
+
+	void reset(bool p_allow_unfreed = false) {
+		if (!p_allow_unfreed || !std::is_trivially_destructible<T>::value) {
+			ERR_FAIL_COND(allocs_available < pages_allocated * page_size);
+		}
+		if (pages_allocated) {
+			for (uint32_t i = 0; i < pages_allocated; i++) {
+				memfree(page_pool[i]);
+				memfree(available_pool[i]);
+			}
+			memfree(page_pool);
+			memfree(available_pool);
+			page_pool = nullptr;
+			available_pool = nullptr;
+			pages_allocated = 0;
+			allocs_available = 0;
+		}
+	}
+	bool is_configured() const {
+		return page_size > 0;
+	}
+
+	void configure(uint32_t p_page_size) {
+		ERR_FAIL_COND(page_pool != nullptr); //sanity check
+		ERR_FAIL_COND(p_page_size == 0);
+		page_size = nearest_power_of_2_templated(p_page_size);
+		page_mask = page_size - 1;
+		page_shift = get_shift_from_power_of_2(page_size);
+	}
+
+	PagedAllocator(uint32_t p_page_size = 4096) { // power of 2 recommended because of alignment with OS page sizes. Even if element is bigger, its still a multiple and get rounded amount of pages
+		configure(p_page_size);
+	}
+
+	~PagedAllocator() {
+		ERR_FAIL_COND_MSG(allocs_available < pages_allocated * page_size, "Pages in use exist at exit in PagedAllocator");
+		reset();
+	}
+};
+
+#endif // PAGED_ALLOCATOR_H

editor/spatial_editor_gizmos.cpp

@@ -30,8 +30,8 @@
 
 #include "spatial_editor_gizmos.h"
 
+#include "core/math/convex_hull.h"
 #include "core/math/geometry.h"
-#include "core/math/quick_hull.h"
 #include "scene/3d/audio_stream_player_3d.h"
 #include "scene/3d/baked_lightmap.h"
 #include "scene/3d/collision_polygon.h"
@@ -3550,7 +3550,7 @@ void CollisionShapeSpatialGizmoPlugin::redraw(EditorSpatialGizmo *p_gizmo) {
 		if (points.size() > 3) {
 			Vector<Vector3> varr = Variant(points);
 			Geometry::MeshData md;
-			Error err = QuickHull::build(varr, md);
+			Error err = ConvexHullComputer::convex_hull(varr, md);
 			if (err == OK) {
 				Vector<Vector3> points2;
 				points2.resize(md.edges.size() * 2);

main/tests/test_physics.cpp

@@ -31,8 +31,8 @@
 #include "test_physics.h"
 
 #include "core/map.h"
+#include "core/math/convex_hull.h"
 #include "core/math/math_funcs.h"
-#include "core/math/quick_hull.h"
 #include "core/os/main_loop.h"
 #include "core/os/os.h"
 #include "core/print_string.h"
@@ -168,7 +168,7 @@ protected:
 
 		RID convex_mesh = vs->mesh_create();
 		Geometry::MeshData convex_data = Geometry::build_convex_mesh(convex_planes);
-		QuickHull::build(convex_data.vertices, convex_data);
+		ConvexHullComputer::convex_hull(convex_data.vertices, convex_data);
 		vs->mesh_add_surface_from_mesh_data(convex_mesh, convex_data);
 
 		type_mesh_map[PhysicsServer::SHAPE_CONVEX_POLYGON] = convex_mesh;

main/tests/test_render.cpp

@@ -30,8 +30,8 @@
 
 #include "test_render.h"
 
+#include "core/math/convex_hull.h"
 #include "core/math/math_funcs.h"
-#include "core/math/quick_hull.h"
 #include "core/os/keyboard.h"
 #include "core/os/main_loop.h"
 #include "core/os/os.h"
@@ -118,7 +118,7 @@ public:
 		vts.push_back(Vector3(-1, -1, -1));
 
 		Geometry::MeshData md;
-		Error err = QuickHull::build(vts, md);
+		Error err = ConvexHullComputer::convex_hull(vts, md);
 		print_line("ERR: " + itos(err));
 		test_cube = vs->mesh_create();
 		vs->mesh_add_surface_from_mesh_data(test_cube, md);

modules/recast/navigation_mesh_generator.cpp

@@ -29,7 +29,7 @@
 /*************************************************************************/
 
 #include "navigation_mesh_generator.h"
-#include "core/math/quick_hull.h"
+#include "core/math/convex_hull.h"
 #include "core/os/thread.h"
 #include "editor/editor_settings.h"
 #include "scene/3d/collision_shape.h"
@@ -213,7 +213,7 @@ void EditorNavigationMeshGenerator::_parse_geometry(Transform p_accumulated_tran
 						Vector<Vector3> varr = Variant(convex_polygon->get_points());
 						Geometry::MeshData md;
 
-						Error err = QuickHull::build(varr, md);
+						Error err = ConvexHullComputer::convex_hull(varr, md);
 
 						if (err == OK) {
 							PoolVector3Array faces;

scene/resources/convex_polygon_shape.cpp

@@ -29,7 +29,7 @@
 /*************************************************************************/
 
 #include "convex_polygon_shape.h"
-#include "core/math/quick_hull.h"
+#include "core/math/convex_hull.h"
 #include "servers/physics_server.h"
 
 Vector<Vector3> ConvexPolygonShape::get_debug_mesh_lines() {
@@ -38,7 +38,7 @@ Vector<Vector3> ConvexPolygonShape::get_debug_mesh_lines() {
 	if (points.size() > 3) {
 		Vector<Vector3> varr = Variant(points);
 		Geometry::MeshData md;
-		Error err = QuickHull::build(varr, md);
+		Error err = ConvexHullComputer::convex_hull(varr, md);
 		if (err == OK) {
 			Vector<Vector3> lines;
 			lines.resize(md.edges.size() * 2);

servers/physics/shape_sw.cpp

@@ -31,8 +31,8 @@
 #include "shape_sw.h"
 
 #include "core/image.h"
+#include "core/math/convex_hull.h"
 #include "core/math/geometry.h"
-#include "core/math/quick_hull.h"
 #include "core/sort_array.h"
 
 // HeightMapShapeSW is based on Bullet btHeightfieldTerrainShape.
@@ -1090,9 +1090,9 @@ Vector3 ConvexPolygonShapeSW::get_moment_of_inertia(real_t p_mass) const {
 }
 
 void ConvexPolygonShapeSW::_setup(const Vector<Vector3> &p_vertices) {
-	Error err = QuickHull::build(p_vertices, mesh);
+	Error err = ConvexHullComputer::convex_hull(p_vertices, mesh);
 	if (err != OK)
-		ERR_PRINT("Failed to build QuickHull");
+		ERR_PRINT("Failed to build convex hull");
 
 	AABB _aabb;