xatlas.cpp

/*
MIT License

Copyright (c) 2018-2020 Jonathan Young

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.
*/
/*
thekla_atlas
https://github.com/Thekla/thekla_atlas
MIT License
Copyright (c) 2013 Thekla, Inc
Copyright NVIDIA Corporation 2006 -- Ignacio Castano <icastano@nvidia.com>

Fast-BVH
https://github.com/brandonpelfrey/Fast-BVH
MIT License
Copyright (c) 2012 Brandon Pelfrey
*/
#include <atomic>
#include <condition_variable>
#include <mutex>
#include <thread>
#include <assert.h>
#include <float.h> // FLT_MAX
#include <limits.h>
#include <math.h>
#define __STDC_LIMIT_MACROS
#include <stdint.h>
#include <stdio.h>
#include <string.h>
#include "xatlas.h"

#define XA_MULTITHREADED 0

#ifndef XA_DEBUG
#ifdef NDEBUG
#define XA_DEBUG 0
#else
#define XA_DEBUG 1
#endif
#endif

#ifndef XA_PROFILE
#define XA_PROFILE 0
#endif
#if XA_PROFILE
#include <time.h>
#endif

#ifndef XA_MULTITHREADED
#define XA_MULTITHREADED 1
#endif

#define XA_STR(x) #x
#define XA_XSTR(x) XA_STR(x)

#ifndef XA_ASSERT
#define XA_ASSERT(exp) if (!(exp)) { XA_PRINT_WARNING("\rASSERT: %s %s %d\n", XA_XSTR(exp), __FILE__, __LINE__); }
#endif

#ifndef XA_DEBUG_ASSERT
#define XA_DEBUG_ASSERT(exp) assert(exp)
#endif

#ifndef XA_PRINT
#define XA_PRINT(...) \
	if (xatlas::internal::s_print && xatlas::internal::s_printVerbose) \
		xatlas::internal::s_print(__VA_ARGS__);
#endif

#ifndef XA_PRINT_WARNING
#define XA_PRINT_WARNING(...) \
	if (xatlas::internal::s_print) \
		xatlas::internal::s_print(__VA_ARGS__);
#endif

#define XA_ALLOC(tag, type) (type *)internal::Realloc(nullptr, sizeof(type), tag, __FILE__, __LINE__)
#define XA_ALLOC_ARRAY(tag, type, num) (type *)internal::Realloc(nullptr, sizeof(type) * (num), tag, __FILE__, __LINE__)
#define XA_REALLOC(tag, ptr, type, num) (type *)internal::Realloc(ptr, sizeof(type) * (num), tag, __FILE__, __LINE__)
#define XA_REALLOC_SIZE(tag, ptr, size) (uint8_t *)internal::Realloc(ptr, size, tag, __FILE__, __LINE__)
#define XA_FREE(ptr) internal::Realloc(ptr, 0, internal::MemTag::Default, __FILE__, __LINE__)
#define XA_NEW(tag, type) new (XA_ALLOC(tag, type)) type()
#define XA_NEW_ARGS(tag, type, ...) new (XA_ALLOC(tag, type)) type(__VA_ARGS__)

#ifdef _MSC_VER
#define XA_INLINE __forceinline
#else
#define XA_INLINE inline
#endif

#if defined(__clang__) || defined(__GNUC__)
#define XA_NODISCARD [[nodiscard]]
#elif defined(_MSC_VER)
#define XA_NODISCARD _Check_return_
#else
#define XA_NODISCARD
#endif

#define XA_UNUSED(a) ((void)(a))

#define XA_MERGE_CHARTS 1
#define XA_MERGE_CHARTS_MIN_NORMAL_DEVIATION 0.5f
#define XA_RECOMPUTE_CHARTS 1
#define XA_CLOSE_HOLES_CHECK_EDGE_INTERSECTION 0
#define XA_FIX_INTERNAL_BOUNDARY_LOOPS 1
#define XA_PRINT_CHART_WARNINGS 0

#define XA_DEBUG_HEAP 0
#define XA_DEBUG_SINGLE_CHART 0
#define XA_DEBUG_ALL_CHARTS_INVALID 0
#define XA_DEBUG_EXPORT_ATLAS_IMAGES 0
#define XA_DEBUG_EXPORT_ATLAS_IMAGES_PER_CHART 0 // Export an atlas image after each chart is added.
#define XA_DEBUG_EXPORT_BOUNDARY_GRID 0
#define XA_DEBUG_EXPORT_TGA (XA_DEBUG_EXPORT_ATLAS_IMAGES || XA_DEBUG_EXPORT_BOUNDARY_GRID)
#define XA_DEBUG_EXPORT_OBJ_FACE_GROUPS 0
#define XA_DEBUG_EXPORT_OBJ_CHART_GROUPS 0
#define XA_DEBUG_EXPORT_OBJ_PLANAR_REGIONS 0
#define XA_DEBUG_EXPORT_OBJ_CHARTS 0
#define XA_DEBUG_EXPORT_OBJ_BEFORE_FIX_TJUNCTION 0
#define XA_DEBUG_EXPORT_OBJ_CLOSE_HOLES_ERROR 0
#define XA_DEBUG_EXPORT_OBJ_CHARTS_AFTER_PARAMETERIZATION 0
#define XA_DEBUG_EXPORT_OBJ_INVALID_PARAMETERIZATION 0
#define XA_DEBUG_EXPORT_OBJ_RECOMPUTED_CHARTS 0

#define XA_DEBUG_EXPORT_OBJ (0 \
	|| XA_DEBUG_EXPORT_OBJ_FACE_GROUPS \
	|| XA_DEBUG_EXPORT_OBJ_CHART_GROUPS \
	|| XA_DEBUG_EXPORT_OBJ_PLANAR_REGIONS \
	|| XA_DEBUG_EXPORT_OBJ_CHARTS \
	|| XA_DEBUG_EXPORT_OBJ_BEFORE_FIX_TJUNCTION \
	|| XA_DEBUG_EXPORT_OBJ_CLOSE_HOLES_ERROR \
	|| XA_DEBUG_EXPORT_OBJ_CHARTS_AFTER_PARAMETERIZATION \
	|| XA_DEBUG_EXPORT_OBJ_INVALID_PARAMETERIZATION \
	|| XA_DEBUG_EXPORT_OBJ_RECOMPUTED_CHARTS)

#ifdef _MSC_VER
#define XA_FOPEN(_file, _filename, _mode) { if (fopen_s(&_file, _filename, _mode) != 0) _file = NULL; }
#define XA_SPRINTF(_buffer, _size, _format, ...) sprintf_s(_buffer, _size, _format, __VA_ARGS__)
#else
#define XA_FOPEN(_file, _filename, _mode) _file = fopen(_filename, _mode)
#define XA_SPRINTF(_buffer, _size, _format, ...) sprintf(_buffer, _format, __VA_ARGS__)
#endif

namespace xatlas {
namespace internal {

static ReallocFunc s_realloc = realloc;
static FreeFunc s_free = free;
static PrintFunc s_print = printf;
static bool s_printVerbose = false;

#if XA_PROFILE
#define XA_PROFILE_START(var) const clock_t var##Start = clock();
#define XA_PROFILE_END(var) internal::s_profile.var += clock() - var##Start;
#define XA_PROFILE_PRINT_AND_RESET(label, var) XA_PRINT("%s%.2f seconds (%g ms)\n", label, internal::clockToSeconds(internal::s_profile.var), internal::clockToMs(internal::s_profile.var)); internal::s_profile.var = 0;
#define XA_PROFILE_ALLOC 0

struct ProfileData
{
#if XA_PROFILE_ALLOC
	std::atomic<clock_t> alloc;
#endif
	clock_t addMeshReal;
	clock_t addMeshCopyData;
	std::atomic<clock_t> addMeshThread;
	std::atomic<clock_t> addMeshCreateColocals;
	clock_t computeChartsReal;
	std::atomic<clock_t> computeChartsThread;
	std::atomic<clock_t> createFaceGroups;
	std::atomic<clock_t> extractInvalidMeshGeometry;
	std::atomic<clock_t> chartGroupComputeChartsReal;
	std::atomic<clock_t> chartGroupComputeChartsThread;
	std::atomic<clock_t> createChartGroupMesh;
	std::atomic<clock_t> createChartGroupMeshColocals;
	std::atomic<clock_t> createChartGroupMeshBoundaries;
	std::atomic<clock_t> buildAtlas;
	std::atomic<clock_t> buildAtlasInit;
	std::atomic<clock_t> planarCharts;
	std::atomic<clock_t> clusteredCharts;
	std::atomic<clock_t> clusteredChartsPlaceSeeds;
	std::atomic<clock_t> clusteredChartsPlaceSeedsBoundaryIntersection;
	std::atomic<clock_t> clusteredChartsRelocateSeeds;
	std::atomic<clock_t> clusteredChartsReset;
	std::atomic<clock_t> clusteredChartsGrow;
	std::atomic<clock_t> clusteredChartsGrowBoundaryIntersection;
	std::atomic<clock_t> clusteredChartsMerge;
	std::atomic<clock_t> clusteredChartsFillHoles;
	std::atomic<clock_t> copyChartFaces;
	clock_t parameterizeChartsReal;
	std::atomic<clock_t> parameterizeChartsThread;
	std::atomic<clock_t> createChartMesh;
	std::atomic<clock_t> fixChartMeshTJunctions;
	std::atomic<clock_t> closeChartMeshHoles;
	std::atomic<clock_t> parameterizeChartsOrthogonal;
	std::atomic<clock_t> parameterizeChartsLSCM;
	std::atomic<clock_t> parameterizeChartsRecompute;
	std::atomic<clock_t> parameterizeChartsPiecewise;
	std::atomic<clock_t> parameterizeChartsPiecewiseBoundaryIntersection;
	std::atomic<clock_t> parameterizeChartsEvaluateQuality;
	clock_t packCharts;
	clock_t packChartsAddCharts;
	std::atomic<clock_t> packChartsAddChartsThread;
	std::atomic<clock_t> packChartsAddChartsRestoreTexcoords;
	clock_t packChartsRasterize;
	clock_t packChartsDilate;
	clock_t packChartsFindLocation;
	clock_t packChartsBlit;
	clock_t buildOutputMeshes;
};

static ProfileData s_profile;

static double clockToMs(clock_t c)
{
	return c * 1000.0 / CLOCKS_PER_SEC;
}

static double clockToSeconds(clock_t c)
{
	return c / (double)CLOCKS_PER_SEC;
}
#else
#define XA_PROFILE_START(var)
#define XA_PROFILE_END(var)
#define XA_PROFILE_PRINT_AND_RESET(label, var)
#define XA_PROFILE_ALLOC 0
#endif

struct MemTag
{
	enum
	{
		Default,
		BitImage,
		BVH,
		Matrix,
		Mesh,
		MeshBoundaries,
		MeshColocals,
		MeshEdgeMap,
		MeshIndices,
		MeshNormals,
		MeshPositions,
		MeshTexcoords,
		OpenNL,
		SegmentAtlasChartCandidates,
		SegmentAtlasChartFaces,
		SegmentAtlasMeshData,
		SegmentAtlasPlanarRegions,
		Count
	};
};

#if XA_DEBUG_HEAP
struct AllocHeader
{
	size_t size;
	const char *file;
	int line;
	int tag;
	uint32_t id;
	AllocHeader *prev, *next;
	bool free;
};

static std::mutex s_allocMutex;
static AllocHeader *s_allocRoot = nullptr;
static size_t s_allocTotalCount = 0, s_allocTotalSize = 0, s_allocPeakSize = 0, s_allocCount[MemTag::Count] = { 0 }, s_allocTotalTagSize[MemTag::Count] = { 0 }, s_allocPeakTagSize[MemTag::Count] = { 0 };
static uint32_t s_allocId =0 ;
static constexpr uint32_t kAllocRedzone = 0x12345678;

static void *Realloc(void *ptr, size_t size, int tag, const char *file, int line)
{
	std::unique_lock<std::mutex> lock(s_allocMutex);
	if (!size && !ptr)
		return nullptr;
	uint8_t *realPtr = nullptr;
	AllocHeader *header = nullptr;
	if (ptr) {
		realPtr = ((uint8_t *)ptr) - sizeof(AllocHeader);
		header = (AllocHeader *)realPtr;
	}
	if (realPtr && size) {
		s_allocTotalSize -= header->size;
		s_allocTotalTagSize[header->tag] -= header->size;
		// realloc, remove.
		if (header->prev)
			header->prev->next = header->next;
		else
			s_allocRoot = header->next;
		if (header->next)
			header->next->prev = header->prev;
	}
	if (!size) {
		s_allocTotalSize -= header->size;
		s_allocTotalTagSize[header->tag] -= header->size;
		XA_ASSERT(!header->free); // double free
		header->free = true;
		return nullptr;
	}
	size += sizeof(AllocHeader) + sizeof(kAllocRedzone);
	uint8_t *newPtr = (uint8_t *)s_realloc(realPtr, size);
	if (!newPtr)
		return nullptr;
	header = (AllocHeader *)newPtr;
	header->size = size;
	header->file = file;
	header->line = line;
	header->tag = tag;
	header->id = s_allocId++;
	header->free = false;
	if (!s_allocRoot) {
		s_allocRoot = header;
		header->prev = header->next = 0;
	} else {
		header->prev = nullptr;
		header->next = s_allocRoot;
		s_allocRoot = header;
		header->next->prev = header;
	}
	s_allocTotalCount++;
	s_allocTotalSize += size;
	if (s_allocTotalSize > s_allocPeakSize)
		s_allocPeakSize = s_allocTotalSize;
	s_allocCount[tag]++;
	s_allocTotalTagSize[tag] += size;
	if (s_allocTotalTagSize[tag] > s_allocPeakTagSize[tag])
		s_allocPeakTagSize[tag] = s_allocTotalTagSize[tag];
	auto redzone = (uint32_t *)(newPtr + size - sizeof(kAllocRedzone));
	*redzone = kAllocRedzone;
	return newPtr + sizeof(AllocHeader);
}

static void ReportLeaks()
{
	printf("Checking for memory leaks...\n");
	bool anyLeaks = false;
	AllocHeader *header = s_allocRoot;
	while (header) {
		if (!header->free) {
			printf("   Leak: ID %u, %zu bytes, %s %d\n", header->id, header->size, header->file, header->line);
			anyLeaks = true;
		}
		auto redzone = (const uint32_t *)((const uint8_t *)header + header->size - sizeof(kAllocRedzone));
		if (*redzone != kAllocRedzone)
			printf("   Redzone corrupted: %zu bytes %s %d\n", header->size, header->file, header->line);
		header = header->next;
	}
	if (!anyLeaks)
		printf("   No memory leaks\n");
	header = s_allocRoot;
	while (header) {
		AllocHeader *destroy = header;
		header = header->next;
		s_realloc(destroy, 0);
	}
	s_allocRoot = nullptr;
	s_allocTotalSize = s_allocPeakSize = 0;
	for (int i = 0; i < MemTag::Count; i++)
		s_allocTotalTagSize[i] = s_allocPeakTagSize[i] = 0;
}

static void PrintMemoryUsage()
{
	XA_PRINT("Total allocations: %zu\n", s_allocTotalCount);
	XA_PRINT("Memory usage: %0.2fMB current, %0.2fMB peak\n", internal::s_allocTotalSize / 1024.0f / 1024.0f, internal::s_allocPeakSize / 1024.0f / 1024.0f);
	static const char *labels[] = { // Sync with MemTag
		"Default",
		"BitImage",
		"BVH",
		"Matrix",
		"Mesh",
		"MeshBoundaries",
		"MeshColocals",
		"MeshEdgeMap",
		"MeshIndices",
		"MeshNormals",
		"MeshPositions",
		"MeshTexcoords",
		"OpenNL",
		"SegmentAtlasChartCandidates",
		"SegmentAtlasChartFaces",
		"SegmentAtlasMeshData",
		"SegmentAtlasPlanarRegions"
	};
	for (int i = 0; i < MemTag::Count; i++) {
		XA_PRINT("   %s: %zu allocations, %0.2fMB current, %0.2fMB peak\n", labels[i], internal::s_allocCount[i], internal::s_allocTotalTagSize[i] / 1024.0f / 1024.0f, internal::s_allocPeakTagSize[i] / 1024.0f / 1024.0f);
	}
}

#define XA_PRINT_MEM_USAGE internal::PrintMemoryUsage();
#else
static void *Realloc(void *ptr, size_t size, int /*tag*/, const char * /*file*/, int /*line*/)
{
	if (size == 0 && !ptr)
		return nullptr;
	if (size == 0 && s_free) {
		s_free(ptr);
		return nullptr;
	}
#if XA_PROFILE_ALLOC
	XA_PROFILE_START(alloc)
#endif
	void *mem = s_realloc(ptr, size);
#if XA_PROFILE_ALLOC
	XA_PROFILE_END(alloc)
#endif
	XA_DEBUG_ASSERT(size <= 0 || (size > 0 && mem));
	return mem;
}
#define XA_PRINT_MEM_USAGE
#endif

static constexpr float kPi = 3.14159265358979323846f;
static constexpr float kPi2 = 6.28318530717958647692f;
static constexpr float kEpsilon = 0.0001f;
static constexpr float kAreaEpsilon = FLT_EPSILON;
static constexpr float kNormalEpsilon = 0.001f;

static int align(int x, int a)
{
	return (x + a - 1) & ~(a - 1);
}

template <typename T>
static T max(const T &a, const T &b)
{
	return a > b ? a : b;
}

template <typename T>
static T min(const T &a, const T &b)
{
	return a < b ? a : b;
}

template <typename T>
static T max3(const T &a, const T &b, const T &c)
{
	return max(a, max(b, c));
}

/// Return the maximum of the three arguments.
template <typename T>
static T min3(const T &a, const T &b, const T &c)
{
	return min(a, min(b, c));
}

/// Clamp between two values.
template <typename T>
static T clamp(const T &x, const T &a, const T &b)
{
	return min(max(x, a), b);
}

template <typename T>
static void swap(T &a, T &b)
{
	T temp = a;
	a = b;
	b = temp;
}

union FloatUint32
{
	float f;
	uint32_t u;
};

static bool isFinite(float f)
{
	FloatUint32 fu;
	fu.f = f;
	return fu.u != 0x7F800000u && fu.u != 0x7F800001u;
}

static bool isNan(float f)
{
	return f != f;
}

// Robust floating point comparisons:
// http://realtimecollisiondetection.net/blog/?p=89
static bool equal(const float f0, const float f1, const float epsilon)
{
	//return fabs(f0-f1) <= epsilon;
	return fabs(f0 - f1) <= epsilon * max3(1.0f, fabsf(f0), fabsf(f1));
}

static int ftoi_ceil(float val)
{
	return (int)ceilf(val);
}

static bool isZero(const float f, const float epsilon)
{
	return fabs(f) <= epsilon;
}

static float square(float f)
{
	return f * f;
}

/** Return the next power of two.
* @see http://graphics.stanford.edu/~seander/bithacks.html
* @warning Behaviour for 0 is undefined.
* @note isPowerOfTwo(x) == true -> nextPowerOfTwo(x) == x
* @note nextPowerOfTwo(x) = 2 << log2(x-1)
*/
static uint32_t nextPowerOfTwo(uint32_t x)
{
	XA_DEBUG_ASSERT( x != 0 );
	// On modern CPUs this is supposed to be as fast as using the bsr instruction.
	x--;
	x |= x >> 1;
	x |= x >> 2;
	x |= x >> 4;
	x |= x >> 8;
	x |= x >> 16;
	return x + 1;
}

class Vector2
{
public:
	Vector2() {}
	explicit Vector2(float f) : x(f), y(f) {}
	Vector2(float x, float y): x(x), y(y) {}

	Vector2 operator-() const
	{
		return Vector2(-x, -y);
	}

	void operator+=(const Vector2 &v)
	{
		x += v.x;
		y += v.y;
	}

	void operator-=(const Vector2 &v)
	{
		x -= v.x;
		y -= v.y;
	}

	void operator*=(float s)
	{
		x *= s;
		y *= s;
	}

	void operator*=(const Vector2 &v)
	{
		x *= v.x;
		y *= v.y;
	}

	float x, y;
};

static bool operator==(const Vector2 &a, const Vector2 &b)
{
	return a.x == b.x && a.y == b.y;
}

static bool operator!=(const Vector2 &a, const Vector2 &b)
{
	return a.x != b.x || a.y != b.y;
}

/*static Vector2 operator+(const Vector2 &a, const Vector2 &b)
{
	return Vector2(a.x + b.x, a.y + b.y);
}*/

static Vector2 operator-(const Vector2 &a, const Vector2 &b)
{
	return Vector2(a.x - b.x, a.y - b.y);
}

static Vector2 operator*(const Vector2 &v, float s)
{
	return Vector2(v.x * s, v.y * s);
}

static float dot(const Vector2 &a, const Vector2 &b)
{
	return a.x * b.x + a.y * b.y;
}

static float lengthSquared(const Vector2 &v)
{
	return v.x * v.x + v.y * v.y;
}

static float length(const Vector2 &v)
{
	return sqrtf(lengthSquared(v));
}

#if XA_DEBUG
static bool isNormalized(const Vector2 &v, float epsilon = kNormalEpsilon)
{
	return equal(length(v), 1, epsilon);
}
#endif

static Vector2 normalize(const Vector2 &v, float epsilon)
{
	float l = length(v);
	XA_DEBUG_ASSERT(!isZero(l, epsilon));
	XA_UNUSED(epsilon);
	Vector2 n = v * (1.0f / l);
	XA_DEBUG_ASSERT(isNormalized(n));
	return n;
}

static Vector2 normalizeSafe(const Vector2 &v, const Vector2 &fallback, float epsilon)
{
	float l = length(v);
	if (isZero(l, epsilon))
		return fallback;
	return v * (1.0f / l);
}

static bool equal(const Vector2 &v1, const Vector2 &v2, float epsilon)
{
	return equal(v1.x, v2.x, epsilon) && equal(v1.y, v2.y, epsilon);
}

static Vector2 min(const Vector2 &a, const Vector2 &b)
{
	return Vector2(min(a.x, b.x), min(a.y, b.y));
}

static Vector2 max(const Vector2 &a, const Vector2 &b)
{
	return Vector2(max(a.x, b.x), max(a.y, b.y));
}

static bool isFinite(const Vector2 &v)
{
	return isFinite(v.x) && isFinite(v.y);
}

static float triangleArea(const Vector2 &a, const Vector2 &b, const Vector2 &c)
{
	// IC: While it may be appealing to use the following expression:
	//return (c.x * a.y + a.x * b.y + b.x * c.y - b.x * a.y - c.x * b.y - a.x * c.y) * 0.5f;
	// That's actually a terrible idea. Small triangles far from the origin can end up producing fairly large floating point
	// numbers and the results becomes very unstable and dependent on the order of the factors.
	// Instead, it's preferable to subtract the vertices first, and multiply the resulting small values together. The result
	// in this case is always much more accurate (as long as the triangle is small) and less dependent of the location of
	// the triangle.
	//return ((a.x - c.x) * (b.y - c.y) - (a.y - c.y) * (b.x - c.x)) * 0.5f;
	const Vector2 v0 = a - c;
	const Vector2 v1 = b - c;
	return (v0.x * v1.y - v0.y * v1.x) * 0.5f;
}

static bool linesIntersect(const Vector2 &a1, const Vector2 &a2, const Vector2 &b1, const Vector2 &b2, float epsilon)
{
	const Vector2 v0 = a2 - a1;
	const Vector2 v1 = b2 - b1;
	const float denom = -v1.x * v0.y + v0.x * v1.y;
	if (equal(denom, 0.0f, epsilon))
		return false;
	const float s = (-v0.y * (a1.x - b1.x) + v0.x * (a1.y - b1.y)) / denom;
	if (s > epsilon && s < 1.0f - epsilon) {
		const float t = ( v1.x * (a1.y - b1.y) - v1.y * (a1.x - b1.x)) / denom;
		return t > epsilon && t < 1.0f - epsilon;
	}
	return false;
}

struct Vector2i
{
	Vector2i() {}
	Vector2i(int32_t x, int32_t y) : x(x), y(y) {}

	int32_t x, y;
};

class Vector3
{
public:
	Vector3() {}
	explicit Vector3(float f) : x(f), y(f), z(f) {}
	Vector3(float x, float y, float z) : x(x), y(y), z(z) {}
	Vector3(const Vector2 &v, float z) : x(v.x), y(v.y), z(z) {}

	Vector2 xy() const
	{
		return Vector2(x, y);
	}

	Vector3 operator-() const
	{
		return Vector3(-x, -y, -z);
	}

	void operator+=(const Vector3 &v)
	{
		x += v.x;
		y += v.y;
		z += v.z;
	}

	void operator-=(const Vector3 &v)
	{
		x -= v.x;
		y -= v.y;
		z -= v.z;
	}

	void operator*=(float s)
	{
		x *= s;
		y *= s;
		z *= s;
	}

	void operator/=(float s)
	{
		float is = 1.0f / s;
		x *= is;
		y *= is;
		z *= is;
	}

	void operator*=(const Vector3 &v)
	{
		x *= v.x;
		y *= v.y;
		z *= v.z;
	}

	void operator/=(const Vector3 &v)
	{
		x /= v.x;
		y /= v.y;
		z /= v.z;
	}

	float x, y, z;
};

static Vector3 operator+(const Vector3 &a, const Vector3 &b)
{
	return Vector3(a.x + b.x, a.y + b.y, a.z + b.z);
}

static Vector3 operator-(const Vector3 &a, const Vector3 &b)
{
	return Vector3(a.x - b.x, a.y - b.y, a.z - b.z);
}

static Vector3 cross(const Vector3 &a, const Vector3 &b)
{
	return Vector3(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
}

static Vector3 operator*(const Vector3 &v, float s)
{
	return Vector3(v.x * s, v.y * s, v.z * s);
}

static Vector3 operator/(const Vector3 &v, float s)
{
	return v * (1.0f / s);
}

static float dot(const Vector3 &a, const Vector3 &b)
{
	return a.x * b.x + a.y * b.y + a.z * b.z;
}

static float lengthSquared(const Vector3 &v)
{
	return v.x * v.x + v.y * v.y + v.z * v.z;
}

static float length(const Vector3 &v)
{
	return sqrtf(lengthSquared(v));
}

static bool isNormalized(const Vector3 &v, float epsilon = kNormalEpsilon)
{
	return equal(length(v), 1, epsilon);
}

static Vector3 normalize(const Vector3 &v, float epsilon)
{
	float l = length(v);
	XA_DEBUG_ASSERT(!isZero(l, epsilon));
	XA_UNUSED(epsilon);
	Vector3 n = v * (1.0f / l);
	XA_DEBUG_ASSERT(isNormalized(n));
	return n;
}

static Vector3 normalizeSafe(const Vector3 &v, const Vector3 &fallback, float epsilon)
{
	float l = length(v);
	if (isZero(l, epsilon)) {
		return fallback;
	}
	return v * (1.0f / l);
}

static bool equal(const Vector3 &v0, const Vector3 &v1, float epsilon)
{
	return fabs(v0.x - v1.x) <= epsilon && fabs(v0.y - v1.y) <= epsilon && fabs(v0.z - v1.z) <= epsilon;
}

static Vector3 min(const Vector3 &a, const Vector3 &b)
{
	return Vector3(min(a.x, b.x), min(a.y, b.y), min(a.z, b.z));
}

static Vector3 max(const Vector3 &a, const Vector3 &b)
{
	return Vector3(max(a.x, b.x), max(a.y, b.y), max(a.z, b.z));
}

#if XA_DEBUG
bool isFinite(const Vector3 &v)
{
	return isFinite(v.x) && isFinite(v.y) && isFinite(v.z);
}
#endif

struct Extents2
{
	Vector2 min, max;

	Extents2() {}
	
	Extents2(Vector2 p1, Vector2 p2)
	{
		min = xatlas::internal::min(p1, p2);
		max = xatlas::internal::max(p1, p2);
	}

	void reset()
	{
		min.x = min.y = FLT_MAX;
		max.x = max.y = -FLT_MAX;
	}

	void add(Vector2 p)
	{
		min = xatlas::internal::min(min, p);
		max = xatlas::internal::max(max, p);
	}

	Vector2 midpoint() const
	{
		return Vector2(min.x + (max.x - min.x) * 0.5f, min.y + (max.y - min.y) * 0.5f);
	}

	static bool intersect(const Extents2 &e1, const Extents2 &e2)
	{
		return e1.min.x <= e2.max.x && e1.max.x >= e2.min.x && e1.min.y <= e2.max.y && e1.max.y >= e2.min.y;
	}
};

struct Plane
{
	Plane() = default;
	
	Plane(const Vector3 &p1, const Vector3 &p2, const Vector3 &p3)
	{
		normal = cross(p2 - p1, p3 - p1);
		dist = dot(normal, p1);
	}

	float distance(const Vector3 &p) const
	{
		return dot(normal, p) - dist;
	}

	void normalize()
	{
		const float len = length(normal);
		if (len > 0.0f) {
			const float il = 1.0f / len;
			normal *= il;
			dist *= il;
		}
	}

	Vector3 normal;
	float dist;
};

static bool lineIntersectsPoint(const Vector3 &point, const Vector3 &lineStart, const Vector3 &lineEnd, float *t, float epsilon)
{
	float tt;
	if (!t)
		t = &tt;
	*t = 0.0f;
	if (equal(lineStart, point, epsilon) || equal(lineEnd, point, epsilon))
		return false; // Vertex lies on either line vertices.
	const Vector3 v01 = point - lineStart;
	const Vector3 v21 = lineEnd - lineStart;
	const float l = length(v21);
	const float d = length(cross(v01, v21)) / l;
	if (!isZero(d, epsilon))
		return false;
	*t = dot(v01, v21) / (l * l);
	return *t > kEpsilon && *t < 1.0f - kEpsilon;
}

static bool sameSide(const Vector3 &p1, const Vector3 &p2, const Vector3 &a, const Vector3 &b)
{
	const Vector3 &ab = b - a;
	return dot(cross(ab, p1 - a), cross(ab, p2 - a)) >= 0.0f;
}

// http://blackpawn.com/texts/pointinpoly/default.html
static bool pointInTriangle(const Vector3 &p, const Vector3 &a, const Vector3 &b, const Vector3 &c)
{
	return sameSide(p, a, b, c) && sameSide(p, b, a, c) && sameSide(p, c, a, b);
}

#if XA_CLOSE_HOLES_CHECK_EDGE_INTERSECTION
// https://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm
static bool rayIntersectsTriangle(const Vector3 &rayOrigin, const Vector3 &rayDir, const Vector3 *tri, float *t)
{
	*t = 0.0f;
	const Vector3 &edge1 = tri[1] - tri[0];
	const Vector3 &edge2 = tri[2] - tri[0];
	const Vector3 h = cross(rayDir, edge2);
	const float a = dot(edge1, h);
	if (a > -kEpsilon && a < kEpsilon)
		return false; // This ray is parallel to this triangle.
	const float f = 1.0f / a;
	const Vector3 s = rayOrigin - tri[0];
	const float u = f * dot(s, h);
	if (u < 0.0f || u > 1.0f)
		return false;
	const Vector3 q = cross(s, edge1);
	const float v = f * dot(rayDir, q);
	if (v < 0.0f || u + v > 1.0f)
		return false;
	// At this stage we can compute t to find out where the intersection point is on the line.
	*t = f * dot(edge2, q);
	if (*t > kEpsilon && *t < 1.0f - kEpsilon)
		return true;
	// This means that there is a line intersection but not a ray intersection.
	return false;
}
#endif

// From Fast-BVH
struct AABB
{
	AABB() : min(FLT_MAX, FLT_MAX, FLT_MAX), max(-FLT_MAX, -FLT_MAX, -FLT_MAX) {}
	AABB(const Vector3 &min, const Vector3 &max) : min(min), max(max) { }
	AABB(const Vector3 &p, float radius = 0.0f) : min(p), max(p) { if (radius > 0.0f) expand(radius); }

	bool intersect(const AABB &other) const
	{
		return min.x <= other.max.x && max.x >= other.min.x && min.y <= other.max.y && max.y >= other.min.y && min.z <= other.max.z && max.z >= other.min.z;
	}

	void expandToInclude(const Vector3 &p)
	{
		min = internal::min(min, p);
		max = internal::max(max, p);
	}

	void expandToInclude(const AABB &aabb)
	{
		min = internal::min(min, aabb.min);
		max = internal::max(max, aabb.max);
	}

	void expand(float amount)
	{
		min -= Vector3(amount);
		max += Vector3(amount);
	}

	Vector3 centroid() const
	{
		return min + (max - min) * 0.5f;
	}

	uint32_t maxDimension() const
	{
		const Vector3 extent = max - min;
		uint32_t result = 0;
		if (extent.y > extent.x) {
			result = 1;
			if (extent.z > extent.y)
				result = 2;
		}
		else if(extent.z > extent.x)
			result = 2;
		return result;
	}

	Vector3 min, max;
};

struct ArrayBase
{
	ArrayBase(uint32_t elementSize, int memTag = MemTag::Default) : buffer(nullptr), elementSize(elementSize), size(0), capacity(0)
	{
#if XA_DEBUG_HEAP
		this->memTag = memTag;
#else
		XA_UNUSED(memTag);
#endif
	}

	~ArrayBase()
	{
		XA_FREE(buffer);
	}

	XA_INLINE void clear()
	{
		size = 0;
	}

	void copyFrom(const uint8_t *data, uint32_t length)
	{
		resize(length, true);
		memcpy(buffer, data, length * elementSize);
	}

	void copyTo(ArrayBase &other) const
	{
		XA_DEBUG_ASSERT(elementSize == other.elementSize);
		other.resize(size, true);
		memcpy(other.buffer, buffer, size * elementSize);
	}

	void destroy()
	{
		size = 0;
		XA_FREE(buffer);
		buffer = nullptr;
		capacity = 0;
		size = 0;
	}

	// Insert the given element at the given index shifting all the elements up.
	void insertAt(uint32_t index, const uint8_t *value)
	{
		XA_DEBUG_ASSERT(index >= 0 && index <= size);
		resize(size + 1, false);
		if (index < size - 1)
			memmove(buffer + elementSize * (index + 1), buffer + elementSize * index, elementSize * (size - 1 - index));
		memcpy(&buffer[index * elementSize], value, elementSize);
	}

	void moveTo(ArrayBase &other)
	{
		XA_DEBUG_ASSERT(elementSize == other.elementSize);
		other.destroy();
		other.buffer = buffer;
		other.elementSize = elementSize;
		other.size = size;
		other.capacity = capacity;
#if XA_DEBUG_HEAP
		other.memTag = memTag;
#endif
		buffer = nullptr;
		elementSize = size = capacity = 0;
	}

	void pop_back()
	{
		XA_DEBUG_ASSERT(size > 0);
		resize(size - 1, false);
	}

	void push_back(const uint8_t *value)
	{
		XA_DEBUG_ASSERT(value < buffer || value >= buffer + size);
		resize(size + 1, false);
		memcpy(&buffer[(size - 1) * elementSize], value, elementSize);
	}

	void push_back(const ArrayBase &other)
	{
		XA_DEBUG_ASSERT(elementSize == other.elementSize);
		if (other.size == 0)
			return;
		const uint32_t oldSize = size;
		resize(size + other.size, false);
		memcpy(buffer + oldSize * elementSize, other.buffer, other.size * other.elementSize);
	}

	// Remove the element at the given index. This is an expensive operation!
	void removeAt(uint32_t index)
	{
		XA_DEBUG_ASSERT(index >= 0 && index < size);
		if (size != 1)
			memmove(buffer + elementSize * index, buffer + elementSize * (index + 1), elementSize * (size - 1 - index));
		size--;
	}

	// Element at index is swapped with the last element, then the array length is decremented.
	void removeAtFast(uint32_t index)
	{
		XA_DEBUG_ASSERT(index >= 0 && index < size);
		if (size != 1 && index != size - 1)
			memcpy(buffer + elementSize * index, buffer + elementSize * (size - 1), elementSize);
		size--;
	}

	void reserve(uint32_t desiredSize)
	{
		if (desiredSize > capacity)
			setArrayCapacity(desiredSize);
	}

	void resize(uint32_t newSize, bool exact)
	{
		size = newSize;
		if (size > capacity) {
			// First allocation is always exact. Otherwise, following allocations grow array to 150% of desired size.
			uint32_t newBufferSize;
			if (capacity == 0 || exact)
				newBufferSize = size;
			else
				newBufferSize = size + (size >> 2);
			setArrayCapacity(newBufferSize);
		}
	}

	void setArrayCapacity(uint32_t newCapacity)
	{
		XA_DEBUG_ASSERT(newCapacity >= size);
		if (newCapacity == 0) {
			// free the buffer.
			if (buffer != nullptr) {
				XA_FREE(buffer);
				buffer = nullptr;
			}
		} else {
			// realloc the buffer
#if XA_DEBUG_HEAP
			buffer = XA_REALLOC_SIZE(memTag, buffer, newCapacity * elementSize);
#else
			buffer = XA_REALLOC_SIZE(MemTag::Default, buffer, newCapacity * elementSize);
#endif
		}
		capacity = newCapacity;
	}

#if XA_DEBUG_HEAP
	void setMemTag(int _memTag)
	{
		this->memTag = _memTag;
	}
#endif

	uint8_t *buffer;
	uint32_t elementSize;
	uint32_t size;
	uint32_t capacity;
#if XA_DEBUG_HEAP
	int memTag;
#endif
};

template<typename T>
class Array
{
public:
	Array(int memTag = MemTag::Default) : m_base(sizeof(T), memTag) {}
	Array(const Array&) = delete;
	Array &operator=(const Array &) = delete;

	XA_INLINE const T &operator[](uint32_t index) const
	{
		XA_DEBUG_ASSERT(index < m_base.size);
		return ((const T *)m_base.buffer)[index];
	}

	XA_INLINE T &operator[](uint32_t index)
	{
		XA_DEBUG_ASSERT(index < m_base.size);
		return ((T *)m_base.buffer)[index];
	}

	XA_INLINE const T &back() const
	{
		XA_DEBUG_ASSERT(!isEmpty());
		return ((const T *)m_base.buffer)[m_base.size - 1];
	}

	XA_INLINE T *begin() { return (T *)m_base.buffer; }
	XA_INLINE void clear() { m_base.clear(); }

	bool contains(const T &value) const
	{
		for (uint32_t i = 0; i < m_base.size; i++) {
			if (((const T *)m_base.buffer)[i] == value)
				return true;
		}
		return false;
	}

	void copyFrom(const T *data, uint32_t length) { m_base.copyFrom((const uint8_t *)data, length); }
	void copyTo(Array &other) const { m_base.copyTo(other.m_base); }
	XA_INLINE const T *data() const { return (const T *)m_base.buffer; }
	XA_INLINE T *data() { return (T *)m_base.buffer; }
	void destroy() { m_base.destroy(); }
	XA_INLINE T *end() { return (T *)m_base.buffer + m_base.size; }
	XA_INLINE bool isEmpty() const { return m_base.size == 0; }
	void insertAt(uint32_t index, const T &value) { m_base.insertAt(index, (const uint8_t *)&value); }
	void moveTo(Array &other) { m_base.moveTo(other.m_base); }
	void push_back(const T &value) { m_base.push_back((const uint8_t *)&value); }
	void push_back(const Array &other) { m_base.push_back(other.m_base); }
	void pop_back() { m_base.pop_back(); }
	void removeAt(uint32_t index) { m_base.removeAt(index); }
	void removeAtFast(uint32_t index) { m_base.removeAtFast(index); }
	void reserve(uint32_t desiredSize) { m_base.reserve(desiredSize); }
	void resize(uint32_t newSize) { m_base.resize(newSize, true); }

	void runCtors()
	{
		for (uint32_t i = 0; i < m_base.size; i++)
			new (&((T *)m_base.buffer)[i]) T;
	}

	void runDtors()
	{
		for (uint32_t i = 0; i < m_base.size; i++)
			((T *)m_base.buffer)[i].~T();
	}

	void fill(const T &value)
	{
		auto buffer = (T *)m_base.buffer;
		for (uint32_t i = 0; i < m_base.size; i++)
			buffer[i] = value;
	}

	void fillBytes(uint8_t value)
	{
		memset(m_base.buffer, (int)value, m_base.size * m_base.elementSize);
	}

#if XA_DEBUG_HEAP
	void setMemTag(int memTag) { m_base.setMemTag(memTag); }
#endif

	XA_INLINE uint32_t size() const { return m_base.size; }
	XA_INLINE void zeroOutMemory() { memset(m_base.buffer, 0, m_base.elementSize * m_base.size); }

private:
	ArrayBase m_base;
};

template<typename T>
struct ArrayView
{
	ArrayView() : data(nullptr), length(0) {}
	ArrayView(Array<T> &a) : data(a.data()), length(a.size()) {}
	ArrayView(T *data, uint32_t length) : data(data), length(length) {}
	ArrayView &operator=(Array<T> &a) { data = a.data(); length = a.size(); return *this; }
	XA_INLINE const T &operator[](uint32_t index) const { XA_DEBUG_ASSERT(index < length); return data[index]; }
	T *data;
	uint32_t length;
};

template<typename T>
struct ConstArrayView
{
	ConstArrayView() : data(nullptr), length(0) {}
	ConstArrayView(const Array<T> &a) : data(a.data()), length(a.size()) {}
	ConstArrayView(const T *data, uint32_t length) : data(data), length(length) {}
	ConstArrayView &operator=(const Array<T> &a) { data = a.data(); length = a.size(); return *this; }
	XA_INLINE const T &operator[](uint32_t index) const { XA_DEBUG_ASSERT(index < length); return data[index]; }
	const T *data;
	uint32_t length;
};

/// Basis class to compute tangent space basis, ortogonalizations and to transform vectors from one space to another.
struct Basis
{
	XA_NODISCARD static Vector3 computeTangent(const Vector3 &normal)
	{
		XA_ASSERT(isNormalized(normal));
		// Choose minimum axis.
		Vector3 tangent;
		if (fabsf(normal.x) < fabsf(normal.y) && fabsf(normal.x) < fabsf(normal.z))
			tangent = Vector3(1, 0, 0);
		else if (fabsf(normal.y) < fabsf(normal.z))
			tangent = Vector3(0, 1, 0);
		else
			tangent = Vector3(0, 0, 1);
		// Ortogonalize
		tangent -= normal * dot(normal, tangent);
		tangent = normalize(tangent, kEpsilon);
		return tangent;
	}

	XA_NODISCARD static Vector3 computeBitangent(const Vector3 &normal, const Vector3 &tangent)
	{
		return cross(normal, tangent);
	}

	Vector3 tangent = Vector3(0.0f);
	Vector3 bitangent = Vector3(0.0f);
	Vector3 normal = Vector3(0.0f);
};

// Simple bit array.
class BitArray
{
public:
	BitArray() : m_size(0) {}

	BitArray(uint32_t sz)
	{
		resize(sz);
	}

	void resize(uint32_t new_size)
	{
		m_size = new_size;
		m_wordArray.resize((m_size + 31) >> 5);
	}

	bool get(uint32_t index) const
	{
		XA_DEBUG_ASSERT(index < m_size);
		return (m_wordArray[index >> 5] & (1 << (index & 31))) != 0;
	}

	void set(uint32_t index)
	{
		XA_DEBUG_ASSERT(index < m_size);
		m_wordArray[index >> 5] |= (1 << (index & 31));
	}

	void unset(uint32_t index)
	{
		XA_DEBUG_ASSERT(index < m_size);
		m_wordArray[index >> 5] &= ~(1 << (index & 31));
	}

	void zeroOutMemory()
	{
		m_wordArray.zeroOutMemory();
	}

private:
	uint32_t m_size; // Number of bits stored.
	Array<uint32_t> m_wordArray;
};

class BitImage
{
public:
	BitImage() : m_width(0), m_height(0), m_rowStride(0), m_data(MemTag::BitImage) {}

	BitImage(uint32_t w, uint32_t h) : m_width(w), m_height(h), m_data(MemTag::BitImage)
	{
		m_rowStride = (m_width + 63) >> 6;
		m_data.resize(m_rowStride * m_height);
		m_data.zeroOutMemory();
	}

	BitImage(const BitImage &other) = delete;
	BitImage &operator=(const BitImage &other) = delete;
	uint32_t width() const { return m_width; }
	uint32_t height() const { return m_height; }

	void copyTo(BitImage &other)
	{
		other.m_width = m_width;
		other.m_height = m_height;
		other.m_rowStride = m_rowStride;
		m_data.copyTo(other.m_data);
	}

	void resize(uint32_t w, uint32_t h, bool discard)
	{
		const uint32_t rowStride = (w + 63) >> 6;
		if (discard) {
			m_data.resize(rowStride * h);
			m_data.zeroOutMemory();
		} else {
			Array<uint64_t> tmp;
			tmp.resize(rowStride * h);
			memset(tmp.data(), 0, tmp.size() * sizeof(uint64_t));
			// If only height has changed, can copy all rows at once.
			if (rowStride == m_rowStride) {
				memcpy(tmp.data(), m_data.data(), m_rowStride * min(m_height, h) * sizeof(uint64_t));
			} else if (m_width > 0 && m_height > 0) {
				const uint32_t height = min(m_height, h);
				for (uint32_t i = 0; i < height; i++)
					memcpy(&tmp[i * rowStride], &m_data[i * m_rowStride], min(rowStride, m_rowStride) * sizeof(uint64_t));
			}
			tmp.moveTo(m_data);
		}
		m_width = w;
		m_height = h;
		m_rowStride = rowStride;
	}

	bool get(uint32_t x, uint32_t y) const
	{
		XA_DEBUG_ASSERT(x < m_width && y < m_height);
		const uint32_t index = (x >> 6) + y * m_rowStride;
		return (m_data[index] & (UINT64_C(1) << (uint64_t(x) & UINT64_C(63)))) != 0;
	}

	void set(uint32_t x, uint32_t y)
	{
		XA_DEBUG_ASSERT(x < m_width && y < m_height);
		const uint32_t index = (x >> 6) + y * m_rowStride;
		m_data[index] |= UINT64_C(1) << (uint64_t(x) & UINT64_C(63));
		XA_DEBUG_ASSERT(get(x, y));
	}

	void zeroOutMemory()
	{
		m_data.zeroOutMemory();
	}

	bool canBlit(const BitImage &image, uint32_t offsetX, uint32_t offsetY) const
	{
		for (uint32_t y = 0; y < image.m_height; y++) {
			const uint32_t thisY = y + offsetY;
			if (thisY >= m_height)
				continue;
			uint32_t x = 0;
			for (;;) {
				const uint32_t thisX = x + offsetX;
				if (thisX >= m_width)
					break;
				const uint32_t thisBlockShift = thisX % 64;
				const uint64_t thisBlock = m_data[(thisX >> 6) + thisY * m_rowStride] >> thisBlockShift;
				const uint32_t blockShift = x % 64;
				const uint64_t block = image.m_data[(x >> 6) + y * image.m_rowStride] >> blockShift;
				if ((thisBlock & block) != 0)
					return false;
				x += 64 - max(thisBlockShift, blockShift);
				if (x >= image.m_width)
					break;
			}
		}
		return true;
	}

	void dilate(uint32_t padding)
	{
		BitImage tmp(m_width, m_height);
		for (uint32_t p = 0; p < padding; p++) {
			tmp.zeroOutMemory();
			for (uint32_t y = 0; y < m_height; y++) {
				for (uint32_t x = 0; x < m_width; x++) {
					bool b = get(x, y);
					if (!b) {
						if (x > 0) {
							b |= get(x - 1, y);
							if (y > 0) b |= get(x - 1, y - 1);
							if (y < m_height - 1) b |= get(x - 1, y + 1);
						}
						if (y > 0) b |= get(x, y - 1);
						if (y < m_height - 1) b |= get(x, y + 1);
						if (x < m_width - 1) {
							b |= get(x + 1, y);
							if (y > 0) b |= get(x + 1, y - 1);
							if (y < m_height - 1) b |= get(x + 1, y + 1);
						}
					}
					if (b)
						tmp.set(x, y);
				}
			}
			tmp.m_data.copyTo(m_data);
		}
	}

private:
	uint32_t m_width;
	uint32_t m_height;
	uint32_t m_rowStride; // In uint64_t's
	Array<uint64_t> m_data;
};

// From Fast-BVH
class BVH
{
public:
	BVH(const Array<AABB> &objectAabbs, uint32_t leafSize = 4) : m_objectIds(MemTag::BVH), m_nodes(MemTag::BVH)
	{
		m_objectAabbs = &objectAabbs;
		if (m_objectAabbs->isEmpty())
			return;
		m_objectIds.resize(objectAabbs.size());
		for (uint32_t i = 0; i < m_objectIds.size(); i++)
			m_objectIds[i] = i;
		BuildEntry todo[128];
		uint32_t stackptr = 0;
		const uint32_t kRoot = 0xfffffffc;
		const uint32_t kUntouched = 0xffffffff;
		const uint32_t kTouchedTwice = 0xfffffffd;
		// Push the root
		todo[stackptr].start = 0;
		todo[stackptr].end = objectAabbs.size();
		todo[stackptr].parent = kRoot;
		stackptr++;
		Node node;
		m_nodes.reserve(objectAabbs.size() * 2);
		uint32_t nNodes = 0;
		while(stackptr > 0) {
			// Pop the next item off of the stack
			const BuildEntry &bnode = todo[--stackptr];
			const uint32_t start = bnode.start;
			const uint32_t end = bnode.end;
			const uint32_t nPrims = end - start;
			nNodes++;
			node.start = start;
			node.nPrims = nPrims;
			node.rightOffset = kUntouched;
			// Calculate the bounding box for this node
			AABB bb(objectAabbs[m_objectIds[start]]);
			AABB bc(objectAabbs[m_objectIds[start]].centroid());
			for(uint32_t p = start + 1; p < end; ++p) {
				bb.expandToInclude(objectAabbs[m_objectIds[p]]);
				bc.expandToInclude(objectAabbs[m_objectIds[p]].centroid());
			}
			node.aabb = bb;
			// If the number of primitives at this point is less than the leaf
			// size, then this will become a leaf. (Signified by rightOffset == 0)
			if (nPrims <= leafSize)
				node.rightOffset = 0;
			m_nodes.push_back(node);
			// Child touches parent...
			// Special case: Don't do this for the root.
			if (bnode.parent != kRoot) {
				m_nodes[bnode.parent].rightOffset--;
				// When this is the second touch, this is the right child.
				// The right child sets up the offset for the flat tree.
				if (m_nodes[bnode.parent].rightOffset == kTouchedTwice )
					m_nodes[bnode.parent].rightOffset = nNodes - 1 - bnode.parent;
			}
			// If this is a leaf, no need to subdivide.
			if (node.rightOffset == 0)
				continue;
			// Set the split dimensions
			const uint32_t split_dim = bc.maxDimension();
			// Split on the center of the longest axis
			const float split_coord = 0.5f * ((&bc.min.x)[split_dim] + (&bc.max.x)[split_dim]);
			// Partition the list of objects on this split
			uint32_t mid = start;
			for (uint32_t i = start; i < end; ++i) {
				const Vector3 centroid(objectAabbs[m_objectIds[i]].centroid());
				if ((&centroid.x)[split_dim] < split_coord) {
					swap(m_objectIds[i], m_objectIds[mid]);
					++mid;
				}
			}
			// If we get a bad split, just choose the center...
			if (mid == start || mid == end)
				mid = start + (end - start) / 2;
			// Push right child
			todo[stackptr].start = mid;
			todo[stackptr].end = end;
			todo[stackptr].parent = nNodes - 1;
			stackptr++;
			// Push left child
			todo[stackptr].start = start;
			todo[stackptr].end = mid;
			todo[stackptr].parent = nNodes - 1;
			stackptr++;
		}
	}

	void query(const AABB &queryAabb, Array<uint32_t> &result) const
	{
		result.clear();
		// Working set
		uint32_t todo[64];
		int32_t stackptr = 0;
		// "Push" on the root node to the working set
		todo[stackptr] = 0;
		while(stackptr >= 0) {
			// Pop off the next node to work on.
			const int ni = todo[stackptr--];
			const Node &node = m_nodes[ni];
			// Is leaf -> Intersect
			if (node.rightOffset == 0) {
				for(uint32_t o = 0; o < node.nPrims; ++o) {
					const uint32_t obj = node.start + o;
					if (queryAabb.intersect((*m_objectAabbs)[m_objectIds[obj]]))
						result.push_back(m_objectIds[obj]);
				}
			} else { // Not a leaf
				const uint32_t left = ni + 1;
				const uint32_t right = ni + node.rightOffset;
				if (queryAabb.intersect(m_nodes[left].aabb))
					todo[++stackptr] = left;
				if (queryAabb.intersect(m_nodes[right].aabb))
					todo[++stackptr] = right;
			}
		}
	}

private:
	struct BuildEntry
	{
		uint32_t parent; // If non-zero then this is the index of the parent. (used in offsets)
		uint32_t start, end; // The range of objects in the object list covered by this node.
	};

	struct Node
	{
		AABB aabb;
		uint32_t start, nPrims, rightOffset;
	};

	const Array<AABB> *m_objectAabbs;
	Array<uint32_t> m_objectIds;
	Array<Node> m_nodes;
};

struct Fit
{
	static bool computeBasis(const Vector3 *points, uint32_t pointsCount, Basis *basis)
	{
		if (computeLeastSquaresNormal(points, pointsCount, &basis->normal)) {
			basis->tangent = Basis::computeTangent(basis->normal);
			basis->bitangent = Basis::computeBitangent(basis->normal, basis->tangent);
			return true;
		}
		return computeEigen(points, pointsCount, basis);
	}

private:
	// Fit a plane to a collection of points.
	// Fast, and accurate to within a few degrees.
	// Returns None if the points do not span a plane.
	// https://www.ilikebigbits.com/2015_03_04_plane_from_points.html
	static bool computeLeastSquaresNormal(const Vector3 *points, uint32_t pointsCount, Vector3 *normal)
	{
		XA_DEBUG_ASSERT(pointsCount >= 3);
		if (pointsCount == 3) {
			*normal = normalize(cross(points[2] - points[0], points[1] - points[0]), kEpsilon);
			return true;
		}
		const float invN = 1.0f / float(pointsCount);
		Vector3 centroid(0.0f);
		for (uint32_t i = 0; i < pointsCount; i++)
			centroid += points[i];
		centroid *= invN;
		// Calculate full 3x3 covariance matrix, excluding symmetries:
		float xx = 0.0f, xy = 0.0f, xz = 0.0f, yy = 0.0f, yz = 0.0f, zz = 0.0f;
		for (uint32_t i = 0; i < pointsCount; i++) {
			Vector3 r = points[i] - centroid;
			xx += r.x * r.x;
			xy += r.x * r.y;
			xz += r.x * r.z;
			yy += r.y * r.y;
			yz += r.y * r.z;
			zz += r.z * r.z;
		}
#if 0
		xx *= invN;
		xy *= invN;
		xz *= invN;
		yy *= invN;
		yz *= invN;
		zz *= invN;
		Vector3 weighted_dir(0.0f);
		{
			float det_x = yy * zz - yz * yz;
			const Vector3 axis_dir(det_x, xz * yz - xy * zz, xy * yz - xz * yy);
			float weight = det_x * det_x;
			if (dot(weighted_dir, axis_dir) < 0.0f)
				weight = -weight;
			weighted_dir += axis_dir * weight;
		}
		{
			float det_y = xx * zz - xz * xz;
			const Vector3 axis_dir(xz * yz - xy * zz, det_y, xy * xz - yz * xx);
			float weight = det_y * det_y;
			if (dot(weighted_dir, axis_dir) < 0.0f)
				weight = -weight;
			weighted_dir += axis_dir * weight;
		}
		{
			float det_z = xx * yy - xy * xy;
			const Vector3 axis_dir(xy * yz - xz * yy, xy * xz - yz * xx, det_z);
			float weight = det_z * det_z;
			if (dot(weighted_dir, axis_dir) < 0.0f)
				weight = -weight;
			weighted_dir += axis_dir * weight;
		}
		*normal = normalize(weighted_dir, kEpsilon);
#else
		const float det_x = yy * zz - yz * yz;
		const float det_y = xx * zz - xz * xz;
		const float det_z = xx * yy - xy * xy;
		const float det_max = max(det_x, max(det_y, det_z));
		if (det_max <= 0.0f)
			return false; // The points don't span a plane
		// Pick path with best conditioning:
		Vector3 dir(0.0f);
		if (det_max == det_x)
			dir = Vector3(det_x,xz * yz - xy * zz,xy * yz - xz * yy);
		else if (det_max == det_y)
			dir = Vector3(xz * yz - xy * zz, det_y, xy * xz - yz * xx);
		else if (det_max == det_z)
			dir = Vector3(xy * yz - xz * yy, xy * xz - yz * xx, det_z);
		const float len = length(dir);
		if (isZero(len, kEpsilon))
			return false;
		*normal = dir * (1.0f / len);
#endif
		return isNormalized(*normal);
	}

	static bool computeEigen(const Vector3 *points, uint32_t pointsCount, Basis *basis)
	{
		float matrix[6];
		computeCovariance(pointsCount, points, matrix);
		if (matrix[0] == 0 && matrix[3] == 0 && matrix[5] == 0)
			return false;
		float eigenValues[3];
		Vector3 eigenVectors[3];
		if (!eigenSolveSymmetric3(matrix, eigenValues, eigenVectors))
			return false;
		basis->normal = normalize(eigenVectors[2], kEpsilon);
		basis->tangent = normalize(eigenVectors[0], kEpsilon);
		basis->bitangent = normalize(eigenVectors[1], kEpsilon);
		return true;
	}

	static Vector3 computeCentroid(int n, const Vector3 * points)
	{
		Vector3 centroid(0.0f);
		for (int i = 0; i < n; i++) {
			centroid += points[i];
		}
		centroid /= float(n);
		return centroid;
	}

	static Vector3 computeCovariance(int n, const Vector3 * points, float * covariance)
	{
		// compute the centroid
		Vector3 centroid = computeCentroid(n, points);
		// compute covariance matrix
		for (int i = 0; i < 6; i++) {
			covariance[i] = 0.0f;
		}
		for (int i = 0; i < n; i++) {
			Vector3 v = points[i] - centroid;
			covariance[0] += v.x * v.x;
			covariance[1] += v.x * v.y;
			covariance[2] += v.x * v.z;
			covariance[3] += v.y * v.y;
			covariance[4] += v.y * v.z;
			covariance[5] += v.z * v.z;
		}
		return centroid;
	}

	// Tridiagonal solver from Charles Bloom.
	// Householder transforms followed by QL decomposition.
	// Seems to be based on the code from Numerical Recipes in C.
	static bool eigenSolveSymmetric3(const float matrix[6], float eigenValues[3], Vector3 eigenVectors[3])
	{
		XA_DEBUG_ASSERT(matrix != nullptr && eigenValues != nullptr && eigenVectors != nullptr);
		float subd[3];
		float diag[3];
		float work[3][3];
		work[0][0] = matrix[0];
		work[0][1] = work[1][0] = matrix[1];
		work[0][2] = work[2][0] = matrix[2];
		work[1][1] = matrix[3];
		work[1][2] = work[2][1] = matrix[4];
		work[2][2] = matrix[5];
		EigenSolver3_Tridiagonal(work, diag, subd);
		if (!EigenSolver3_QLAlgorithm(work, diag, subd)) {
			for (int i = 0; i < 3; i++) {
				eigenValues[i] = 0;
				eigenVectors[i] = Vector3(0);
			}
			return false;
		}
		for (int i = 0; i < 3; i++) {
			eigenValues[i] = (float)diag[i];
		}
		// eigenvectors are the columns; make them the rows :
		for (int i = 0; i < 3; i++) {
			for (int j = 0; j < 3; j++) {
				(&eigenVectors[j].x)[i] = (float) work[i][j];
			}
		}
		// shuffle to sort by singular value :
		if (eigenValues[2] > eigenValues[0] && eigenValues[2] > eigenValues[1]) {
			swap(eigenValues[0], eigenValues[2]);
			swap(eigenVectors[0], eigenVectors[2]);
		}
		if (eigenValues[1] > eigenValues[0]) {
			swap(eigenValues[0], eigenValues[1]);
			swap(eigenVectors[0], eigenVectors[1]);
		}
		if (eigenValues[2] > eigenValues[1]) {
			swap(eigenValues[1], eigenValues[2]);
			swap(eigenVectors[1], eigenVectors[2]);
		}
		XA_DEBUG_ASSERT(eigenValues[0] >= eigenValues[1] && eigenValues[0] >= eigenValues[2]);
		XA_DEBUG_ASSERT(eigenValues[1] >= eigenValues[2]);
		return true;
	}

private:
	static void EigenSolver3_Tridiagonal(float mat[3][3], float *diag, float *subd)
	{
		// Householder reduction T = Q^t M Q
		//   Input:
		//     mat, symmetric 3x3 matrix M
		//   Output:
		//     mat, orthogonal matrix Q
		//     diag, diagonal entries of T
		//     subd, subdiagonal entries of T (T is symmetric)
		const float epsilon = 1e-08f;
		float a = mat[0][0];
		float b = mat[0][1];
		float c = mat[0][2];
		float d = mat[1][1];
		float e = mat[1][2];
		float f = mat[2][2];
		diag[0] = a;
		subd[2] = 0.f;
		if (fabsf(c) >= epsilon) {
			const float ell = sqrtf(b * b + c * c);
			b /= ell;
			c /= ell;
			const float q = 2 * b * e + c * (f - d);
			diag[1] = d + c * q;
			diag[2] = f - c * q;
			subd[0] = ell;
			subd[1] = e - b * q;
			mat[0][0] = 1;
			mat[0][1] = 0;
			mat[0][2] = 0;
			mat[1][0] = 0;
			mat[1][1] = b;
			mat[1][2] = c;
			mat[2][0] = 0;
			mat[2][1] = c;
			mat[2][2] = -b;
		} else {
			diag[1] = d;
			diag[2] = f;
			subd[0] = b;
			subd[1] = e;
			mat[0][0] = 1;
			mat[0][1] = 0;
			mat[0][2] = 0;
			mat[1][0] = 0;
			mat[1][1] = 1;
			mat[1][2] = 0;
			mat[2][0] = 0;
			mat[2][1] = 0;
			mat[2][2] = 1;
		}
	}

	static bool EigenSolver3_QLAlgorithm(float mat[3][3], float *diag, float *subd)
	{
		// QL iteration with implicit shifting to reduce matrix from tridiagonal
		// to diagonal
		const int maxiter = 32;
		for (int ell = 0; ell < 3; ell++) {
			int iter;
			for (iter = 0; iter < maxiter; iter++) {
				int m;
				for (m = ell; m <= 1; m++) {
					float dd = fabsf(diag[m]) + fabsf(diag[m + 1]);
					if ( fabsf(subd[m]) + dd == dd )
						break;
				}
				if ( m == ell )
					break;
				float g = (diag[ell + 1] - diag[ell]) / (2 * subd[ell]);
				float r = sqrtf(g * g + 1);
				if ( g < 0 )
					g = diag[m] - diag[ell] + subd[ell] / (g - r);
				else
					g = diag[m] - diag[ell] + subd[ell] / (g + r);
				float s = 1, c = 1, p = 0;
				for (int i = m - 1; i >= ell; i--) {
					float f = s * subd[i], b = c * subd[i];
					if ( fabsf(f) >= fabsf(g) ) {
						c = g / f;
						r = sqrtf(c * c + 1);
						subd[i + 1] = f * r;
						c *= (s = 1 / r);
					} else {
						s = f / g;
						r = sqrtf(s * s + 1);
						subd[i + 1] = g * r;
						s *= (c = 1 / r);
					}
					g = diag[i + 1] - p;
					r = (diag[i] - g) * s + 2 * b * c;
					p = s * r;
					diag[i + 1] = g + p;
					g = c * r - b;
					for (int k = 0; k < 3; k++) {
						f = mat[k][i + 1];
						mat[k][i + 1] = s * mat[k][i] + c * f;
						mat[k][i] = c * mat[k][i] - s * f;
					}
				}
				diag[ell] -= p;
				subd[ell] = g;
				subd[m] = 0;
			}
			if ( iter == maxiter )
				// should not get here under normal circumstances
				return false;
		}
		return true;
	}
};

static uint32_t sdbmHash(const void *data_in, uint32_t size, uint32_t h = 5381)
{
	const uint8_t *data = (const uint8_t *) data_in;
	uint32_t i = 0;
	while (i < size) {
		h = (h << 16) + (h << 6) - h + (uint32_t ) data[i++];
	}
	return h;
}

template <typename T>
static uint32_t hash(const T &t, uint32_t h = 5381)
{
	return sdbmHash(&t, sizeof(T), h);
}

template <typename Key>
struct Hash
{
	uint32_t operator()(const Key &k) const { return hash(k); }
};

template <typename Key>
struct PassthroughHash
{
	uint32_t operator()(const Key &k) const { return (uint32_t)k; }
};

template <typename Key>
struct Equal
{
	bool operator()(const Key &k0, const Key &k1) const { return k0 == k1; }
};

template<typename Key, typename H = Hash<Key>, typename E = Equal<Key> >
class HashMap
{
public:
	HashMap(int memTag, uint32_t size) : m_memTag(memTag), m_size(size), m_numSlots(0), m_slots(nullptr), m_keys(memTag), m_next(memTag)
	{
	}

	~HashMap()
	{
		if (m_slots)
			XA_FREE(m_slots);
	}

	void destroy()
	{
		if (m_slots) {
			XA_FREE(m_slots);
			m_slots = nullptr;
		}
		m_keys.destroy();
		m_next.destroy();
	}

	uint32_t add(const Key &key)
	{
		if (!m_slots)
			alloc();
		const uint32_t hash = computeHash(key);
		m_keys.push_back(key);
		m_next.push_back(m_slots[hash]);
		m_slots[hash] = m_next.size() - 1;
		return m_keys.size() - 1;
	}

	uint32_t get(const Key &key) const
	{
		if (!m_slots)
			return UINT32_MAX;
		const uint32_t hash = computeHash(key);
		uint32_t i = m_slots[hash];
		E equal;
		while (i != UINT32_MAX) {
			if (equal(m_keys[i], key))
				return i;
			i = m_next[i];
		}
		return UINT32_MAX;
	}

	uint32_t getNext(uint32_t current) const
	{
		uint32_t i = m_next[current];
		E equal;
		while (i != UINT32_MAX) {
			if (equal(m_keys[i], m_keys[current]))
				return i;
			i = m_next[i];
		}
		return UINT32_MAX;
	}

private:
	void alloc()
	{
		XA_DEBUG_ASSERT(m_size > 0);
		m_numSlots = nextPowerOfTwo(m_size);
		auto minNumSlots = uint32_t(m_size * 1.3);
		if (m_numSlots < minNumSlots)
			m_numSlots = nextPowerOfTwo(minNumSlots);
		m_slots = XA_ALLOC_ARRAY(m_memTag, uint32_t, m_numSlots);
		for (uint32_t i = 0; i < m_numSlots; i++)
			m_slots[i] = UINT32_MAX;
		m_keys.reserve(m_size);
		m_next.reserve(m_size);
	}

	uint32_t computeHash(const Key &key) const
	{
		H hash;
		return hash(key) & (m_numSlots - 1);
	}

	int m_memTag;
	uint32_t m_size;
	uint32_t m_numSlots;
	uint32_t *m_slots;
	Array<Key> m_keys;
	Array<uint32_t> m_next;
};

template<typename T>
static void insertionSort(T *data, uint32_t length)
{
	for (int32_t i = 1; i < (int32_t)length; i++) {
		T x = data[i];
		int32_t j = i - 1;
		while (j >= 0 && x < data[j]) {
			data[j + 1] = data[j];
			j--;
		}
		data[j + 1] = x;
	}
}

class KISSRng
{
public:
	KISSRng() { reset(); }

	void reset()
	{
		x = 123456789;
		y = 362436000;
		z = 521288629;
		c = 7654321;
	}

	uint32_t getRange(uint32_t range)
	{
		if (range == 0)
			return 0;
		x = 69069 * x + 12345;
		y ^= (y << 13);
		y ^= (y >> 17);
		y ^= (y << 5);
		uint64_t t = 698769069ULL * z + c;
		c = (t >> 32);
		return (x + y + (z = (uint32_t)t)) % range;
	}

private:
	uint32_t x, y, z, c;
};

// Based on Pierre Terdiman's and Michael Herf's source code.
// http://www.codercorner.com/RadixSortRevisited.htm
// http://www.stereopsis.com/radix.html
class RadixSort
{
public:
	void sort(const float *input, uint32_t count)
	{
		if (input == nullptr || count == 0) {
			m_buffer1.clear();
			m_buffer2.clear();
			m_ranks = m_buffer1.data();
			m_ranks2 = m_buffer2.data();
			return;
		}
		// Resize lists if needed
		m_buffer1.resize(count);
		m_buffer2.resize(count);
		m_ranks = m_buffer1.data();
		m_ranks2 = m_buffer2.data();
		m_validRanks = false;
		if (count < 32)
			insertionSort(input, count);
		else {
			// @@ Avoid touching the input multiple times.
			for (uint32_t i = 0; i < count; i++) {
				floatFlip((uint32_t &)input[i]);
			}
			radixSort<uint32_t>((const uint32_t *)input, count);
			for (uint32_t i = 0; i < count; i++) {
				ifloatFlip((uint32_t &)input[i]);
			}
		}
	}

	void sort(const Array<float> &input)
	{
		sort(input.data(), input.size());
	}

	// Access to results. m_ranks is a list of indices in sorted order, i.e. in the order you may further process your data
	const uint32_t *ranks() const
	{
		XA_DEBUG_ASSERT(m_validRanks);
		return m_ranks;
	}

private:
	uint32_t *m_ranks, *m_ranks2;
	Array<uint32_t> m_buffer1, m_buffer2;
	bool m_validRanks;

	void floatFlip(uint32_t &f)
	{
		int32_t mask = (int32_t(f) >> 31) | 0x80000000; // Warren Hunt, Manchor Ko.
		f ^= mask;
	}

	void ifloatFlip(uint32_t &f)
	{
		uint32_t mask = ((f >> 31) - 1) | 0x80000000; // Michael Herf.
		f ^= mask;
	}

	template<typename T>
	void createHistograms(const T *buffer, uint32_t count, uint32_t *histogram)
	{
		const uint32_t bucketCount = sizeof(T); // (8 * sizeof(T)) / log2(radix)
		// Init bucket pointers.
		uint32_t *h[bucketCount];
		for (uint32_t i = 0; i < bucketCount; i++) {
			h[i] = histogram + 256 * i;
		}
		// Clear histograms.
		memset(histogram, 0, 256 * bucketCount * sizeof(uint32_t ));
		// @@ Add support for signed integers.
		// Build histograms.
		const uint8_t *p = (const uint8_t *)buffer;  // @@ Does this break aliasing rules?
		const uint8_t *pe = p + count * sizeof(T);
		while (p != pe) {
			h[0][*p++]++, h[1][*p++]++, h[2][*p++]++, h[3][*p++]++;
#ifdef _MSC_VER
#pragma warning(push)
#pragma warning(disable : 4127)
#endif
			if (bucketCount == 8) h[4][*p++]++, h[5][*p++]++, h[6][*p++]++, h[7][*p++]++;
#ifdef _MSC_VER
#pragma warning(pop)
#endif
		}
	}

	template <typename T>
	void insertionSort(const T *input, uint32_t count)
	{
		if (!m_validRanks) {
			m_ranks[0] = 0;
			for (uint32_t i = 1; i != count; ++i) {
				int rank = m_ranks[i] = i;
				uint32_t j = i;
				while (j != 0 && input[rank] < input[m_ranks[j - 1]]) {
					m_ranks[j] = m_ranks[j - 1];
					--j;
				}
				if (i != j) {
					m_ranks[j] = rank;
				}
			}
			m_validRanks = true;
		} else {
			for (uint32_t i = 1; i != count; ++i) {
				int rank = m_ranks[i];
				uint32_t j = i;
				while (j != 0 && input[rank] < input[m_ranks[j - 1]]) {
					m_ranks[j] = m_ranks[j - 1];
					--j;
				}
				if (i != j) {
					m_ranks[j] = rank;
				}
			}
		}
	}

	template <typename T>
	void radixSort(const T *input, uint32_t count)
	{
		const uint32_t P = sizeof(T); // pass count
		// Allocate histograms & offsets on the stack
		uint32_t histogram[256 * P];
		uint32_t *link[256];
		createHistograms(input, count, histogram);
		// Radix sort, j is the pass number (0=LSB, P=MSB)
		for (uint32_t j = 0; j < P; j++) {
			// Pointer to this bucket.
			const uint32_t *h = &histogram[j * 256];
			const uint8_t *inputBytes = (const uint8_t *)input; // @@ Is this aliasing legal?
			inputBytes += j;
			if (h[inputBytes[0]] == count) {
				// Skip this pass, all values are the same.
				continue;
			}
			// Create offsets
			link[0] = m_ranks2;
			for (uint32_t i = 1; i < 256; i++) link[i] = link[i - 1] + h[i - 1];
			// Perform Radix Sort
			if (!m_validRanks) {
				for (uint32_t i = 0; i < count; i++) {
					*link[inputBytes[i * P]]++ = i;
				}
				m_validRanks = true;
			} else {
				for (uint32_t i = 0; i < count; i++) {
					const uint32_t idx = m_ranks[i];
					*link[inputBytes[idx * P]]++ = idx;
				}
			}
			// Swap pointers for next pass. Valid indices - the most recent ones - are in m_ranks after the swap.
			swap(m_ranks, m_ranks2);
		}
		// All values were equal, generate linear ranks.
		if (!m_validRanks) {
			for (uint32_t i = 0; i < count; i++)
				m_ranks[i] = i;
			m_validRanks = true;
		}
	}
};

// Wrapping this in a class allows temporary arrays to be re-used.
class BoundingBox2D
{
public:
	Vector2 majorAxis, minorAxis, minCorner, maxCorner;

	void clear()
	{
		m_boundaryVertices.clear();
	}

	void appendBoundaryVertex(Vector2 v)
	{
		m_boundaryVertices.push_back(v);
	}

	// This should compute convex hull and use rotating calipers to find the best box. Currently it uses a brute force method.
	// If vertices is null or vertexCount is 0, the boundary vertices are used.
	void compute(const Vector2 *vertices = nullptr, uint32_t vertexCount = 0)
	{
		if (!vertices || vertexCount == 0) {
			vertices = m_boundaryVertices.data();
			vertexCount = m_boundaryVertices.size();
		}
		convexHull(m_boundaryVertices.data(), m_boundaryVertices.size(), m_hull, 0.00001f);
		// @@ Ideally I should use rotating calipers to find the best box. Using brute force for now.
		float best_area = FLT_MAX;
		Vector2 best_min(0);
		Vector2 best_max(0);
		Vector2 best_axis(0);
		const uint32_t hullCount = m_hull.size();
		for (uint32_t i = 0, j = hullCount - 1; i < hullCount; j = i, i++) {
			if (equal(m_hull[i], m_hull[j], kEpsilon))
				continue;
			Vector2 axis = normalize(m_hull[i] - m_hull[j], 0.0f);
			XA_DEBUG_ASSERT(isFinite(axis));
			// Compute bounding box.
			Vector2 box_min(FLT_MAX, FLT_MAX);
			Vector2 box_max(-FLT_MAX, -FLT_MAX);
			// Consider all points, not only boundary points, in case the input chart is malformed.
			for (uint32_t v = 0; v < vertexCount; v++) {
				const Vector2 &point = vertices[v];
				const float x = dot(axis, point);
				const float y = dot(Vector2(-axis.y, axis.x), point);
				box_min.x = min(box_min.x, x);
				box_max.x = max(box_max.x, x);
				box_min.y = min(box_min.y, y);
				box_max.y = max(box_max.y, y);
			}
			// Compute box area.
			const float area = (box_max.x - box_min.x) * (box_max.y - box_min.y);
			if (area < best_area) {
				best_area = area;
				best_min = box_min;
				best_max = box_max;
				best_axis = axis;
			}
		}
		majorAxis = best_axis;
		minorAxis = Vector2(-best_axis.y, best_axis.x);
		minCorner = best_min;
		maxCorner = best_max;
		XA_ASSERT(isFinite(majorAxis) && isFinite(minorAxis) && isFinite(minCorner));
	}

private:
	// Compute the convex hull using Graham Scan.
	void convexHull(const Vector2 *input, uint32_t inputCount, Array<Vector2> &output, float epsilon)
	{
		m_coords.resize(inputCount);
		for (uint32_t i = 0; i < inputCount; i++)
			m_coords[i] = input[i].x;
		m_radix.sort(m_coords);
		const uint32_t *ranks = m_radix.ranks();
		m_top.clear();
		m_bottom.clear();
		m_top.reserve(inputCount);
		m_bottom.reserve(inputCount);
		Vector2 P = input[ranks[0]];
		Vector2 Q = input[ranks[inputCount - 1]];
		float topy = max(P.y, Q.y);
		float boty = min(P.y, Q.y);
		for (uint32_t i = 0; i < inputCount; i++) {
			Vector2 p = input[ranks[i]];
			if (p.y >= boty)
				m_top.push_back(p);
		}
		for (uint32_t i = 0; i < inputCount; i++) {
			Vector2 p = input[ranks[inputCount - 1 - i]];
			if (p.y <= topy)
				m_bottom.push_back(p);
		}
		// Filter top list.
		output.clear();
		XA_DEBUG_ASSERT(m_top.size() >= 2);
		output.push_back(m_top[0]);
		output.push_back(m_top[1]);
		for (uint32_t i = 2; i < m_top.size(); ) {
			Vector2 a = output[output.size() - 2];
			Vector2 b = output[output.size() - 1];
			Vector2 c = m_top[i];
			float area = triangleArea(a, b, c);
			if (area >= -epsilon)
				output.pop_back();
			if (area < -epsilon || output.size() == 1) {
				output.push_back(c);
				i++;
			}
		}
		uint32_t top_count = output.size();
		XA_DEBUG_ASSERT(m_bottom.size() >= 2);
		output.push_back(m_bottom[1]);
		// Filter bottom list.
		for (uint32_t i = 2; i < m_bottom.size(); ) {
			Vector2 a = output[output.size() - 2];
			Vector2 b = output[output.size() - 1];
			Vector2 c = m_bottom[i];
			float area = triangleArea(a, b, c);
			if (area >= -epsilon)
				output.pop_back();
			if (area < -epsilon || output.size() == top_count) {
				output.push_back(c);
				i++;
			}
		}
		// Remove duplicate element.
		XA_DEBUG_ASSERT(output.size() > 0);
		output.pop_back();
	}

	Array<Vector2> m_boundaryVertices;
	Array<float> m_coords;
	Array<Vector2> m_top, m_bottom, m_hull;
	RadixSort m_radix;
};

static uint32_t meshEdgeFace(uint32_t edge) { return edge / 3; }
static uint32_t meshEdgeIndex0(uint32_t edge) { return edge; }

static uint32_t meshEdgeIndex1(uint32_t edge)
{
	const uint32_t faceFirstEdge = edge / 3 * 3;
	return faceFirstEdge + (edge - faceFirstEdge + 1) % 3;
}

struct MeshFlags
{
	enum
	{
		HasIgnoredFaces = 1<<0,
		HasNormals = 1<<1
	};
};

class Mesh;
static void meshGetBoundaryLoops(const Mesh &mesh, Array<uint32_t> &boundaryLoops);

class Mesh
{
public:
	Mesh(float epsilon, uint32_t approxVertexCount, uint32_t approxFaceCount, uint32_t flags = 0, uint32_t id = UINT32_MAX) : m_epsilon(epsilon), m_flags(flags), m_id(id), m_faceIgnore(MemTag::Mesh), m_indices(MemTag::MeshIndices), m_positions(MemTag::MeshPositions), m_normals(MemTag::MeshNormals), m_texcoords(MemTag::MeshTexcoords), m_nextColocalVertex(MemTag::MeshColocals), m_boundaryEdges(MemTag::MeshBoundaries), m_oppositeEdges(MemTag::MeshBoundaries), m_nextBoundaryEdges(MemTag::MeshBoundaries), m_edgeMap(MemTag::MeshEdgeMap, approxFaceCount * 3)
	{
		m_indices.reserve(approxFaceCount * 3);
		m_positions.reserve(approxVertexCount);
		m_texcoords.reserve(approxVertexCount);
		if (m_flags & MeshFlags::HasIgnoredFaces)
			m_faceIgnore.reserve(approxFaceCount);
		if (m_flags & MeshFlags::HasNormals)
			m_normals.reserve(approxVertexCount);
	}

	uint32_t flags() const { return m_flags; }
	uint32_t id() const { return m_id; }

	void addVertex(const Vector3 &pos, const Vector3 &normal = Vector3(0.0f), const Vector2 &texcoord = Vector2(0.0f))
	{
		XA_DEBUG_ASSERT(isFinite(pos));
		m_positions.push_back(pos);
		if (m_flags & MeshFlags::HasNormals)
			m_normals.push_back(normal);
		m_texcoords.push_back(texcoord);
	}

	struct AddFaceResult
	{
		enum Enum
		{
			OK,
			DuplicateEdge = 1
		};
	};

	AddFaceResult::Enum addFace(uint32_t v0, uint32_t v1, uint32_t v2, bool ignore = false)
	{
		uint32_t indexArray[3];
		indexArray[0] = v0;
		indexArray[1] = v1;
		indexArray[2] = v2;
		return addFace(indexArray, ignore);
	}

	AddFaceResult::Enum addFace(const uint32_t *indices, bool ignore = false)
	{
		AddFaceResult::Enum result = AddFaceResult::OK;
		if (m_flags & MeshFlags::HasIgnoredFaces)
			m_faceIgnore.push_back(ignore);
		const uint32_t firstIndex = m_indices.size();
		for (uint32_t i = 0; i < 3; i++)
			m_indices.push_back(indices[i]);
		for (uint32_t i = 0; i < 3; i++) {
			const uint32_t vertex0 = m_indices[firstIndex + i];
			const uint32_t vertex1 = m_indices[firstIndex + (i + 1) % 3];
			const EdgeKey key(vertex0, vertex1);
			if (m_edgeMap.get(key) != UINT32_MAX)
				result = AddFaceResult::DuplicateEdge;
			m_edgeMap.add(key);
		}
		return result;
	}

	void createColocals()
	{
		const uint32_t vertexCount = m_positions.size();
		Array<AABB> aabbs(MemTag::BVH);
		aabbs.resize(vertexCount);
		for (uint32_t i = 0; i < m_positions.size(); i++)
			aabbs[i] = AABB(m_positions[i], m_epsilon);
		BVH bvh(aabbs);
		Array<uint32_t> colocals(MemTag::MeshColocals);
		Array<uint32_t> potential(MemTag::MeshColocals);
		m_nextColocalVertex.resize(vertexCount);
		m_nextColocalVertex.fillBytes(0xff);
		for (uint32_t i = 0; i < vertexCount; i++) {
			if (m_nextColocalVertex[i] != UINT32_MAX)
				continue; // Already linked.
			// Find other vertices colocal to this one.
			colocals.clear();
			colocals.push_back(i); // Always add this vertex.
			bvh.query(AABB(m_positions[i], m_epsilon), potential);
			for (uint32_t j = 0; j < potential.size(); j++) {
				const uint32_t otherVertex = potential[j];
				if (otherVertex != i && equal(m_positions[i], m_positions[otherVertex], m_epsilon) && m_nextColocalVertex[otherVertex] == UINT32_MAX)
					colocals.push_back(otherVertex);
			}
			if (colocals.size() == 1) {
				// No colocals for this vertex.
				m_nextColocalVertex[i] = i;
				continue; 
			}
			// Link in ascending order.
			insertionSort(colocals.data(), colocals.size());
			for (uint32_t j = 0; j < colocals.size(); j++)
				m_nextColocalVertex[colocals[j]] = colocals[(j + 1) % colocals.size()];
			XA_DEBUG_ASSERT(m_nextColocalVertex[i] != UINT32_MAX);
		}
	}

	void createBoundaries()
	{
		const uint32_t edgeCount = m_indices.size();
		const uint32_t vertexCount = m_positions.size();
		m_oppositeEdges.resize(edgeCount);
		m_boundaryEdges.reserve(uint32_t(edgeCount * 0.1f));
		m_isBoundaryVertex.resize(vertexCount);
		m_isBoundaryVertex.zeroOutMemory();
		for (uint32_t i = 0; i < edgeCount; i++)
			m_oppositeEdges[i] = UINT32_MAX;
		const uint32_t faceCount = m_indices.size() / 3;
		for (uint32_t i = 0; i < faceCount; i++) {
			if (isFaceIgnored(i))
				continue;
			for (uint32_t j = 0; j < 3; j++) {
				const uint32_t edge = i * 3 + j;
				const uint32_t vertex0 = m_indices[edge];
				const uint32_t vertex1 = m_indices[i * 3 + (j + 1) % 3];
				// If there is an edge with opposite winding to this one, the edge isn't on a boundary.
				const uint32_t oppositeEdge = findEdge(vertex1, vertex0);
				if (oppositeEdge != UINT32_MAX) {
					m_oppositeEdges[edge] = oppositeEdge;
				} else {
					m_boundaryEdges.push_back(edge);
					m_isBoundaryVertex.set(vertex0);
					m_isBoundaryVertex.set(vertex1);
				}
			}
		}
	}

	void linkBoundaries()
	{
		const uint32_t edgeCount = m_indices.size();
		HashMap<uint32_t> vertexToEdgeMap(MemTag::Mesh, edgeCount); // Edge is index / 2
		for (uint32_t i = 0; i < edgeCount; i++) {
			vertexToEdgeMap.add(m_indices[meshEdgeIndex0(i)]);
			vertexToEdgeMap.add(m_indices[meshEdgeIndex1(i)]);
		}
		m_nextBoundaryEdges.resize(edgeCount);
		for (uint32_t i = 0; i < edgeCount; i++)
			m_nextBoundaryEdges[i] = UINT32_MAX;
		uint32_t numBoundaryLoops = 0, numUnclosedBoundaries = 0;
		BitArray linkedEdges(edgeCount);
		linkedEdges.zeroOutMemory();
		for (;;) {
			// Find the first boundary edge that hasn't been linked yet.
			uint32_t firstEdge = UINT32_MAX;
			for (uint32_t i = 0; i < edgeCount; i++) {
				if (m_oppositeEdges[i] == UINT32_MAX && !linkedEdges.get(i)) {
					firstEdge = i;
					break;
				}
			}
			if (firstEdge == UINT32_MAX)
				break;
			uint32_t currentEdge = firstEdge;
			for (;;) {
				// Find the next boundary edge. The first vertex will be the same as (or colocal to) the current edge second vertex.
				const uint32_t startVertex = m_indices[meshEdgeIndex1(currentEdge)];
				uint32_t bestNextEdge = UINT32_MAX;
				for (ColocalVertexIterator it(this, startVertex); !it.isDone(); it.advance()) {
					uint32_t mapIndex = vertexToEdgeMap.get(it.vertex());
					while (mapIndex != UINT32_MAX) {
						const uint32_t otherEdge = mapIndex / 2; // Two vertices added per edge.
						if (m_oppositeEdges[otherEdge] != UINT32_MAX)
							goto next; // Not a boundary edge.
						if (linkedEdges.get(otherEdge))
							goto next; // Already linked.
						if (m_indices[meshEdgeIndex0(otherEdge)] != it.vertex())
							goto next; // Edge contains the vertex, but it's the wrong one.
						// First edge (closing the boundary loop) has the highest priority.
						// Non-colocal vertex has the next highest.
						if (bestNextEdge != firstEdge && (bestNextEdge == UINT32_MAX || it.vertex() == startVertex))
							bestNextEdge = otherEdge;
					next:
						mapIndex = vertexToEdgeMap.getNext(mapIndex);
					}
				}
				if (bestNextEdge == UINT32_MAX) {
					numUnclosedBoundaries++;
					if (currentEdge == firstEdge)
						linkedEdges.set(firstEdge); // Only 1 edge in this boundary "loop".
					break; // Can't find a next edge.
				}
				m_nextBoundaryEdges[currentEdge] = bestNextEdge;
				linkedEdges.set(bestNextEdge);
				currentEdge = bestNextEdge;
				if (currentEdge == firstEdge) {
					numBoundaryLoops++;
					break; // Closed the boundary loop.
				}
			}
		}
#if XA_FIX_INTERNAL_BOUNDARY_LOOPS
		// Find internal boundary loops and separate them.
		// Detect by finding two edges in a boundary loop that have a colocal end vertex.
		// Fix by swapping their next boundary edge.
		// Need to start over after every fix since known boundary loops have changed.
		Array<uint32_t> boundaryLoops;
	fixInternalBoundary:
		meshGetBoundaryLoops(*this, boundaryLoops);
		for (uint32_t loop = 0; loop < boundaryLoops.size(); loop++) {
			linkedEdges.zeroOutMemory();
			for (Mesh::BoundaryLoopEdgeIterator it1(this, boundaryLoops[loop]); !it1.isDone(); it1.advance()) {
				const uint32_t e1 = it1.edge();
				if (linkedEdges.get(e1))
					continue;
				for (Mesh::BoundaryLoopEdgeIterator it2(this, boundaryLoops[loop]); !it2.isDone(); it2.advance()) {
					const uint32_t e2 = it2.edge();
					if (e1 == e2 || !isBoundaryEdge(e2) || linkedEdges.get(e2))
						continue;
					if (!areColocal(m_indices[meshEdgeIndex1(e1)], m_indices[meshEdgeIndex1(e2)]))
						continue;
					swap(m_nextBoundaryEdges[e1], m_nextBoundaryEdges[e2]);
					linkedEdges.set(e1);
					linkedEdges.set(e2);
					goto fixInternalBoundary; // start over
				}
			}
		}
#endif
	}

	/// Find edge, test all colocals.
	uint32_t findEdge(uint32_t vertex0, uint32_t vertex1) const
	{
		uint32_t result = UINT32_MAX;
		if (m_nextColocalVertex.isEmpty()) {
			EdgeKey key(vertex0, vertex1);
			uint32_t edge = m_edgeMap.get(key);
			while (edge != UINT32_MAX) {
				// Don't find edges of ignored faces.
				if (!isFaceIgnored(meshEdgeFace(edge))) {
					//XA_DEBUG_ASSERT(m_id != UINT32_MAX || (m_id == UINT32_MAX && result == UINT32_MAX)); // duplicate edge - ignore on initial meshes
					result = edge;
#if !XA_DEBUG
					return result;
#endif
				}
				edge = m_edgeMap.getNext(edge);
			}
		} else {
			for (ColocalVertexIterator it0(this, vertex0); !it0.isDone(); it0.advance()) {
				for (ColocalVertexIterator it1(this, vertex1); !it1.isDone(); it1.advance()) {
					EdgeKey key(it0.vertex(), it1.vertex());
					uint32_t edge = m_edgeMap.get(key);
					while (edge != UINT32_MAX) {
						// Don't find edges of ignored faces.
						if (!isFaceIgnored(meshEdgeFace(edge))) {
							XA_DEBUG_ASSERT(m_id != UINT32_MAX || (m_id == UINT32_MAX && result == UINT32_MAX)); // duplicate edge - ignore on initial meshes
							result = edge;
#if !XA_DEBUG
							return result;
#endif
						}
						edge = m_edgeMap.getNext(edge);
					}
				}
			}
		}
		return result;
	}

	// Edge map can be destroyed when no longer used to reduce memory usage. It's used by:
	//   * Mesh::createBoundaries()
	//   * Mesh::ColocalEdgeIterator (used by MeshFaceGroups)
	//   * meshCloseHole()
	void destroyEdgeMap()
	{
		m_edgeMap.destroy();
	}

#if XA_DEBUG_EXPORT_OBJ
	void writeObjVertices(FILE *file) const
	{
		for (uint32_t i = 0; i < m_positions.size(); i++)
			fprintf(file, "v %g %g %g\n", m_positions[i].x, m_positions[i].y, m_positions[i].z);
		if (m_flags & MeshFlags::HasNormals) {
			for (uint32_t i = 0; i < m_normals.size(); i++)
				fprintf(file, "vn %g %g %g\n", m_normals[i].x, m_normals[i].y, m_normals[i].z);
		}
		for (uint32_t i = 0; i < m_texcoords.size(); i++)
			fprintf(file, "vt %g %g\n", m_texcoords[i].x, m_texcoords[i].y);
	}

	void writeObjFace(FILE *file, uint32_t face, uint32_t offset = 0) const
	{
		fprintf(file, "f ");
		for (uint32_t j = 0; j < 3; j++) {
			const uint32_t index = m_indices[face * 3 + j] + 1 + offset; // 1-indexed
			fprintf(file, "%d/%d/%d%c", index, index, index, j == 2 ? '\n' : ' ');
		}
	}

	void writeObjBoundaryEges(FILE *file) const
	{
		if (m_oppositeEdges.isEmpty())
			return; // Boundaries haven't been created.
		fprintf(file, "o boundary_edges\n");
		for (uint32_t i = 0; i < edgeCount(); i++) {
			if (m_oppositeEdges[i] != UINT32_MAX)
				continue;
			fprintf(file, "l %d %d\n", m_indices[meshEdgeIndex0(i)] + 1, m_indices[meshEdgeIndex1(i)] + 1); // 1-indexed
		}
	}

	void writeObjLinkedBoundaries(FILE *file) const
	{
		if (m_oppositeEdges.isEmpty() || m_nextBoundaryEdges.isEmpty())
			return; // Boundaries haven't been created and/or linked.
		Array<uint32_t> boundaryLoops;
		meshGetBoundaryLoops(*this, boundaryLoops);
		for (uint32_t i = 0; i < boundaryLoops.size(); i++) {
			uint32_t edge = boundaryLoops[i];
			fprintf(file, "o boundary_%04d\n", i);
			fprintf(file, "l");
			for (;;) {
				const uint32_t vertex0 = m_indices[meshEdgeIndex0(edge)];
				const uint32_t vertex1 = m_indices[meshEdgeIndex1(edge)];
				fprintf(file, " %d", vertex0 + 1); // 1-indexed
				edge = m_nextBoundaryEdges[edge];
				if (edge == boundaryLoops[i] || edge == UINT32_MAX) {
					fprintf(file, " %d\n", vertex1 + 1); // 1-indexed
					break;
				}
			}
		}
	}

	void writeObjFile(const char *filename) const
	{
		FILE *file;
		XA_FOPEN(file, filename, "w");
		if (!file)
			return;
		writeObjVertices(file);
		fprintf(file, "s off\n");
		fprintf(file, "o object\n");
		for (uint32_t i = 0; i < faceCount(); i++)
			writeObjFace(file, i);
		writeObjBoundaryEges(file);
		writeObjLinkedBoundaries(file);
		fclose(file);
	}
#endif

	float computeSurfaceArea() const
	{
		float area = 0;
		for (uint32_t f = 0; f < faceCount(); f++)
			area += computeFaceArea(f);
		XA_DEBUG_ASSERT(area >= 0);
		return area;
	}

	// Returned value is always positive, even if some triangles are flipped.
	float computeParametricArea() const
	{
		float area = 0;
		for (uint32_t f = 0; f < faceCount(); f++)
			area += fabsf(computeFaceParametricArea(f)); // May be negative, depends on texcoord winding.
		return area; 
	}

	float computeFaceArea(uint32_t face) const
	{
		const Vector3 &p0 = m_positions[m_indices[face * 3 + 0]];
		const Vector3 &p1 = m_positions[m_indices[face * 3 + 1]];
		const Vector3 &p2 = m_positions[m_indices[face * 3 + 2]];
		return length(cross(p1 - p0, p2 - p0)) * 0.5f;
	}

	Vector3 computeFaceCentroid(uint32_t face) const
	{
		Vector3 sum(0.0f);
		for (uint32_t i = 0; i < 3; i++)
			sum += m_positions[m_indices[face * 3 + i]];
		return sum / 3.0f;
	}

	// Average of the edge midpoints weighted by the edge length.
	// I want a point inside the triangle, but closer to the cirumcenter.
	Vector3 computeFaceCenter(uint32_t face) const
	{
		const Vector3 &p0 = m_positions[m_indices[face * 3 + 0]];
		const Vector3 &p1 = m_positions[m_indices[face * 3 + 1]];
		const Vector3 &p2 = m_positions[m_indices[face * 3 + 2]];
		const float l0 = length(p1 - p0);
		const float l1 = length(p2 - p1);
		const float l2 = length(p0 - p2);
		const Vector3 m0 = (p0 + p1) * l0 / (l0 + l1 + l2);
		const Vector3 m1 = (p1 + p2) * l1 / (l0 + l1 + l2);
		const Vector3 m2 = (p2 + p0) * l2 / (l0 + l1 + l2);
		return m0 + m1 + m2;
	}

	Vector3 computeFaceNormal(uint32_t face) const
	{
		const Vector3 &p0 = m_positions[m_indices[face * 3 + 0]];
		const Vector3 &p1 = m_positions[m_indices[face * 3 + 1]];
		const Vector3 &p2 = m_positions[m_indices[face * 3 + 2]];
		const Vector3 e0 = p2 - p0;
		const Vector3 e1 = p1 - p0;
		const Vector3 normalAreaScaled = cross(e0, e1);
		return normalizeSafe(normalAreaScaled, Vector3(0, 0, 1), 0.0f);
	}

	float computeFaceParametricArea(uint32_t face) const
	{
		const Vector2 &t0 = m_texcoords[m_indices[face * 3 + 0]];
		const Vector2 &t1 = m_texcoords[m_indices[face * 3 + 1]];
		const Vector2 &t2 = m_texcoords[m_indices[face * 3 + 2]];
		return triangleArea(t0, t1, t2);
	}
	
	// @@ This is not exactly accurate, we should compare the texture coordinates...
	bool isSeam(uint32_t edge) const
	{
		const uint32_t oppositeEdge = m_oppositeEdges[edge];
		if (oppositeEdge == UINT32_MAX)
			return false; // boundary edge
		const uint32_t e0 = meshEdgeIndex0(edge);
		const uint32_t e1 = meshEdgeIndex1(edge);
		const uint32_t oe0 = meshEdgeIndex0(oppositeEdge);
		const uint32_t oe1 = meshEdgeIndex1(oppositeEdge);
		return m_indices[e0] != m_indices[oe1] || m_indices[e1] != m_indices[oe0];
	}

	bool isTextureSeam(uint32_t edge) const
	{
		const uint32_t oppositeEdge = m_oppositeEdges[edge];
		if (oppositeEdge == UINT32_MAX)
			return false; // boundary edge
		const uint32_t e0 = meshEdgeIndex0(edge);
		const uint32_t e1 = meshEdgeIndex1(edge);
		const uint32_t oe0 = meshEdgeIndex0(oppositeEdge);
		const uint32_t oe1 = meshEdgeIndex1(oppositeEdge);
		return m_texcoords[m_indices[e0]] != m_texcoords[m_indices[oe1]] || m_texcoords[m_indices[e1]] != m_texcoords[m_indices[oe0]];
	}

	uint32_t firstColocal(uint32_t vertex) const
	{
		for (ColocalVertexIterator it(this, vertex); !it.isDone(); it.advance()) {
			if (it.vertex() < vertex)
				vertex = it.vertex();
		}
		return vertex;
	}

	bool areColocal(uint32_t vertex0, uint32_t vertex1) const
	{
		if (vertex0 == vertex1)
			return true;
		if (m_nextColocalVertex.isEmpty())
			return false;
		for (ColocalVertexIterator it(this, vertex0); !it.isDone(); it.advance()) {
			if (it.vertex() == vertex1)
				return true;
		}
		return false;
	}

	XA_INLINE float epsilon() const { return m_epsilon; }
	XA_INLINE uint32_t edgeCount() const { return m_indices.size(); }
	XA_INLINE uint32_t oppositeEdge(uint32_t edge) const { return m_oppositeEdges[edge]; }
	XA_INLINE bool isBoundaryEdge(uint32_t edge) const { return m_oppositeEdges[edge] == UINT32_MAX; }
	XA_INLINE const Array<uint32_t> &boundaryEdges() const { return m_boundaryEdges; }
	XA_INLINE bool isBoundaryVertex(uint32_t vertex) const { return m_isBoundaryVertex.get(vertex); }
	XA_INLINE uint32_t vertexCount() const { return m_positions.size(); }
	XA_INLINE uint32_t vertexAt(uint32_t i) const { return m_indices[i]; }
	XA_INLINE const Vector3 &position(uint32_t vertex) const { return m_positions[vertex]; }
	XA_INLINE const Vector3 *positions() const { return m_positions.data(); }
	XA_INLINE const Vector3 &normal(uint32_t vertex) const { XA_DEBUG_ASSERT(m_flags & MeshFlags::HasNormals); return m_normals[vertex]; }
	XA_INLINE const Vector2 &texcoord(uint32_t vertex) const { return m_texcoords[vertex]; }
	XA_INLINE Vector2 &texcoord(uint32_t vertex) { return m_texcoords[vertex]; }
	XA_INLINE const Vector2 *texcoords() const { return m_texcoords.data(); }
	XA_INLINE Vector2 *texcoords() { return m_texcoords.data(); }
	XA_INLINE uint32_t faceCount() const { return m_indices.size() / 3; }
	XA_INLINE const uint32_t *indices() const { return m_indices.data(); }
	XA_INLINE uint32_t indexCount() const { return m_indices.size(); }
	XA_INLINE bool isFaceIgnored(uint32_t face) const { return (m_flags & MeshFlags::HasIgnoredFaces) && m_faceIgnore[face]; }

private:

	float m_epsilon;
	uint32_t m_flags;
	uint32_t m_id;
	Array<bool> m_faceIgnore;
	Array<uint32_t> m_indices;
	Array<Vector3> m_positions;
	Array<Vector3> m_normals;
	Array<Vector2> m_texcoords;

	// Populated by createColocals
	Array<uint32_t> m_nextColocalVertex; // In: vertex index. Out: the vertex index of the next colocal position.

	// Populated by createBoundaries
	BitArray m_isBoundaryVertex;
	Array<uint32_t> m_boundaryEdges;
	Array<uint32_t> m_oppositeEdges; // In: edge index. Out: the index of the opposite edge (i.e. wound the opposite direction). UINT32_MAX if the input edge is a boundary edge.

	// Populated by linkBoundaries
	Array<uint32_t> m_nextBoundaryEdges; // The index of the next boundary edge. UINT32_MAX if the edge is not a boundary edge.

	struct EdgeKey
	{
		EdgeKey(const EdgeKey &k) : v0(k.v0), v1(k.v1) {}
		EdgeKey(uint32_t v0, uint32_t v1) : v0(v0), v1(v1) {}
		bool operator==(const EdgeKey &k) const { return v0 == k.v0 && v1 == k.v1; }

		uint32_t v0;
		uint32_t v1;
	};

	struct EdgeHash
	{
		uint32_t operator()(const EdgeKey &k) const { return k.v0 * 32768u + k.v1; }
	};

	HashMap<EdgeKey, EdgeHash> m_edgeMap;

public:
	class BoundaryLoopEdgeIterator
	{
	public:
		BoundaryLoopEdgeIterator(const Mesh *mesh, uint32_t edge) : m_mesh(mesh), m_first(UINT32_MAX), m_current(edge) {}

		void advance()
		{
			if (m_first == UINT32_MAX)
				m_first = m_current;
			m_current = m_mesh->m_nextBoundaryEdges[m_current];
		}

		bool isDone() const
		{
			return m_first == m_current || m_current == UINT32_MAX;
		}

		uint32_t edge() const
		{
			return m_current;
		}

		uint32_t nextEdge() const
		{
			return m_mesh->m_nextBoundaryEdges[m_current];
		}

	private:
		const Mesh *m_mesh;
		uint32_t m_first;
		uint32_t m_current;
	};

	class ColocalVertexIterator
	{
	public:
		ColocalVertexIterator(const Mesh *mesh, uint32_t v) : m_mesh(mesh), m_first(UINT32_MAX), m_current(v) {}

		void advance()
		{
			if (m_first == UINT32_MAX)
				m_first = m_current;
			if (!m_mesh->m_nextColocalVertex.isEmpty())
				m_current = m_mesh->m_nextColocalVertex[m_current];
		}

		bool isDone() const
		{
			return m_first == m_current;
		}

		uint32_t vertex() const
		{
			return m_current;
		}

		const Vector3 *pos() const
		{
			return &m_mesh->m_positions[m_current];
		}

	private:
		const Mesh *m_mesh;
		uint32_t m_first;
		uint32_t m_current;
	};

	class ColocalEdgeIterator
	{
	public:
		ColocalEdgeIterator(const Mesh *mesh, uint32_t vertex0, uint32_t vertex1) : m_mesh(mesh), m_vertex0It(mesh, vertex0), m_vertex1It(mesh, vertex1), m_vertex1(vertex1)
		{
			do {
				if (!resetElement()) {
					advanceVertex1();
				}
				else {
					break;
				}
			} while (!isDone());
		}

		void advance()
		{
			advanceElement();
		}

		bool isDone() const
		{
			return m_vertex0It.isDone() && m_vertex1It.isDone() && m_edge == UINT32_MAX;
		}

		uint32_t edge() const
		{
			return m_edge;
		}

	private:
		bool resetElement()
		{
			m_edge = m_mesh->m_edgeMap.get(Mesh::EdgeKey(m_vertex0It.vertex(), m_vertex1It.vertex()));
			while (m_edge != UINT32_MAX) {
				if (!isIgnoredFace())
					break;
				m_edge = m_mesh->m_edgeMap.getNext(m_edge);
			}
			if (m_edge == UINT32_MAX) {
				return false;
			}
			return true;
		}

		void advanceElement()
		{
			for (;;) {
				m_edge = m_mesh->m_edgeMap.getNext(m_edge);
				if (m_edge == UINT32_MAX)
					break;
				if (!isIgnoredFace())
					break;
			}
			if (m_edge == UINT32_MAX)
				advanceVertex1();
		}

		void advanceVertex1()
		{
			auto successful = false;
			while (!successful)	{
				m_vertex1It.advance();
				if (m_vertex1It.isDone()) {
					if (!m_vertex0It.isDone()) {
						m_vertex0It.advance();
						m_vertex1It = ColocalVertexIterator(m_mesh, m_vertex1);
					}
					else {
						return;
					}
				}
				successful = resetElement();
			}
		}

		bool isIgnoredFace() const
		{
			return m_mesh->m_faceIgnore[meshEdgeFace(m_edge)];
		}

		const Mesh *m_mesh;
		ColocalVertexIterator m_vertex0It, m_vertex1It;
		const uint32_t m_vertex1;
		uint32_t m_edge;
	};

	class FaceEdgeIterator 
	{
	public:
		FaceEdgeIterator (const Mesh *mesh, uint32_t face) : m_mesh(mesh), m_face(face), m_relativeEdge(0)
		{
			m_edge = m_face * 3;
		}

		void advance()
		{
			if (m_relativeEdge < 3) {
				m_edge++;
				m_relativeEdge++;
			}
		}

		bool isDone() const
		{
			return m_relativeEdge == 3;
		}

		bool isBoundary() const { return m_mesh->m_oppositeEdges[m_edge] == UINT32_MAX; }
		bool isSeam() const { return m_mesh->isSeam(m_edge); }
		bool isTextureSeam() const { return m_mesh->isTextureSeam(m_edge); }
		uint32_t edge() const { return m_edge; }
		uint32_t relativeEdge() const { return m_relativeEdge; }
		uint32_t face() const { return m_face; }
		uint32_t oppositeEdge() const { return m_mesh->m_oppositeEdges[m_edge]; }
		
		uint32_t oppositeFace() const
		{
			const uint32_t oedge = m_mesh->m_oppositeEdges[m_edge];
			if (oedge == UINT32_MAX)
				return UINT32_MAX;
			return meshEdgeFace(oedge);
		}

		uint32_t vertex0() const { return m_mesh->m_indices[m_face * 3 + m_relativeEdge]; }
		uint32_t vertex1() const { return m_mesh->m_indices[m_face * 3 + (m_relativeEdge + 1) % 3]; }
		const Vector3 &position0() const { return m_mesh->m_positions[vertex0()]; }
		const Vector3 &position1() const { return m_mesh->m_positions[vertex1()]; }
		const Vector3 &normal0() const { return m_mesh->m_normals[vertex0()]; }
		const Vector3 &normal1() const { return m_mesh->m_normals[vertex1()]; }
		const Vector2 &texcoord0() const { return m_mesh->m_texcoords[vertex0()]; }
		const Vector2 &texcoord1() const { return m_mesh->m_texcoords[vertex1()]; }

	private:
		const Mesh *m_mesh;
		uint32_t m_face;
		uint32_t m_edge;
		uint32_t m_relativeEdge;
	};
};

struct MeshFaceGroups
{
	typedef uint32_t Handle;
	static constexpr Handle kInvalid = UINT32_MAX;

	MeshFaceGroups(const Mesh *mesh) : m_mesh(mesh), m_groups(MemTag::Mesh), m_firstFace(MemTag::Mesh), m_nextFace(MemTag::Mesh), m_faceCount(MemTag::Mesh) {}
	XA_INLINE Handle groupAt(uint32_t face) const { return m_groups[face]; }
	XA_INLINE uint32_t groupCount() const { return m_faceCount.size(); }
	XA_INLINE uint32_t nextFace(uint32_t face) const { return m_nextFace[face]; }
	XA_INLINE uint32_t faceCount(uint32_t group) const { return m_faceCount[group]; }

	void compute()
	{
		m_groups.resize(m_mesh->faceCount());
		m_groups.fillBytes(0xff); // Set all faces to kInvalid
		uint32_t firstUnassignedFace = 0;
		Handle group = 0;
		Array<uint32_t> growFaces;
		const uint32_t n = m_mesh->faceCount();
		m_nextFace.resize(n);
		for (;;) {
			// Find an unassigned face.
			uint32_t face = UINT32_MAX;
			for (uint32_t f = firstUnassignedFace; f < n; f++) {
				if (m_groups[f] == kInvalid && !m_mesh->isFaceIgnored(f)) {
					face = f;
					firstUnassignedFace = f + 1;
					break;
				}
			}
			if (face == UINT32_MAX)
				break; // All faces assigned to a group (except ignored faces).
			m_groups[face] = group;
			m_nextFace[face] = UINT32_MAX;
			m_firstFace.push_back(face);
			growFaces.clear();
			growFaces.push_back(face);
			uint32_t prevFace = face, groupFaceCount = 1;
			// Find faces connected to the face and assign them to the same group as the face, unless they are already assigned to another group.
			for (;;) {
				if (growFaces.isEmpty())
					break;
				const uint32_t f = growFaces.back();
				growFaces.pop_back();
				for (Mesh::FaceEdgeIterator edgeIt(m_mesh, f); !edgeIt.isDone(); edgeIt.advance()) {
					// Iterate opposite edges. There may be more than one - non-manifold geometry can have duplicate edges.
					// Prioritize the one with exact vertex match, not just colocal.
					// If *any* of the opposite edges are already assigned to this group, don't do anything.
					bool alreadyAssignedToThisGroup = false;
					uint32_t bestConnectedFace = UINT32_MAX;
					for (Mesh::ColocalEdgeIterator oppositeEdgeIt(m_mesh, edgeIt.vertex1(), edgeIt.vertex0()); !oppositeEdgeIt.isDone(); oppositeEdgeIt.advance()) {
						const uint32_t oppositeEdge = oppositeEdgeIt.edge();
						const uint32_t oppositeFace = meshEdgeFace(oppositeEdge);
#if 0
						// Reject opposite face if dihedral angle >= 90 degrees.
						{
							Vector3 a = m_mesh->computeFaceNormal(f);
							Vector3 b = m_mesh->computeFaceNormal(oppositeFace);
							if (dot(a, b) <= 0.0f)
								continue;
						}
#endif
						if (m_mesh->isFaceIgnored(oppositeFace))
							continue; // Don't add ignored faces to group.
						if (m_groups[oppositeFace] == group) {
							alreadyAssignedToThisGroup = true;
							break;
						}
						if (m_groups[oppositeFace] != kInvalid)
							continue; // Connected face is already assigned to another group.
						if (faceDuplicatesGroupEdge(group, oppositeFace))
							continue; // Don't want duplicate edges in a group.
						const uint32_t oppositeVertex0 = m_mesh->vertexAt(meshEdgeIndex0(oppositeEdge));
						const uint32_t oppositeVertex1 = m_mesh->vertexAt(meshEdgeIndex1(oppositeEdge));
						if (bestConnectedFace == UINT32_MAX || (oppositeVertex0 == edgeIt.vertex1() && oppositeVertex1 == edgeIt.vertex0()))
							bestConnectedFace = oppositeFace;
#if 0
						else {
							// Choose the opposite face with the smallest dihedral angle.
							const float d1 = 1.0f - dot(computeFaceNormal(f), computeFaceNormal(bestConnectedFace));
							const float d2 = 1.0f - dot(computeFaceNormal(f), computeFaceNormal(oppositeFace));
							if (d2 < d1)
								bestConnectedFace = oppositeFace;
						}
#endif
					}
					if (!alreadyAssignedToThisGroup && bestConnectedFace != UINT32_MAX) {
						m_groups[bestConnectedFace] = group;
						m_nextFace[bestConnectedFace] = UINT32_MAX;
						if (prevFace != UINT32_MAX)
							m_nextFace[prevFace] = bestConnectedFace;
						prevFace = bestConnectedFace;
						groupFaceCount++;
						growFaces.push_back(bestConnectedFace);
					}
				}
			}
			m_faceCount.push_back(groupFaceCount);
			group++;
			XA_ASSERT(group < kInvalid);
		}
	}

	class Iterator
	{
	public:
		Iterator(const MeshFaceGroups *meshFaceGroups, Handle group) : m_meshFaceGroups(meshFaceGroups)
		{
			XA_DEBUG_ASSERT(group != kInvalid);
			m_current = m_meshFaceGroups->m_firstFace[group];
		}

		void advance()
		{
			m_current = m_meshFaceGroups->m_nextFace[m_current];
		}

		bool isDone() const
		{
			return m_current == UINT32_MAX;
		}

		uint32_t face() const
		{
			return m_current;
		}

	private:
		const MeshFaceGroups *m_meshFaceGroups;
		uint32_t m_current;
	};

private:
	// Check if the face duplicates any edges of any face already in the group.
	bool faceDuplicatesGroupEdge(Handle group, uint32_t face) const
	{
		for (Mesh::FaceEdgeIterator edgeIt(m_mesh, face); !edgeIt.isDone(); edgeIt.advance()) {
			for (Mesh::ColocalEdgeIterator colocalEdgeIt(m_mesh, edgeIt.vertex0(), edgeIt.vertex1()); !colocalEdgeIt.isDone(); colocalEdgeIt.advance()) {
				if (m_groups[meshEdgeFace(colocalEdgeIt.edge())] == group)
					return true;
			}
		}
		return false;
	}

	const Mesh *m_mesh;
	Array<Handle> m_groups;
	Array<uint32_t> m_firstFace;
	Array<uint32_t> m_nextFace; // In: face. Out: the next face in the same group.
	Array<uint32_t> m_faceCount; // In: face group. Out: number of faces in the group.
};

constexpr MeshFaceGroups::Handle MeshFaceGroups::kInvalid;

static bool meshCloseHole(Mesh *mesh, const Array<uint32_t> &holeVertices, const Vector3 &normal)
{
#if XA_CLOSE_HOLES_CHECK_EDGE_INTERSECTION
	const uint32_t faceCount = mesh->faceCount();
#endif
	const bool compareNormal = equal(normal, Vector3(0.0f), FLT_EPSILON);
	uint32_t frontCount = holeVertices.size();
	Array<uint32_t> frontVertices;
	Array<Vector3> frontPoints;
	Array<float> frontAngles;
	frontVertices.resize(frontCount);
	frontPoints.resize(frontCount);
	for (uint32_t i = 0; i < frontCount; i++) {
		frontVertices[i] = holeVertices[i];
		frontPoints[i] = mesh->position(frontVertices[i]);
	}
	while (frontCount >= 3) {
		frontAngles.resize(frontCount);
		float smallestAngle = kPi2, smallestAngleIgnoringNormal = kPi2;
		uint32_t smallestAngleIndex = UINT32_MAX, smallestAngleIndexIgnoringNormal = UINT32_MAX;
		for (uint32_t i = 0; i < frontCount; i++) {
			const uint32_t i1 = i == 0 ? frontCount - 1 : i - 1;
			const uint32_t i2 = i;
			const uint32_t i3 = (i + 1) % frontCount;
			const Vector3 edge1 = frontPoints[i1] - frontPoints[i2];
			const Vector3 edge2 = frontPoints[i3] - frontPoints[i2];
			frontAngles[i] = atan2f(length(cross(edge1, edge2)), dot(edge1, edge2));
			if (frontAngles[i] >= smallestAngle || isNan(frontAngles[i]))
				continue;
			// Don't duplicate edges.
			if (mesh->findEdge(frontVertices[i1], frontVertices[i2]) != UINT32_MAX)
				continue;
			if (mesh->findEdge(frontVertices[i2], frontVertices[i3]) != UINT32_MAX)
				continue;
			if (mesh->findEdge(frontVertices[i3], frontVertices[i1]) != UINT32_MAX)
				continue;
			/*
			Make sure he new edge that would be formed by (i3, i1) doesn't intersect any vertices. This often happens when fixing t-junctions.

			       i2
			       *
			      / \
			     /   \
			 i1 *--*--* i3
			     \ | /
				  \|/
				   *
			*/
			bool intersection = false;
			for (uint32_t j = 0; j < frontCount; j++) {
				if (j == i1 || j == i2 || j == i3)
					continue;
				if (lineIntersectsPoint(frontPoints[j], frontPoints[i3], frontPoints[i1], nullptr, mesh->epsilon())) {
					intersection = true;
					break;
				}
			}
			if (intersection)
				continue;
			// Don't add the triangle if a boundary point lies on the same plane as the triangle, and is inside it.
			intersection = false;
			const Plane plane(frontPoints[i1], frontPoints[i2], frontPoints[i3]);
			for (uint32_t j = 0; j < frontCount; j++) {
				if (j == i1 || j == i2 || j == i3)
					continue;
				if (!isZero(plane.distance(frontPoints[j]), mesh->epsilon()))
					continue;
				if (pointInTriangle(frontPoints[j], frontPoints[i1], frontPoints[i2], frontPoints[i3])) {
					intersection = true;
					break;
				}
			}
			if (intersection)
				continue;
#if XA_CLOSE_HOLES_CHECK_EDGE_INTERSECTION
			// Don't add the triangle if the new edge (i3, i1), intersects any other triangle that isn't part of the filled hole.
			intersection = false;
			const Vector3 newEdgeVector = frontPoints[i1] - frontPoints[i3];
			for (uint32_t f = 0; f < faceCount; f++) {
				Vector3 tri[3];
				for (uint32_t j = 0; j < 3; j++)
					tri[j] = mesh->position(mesh->vertexAt(f * 3 + j));
				float t;
				if (rayIntersectsTriangle(frontPoints[i3], newEdgeVector, tri, &t)) {
					intersection = true;
					break;
				}
			}
			if (intersection)
				continue;
#endif
			// Skip backwards facing triangles.
			if (compareNormal) {
				if (frontAngles[i] < smallestAngleIgnoringNormal) {
					smallestAngleIgnoringNormal = frontAngles[i];
					smallestAngleIndexIgnoringNormal = i;
				}
				const Vector3 e0 = frontPoints[i3] - frontPoints[i1];
				const Vector3 e1 = frontPoints[i2] - frontPoints[i1];
				const Vector3 triNormal = normalizeSafe(cross(e0, e1), Vector3(0.0f), mesh->epsilon());
				if (dot(normal, triNormal) <= 0.0f)
					continue;
			}
			smallestAngle = smallestAngleIgnoringNormal = frontAngles[i];
			smallestAngleIndex = smallestAngleIndexIgnoringNormal = i;
		}
		// Closing holes failed if we don't have a smallest angle.
		// Fallback to ignoring the backwards facing normal test if possible.
		if (smallestAngleIndex == UINT32_MAX || smallestAngle <= 0.0f || smallestAngle >= kPi) {
			if (smallestAngleIgnoringNormal == UINT32_MAX || smallestAngleIgnoringNormal <= 0.0f || smallestAngleIgnoringNormal >= kPi)
				return false;
			else
				smallestAngleIndex = smallestAngleIndexIgnoringNormal;
		}
		const uint32_t i1 = smallestAngleIndex == 0 ? frontCount - 1 : smallestAngleIndex - 1;
		const uint32_t i2 = smallestAngleIndex;
		const uint32_t i3 = (smallestAngleIndex + 1) % frontCount;
		const Mesh::AddFaceResult::Enum result = mesh->addFace(frontVertices[i1], frontVertices[i2], frontVertices[i3]);
		XA_DEBUG_ASSERT(result == Mesh::AddFaceResult::OK); // Shouldn't happen due to the findEdge calls above.
		XA_UNUSED(result);
		frontVertices.removeAt(i2);
		frontPoints.removeAt(i2);
		frontCount = frontVertices.size();
	}
	return true;
}

static bool meshCloseHoles(Mesh *mesh, const Array<uint32_t> &boundaryLoops, const Vector3 &normal, uint32_t *holeCount, Array<uint32_t> *holeFaceCounts)
{
	if (holeFaceCounts)
		holeFaceCounts->clear();
	// Compute lengths.
	const uint32_t boundaryCount = boundaryLoops.size();
	Array<float> boundaryLengths;
	Array<uint32_t> boundaryEdgeCounts;
	boundaryEdgeCounts.resize(boundaryCount);
	for (uint32_t i = 0; i < boundaryCount; i++) {
		float boundaryLength = 0.0f;
		boundaryEdgeCounts[i] = 0;
		for (Mesh::BoundaryLoopEdgeIterator it(mesh, boundaryLoops[i]); !it.isDone(); it.advance()) {
			const Vector3 &t0 = mesh->position(mesh->vertexAt(meshEdgeIndex0(it.edge())));
			const Vector3 &t1 = mesh->position(mesh->vertexAt(meshEdgeIndex1(it.edge())));
			boundaryLength += length(t1 - t0);
			boundaryEdgeCounts[i]++;
		}
		boundaryLengths.push_back(boundaryLength);
	}
	// Find disk boundary.
	uint32_t diskBoundary = 0;
	float maxLength = boundaryLengths[0];
	for (uint32_t i = 1; i < boundaryCount; i++) {
		if (boundaryLengths[i] > maxLength) {
			maxLength = boundaryLengths[i];
			diskBoundary = i;
		}
	}
	// Close holes.
	Array<uint32_t> holeVertices;
	Array<Vector3> holePoints;
	bool result = true;
	for (uint32_t i = 0; i < boundaryCount; i++) {
		if (diskBoundary == i)
			continue; // Skip disk boundary.
		holeVertices.resize(boundaryEdgeCounts[i]);
		holePoints.resize(boundaryEdgeCounts[i]);
		// Winding is backwards for internal boundaries.
		uint32_t e = 0;
		for (Mesh::BoundaryLoopEdgeIterator it(mesh, boundaryLoops[i]); !it.isDone(); it.advance()) {
			const uint32_t vertex = mesh->vertexAt(meshEdgeIndex0(it.edge()));
			holeVertices[boundaryEdgeCounts[i] - 1 - e] = vertex;
			holePoints[boundaryEdgeCounts[i] - 1 - e] = mesh->position(vertex);
			e++;
		}
		const uint32_t oldFaceCount = mesh->faceCount();
		if (!meshCloseHole(mesh, holeVertices, normal))
			result = false; // Return false if any hole failed to close, but keep trying to close other holes.
		if (holeCount)
			(*holeCount)++;
		if (holeFaceCounts)
			holeFaceCounts->push_back(mesh->faceCount() - oldFaceCount);
	}
	return result;
}

static bool meshIsPlanar(const Mesh &mesh)
{
	const Vector3 p1 = mesh.position(mesh.vertexAt(0));
	const Vector3 p2 = mesh.position(mesh.vertexAt(1));
	const Vector3 p3 = mesh.position(mesh.vertexAt(2));
	const Plane plane(p1, p2, p3);
	const uint32_t vertexCount = mesh.vertexCount();
	for (uint32_t v = 0; v < vertexCount; v++) {
		const float d = plane.distance(mesh.position(v));
		if (!isZero(d, mesh.epsilon()))
			return false;
	}
	return true;
}

/*
Fixing T-junctions.

- Find T-junctions. Find  vertices that are on an edge.
- This test is approximate.
- Insert edges on a spatial index to speedup queries.
- Consider only open edges, that is edges that have no pairs.
- Consider only vertices on boundaries.
- Close T-junction.
- Split edge.

*/
struct SplitEdge
{
	uint32_t edge;
	float t;
	uint32_t vertex;

	bool operator<(const SplitEdge &other) const
	{
		if (edge < other.edge)
			return true;
		else if (edge == other.edge) {
			if (t < other.t)
				return true;
		}
		return false;
	}
};

// Returns nullptr if there were no t-junctions to fix.
static Mesh *meshFixTJunctions(const Mesh &inputMesh, bool *duplicatedEdge, bool *failed, uint32_t *fixedTJunctionsCount)
{
	if (duplicatedEdge)
		*duplicatedEdge = false;
	if (failed)
		*failed = false;
	Array<SplitEdge> splitEdges;
	const uint32_t vertexCount = inputMesh.vertexCount();
	const uint32_t edgeCount = inputMesh.edgeCount();
	for (uint32_t v = 0; v < vertexCount; v++) {
		if (!inputMesh.isBoundaryVertex(v))
			continue;
		// Find edges that this vertex overlaps with.
		const Vector3 &pos = inputMesh.position(v);
		for (uint32_t e = 0; e < edgeCount; e++) {
			if (!inputMesh.isBoundaryEdge(e))
				continue;
			const Vector3 &edgePos1 = inputMesh.position(inputMesh.vertexAt(meshEdgeIndex0(e)));
			const Vector3 &edgePos2 = inputMesh.position(inputMesh.vertexAt(meshEdgeIndex1(e)));
			float t;
			if (!lineIntersectsPoint(pos, edgePos1, edgePos2, &t, inputMesh.epsilon()))
				continue;
			SplitEdge splitEdge;
			splitEdge.edge = e;
			splitEdge.t = t;
			splitEdge.vertex = v;
			splitEdges.push_back(splitEdge);
		}
	}
	if (splitEdges.isEmpty())
		return nullptr;
	const uint32_t faceCount = inputMesh.faceCount();
	Mesh *mesh = XA_NEW_ARGS(MemTag::Mesh, Mesh, inputMesh.epsilon(), vertexCount + splitEdges.size(), faceCount);
	for (uint32_t v = 0; v < vertexCount; v++)
		mesh->addVertex(inputMesh.position(v));
	Array<uint32_t> indexArray;
	indexArray.reserve(4);
	Array<SplitEdge> faceSplitEdges;
	faceSplitEdges.reserve(4);
	for (uint32_t f = 0; f < faceCount; f++) {
		// Find t-junctions in this face.
		faceSplitEdges.clear();
		for (uint32_t i = 0; i < splitEdges.size(); i++) {
			if (meshEdgeFace(splitEdges[i].edge) == f)
				faceSplitEdges.push_back(splitEdges[i]);
		}
		if (!faceSplitEdges.isEmpty()) {
			// Need to split edges in winding order when a single edge has multiple t-junctions.
			insertionSort(faceSplitEdges.data(), faceSplitEdges.size());
			indexArray.clear();
			for (Mesh::FaceEdgeIterator it(&inputMesh, f); !it.isDone(); it.advance()) {
				indexArray.push_back(it.vertex0());
				for (uint32_t se = 0; se < faceSplitEdges.size(); se++) {
					const SplitEdge &splitEdge = faceSplitEdges[se];
					if (splitEdge.edge == it.edge())
						indexArray.push_back(splitEdge.vertex);
				}
			}
			if (!meshCloseHole(mesh, indexArray, Vector3(0.0f))) {
				if (failed)
					*failed = true;
			}
		} else {
			// No t-junctions in this face. Copy from input mesh.
			if (mesh->addFace(&inputMesh.indices()[f * 3]) == Mesh::AddFaceResult::DuplicateEdge) {
				if (duplicatedEdge)
					*duplicatedEdge = true;
			}
		}
	}
	if (fixedTJunctionsCount)
		*fixedTJunctionsCount = splitEdges.size();
	return mesh;
}

// boundaryLoops are the first edges for each boundary loop.
static void meshGetBoundaryLoops(const Mesh &mesh, Array<uint32_t> &boundaryLoops)
{
	const uint32_t edgeCount = mesh.edgeCount();
	BitArray bitFlags(edgeCount);
	bitFlags.zeroOutMemory();
	boundaryLoops.clear();
	// Search for boundary edges. Mark all the edges that belong to the same boundary.
	for (uint32_t e = 0; e < edgeCount; e++) {
		if (bitFlags.get(e) || !mesh.isBoundaryEdge(e))
			continue;
		for (Mesh::BoundaryLoopEdgeIterator it(&mesh, e); !it.isDone(); it.advance())
			bitFlags.set(it.edge());
		boundaryLoops.push_back(e);
	}
}

struct Progress
{
	Progress(ProgressCategory::Enum category, ProgressFunc func, void *userData, uint32_t maxValue) : value(0), cancel(false), m_category(category), m_func(func), m_userData(userData), m_maxValue(maxValue), m_progress(0)
	{
		if (m_func) {
			if (!m_func(category, 0, userData))
				cancel = true;
		}
	}

	~Progress()
	{
		if (m_func) {
			if (!m_func(m_category, 100, m_userData))
				cancel = true;
		}
	}

	void update()
	{
		if (!m_func)
			return;
		m_mutex.lock();
		const uint32_t newProgress = uint32_t(ceilf(value.load() / (float)m_maxValue * 100.0f));
		if (newProgress != m_progress && newProgress < 100) {
			m_progress = newProgress;
			if (!m_func(m_category, m_progress, m_userData))
				cancel = true;
		}
		m_mutex.unlock();
	}

	void setMaxValue(uint32_t maxValue)
	{
		m_mutex.lock();
		m_maxValue = maxValue;
		m_mutex.unlock();
	}

	std::atomic<uint32_t> value;
	std::atomic<bool> cancel;

private:
	ProgressCategory::Enum m_category;
	ProgressFunc m_func;
	void *m_userData;
	uint32_t m_maxValue;
	uint32_t m_progress;
	std::mutex m_mutex;
};

struct Spinlock
{
	void lock() { while(m_lock.test_and_set(std::memory_order_acquire)) {} }
	void unlock() { m_lock.clear(std::memory_order_release); }

private:
	std::atomic_flag m_lock = ATOMIC_FLAG_INIT;
};

struct TaskGroupHandle
{
	uint32_t value = UINT32_MAX;
};

struct Task
{
	void (*func)(void *userData);
	void *userData;
};

#if XA_MULTITHREADED
class TaskScheduler
{
public:
	TaskScheduler() : m_shutdown(false)
	{
		m_threadIndex = 0;
		// Max with current task scheduler usage is 1 per thread + 1 deep nesting, but allow for some slop.
		m_maxGroups = std::thread::hardware_concurrency() * 4;
		m_groups = XA_ALLOC_ARRAY(MemTag::Default, TaskGroup, m_maxGroups);
		for (uint32_t i = 0; i < m_maxGroups; i++) {
			new (&m_groups[i]) TaskGroup();
			m_groups[i].free = true;
			m_groups[i].ref = 0;
		}
		m_workers.resize(std::thread::hardware_concurrency() <= 1 ? 1 : std::thread::hardware_concurrency() - 1);
		for (uint32_t i = 0; i < m_workers.size(); i++) {
			new (&m_workers[i]) Worker();
			m_workers[i].wakeup = false;
			m_workers[i].thread = XA_NEW_ARGS(MemTag::Default, std::thread, workerThread, this, &m_workers[i], i + 1);
		}
	}

	~TaskScheduler()
	{
		m_shutdown = true;
		for (uint32_t i = 0; i < m_workers.size(); i++) {
			Worker &worker = m_workers[i];
			XA_DEBUG_ASSERT(worker.thread);
			worker.wakeup = true;
			worker.cv.notify_one();
			if (worker.thread->joinable())
				worker.thread->join();
			worker.thread->~thread();
			XA_FREE(worker.thread);
			worker.~Worker();
		}
		for (uint32_t i = 0; i < m_maxGroups; i++)
			m_groups[i].~TaskGroup();
		XA_FREE(m_groups);
	}

	uint32_t threadCount() const
	{
		return max(1u, std::thread::hardware_concurrency()); // Including the main thread.
	}

	TaskGroupHandle createTaskGroup(uint32_t reserveSize = 0)
	{
		// Claim the first free group.
		for (uint32_t i = 0; i < m_maxGroups; i++) {
			TaskGroup &group = m_groups[i];
			bool expected = true;
			if (!group.free.compare_exchange_strong(expected, false))
				continue;
			group.queueLock.lock();
			group.queueHead = 0;
			group.queue.clear();
			group.queue.reserve(reserveSize);
			group.queueLock.unlock();
			TaskGroupHandle handle;
			handle.value = i;
			return handle;
		}
		XA_DEBUG_ASSERT(false);
		TaskGroupHandle handle;
		handle.value = UINT32_MAX;
		return handle;
	}

	void run(TaskGroupHandle handle, const Task &task)
	{
		XA_DEBUG_ASSERT(handle.value != UINT32_MAX);
		TaskGroup &group = m_groups[handle.value];
		group.queueLock.lock();
		group.queue.push_back(task);
		group.queueLock.unlock();
		group.ref++;
		// Wake up a worker to run this task.
		for (uint32_t i = 0; i < m_workers.size(); i++) {
			m_workers[i].wakeup = true;
			m_workers[i].cv.notify_one();
		}
	}

	void wait(TaskGroupHandle *handle)
	{
		if (handle->value == UINT32_MAX) {
			XA_DEBUG_ASSERT(false);
			return;
		}
		// Run tasks from the group queue until empty.
		TaskGroup &group = m_groups[handle->value];
		for (;;) {
			Task *task = nullptr;
			group.queueLock.lock();
			if (group.queueHead < group.queue.size())
				task = &group.queue[group.queueHead++];
			group.queueLock.unlock();
			if (!task)
				break;
			task->func(task->userData);
			group.ref--;
		}
		// Even though the task queue is empty, workers can still be running tasks.
		while (group.ref > 0)
			std::this_thread::yield();
		group.free = true;
		handle->value = UINT32_MAX;
	}

	static uint32_t currentThreadIndex() { return m_threadIndex; }

private:
	struct TaskGroup
	{
		std::atomic<bool> free;
		Array<Task> queue; // Items are never removed. queueHead is incremented to pop items.
		uint32_t queueHead = 0;
		Spinlock queueLock;
		std::atomic<uint32_t> ref; // Increment when a task is enqueued, decrement when a task finishes.
	};

	struct Worker
	{
		std::thread *thread = nullptr;
		std::mutex mutex;
		std::condition_variable cv;
		std::atomic<bool> wakeup;
	};

	TaskGroup *m_groups;
	Array<Worker> m_workers;
	std::atomic<bool> m_shutdown;
	uint32_t m_maxGroups;
	static thread_local uint32_t m_threadIndex;

	static void workerThread(TaskScheduler *scheduler, Worker *worker, uint32_t threadIndex)
	{
		m_threadIndex = threadIndex;
		std::unique_lock<std::mutex> lock(worker->mutex);
		for (;;) {
			worker->cv.wait(lock, [=]{ return worker->wakeup.load(); });
			worker->wakeup = false;
			for (;;) {
				if (scheduler->m_shutdown)
					return;
				// Look for a task in any of the groups and run it.
				TaskGroup *group = nullptr;
				Task *task = nullptr;
				for (uint32_t i = 0; i < scheduler->m_maxGroups; i++) {
					group = &scheduler->m_groups[i];
					if (group->free || group->ref == 0)
						continue;
					group->queueLock.lock();
					if (group->queueHead < group->queue.size()) {
						task = &group->queue[group->queueHead++];
						group->queueLock.unlock();
						break;
					}
					group->queueLock.unlock();
				}
				if (!task)
					break;
				task->func(task->userData);
				group->ref--;
			}
		}
	}
};

thread_local uint32_t TaskScheduler::m_threadIndex;
#else
class TaskScheduler
{
public:
	~TaskScheduler()
	{
		for (uint32_t i = 0; i < m_groups.size(); i++) {
			TaskGroupHandle tgh;
			tgh.value = i;
			destroyGroup(tgh);
		}
	}

	uint32_t threadCount() const
	{
		return 1;
	}

	TaskGroupHandle createTaskGroup(uint32_t reserveSize = 0)
	{
		TaskGroup *group = XA_NEW(MemTag::Default, TaskGroup);
		group->queue.reserve(reserveSize);
		m_groups.push_back(group);
		TaskGroupHandle handle;
		handle.value = m_groups.size() - 1;
		return handle;
	}

	void run(TaskGroupHandle handle, Task task)
	{
		m_groups[handle.value]->queue.push_back(task);
	}

	void wait(TaskGroupHandle *handle)
	{
		if (handle->value == UINT32_MAX) {
			XA_DEBUG_ASSERT(false);
			return;
		}
		TaskGroup *group = m_groups[handle->value];
		for (uint32_t i = 0; i < group->queue.size(); i++)
			group->queue[i].func(group->queue[i].userData);
		group->queue.clear();
		destroyGroup(*handle);
		handle->value = UINT32_MAX;
	}

	static uint32_t currentThreadIndex() { return 0; }

private:
	void destroyGroup(TaskGroupHandle handle)
	{
		TaskGroup *group = m_groups[handle.value];
		if (group) {
			group->~TaskGroup();
			XA_FREE(group);
			m_groups[handle.value] = nullptr;
		}
	}

	struct TaskGroup
	{
		Array<Task> queue;
	};

	Array<TaskGroup *> m_groups;
};
#endif

#if XA_DEBUG_EXPORT_TGA
const uint8_t TGA_TYPE_RGB = 2;
const uint8_t TGA_ORIGIN_UPPER = 0x20;

#pragma pack(push, 1)
struct TgaHeader
{
	uint8_t id_length;
	uint8_t colormap_type;
	uint8_t image_type;
	uint16_t colormap_index;
	uint16_t colormap_length;
	uint8_t colormap_size;
	uint16_t x_origin;
	uint16_t y_origin;
	uint16_t width;
	uint16_t height;
	uint8_t pixel_size;
	uint8_t flags;
	enum { Size = 18 };
};
#pragma pack(pop)

static void WriteTga(const char *filename, const uint8_t *data, uint32_t width, uint32_t height)
{
	XA_DEBUG_ASSERT(sizeof(TgaHeader) == TgaHeader::Size);
	FILE *f;
	XA_FOPEN(f, filename, "wb");
	if (!f)
		return;
	TgaHeader tga;
	tga.id_length = 0;
	tga.colormap_type = 0;
	tga.image_type = TGA_TYPE_RGB;
	tga.colormap_index = 0;
	tga.colormap_length = 0;
	tga.colormap_size = 0;
	tga.x_origin = 0;
	tga.y_origin = 0;
	tga.width = (uint16_t)width;
	tga.height = (uint16_t)height;
	tga.pixel_size = 24;
	tga.flags = TGA_ORIGIN_UPPER;
	fwrite(&tga, sizeof(TgaHeader), 1, f);
	fwrite(data, sizeof(uint8_t), width * height * 3, f);
	fclose(f);
}
#endif

template<typename T>
class ThreadLocal
{
public:
	ThreadLocal()
	{
#if XA_MULTITHREADED
		const uint32_t n = std::thread::hardware_concurrency();
#else
		const uint32_t n = 1;
#endif
		m_array = XA_ALLOC_ARRAY(MemTag::Default, T, n);
		for (uint32_t i = 0; i < n; i++)
			new (&m_array[i]) T;
	}

	~ThreadLocal()
	{
#if XA_MULTITHREADED
		const uint32_t n = std::thread::hardware_concurrency();
#else
		const uint32_t n = 1;
#endif
		for (uint32_t i = 0; i < n; i++)
			m_array[i].~T();
		XA_FREE(m_array);
	}

	T &get() const
	{
		return m_array[TaskScheduler::currentThreadIndex()];
	}

private:
	T *m_array;
};

class UniformGrid2
{
public:
	void reset(const Vector2 *positions, const uint32_t *indices = nullptr, uint32_t reserveEdgeCount = 0)
	{
		m_edges.clear();
		if (reserveEdgeCount > 0)
			m_edges.reserve(reserveEdgeCount);
		m_positions = positions;
		m_indices = indices;
		m_cellDataOffsets.clear();
	}

	void append(uint32_t edge)
	{
		XA_DEBUG_ASSERT(m_cellDataOffsets.isEmpty());
		m_edges.push_back(edge);
	}

	bool intersect(Vector2 v1, Vector2 v2, float epsilon)
	{
		const uint32_t edgeCount = m_edges.size();
		bool bruteForce = edgeCount <= 20;
		if (!bruteForce && m_cellDataOffsets.isEmpty())
			bruteForce = !createGrid();
		if (bruteForce) {
			for (uint32_t j = 0; j < edgeCount; j++) {
				const uint32_t edge = m_edges[j];
				if (linesIntersect(v1, v2, edgePosition0(edge), edgePosition1(edge), epsilon))
					return true;
			}
		} else {
			computePotentialEdges(v1, v2);
			uint32_t prevEdge = UINT32_MAX;
			for (uint32_t j = 0; j < m_potentialEdges.size(); j++) {
				const uint32_t edge = m_potentialEdges[j];
				if (edge == prevEdge)
					continue;
				if (linesIntersect(v1, v2, edgePosition0(edge), edgePosition1(edge), epsilon))
					return true;
				prevEdge = edge;
			}
		}
		return false;
	}

	// If edges is empty, checks for intersection with all edges in the grid.
	bool intersect(float epsilon, ConstArrayView<uint32_t> edges = ConstArrayView<uint32_t>(), ConstArrayView<uint32_t> ignoreEdges = ConstArrayView<uint32_t>())
	{
		bool bruteForce = m_edges.size() <= 20;
		if (!bruteForce && m_cellDataOffsets.isEmpty())
			bruteForce = !createGrid();
		const uint32_t *edges1, *edges2 = nullptr;
		uint32_t edges1Count, edges2Count = 0;
		if (edges.length == 0) {
			edges1 = m_edges.data();
			edges1Count = m_edges.size();
		} else {
			edges1 = edges.data;
			edges1Count = edges.length;
		}
		if (bruteForce) {
			edges2 = m_edges.data();
			edges2Count = m_edges.size();
		}
		for (uint32_t i = 0; i < edges1Count; i++) {
			const uint32_t edge1 = edges1[i];
			const uint32_t edge1Vertex[2] = { vertexAt(meshEdgeIndex0(edge1)), vertexAt(meshEdgeIndex1(edge1)) };
			const Vector2 &edge1Position1 = m_positions[edge1Vertex[0]];
			const Vector2 &edge1Position2 = m_positions[edge1Vertex[1]];
			const Extents2 edge1Extents(edge1Position1, edge1Position2);
			uint32_t j = 0;
			if (bruteForce) {
				// If checking against self, test each edge pair only once.
				if (edges.length == 0) {
					j = i + 1;
					if (j == edges1Count)
						break;
				}
			} else {
				computePotentialEdges(edgePosition0(edge1), edgePosition1(edge1));
				edges2 = m_potentialEdges.data();
				edges2Count = m_potentialEdges.size();
			}
			uint32_t prevEdge = UINT32_MAX; // Handle potential edges duplicates.
			for (; j < edges2Count; j++) {
				const uint32_t edge2 = edges2[j];
				if (edge1 == edge2)
					continue;
				if (edge2 == prevEdge)
					continue;
				prevEdge = edge2;
				// Check if edge2 is ignored.
				bool ignore = false;
				for (uint32_t k = 0; k < ignoreEdges.length; k++) {
					if (edge2 == ignoreEdges[k]) {
						ignore = true;
						break;
					}
				}
				if (ignore)
					continue;
				const uint32_t edge2Vertex[2] = { vertexAt(meshEdgeIndex0(edge2)), vertexAt(meshEdgeIndex1(edge2)) };
				// Ignore connected edges, since they can't intersect (only overlap), and may be detected as false positives.
				if (edge1Vertex[0] == edge2Vertex[0] || edge1Vertex[0] == edge2Vertex[1] || edge1Vertex[1] == edge2Vertex[0] || edge1Vertex[1] == edge2Vertex[1])
					continue;
				const Vector2 &edge2Position1 = m_positions[edge2Vertex[0]];
				const Vector2 &edge2Position2 = m_positions[edge2Vertex[1]];
				if (!Extents2::intersect(edge1Extents, Extents2(edge2Position1, edge2Position2)))
					continue;
				if (linesIntersect(edge1Position1, edge1Position2, edge2Position1, edge2Position2, epsilon))
					return true;
			}
		}
		return false;
	}

#if XA_DEBUG_EXPORT_BOUNDARY_GRID
	void debugExport(const char *filename)
	{
		Array<uint8_t> image;
		image.resize(m_gridWidth * m_gridHeight * 3);
		for (uint32_t y = 0; y < m_gridHeight; y++) {
			for (uint32_t x = 0; x < m_gridWidth; x++) {
				uint8_t *bgr = &image[(x + y * m_gridWidth) * 3];
				bgr[0] = bgr[1] = bgr[2] = 32;
				uint32_t offset = m_cellDataOffsets[x + y * m_gridWidth];
				while (offset != UINT32_MAX) {
					const uint32_t edge2 = m_cellData[offset];
					srand(edge2);
					for (uint32_t i = 0; i < 3; i++)
						bgr[i] = uint8_t(bgr[i] * 0.5f + (rand() % 255) * 0.5f);
					offset = m_cellData[offset + 1];
				}
			}
		}
		WriteTga(filename, image.data(), m_gridWidth, m_gridHeight);
	}
#endif

private:
	bool createGrid()
	{
		// Compute edge extents. Min will be the grid origin.
		const uint32_t edgeCount = m_edges.size();
		Extents2 edgeExtents;
		edgeExtents.reset();
		for (uint32_t i = 0; i < edgeCount; i++) {
			const uint32_t edge = m_edges[i];
			edgeExtents.add(edgePosition0(edge));
			edgeExtents.add(edgePosition1(edge));
		}
		m_gridOrigin = edgeExtents.min;
		// Size grid to approximately one edge per cell.
		const Vector2 extentsSize(edgeExtents.max - edgeExtents.min);
		m_cellSize = min(extentsSize.x, extentsSize.y) / sqrtf((float)edgeCount);
		if (m_cellSize <= 0.0f)
			return false;
		m_gridWidth = uint32_t(ceilf(extentsSize.x / m_cellSize));
		m_gridHeight = uint32_t(ceilf(extentsSize.y / m_cellSize));
		if (m_gridWidth == 0 || m_gridHeight == 0)
			return false;
		// Insert edges into cells.
		m_cellDataOffsets.resize(m_gridWidth * m_gridHeight);
		for (uint32_t i = 0; i < m_cellDataOffsets.size(); i++)
			m_cellDataOffsets[i] = UINT32_MAX;
		m_cellData.clear();
		m_cellData.reserve(edgeCount * 2);
		for (uint32_t i = 0; i < edgeCount; i++) {
			const uint32_t edge = m_edges[i];
			traverse(edgePosition0(edge), edgePosition1(edge));
			XA_DEBUG_ASSERT(!m_traversedCellOffsets.isEmpty());
			for (uint32_t j = 0; j < m_traversedCellOffsets.size(); j++) {
				const uint32_t cell = m_traversedCellOffsets[j];
				uint32_t offset = m_cellDataOffsets[cell];
				if (offset == UINT32_MAX)
					m_cellDataOffsets[cell] = m_cellData.size();
				else {
					for (;;) {
						uint32_t &nextOffset = m_cellData[offset + 1];
						if (nextOffset == UINT32_MAX) {
							nextOffset = m_cellData.size();
							break;
						}
						offset = nextOffset;
					}
				}
				m_cellData.push_back(edge);
				m_cellData.push_back(UINT32_MAX);
			}
		}
		return true;
	}

	void computePotentialEdges(Vector2 p1, Vector2 p2)
	{
		m_potentialEdges.clear();
		traverse(p1, p2);
		for (uint32_t j = 0; j < m_traversedCellOffsets.size(); j++) {
			const uint32_t cell = m_traversedCellOffsets[j];
			uint32_t offset = m_cellDataOffsets[cell];
			while (offset != UINT32_MAX) {
				const uint32_t edge2 = m_cellData[offset];
				m_potentialEdges.push_back(edge2);
				offset = m_cellData[offset + 1];
			}
		}
		if (m_potentialEdges.isEmpty())
			return;
		insertionSort(m_potentialEdges.data(), m_potentialEdges.size());
	}

	// "A Fast Voxel Traversal Algorithm for Ray Tracing"
	void traverse(Vector2 p1, Vector2 p2)
	{
		const Vector2 dir = p2 - p1;
		const Vector2 normal = normalizeSafe(dir, Vector2(0.0f), kEpsilon);
		const int stepX = dir.x >= 0 ? 1 : -1;
		const int stepY = dir.y >= 0 ? 1 : -1;
		const uint32_t firstCell[2] = { cellX(p1.x), cellY(p1.y) };
		const uint32_t lastCell[2] = { cellX(p2.x), cellY(p2.y) };
		float distToNextCellX;
		if (stepX == 1)
			distToNextCellX = (firstCell[0] + 1) * m_cellSize - (p1.x - m_gridOrigin.x);
		else
			distToNextCellX = (p1.x - m_gridOrigin.x) - firstCell[0] * m_cellSize;
		float distToNextCellY;
		if (stepY == 1)
			distToNextCellY = (firstCell[1] + 1) * m_cellSize - (p1.y - m_gridOrigin.y);
		else
			distToNextCellY = (p1.y - m_gridOrigin.y) - firstCell[1] * m_cellSize;
		float tMaxX, tMaxY, tDeltaX, tDeltaY;
		if (normal.x > kEpsilon || normal.x < -kEpsilon) {
			tMaxX = (distToNextCellX * stepX) / normal.x;
			tDeltaX = (m_cellSize * stepX) / normal.x;
		}
		else
			tMaxX = tDeltaX = FLT_MAX;
		if (normal.y > kEpsilon || normal.y < -kEpsilon) {
			tMaxY = (distToNextCellY * stepY) / normal.y;
			tDeltaY = (m_cellSize * stepY) / normal.y;
		}
		else
			tMaxY = tDeltaY = FLT_MAX;
		m_traversedCellOffsets.clear();
		m_traversedCellOffsets.push_back(firstCell[0] + firstCell[1] * m_gridWidth);
		uint32_t currentCell[2] = { firstCell[0], firstCell[1] };
		while (!(currentCell[0] == lastCell[0] && currentCell[1] == lastCell[1])) {
			if (tMaxX < tMaxY) {
				tMaxX += tDeltaX;
				currentCell[0] += stepX;
			} else {
				tMaxY += tDeltaY;
				currentCell[1] += stepY;
			}
			if (currentCell[0] >= m_gridWidth || currentCell[1] >= m_gridHeight)
				break;
			if (stepX == -1 && currentCell[0] < lastCell[0])
				break;
			if (stepX == 1 && currentCell[0] > lastCell[0])
				break;
			if (stepY == -1 && currentCell[1] < lastCell[1])
				break;
			if (stepY == 1 && currentCell[1] > lastCell[1])
				break;
			m_traversedCellOffsets.push_back(currentCell[0] + currentCell[1] * m_gridWidth);
		}
	}

	uint32_t cellX(float x) const
	{
		return min((uint32_t)max(0.0f, (x - m_gridOrigin.x) / m_cellSize), m_gridWidth - 1u);
	}

	uint32_t cellY(float y) const
	{
		return min((uint32_t)max(0.0f, (y - m_gridOrigin.y) / m_cellSize), m_gridHeight - 1u);
	}

	Vector2 edgePosition0(uint32_t edge) const
	{
		return m_positions[vertexAt(meshEdgeIndex0(edge))];
	}

	Vector2 edgePosition1(uint32_t edge) const
	{
		return m_positions[vertexAt(meshEdgeIndex1(edge))];
	}

	uint32_t vertexAt(uint32_t index) const
	{
		return m_indices ? m_indices[index] : index;
	}

	Array<uint32_t> m_edges;
	const Vector2 *m_positions;
	const uint32_t *m_indices; // Optional
	float m_cellSize;
	Vector2 m_gridOrigin;
	uint32_t m_gridWidth, m_gridHeight; // in cells
	Array<uint32_t> m_cellDataOffsets;
	Array<uint32_t> m_cellData;
	Array<uint32_t> m_potentialEdges;
	Array<uint32_t> m_traversedCellOffsets;
};

struct UvMeshChart
{
	Array<uint32_t> faces;
	Array<uint32_t> indices;
	uint32_t material;
};

struct UvMesh
{
	UvMeshDecl decl;
	Array<uint32_t> indices;
	Array<UvMeshChart *> charts;
	Array<uint32_t> vertexToChartMap;
};

struct UvMeshInstance
{
	UvMesh *mesh;
	Array<Vector2> texcoords;
	bool rotateCharts;
};

/*
 *  Copyright (c) 2004-2010, Bruno Levy
 *  All rights reserved.
 *
 *  Redistribution and use in source and binary forms, with or without
 *  modification, are permitted provided that the following conditions are met:
 *
 *  * Redistributions of source code must retain the above copyright notice,
 *  this list of conditions and the following disclaimer.
 *  * Redistributions in binary form must reproduce the above copyright notice,
 *  this list of conditions and the following disclaimer in the documentation
 *  and/or other materials provided with the distribution.
 *  * Neither the name of the ALICE Project-Team nor the names of its
 *  contributors may be used to endorse or promote products derived from this
 *  software without specific prior written permission.
 *
 *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 *  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 *  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 *  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 *  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 *  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 *  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 *  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 *  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 *  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 *  POSSIBILITY OF SUCH DAMAGE.
 *
 *  If you modify this software, you should include a notice giving the
 *  name of the person performing the modification, the date of modification,
 *  and the reason for such modification.
 *
 *  Contact: Bruno Levy
 *
 *     levy@loria.fr
 *
 *     ALICE Project
 *     LORIA, INRIA Lorraine,
 *     Campus Scientifique, BP 239
 *     54506 VANDOEUVRE LES NANCY CEDEX
 *     FRANCE
 */
namespace opennl {
#define NL_NEW(T)              XA_ALLOC(MemTag::OpenNL, T)
#define NL_NEW_ARRAY(T,NB)     XA_ALLOC_ARRAY(MemTag::OpenNL, T, NB)
#define NL_RENEW_ARRAY(T,x,NB) XA_REALLOC(MemTag::OpenNL, x, T, NB)
#define NL_DELETE(x)           XA_FREE(x); x = nullptr 
#define NL_DELETE_ARRAY(x)     XA_FREE(x); x = nullptr
#define NL_CLEAR(x, T)         memset(x, 0, sizeof(T));
#define NL_CLEAR_ARRAY(T,x,NB) memset(x, 0, (size_t)(NB)*sizeof(T)) 
#define NL_NEW_VECTOR(dim)     XA_ALLOC_ARRAY(MemTag::OpenNL, double, dim)
#define NL_DELETE_VECTOR(ptr)  XA_FREE(ptr)

struct NLMatrixStruct;
typedef NLMatrixStruct * NLMatrix;
typedef void (*NLDestroyMatrixFunc)(NLMatrix M);
typedef void (*NLMultMatrixVectorFunc)(NLMatrix M, const double* x, double* y);

#define NL_MATRIX_SPARSE_DYNAMIC 0x1001
#define NL_MATRIX_CRS            0x1002
#define NL_MATRIX_OTHER          0x1006

struct NLMatrixStruct
{
	uint32_t m;
	uint32_t n;
	uint32_t type;
	NLDestroyMatrixFunc destroy_func;
	NLMultMatrixVectorFunc mult_func;
};

/* Dynamic arrays for sparse row/columns */

struct NLCoeff
{
	uint32_t index;
	double value;
};

struct NLRowColumn
{
	uint32_t size;
	uint32_t capacity;
	NLCoeff* coeff;
};

/* Compressed Row Storage */

struct NLCRSMatrix
{
	uint32_t m;
	uint32_t n;
	uint32_t type;
	NLDestroyMatrixFunc destroy_func;
	NLMultMatrixVectorFunc mult_func;
	double* val;
	uint32_t* rowptr;
	uint32_t* colind;
	uint32_t nslices;
	uint32_t* sliceptr;
};

/* SparseMatrix data structure */

struct NLSparseMatrix
{
	uint32_t m;
	uint32_t n;
	uint32_t type;
	NLDestroyMatrixFunc destroy_func;
	NLMultMatrixVectorFunc mult_func;
	uint32_t diag_size;
	uint32_t diag_capacity;
	NLRowColumn* row;
	NLRowColumn* column;
	double*    diag;
	uint32_t row_capacity;
	uint32_t column_capacity;
};

/* NLContext data structure */

struct NLBufferBinding
{
	void* base_address;
	uint32_t stride;
};

#define NL_BUFFER_ITEM(B,i) *(double*)((void*)((char*)((B).base_address)+((i)*(B).stride)))

struct NLContext
{
	NLBufferBinding *variable_buffer;
	double *variable_value;
	bool *variable_is_locked;
	uint32_t *variable_index;
	uint32_t n;
	NLMatrix M;
	NLMatrix P;
	NLMatrix B;
	NLRowColumn af;
	NLRowColumn al;
	double *x;
	double *b;
	uint32_t nb_variables;
	uint32_t nb_systems;
	uint32_t current_row;
	uint32_t max_iterations;
	bool max_iterations_defined;
	double threshold;
	double omega;
	uint32_t used_iterations;
	double error;
};

static void nlDeleteMatrix(NLMatrix M)
{
	if (!M)
		return;
	M->destroy_func(M);
	NL_DELETE(M);
}

static void nlMultMatrixVector(NLMatrix M, const double* x, double* y)
{
	M->mult_func(M, x, y);
}

static void nlRowColumnConstruct(NLRowColumn* c)
{
	c->size = 0;
	c->capacity = 0;
	c->coeff = nullptr;
}

static void nlRowColumnDestroy(NLRowColumn* c)
{
	NL_DELETE_ARRAY(c->coeff);
	c->size = 0;
	c->capacity = 0;
}

static void nlRowColumnGrow(NLRowColumn* c)
{
	if (c->capacity != 0) {
		c->capacity = 2 * c->capacity;
		c->coeff = NL_RENEW_ARRAY(NLCoeff, c->coeff, c->capacity);
	} else {
		c->capacity = 4;
		c->coeff = NL_NEW_ARRAY(NLCoeff, c->capacity);
		NL_CLEAR_ARRAY(NLCoeff, c->coeff, c->capacity);
	}
}

static void nlRowColumnAdd(NLRowColumn* c, uint32_t index, double value)
{
	for (uint32_t i = 0; i < c->size; i++) {
		if (c->coeff[i].index == index) {
			c->coeff[i].value += value;
			return;
		}
	}
	if (c->size == c->capacity)
		nlRowColumnGrow(c);
	c->coeff[c->size].index = index;
	c->coeff[c->size].value = value;
	c->size++;
}

/* Does not check whether the index already exists */
static void nlRowColumnAppend(NLRowColumn* c, uint32_t index, double value)
{
	if (c->size == c->capacity)
		nlRowColumnGrow(c);
	c->coeff[c->size].index = index;
	c->coeff[c->size].value = value;
	c->size++;
}

static void nlRowColumnZero(NLRowColumn* c)
{
	c->size = 0;
}

static void nlRowColumnClear(NLRowColumn* c)
{
	c->size = 0;
	c->capacity = 0;
	NL_DELETE_ARRAY(c->coeff);
}

static int nlCoeffCompare(const void* p1, const void* p2)
{
	return (((NLCoeff*)(p2))->index < ((NLCoeff*)(p1))->index);
}

static void nlRowColumnSort(NLRowColumn* c)
{
	qsort(c->coeff, c->size, sizeof(NLCoeff), nlCoeffCompare);
}

/* CRSMatrix data structure */

static void nlCRSMatrixDestroy(NLCRSMatrix* M)
{
	NL_DELETE_ARRAY(M->val);
	NL_DELETE_ARRAY(M->rowptr);
	NL_DELETE_ARRAY(M->colind);
	NL_DELETE_ARRAY(M->sliceptr);
	M->m = 0;
	M->n = 0;
	M->nslices = 0;
}

static void nlCRSMatrixMultSlice(NLCRSMatrix* M, const double* x, double* y, uint32_t Ibegin, uint32_t Iend)
{
	for (uint32_t i = Ibegin; i < Iend; ++i) {
		double sum = 0.0;
		for (uint32_t j = M->rowptr[i]; j < M->rowptr[i + 1]; ++j)
			sum += M->val[j] * x[M->colind[j]];
		y[i] = sum;
	}
}

static void nlCRSMatrixMult(NLCRSMatrix* M, const double* x, double* y)
{
	int nslices = (int)(M->nslices);
	for (int slice = 0; slice < nslices; ++slice)
		nlCRSMatrixMultSlice(M, x, y, M->sliceptr[slice], M->sliceptr[slice + 1]);
}

static void nlCRSMatrixConstruct(NLCRSMatrix* M, uint32_t m, uint32_t n, uint32_t nnz, uint32_t nslices)
{
	M->m = m;
	M->n = n;
	M->type = NL_MATRIX_CRS;
	M->destroy_func = (NLDestroyMatrixFunc)nlCRSMatrixDestroy;
	M->mult_func = (NLMultMatrixVectorFunc)nlCRSMatrixMult;
	M->nslices = nslices;
	M->val = NL_NEW_ARRAY(double, nnz);
	NL_CLEAR_ARRAY(double, M->val, nnz);
	M->rowptr = NL_NEW_ARRAY(uint32_t, m + 1);
	NL_CLEAR_ARRAY(uint32_t, M->rowptr, m + 1);
	M->colind = NL_NEW_ARRAY(uint32_t, nnz);
	NL_CLEAR_ARRAY(uint32_t, M->colind, nnz);
	M->sliceptr = NL_NEW_ARRAY(uint32_t, nslices + 1);
	NL_CLEAR_ARRAY(uint32_t, M->sliceptr, nslices + 1);
}

/* SparseMatrix data structure */

static void nlSparseMatrixDestroyRowColumns(NLSparseMatrix* M)
{
	for (uint32_t i = 0; i < M->m; i++)
		nlRowColumnDestroy(&(M->row[i]));
	NL_DELETE_ARRAY(M->row);
}

static void nlSparseMatrixDestroy(NLSparseMatrix* M)
{
	XA_DEBUG_ASSERT(M->type == NL_MATRIX_SPARSE_DYNAMIC);
	nlSparseMatrixDestroyRowColumns(M);
	NL_DELETE_ARRAY(M->diag);
}

static void nlSparseMatrixAdd(NLSparseMatrix* M, uint32_t i, uint32_t j, double value)
{
	XA_DEBUG_ASSERT(i >= 0 && i <= M->m - 1);
	XA_DEBUG_ASSERT(j >= 0 && j <= M->n - 1);
	if (i == j)
		M->diag[i] += value;
	nlRowColumnAdd(&(M->row[i]), j, value);
}

/* Returns the number of non-zero coefficients */
static uint32_t nlSparseMatrixNNZ(NLSparseMatrix* M)
{
	uint32_t nnz = 0;
	for (uint32_t i = 0; i < M->m; i++)
		nnz += M->row[i].size;
	return nnz;
}

static void nlSparseMatrixSort(NLSparseMatrix* M)
{
	for (uint32_t i = 0; i < M->m; i++)
		nlRowColumnSort(&(M->row[i]));
}

/* SparseMatrix x Vector routines, internal helper routines */

static void nlSparseMatrix_mult_rows(NLSparseMatrix* A,	const double* x, double* y)
{
	/*
	 * Note: OpenMP does not like unsigned ints
	 * (causes some floating point exceptions),
	 * therefore I use here signed ints for all
	 * indices.
	 */
	int m = (int)(A->m);
	NLCoeff* c = nullptr;
	NLRowColumn* Ri = nullptr;
	for (int i = 0; i < m; i++) {
		Ri = &(A->row[i]);
		y[i] = 0;
		for (int ij = 0; ij < (int)(Ri->size); ij++) {
			c = &(Ri->coeff[ij]);
			y[i] += c->value * x[c->index];
		}
	}
}

static void nlSparseMatrixMult(NLSparseMatrix* A, const double* x, double* y)
{
	XA_DEBUG_ASSERT(A->type == NL_MATRIX_SPARSE_DYNAMIC);
	nlSparseMatrix_mult_rows(A, x, y);
}

static void nlSparseMatrixConstruct(NLSparseMatrix* M, uint32_t m, uint32_t n)
{
	M->m = m;
	M->n = n;
	M->type = NL_MATRIX_SPARSE_DYNAMIC;
	M->destroy_func = (NLDestroyMatrixFunc)nlSparseMatrixDestroy;
	M->mult_func = (NLMultMatrixVectorFunc)nlSparseMatrixMult;
	M->row = NL_NEW_ARRAY(NLRowColumn, m);
	NL_CLEAR_ARRAY(NLRowColumn, M->row, m);
	M->row_capacity = m;
	for (uint32_t i = 0; i < n; i++)
		nlRowColumnConstruct(&(M->row[i]));
	M->row_capacity = 0;
	M->column = nullptr;
	M->column_capacity = 0;
	M->diag_size = min(m, n);
	M->diag_capacity = M->diag_size;
	M->diag = NL_NEW_ARRAY(double, M->diag_size);
	NL_CLEAR_ARRAY(double, M->diag, M->diag_size);
}

static NLMatrix nlCRSMatrixNewFromSparseMatrix(NLSparseMatrix* M)
{
	uint32_t nnz = nlSparseMatrixNNZ(M);
	uint32_t nslices = 8; /* TODO: get number of cores */
	uint32_t slice, cur_bound, cur_NNZ, cur_row;
	uint32_t k;
	uint32_t slice_size = nnz / nslices;
	NLCRSMatrix* CRS = NL_NEW(NLCRSMatrix);
	NL_CLEAR(CRS, NLCRSMatrix);
	nlCRSMatrixConstruct(CRS, M->m, M->n, nnz, nslices);
	nlSparseMatrixSort(M);
	/* Convert matrix to CRS format */
	k = 0;
	for (uint32_t i = 0; i < M->m; ++i) {
		NLRowColumn* Ri = &(M->row[i]);
		CRS->rowptr[i] = k;
		for (uint32_t ij = 0; ij < Ri->size; ij++) {
			NLCoeff* c = &(Ri->coeff[ij]);
			CRS->val[k] = c->value;
			CRS->colind[k] = c->index;
			++k;
		}
	}
	CRS->rowptr[M->m] = k;
	/* Create "slices" to be used by parallel sparse matrix vector product */
	if (CRS->sliceptr) {
		cur_bound = slice_size;
		cur_NNZ = 0;
		cur_row = 0;
		CRS->sliceptr[0] = 0;
		for (slice = 1; slice < nslices; ++slice) {
			while (cur_NNZ < cur_bound && cur_row < M->m) {
				++cur_row;
				cur_NNZ += CRS->rowptr[cur_row + 1] - CRS->rowptr[cur_row];
			}
			CRS->sliceptr[slice] = cur_row;
			cur_bound += slice_size;
		}
		CRS->sliceptr[nslices] = M->m;
	}
	return (NLMatrix)CRS;
}

static void nlMatrixCompress(NLMatrix* M)
{
	NLMatrix CRS = nullptr;
	if ((*M)->type != NL_MATRIX_SPARSE_DYNAMIC)
		return;
	CRS = nlCRSMatrixNewFromSparseMatrix((NLSparseMatrix*)*M);
	nlDeleteMatrix(*M);
	*M = CRS;
}

static NLContext *nlNewContext()
{
	NLContext* result = NL_NEW(NLContext);
	NL_CLEAR(result, NLContext);
	result->max_iterations = 100;
	result->threshold = 1e-6;
	result->omega = 1.5;
	result->nb_systems = 1;
	return result;
}

static void nlDeleteContext(NLContext *context)
{
	nlDeleteMatrix(context->M);
	context->M = nullptr;
	nlDeleteMatrix(context->P);
	context->P = nullptr;
	nlDeleteMatrix(context->B);
	context->B = nullptr;
	nlRowColumnDestroy(&context->af);
	nlRowColumnDestroy(&context->al);
	NL_DELETE_ARRAY(context->variable_value);
	NL_DELETE_ARRAY(context->variable_buffer);
	NL_DELETE_ARRAY(context->variable_is_locked);
	NL_DELETE_ARRAY(context->variable_index);
	NL_DELETE_ARRAY(context->x);
	NL_DELETE_ARRAY(context->b);
	NL_DELETE(context);
}

static double ddot(int n, const double *x, const double *y)
{
	double sum = 0.0;
	for (int i = 0; i < n; i++)
		sum += x[i] * y[i];
	return sum;
}

static void daxpy(int n, double a, const double *x, double *y)
{
	for (int i = 0; i < n; i++)
		y[i] = a * x[i] + y[i];
}

static void dscal(int n, double a, double *x)
{
	for (int i = 0; i < n; i++)
		x[i] *= a;
}

/*
 * The implementation of the solvers is inspired by
 * the lsolver library, by Christian Badura, available from:
 * http://www.mathematik.uni-freiburg.de
 * /IAM/Research/projectskr/lin_solver/
 *
 * About the Conjugate Gradient, details can be found in:
 *  Ashby, Manteuffel, Saylor
 *     A taxononmy for conjugate gradient methods
 *     SIAM J Numer Anal 27, 1542-1568 (1990)
 *
 *  This version is completely abstract, the same code can be used for
 * CPU/GPU, dense matrix / sparse matrix etc...
 *  Abstraction is realized through:
  *   - Abstract matrix interface (NLMatrix), that can implement different
 *     versions of matrix x vector product (CPU/GPU, sparse/dense ...)
 */

static uint32_t nlSolveSystem_PRE_CG(NLMatrix M, NLMatrix P, double* b, double* x, double eps, uint32_t max_iter, double *sq_bnorm, double *sq_rnorm)
{
	int     N = (int)M->n;
	double* r = NL_NEW_VECTOR(N);
	double* d = NL_NEW_VECTOR(N);
	double* h = NL_NEW_VECTOR(N);
	double *Ad = h;
	uint32_t its = 0;
	double rh, alpha, beta;
	double b_square = ddot(N, b, b);
	double err = eps * eps*b_square;
	double curr_err;
	nlMultMatrixVector(M, x, r);
	daxpy(N, -1., b, r);
	nlMultMatrixVector(P, r, d);
	memcpy(h, d, N * sizeof(double));
	rh = ddot(N, r, h);
	curr_err = ddot(N, r, r);
	while (curr_err > err && its < max_iter) {
		nlMultMatrixVector(M, d, Ad);
		alpha = rh / ddot(N, d, Ad);
		daxpy(N, -alpha, d, x);
		daxpy(N, -alpha, Ad, r);
		nlMultMatrixVector(P, r, h);
		beta = 1. / rh;
		rh = ddot(N, r, h);
		beta *= rh;
		dscal(N, beta, d);
		daxpy(N, 1., h, d);
		++its;
		curr_err = ddot(N, r, r);
	}
	NL_DELETE_VECTOR(r);
	NL_DELETE_VECTOR(d);
	NL_DELETE_VECTOR(h);
	*sq_bnorm = b_square;
	*sq_rnorm = curr_err;
	return its;
}

static uint32_t nlSolveSystemIterative(NLContext *context, NLMatrix M, NLMatrix P, double* b_in, double* x_in, double eps, uint32_t max_iter)
{
	uint32_t result = 0;
	double rnorm = 0.0;
	double bnorm = 0.0;
	double* b = b_in;
	double* x = x_in;
	XA_DEBUG_ASSERT(M->m == M->n);
	double sq_bnorm, sq_rnorm;
	result = nlSolveSystem_PRE_CG(M, P, b, x, eps, max_iter, &sq_bnorm, &sq_rnorm);
	/* Get residual norm and rhs norm */
	bnorm = sqrt(sq_bnorm);
	rnorm = sqrt(sq_rnorm);
	if (bnorm == 0.0)
		context->error = rnorm;
	else
		context->error = rnorm / bnorm;
	context->used_iterations = result;
	return result;
}

static bool nlSolveIterative(NLContext *context)
{
	double* b = context->b;
	double* x = context->x;
	uint32_t n = context->n;
	NLMatrix M = context->M;
	NLMatrix P = context->P;
	for (uint32_t k = 0; k < context->nb_systems; ++k) {
		nlSolveSystemIterative(context, M, P, b, x, context->threshold, context->max_iterations);
		b += n;
		x += n;
	}
	return true;
}

struct NLJacobiPreconditioner
{
	uint32_t m;
	uint32_t n;
	uint32_t type;
	NLDestroyMatrixFunc destroy_func;
	NLMultMatrixVectorFunc mult_func;
	double* diag_inv;
};

static void nlJacobiPreconditionerDestroy(NLJacobiPreconditioner* M)
{
	NL_DELETE_ARRAY(M->diag_inv);
}

static void nlJacobiPreconditionerMult(NLJacobiPreconditioner* M, const double* x, double* y)
{
	for (uint32_t i = 0; i < M->n; ++i)
		y[i] = x[i] * M->diag_inv[i];
}

static NLMatrix nlNewJacobiPreconditioner(NLMatrix M_in)
{
	NLSparseMatrix* M = nullptr;
	NLJacobiPreconditioner* result = nullptr;
	XA_DEBUG_ASSERT(M_in->type == NL_MATRIX_SPARSE_DYNAMIC);
	XA_DEBUG_ASSERT(M_in->m == M_in->n);
	M = (NLSparseMatrix*)M_in;
	result = NL_NEW(NLJacobiPreconditioner);
	NL_CLEAR(result, NLJacobiPreconditioner);
	result->m = M->m;
	result->n = M->n;
	result->type = NL_MATRIX_OTHER;
	result->destroy_func = (NLDestroyMatrixFunc)nlJacobiPreconditionerDestroy;
	result->mult_func = (NLMultMatrixVectorFunc)nlJacobiPreconditionerMult;
	result->diag_inv = NL_NEW_ARRAY(double, M->n);
	NL_CLEAR_ARRAY(double, result->diag_inv, M->n);
	for (uint32_t i = 0; i < M->n; ++i)
		result->diag_inv[i] = (M->diag[i] == 0.0) ? 1.0 : 1.0 / M->diag[i];
	return (NLMatrix)result;
}

#define NL_NB_VARIABLES 0x101
#define NL_MAX_ITERATIONS 0x103

static void nlSolverParameteri(NLContext *context, uint32_t pname, int param)
{
	if (pname == NL_NB_VARIABLES) {
		XA_DEBUG_ASSERT(param > 0);
		context->nb_variables = (uint32_t)param;
	} else if (pname == NL_MAX_ITERATIONS) {
		XA_DEBUG_ASSERT(param > 0);
		context->max_iterations = (uint32_t)param;
		context->max_iterations_defined = true;
	}
}

static void nlSetVariable(NLContext *context, uint32_t index, double value)
{
	XA_DEBUG_ASSERT(index >= 0 && index <= context->nb_variables - 1);
	NL_BUFFER_ITEM(context->variable_buffer[0], index) = value;
}

static double nlGetVariable(NLContext *context, uint32_t index)
{
	XA_DEBUG_ASSERT(index >= 0 && index <= context->nb_variables - 1);
	return NL_BUFFER_ITEM(context->variable_buffer[0], index);
}

static void nlLockVariable(NLContext *context, uint32_t index)
{
	XA_DEBUG_ASSERT(index >= 0 && index <= context->nb_variables - 1);
	context->variable_is_locked[index] = true;
}

static void nlVariablesToVector(NLContext *context)
{
	uint32_t n = context->n;
	XA_DEBUG_ASSERT(context->x);
	for (uint32_t k = 0; k < context->nb_systems; ++k) {
		for (uint32_t i = 0; i < context->nb_variables; ++i) {
			if (!context->variable_is_locked[i]) {
				uint32_t index = context->variable_index[i];
				XA_DEBUG_ASSERT(index < context->n);
				double value = NL_BUFFER_ITEM(context->variable_buffer[k], i);
				context->x[index + k * n] = value;
			}
		}
	}
}

static void nlVectorToVariables(NLContext *context)
{
	uint32_t n = context->n;
	XA_DEBUG_ASSERT(context->x);
	for (uint32_t k = 0; k < context->nb_systems; ++k) {
		for (uint32_t i = 0; i < context->nb_variables; ++i) {
			if (!context->variable_is_locked[i]) {
				uint32_t index = context->variable_index[i];
				XA_DEBUG_ASSERT(index < context->n);
				double value = context->x[index + k * n];
				NL_BUFFER_ITEM(context->variable_buffer[k], i) = value;
			}
		}
	}
}

static void nlCoefficient(NLContext *context, uint32_t index, double value)
{
	XA_DEBUG_ASSERT(index >= 0 && index <= context->nb_variables - 1);
	if (context->variable_is_locked[index]) {
		/*
		 * Note: in al, indices are NLvariable indices,
		 * within [0..nb_variables-1]
		 */
		nlRowColumnAppend(&(context->al), index, value);
	} else {
		/*
		 * Note: in af, indices are system indices,
		 * within [0..n-1]
		 */
		nlRowColumnAppend(&(context->af), context->variable_index[index], value);
	}
}

#define NL_SYSTEM  0x0
#define NL_MATRIX  0x1
#define NL_ROW     0x2

static void nlBegin(NLContext *context, uint32_t prim)
{
	if (prim == NL_SYSTEM) {
		XA_DEBUG_ASSERT(context->nb_variables > 0);
		context->variable_buffer = NL_NEW_ARRAY(NLBufferBinding, context->nb_systems);
		NL_CLEAR_ARRAY(NLBufferBinding, context->variable_buffer, context->nb_systems);
		context->variable_value = NL_NEW_ARRAY(double, context->nb_variables * context->nb_systems);
		NL_CLEAR_ARRAY(double, context->variable_value, context->nb_variables * context->nb_systems);
		for (uint32_t k = 0; k < context->nb_systems; ++k) {
			context->variable_buffer[k].base_address =
				context->variable_value +
				k * context->nb_variables;
			context->variable_buffer[k].stride = sizeof(double);
		}
		context->variable_is_locked = NL_NEW_ARRAY(bool, context->nb_variables);
		NL_CLEAR_ARRAY(bool, context->variable_is_locked, context->nb_variables);
		context->variable_index = NL_NEW_ARRAY(uint32_t, context->nb_variables);
		NL_CLEAR_ARRAY(uint32_t, context->variable_index, context->nb_variables);
	} else if (prim == NL_MATRIX) {
		if (context->M)
			return;
		uint32_t n = 0;
		for (uint32_t i = 0; i < context->nb_variables; i++) {
			if (!context->variable_is_locked[i]) {
				context->variable_index[i] = n;
				n++;
			} else
				context->variable_index[i] = (uint32_t)~0;
		}
		context->n = n;
		if (!context->max_iterations_defined)
			context->max_iterations = n * 5;
		context->M = (NLMatrix)(NL_NEW(NLSparseMatrix));
		NL_CLEAR(context->M, NLSparseMatrix);
		nlSparseMatrixConstruct((NLSparseMatrix*)(context->M), n, n);
		context->x = NL_NEW_ARRAY(double, n*context->nb_systems);
		NL_CLEAR_ARRAY(double, context->x, n*context->nb_systems);
		context->b = NL_NEW_ARRAY(double, n*context->nb_systems);
		NL_CLEAR_ARRAY(double, context->b, n*context->nb_systems);
		nlVariablesToVector(context);
		nlRowColumnConstruct(&context->af);
		nlRowColumnConstruct(&context->al);
		context->current_row = 0;
	} else if (prim == NL_ROW) {
		nlRowColumnZero(&context->af);
		nlRowColumnZero(&context->al);
	}
}

static void nlEnd(NLContext *context, uint32_t prim)
{
	if (prim == NL_MATRIX) {
		nlRowColumnClear(&context->af);
		nlRowColumnClear(&context->al);
	} else if (prim == NL_ROW) {
		NLRowColumn*    af = &context->af;
		NLRowColumn*    al = &context->al;
		NLSparseMatrix* M = (NLSparseMatrix*)context->M;
		double* b = context->b;
		uint32_t nf = af->size;
		uint32_t nl = al->size;
		uint32_t n = context->n;
		double S;
		/*
		 * least_squares : we want to solve
		 * A'A x = A'b
		 */
		for (uint32_t i = 0; i < nf; i++) {
			for (uint32_t j = 0; j < nf; j++) {
				nlSparseMatrixAdd(M, af->coeff[i].index, af->coeff[j].index, af->coeff[i].value * af->coeff[j].value);
			}
		}
		for (uint32_t k = 0; k < context->nb_systems; ++k) {
			S = 0.0;
			for (uint32_t jj = 0; jj < nl; ++jj) {
				uint32_t j = al->coeff[jj].index;
				S += al->coeff[jj].value * NL_BUFFER_ITEM(context->variable_buffer[k], j);
			}
			for (uint32_t jj = 0; jj < nf; jj++)
				b[k*n + af->coeff[jj].index] -= af->coeff[jj].value * S;
		}
		context->current_row++;
	}
}

static bool nlSolve(NLContext *context)
{
	nlDeleteMatrix(context->P);
	context->P = nlNewJacobiPreconditioner(context->M);
	nlMatrixCompress(&context->M);
	bool result = nlSolveIterative(context);
	nlVectorToVariables(context);
	return result;
}
} // namespace opennl

namespace raster {
class ClippedTriangle
{
public:
	ClippedTriangle(const Vector2 &a, const Vector2 &b, const Vector2 &c)
	{
		m_numVertices = 3;
		m_activeVertexBuffer = 0;
		m_verticesA[0] = a;
		m_verticesA[1] = b;
		m_verticesA[2] = c;
		m_vertexBuffers[0] = m_verticesA;
		m_vertexBuffers[1] = m_verticesB;
		m_area = 0;
	}

	void clipHorizontalPlane(float offset, float clipdirection)
	{
		Vector2 *v  = m_vertexBuffers[m_activeVertexBuffer];
		m_activeVertexBuffer ^= 1;
		Vector2 *v2 = m_vertexBuffers[m_activeVertexBuffer];
		v[m_numVertices] = v[0];
		float dy2,   dy1 = offset - v[0].y;
		int   dy2in, dy1in = clipdirection * dy1 >= 0;
		uint32_t  p = 0;
		for (uint32_t k = 0; k < m_numVertices; k++) {
			dy2   = offset - v[k + 1].y;
			dy2in = clipdirection * dy2 >= 0;
			if (dy1in) v2[p++] = v[k];
			if ( dy1in + dy2in == 1 ) { // not both in/out
				float dx = v[k + 1].x - v[k].x;
				float dy = v[k + 1].y - v[k].y;
				v2[p++] = Vector2(v[k].x + dy1 * (dx / dy), offset);
			}
			dy1 = dy2;
			dy1in = dy2in;
		}
		m_numVertices = p;
	}

	void clipVerticalPlane(float offset, float clipdirection)
	{
		Vector2 *v  = m_vertexBuffers[m_activeVertexBuffer];
		m_activeVertexBuffer ^= 1;
		Vector2 *v2 = m_vertexBuffers[m_activeVertexBuffer];
		v[m_numVertices] = v[0];
		float dx2,   dx1   = offset - v[0].x;
		int   dx2in, dx1in = clipdirection * dx1 >= 0;
		uint32_t  p = 0;
		for (uint32_t k = 0; k < m_numVertices; k++) {
			dx2 = offset - v[k + 1].x;
			dx2in = clipdirection * dx2 >= 0;
			if (dx1in) v2[p++] = v[k];
			if ( dx1in + dx2in == 1 ) { // not both in/out
				float dx = v[k + 1].x - v[k].x;
				float dy = v[k + 1].y - v[k].y;
				v2[p++] = Vector2(offset, v[k].y + dx1 * (dy / dx));
			}
			dx1 = dx2;
			dx1in = dx2in;
		}
		m_numVertices = p;
	}

	void computeArea()
	{
		Vector2 *v  = m_vertexBuffers[m_activeVertexBuffer];
		v[m_numVertices] = v[0];
		m_area = 0;
		float centroidx = 0, centroidy = 0;
		for (uint32_t k = 0; k < m_numVertices; k++) {
			// http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
			float f = v[k].x * v[k + 1].y - v[k + 1].x * v[k].y;
			m_area += f;
			centroidx += f * (v[k].x + v[k + 1].x);
			centroidy += f * (v[k].y + v[k + 1].y);
		}
		m_area = 0.5f * fabsf(m_area);
	}

	void clipAABox(float x0, float y0, float x1, float y1)
	{
		clipVerticalPlane(x0, -1);
		clipHorizontalPlane(y0, -1);
		clipVerticalPlane(x1, 1);
		clipHorizontalPlane(y1, 1);
		computeArea();
	}

	float area() const
	{
		return m_area;
	}

private:
	Vector2 m_verticesA[7 + 1];
	Vector2 m_verticesB[7 + 1];
	Vector2 *m_vertexBuffers[2];
	uint32_t m_numVertices;
	uint32_t m_activeVertexBuffer;
	float m_area;
};

/// A callback to sample the environment. Return false to terminate rasterization.
typedef bool (*SamplingCallback)(void *param, int x, int y);

/// A triangle for rasterization.
struct Triangle
{
	Triangle(const Vector2 &_v0, const Vector2 &_v1, const Vector2 &_v2) : v1(_v0), v2(_v2), v3(_v1)
	{
		// make sure every triangle is front facing.
		flipBackface();
		// Compute deltas.
		if (isValid())
			computeUnitInwardNormals();
	}

	bool isValid()
	{
		const Vector2 e0 = v3 - v1;
		const Vector2 e1 = v2 - v1;
		const float area = e0.y * e1.x - e1.y * e0.x;
		return area != 0.0f;
	}

	// extents has to be multiple of BK_SIZE!!
	bool drawAA(const Vector2 &extents, SamplingCallback cb, void *param)
	{
		const float PX_INSIDE = 1.0f/sqrtf(2.0f);
		const float PX_OUTSIDE = -1.0f/sqrtf(2.0f);
		const float BK_SIZE = 8;
		const float BK_INSIDE = sqrtf(BK_SIZE*BK_SIZE/2.0f);
		const float BK_OUTSIDE = -sqrtf(BK_SIZE*BK_SIZE/2.0f);
		// Bounding rectangle
		float minx = floorf(max(min3(v1.x, v2.x, v3.x), 0.0f));
		float miny = floorf(max(min3(v1.y, v2.y, v3.y), 0.0f));
		float maxx = ceilf( min(max3(v1.x, v2.x, v3.x), extents.x - 1.0f));
		float maxy = ceilf( min(max3(v1.y, v2.y, v3.y), extents.y - 1.0f));
		// There's no reason to align the blocks to the viewport, instead we align them to the origin of the triangle bounds.
		minx = floorf(minx);
		miny = floorf(miny);
		//minx = (float)(((int)minx) & (~((int)BK_SIZE - 1))); // align to blocksize (we don't need to worry about blocks partially out of viewport)
		//miny = (float)(((int)miny) & (~((int)BK_SIZE - 1)));
		minx += 0.5;
		miny += 0.5; // sampling at texel centers!
		maxx += 0.5;
		maxy += 0.5;
		// Half-edge constants
		float C1 = n1.x * (-v1.x) + n1.y * (-v1.y);
		float C2 = n2.x * (-v2.x) + n2.y * (-v2.y);
		float C3 = n3.x * (-v3.x) + n3.y * (-v3.y);
		// Loop through blocks
		for (float y0 = miny; y0 <= maxy; y0 += BK_SIZE) {
			for (float x0 = minx; x0 <= maxx; x0 += BK_SIZE) {
				// Corners of block
				float xc = (x0 + (BK_SIZE - 1) / 2.0f);
				float yc = (y0 + (BK_SIZE - 1) / 2.0f);
				// Evaluate half-space functions
				float aC = C1 + n1.x * xc + n1.y * yc;
				float bC = C2 + n2.x * xc + n2.y * yc;
				float cC = C3 + n3.x * xc + n3.y * yc;
				// Skip block when outside an edge
				if ( (aC <= BK_OUTSIDE) || (bC <= BK_OUTSIDE) || (cC <= BK_OUTSIDE) ) continue;
				// Accept whole block when totally covered
				if ( (aC >= BK_INSIDE) && (bC >= BK_INSIDE) && (cC >= BK_INSIDE) ) {
					for (float y = y0; y < y0 + BK_SIZE; y++) {
						for (float x = x0; x < x0 + BK_SIZE; x++) {
							if (!cb(param, (int)x, (int)y))
								return false;
						}
					}
				} else { // Partially covered block
					float CY1 = C1 + n1.x * x0 + n1.y * y0;
					float CY2 = C2 + n2.x * x0 + n2.y * y0;
					float CY3 = C3 + n3.x * x0 + n3.y * y0;
					for (float y = y0; y < y0 + BK_SIZE; y++) { // @@ This is not clipping to scissor rectangle correctly.
						float CX1 = CY1;
						float CX2 = CY2;
						float CX3 = CY3;
						for (float x = x0; x < x0 + BK_SIZE; x++) { // @@ This is not clipping to scissor rectangle correctly.
							if (CX1 >= PX_INSIDE && CX2 >= PX_INSIDE && CX3 >= PX_INSIDE) {
								if (!cb(param, (int)x, (int)y))
									return false;
							} else if ((CX1 >= PX_OUTSIDE) && (CX2 >= PX_OUTSIDE) && (CX3 >= PX_OUTSIDE)) {
								// triangle partially covers pixel. do clipping.
								ClippedTriangle ct(v1 - Vector2(x, y), v2 - Vector2(x, y), v3 - Vector2(x, y));
								ct.clipAABox(-0.5, -0.5, 0.5, 0.5);
								if (ct.area() > 0.0f) {
									if (!cb(param, (int)x, (int)y))
										return false;
								}
							}
							CX1 += n1.x;
							CX2 += n2.x;
							CX3 += n3.x;
						}
						CY1 += n1.y;
						CY2 += n2.y;
						CY3 += n3.y;
					}
				}
			}
		}
		return true;
	}

private:
	void flipBackface()
	{
		// check if triangle is backfacing, if so, swap two vertices
		if ( ((v3.x - v1.x) * (v2.y - v1.y) - (v3.y - v1.y) * (v2.x - v1.x)) < 0 ) {
			Vector2 hv = v1;
			v1 = v2;
			v2 = hv; // swap pos
		}
	}

	// compute unit inward normals for each edge.
	void computeUnitInwardNormals()
	{
		n1 = v1 - v2;
		n1 = Vector2(-n1.y, n1.x);
		n1 = n1 * (1.0f / sqrtf(dot(n1, n1)));
		n2 = v2 - v3;
		n2 = Vector2(-n2.y, n2.x);
		n2 = n2 * (1.0f / sqrtf(dot(n2, n2)));
		n3 = v3 - v1;
		n3 = Vector2(-n3.y, n3.x);
		n3 = n3 * (1.0f / sqrtf(dot(n3, n3)));
	}

	// Vertices.
	Vector2 v1, v2, v3;
	Vector2 n1, n2, n3; // unit inward normals
};

// Process the given triangle. Returns false if rasterization was interrupted by the callback.
static bool drawTriangle(const Vector2 &extents, const Vector2 v[3], SamplingCallback cb, void *param)
{
	Triangle tri(v[0], v[1], v[2]);
	// @@ It would be nice to have a conservative drawing mode that enlarges the triangle extents by one texel and is able to handle degenerate triangles.
	// @@ Maybe the simplest thing to do would be raster triangle edges.
	if (tri.isValid())
		return tri.drawAA(extents, cb, param);
	return true;
}

} // namespace raster

namespace segment {

// - Insertion is o(n)
// - Smallest element goes at the end, so that popping it is o(1).
struct CostQueue
{
	CostQueue(uint32_t size = UINT32_MAX) : m_maxSize(size), m_pairs(MemTag::SegmentAtlasChartCandidates) {}

	float peekCost() const
	{
		return m_pairs.back().cost;
	}

	uint32_t peekFace() const
	{
		return m_pairs.back().face;
	}

	void push(float cost, uint32_t face)
	{
		const Pair p = { cost, face };
		if (m_pairs.isEmpty() || cost < peekCost())
			m_pairs.push_back(p);
		else {
			uint32_t i = 0;
			const uint32_t count = m_pairs.size();
			for (; i < count; i++) {
				if (m_pairs[i].cost < cost)
					break;
			}
			m_pairs.insertAt(i, p);
			if (m_pairs.size() > m_maxSize)
				m_pairs.removeAt(0);
		}
	}

	uint32_t pop()
	{
		XA_DEBUG_ASSERT(!m_pairs.isEmpty());
		uint32_t f = m_pairs.back().face;
		m_pairs.pop_back();
		return f;
	}

	XA_INLINE void clear()
	{
		m_pairs.clear();
	}

	XA_INLINE uint32_t count() const
	{
		return m_pairs.size();
	}

private:
	const uint32_t m_maxSize;

	struct Pair
	{
		float cost;
		uint32_t face;
	};

	Array<Pair> m_pairs;
};

struct AtlasData
{
	ChartOptions options;
	const Mesh *mesh = nullptr;
	Array<float> edgeDihedralAngles;
	Array<float> edgeLengths;
	Array<float> faceAreas;
	Array<Vector3> faceNormals;
	BitArray isFaceInChart;

	AtlasData() : edgeDihedralAngles(MemTag::SegmentAtlasMeshData), edgeLengths(MemTag::SegmentAtlasMeshData), faceAreas(MemTag::SegmentAtlasMeshData), faceNormals(MemTag::SegmentAtlasMeshData) {}

	void compute()
	{
		const uint32_t faceCount = mesh->faceCount();
		const uint32_t edgeCount = mesh->edgeCount();
		edgeDihedralAngles.resize(edgeCount);
		edgeLengths.resize(edgeCount);
		faceAreas.resize(faceCount);
		faceNormals.resize(faceCount);
		isFaceInChart.resize(faceCount);
		isFaceInChart.zeroOutMemory();
		for (uint32_t f = 0; f < faceCount; f++) {
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t edge = f * 3 + i;
				const Vector3 &p0 = mesh->position(mesh->vertexAt(meshEdgeIndex0(edge)));
				const Vector3 &p1 = mesh->position(mesh->vertexAt(meshEdgeIndex1(edge)));
				edgeLengths[edge] = length(p1 - p0);
				XA_DEBUG_ASSERT(edgeLengths[edge] > 0.0f);
			}
			faceAreas[f] = mesh->computeFaceArea(f);
			XA_DEBUG_ASSERT(faceAreas[f] > 0.0f);
			faceNormals[f] = mesh->computeFaceNormal(f);
		}
		for (uint32_t face = 0; face < faceCount; face++) {
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t edge = face * 3 + i;
				const uint32_t oedge = mesh->oppositeEdge(edge);
				if (oedge == UINT32_MAX)
					edgeDihedralAngles[edge] = FLT_MAX;
				else {
					const uint32_t oface = meshEdgeFace(oedge);
					edgeDihedralAngles[edge] = edgeDihedralAngles[oedge] = dot(faceNormals[face], faceNormals[oface]);
				}
			}
		}
	}
};

#if XA_DEBUG_EXPORT_OBJ_PLANAR_REGIONS
static uint32_t s_planarRegionsCurrentRegion;
static uint32_t s_planarRegionsCurrentVertex;
#endif

struct PlanarCharts
{
	PlanarCharts(AtlasData &data) : m_data(data), m_nextRegionFace(MemTag::SegmentAtlasPlanarRegions), m_faceToRegionId(MemTag::SegmentAtlasPlanarRegions) {}
	const Basis &chartBasis(uint32_t chartIndex) const { return m_chartBasis[chartIndex]; }
	uint32_t chartCount() const { return m_charts.size(); }
	
	ConstArrayView<uint32_t> chartFaces(uint32_t chartIndex) const
	{
		const Chart &chart = m_charts[chartIndex];
		return ConstArrayView<uint32_t>(&m_chartFaces[chart.firstFace], chart.faceCount);
	}

	uint32_t regionIdFromFace(uint32_t face) const { return m_faceToRegionId[face]; }
	uint32_t nextRegionFace(uint32_t face) const { return m_nextRegionFace[face]; }
	float regionArea(uint32_t region) const { return m_regionAreas[region]; }

	void compute()
	{
		const uint32_t faceCount = m_data.mesh->faceCount();
		// Precompute regions of coplanar incident faces.
		m_regionFirstFace.clear();
		m_nextRegionFace.resize(faceCount);
		m_faceToRegionId.resize(faceCount);
		for (uint32_t f = 0; f < faceCount; f++) {
			m_nextRegionFace[f] = f;
			m_faceToRegionId[f] = UINT32_MAX;
		}
		Array<uint32_t> faceStack;
		faceStack.reserve(min(faceCount, 16u));
		uint32_t regionCount = 0;
		for (uint32_t f = 0; f < faceCount; f++) {
			if (m_nextRegionFace[f] != f)
				continue; // Already assigned.
			faceStack.clear();
			faceStack.push_back(f);
			for (;;) {
				if (faceStack.isEmpty())
					break;
				const uint32_t face = faceStack.back();
				m_faceToRegionId[face] = regionCount;
				faceStack.pop_back();
				for (Mesh::FaceEdgeIterator it(m_data.mesh, face); !it.isDone(); it.advance()) {
					const uint32_t oface = it.oppositeFace();
					if (it.isBoundary())
						continue;
					if (m_nextRegionFace[oface] != oface)
						continue; // Already assigned.
					if (!equal(dot(m_data.faceNormals[face], m_data.faceNormals[oface]), 1.0f, kEpsilon))
						continue; // Not coplanar.
					const uint32_t next = m_nextRegionFace[face];
					m_nextRegionFace[face] = oface;
					m_nextRegionFace[oface] = next;
					m_faceToRegionId[oface] = regionCount;
					faceStack.push_back(oface);
				}
			}
			m_regionFirstFace.push_back(f);
			regionCount++;
		}
#if XA_DEBUG_EXPORT_OBJ_PLANAR_REGIONS
		static std::mutex s_mutex;
		{
			std::lock_guard<std::mutex> lock(s_mutex);
			FILE *file;
			XA_FOPEN(file, "debug_mesh_planar_regions.obj", s_planarRegionsCurrentRegion == 0 ? "w" : "a");
			if (file) {
				m_data.mesh->writeObjVertices(file);
				fprintf(file, "s off\n");
				for (uint32_t i = 0; i < regionCount; i++) {
					fprintf(file, "o region%u\n", s_planarRegionsCurrentRegion);
					for (uint32_t j = 0; j < faceCount; j++) {
						if (m_faceToRegionId[j] == i)
							m_data.mesh->writeObjFace(file, j, s_planarRegionsCurrentVertex);
					}
					s_planarRegionsCurrentRegion++;
				}
				s_planarRegionsCurrentVertex += m_data.mesh->vertexCount();
				fclose(file);
			}
		}
#endif
		// Precompute planar region areas.
		m_regionAreas.resize(regionCount);
		m_regionAreas.zeroOutMemory();
		for (uint32_t f = 0; f < faceCount; f++)
			m_regionAreas[m_faceToRegionId[f]] += m_data.faceAreas[f];
		// Create charts from suitable planar regions.
		// The dihedral angle of all boundary edges must be >= 90 degrees.
		m_charts.clear();
		m_chartFaces.clear();
		for (uint32_t region = 0; region < regionCount; region++) {
			const uint32_t firstRegionFace = m_regionFirstFace[region];
			uint32_t face = firstRegionFace;
			bool createChart = true;
			do {
				for (Mesh::FaceEdgeIterator it(m_data.mesh, face); !it.isDone(); it.advance()) {
					if (it.isBoundary())
						continue; // Ignore mesh boundary edges.
					const uint32_t oface = it.oppositeFace();
					if (m_faceToRegionId[oface] == region)
						continue; // Ignore internal edges.
					const float angle = m_data.edgeDihedralAngles[it.edge()];
					if (angle > 0.0f && angle < FLT_MAX) { // FLT_MAX on boundaries.
						createChart = false;
						break;
					}
				}
				if (!createChart)
					break;
				face = m_nextRegionFace[face];
			}
			while (face != firstRegionFace);
			// Create a chart.
			if (createChart) {
				Chart chart;
				chart.firstFace = m_chartFaces.size();
				chart.faceCount = 0;
				face = firstRegionFace;
				do {
					m_data.isFaceInChart.set(face);
					m_chartFaces.push_back(face);
					chart.faceCount++;
					face = m_nextRegionFace[face];
				}
				while (face != firstRegionFace);
				m_charts.push_back(chart);
			}
		}
		// Compute basis for each chart using the first face normal (all faces have the same normal).
		m_chartBasis.resize(m_charts.size());
		for (uint32_t c = 0; c < m_charts.size(); c++)
		{
			const uint32_t face = m_chartFaces[m_charts[c].firstFace];
			Basis &basis = m_chartBasis[c];
			basis.normal = m_data.faceNormals[face];
			basis.tangent = Basis::computeTangent(basis.normal);
			basis.bitangent = Basis::computeBitangent(basis.normal, basis.tangent);
		}
	}

private:
	struct Chart
	{
		uint32_t firstFace, faceCount;
	};

	AtlasData &m_data;
	Array<uint32_t> m_regionFirstFace;
	Array<uint32_t> m_nextRegionFace;
	Array<uint32_t> m_faceToRegionId;
	Array<float> m_regionAreas;
	Array<Chart> m_charts;
	Array<uint32_t> m_chartFaces;
	Array<Basis> m_chartBasis;
};

struct ClusteredCharts
{
	ClusteredCharts(AtlasData &data, const PlanarCharts &planarCharts) : m_data(data), m_planarCharts(planarCharts), m_texcoords(MemTag::SegmentAtlasMeshData), m_bestTriangles(10), m_placingSeeds(false) {}

	~ClusteredCharts()
	{
		const uint32_t chartCount = m_charts.size();
		for (uint32_t i = 0; i < chartCount; i++) {
			m_charts[i]->~Chart();
			XA_FREE(m_charts[i]);
		}
	}

	uint32_t chartCount() const { return m_charts.size(); }
	ConstArrayView<uint32_t> chartFaces(uint32_t chartIndex) const { return m_charts[chartIndex]->faces; }
	const Basis &chartBasis(uint32_t chartIndex) const { return m_charts[chartIndex]->basis; }

	void compute()
	{
		const uint32_t faceCount = m_data.mesh->faceCount();
		m_facesLeft = 0;
		for (uint32_t i = 0; i < faceCount; i++) {
			if (!m_data.isFaceInChart.get(i))
				m_facesLeft++;
		}
		const uint32_t chartCount = m_charts.size();
		for (uint32_t i = 0; i < chartCount; i++) {
			m_charts[i]->~Chart();
			XA_FREE(m_charts[i]);
		}
		m_charts.clear();
		m_faceCharts.resize(faceCount);
		m_faceCharts.fill(-1);
		m_texcoords.resize(faceCount * 3);
		if (m_facesLeft == 0)
			return;
		// Create initial charts greedely.
		placeSeeds(m_data.options.maxCost * 0.5f);
		if (m_data.options.maxIterations == 0) {
			XA_DEBUG_ASSERT(m_facesLeft == 0);
			return;
		}
		relocateSeeds();
		resetCharts();
		// Restart process growing charts in parallel.
		uint32_t iteration = 0;
		for (;;) {
			growCharts(m_data.options.maxCost);
			// When charts cannot grow more: fill holes, merge charts, relocate seeds and start new iteration.
			fillHoles(m_data.options.maxCost * 0.5f);
#if XA_MERGE_CHARTS
			mergeCharts();
#endif
			if (++iteration == m_data.options.maxIterations)
				break;
			if (!relocateSeeds())
				break;
			resetCharts();
		}
		// Make sure no holes are left!
		XA_DEBUG_ASSERT(m_facesLeft == 0);
	}

private:
	struct Chart
	{
		Chart() : faces(MemTag::SegmentAtlasChartFaces) {}

		int id = -1;
		Basis basis; // Best fit normal.
		float area = 0.0f;
		float boundaryLength = 0.0f;
		Vector3 centroidSum = Vector3(0.0f); // Sum of chart face centroids.
		Vector3 centroid = Vector3(0.0f); // Average centroid of chart faces.
		Array<uint32_t> faces;
		Array<uint32_t> failedPlanarRegions;
		CostQueue candidates;
		uint32_t seed;
	};

	void placeSeeds(float threshold)
	{
		XA_PROFILE_START(clusteredChartsPlaceSeeds)
		m_placingSeeds = true;
		// Instead of using a predefiened number of seeds:
		// - Add seeds one by one, growing chart until a certain treshold.
		// - Undo charts and restart growing process.
		// @@ How can we give preference to faces far from sharp features as in the LSCM paper?
		//   - those points can be found using a simple flood filling algorithm.
		//   - how do we weight the probabilities?
		while (m_facesLeft > 0)
			createChart(threshold);
		m_placingSeeds = false;
		XA_PROFILE_END(clusteredChartsPlaceSeeds)
	}

	// Returns true if any of the charts can grow more.
	void growCharts(float threshold)
	{
		XA_PROFILE_START(clusteredChartsGrow)
		for (;;) {
			if (m_facesLeft == 0)
				break;
			// Get the single best candidate out of the chart best candidates.
			uint32_t bestFace = UINT32_MAX, bestChart = UINT32_MAX;
			float lowestCost = FLT_MAX;
			for (uint32_t i = 0; i < m_charts.size(); i++) {
				Chart *chart = m_charts[i];
				// Get the best candidate from the chart.
				// Cleanup any best candidates that have been claimed by another chart.
				uint32_t face = UINT32_MAX;
				float cost = FLT_MAX;
				for (;;) {
					if (chart->candidates.count() == 0)
						break;
					cost = chart->candidates.peekCost();
					face = chart->candidates.peekFace();
					if (!m_data.isFaceInChart.get(face))
						break;
					else {
						// Face belongs to another chart. Pop from queue so the next best candidate can be retrieved.
						chart->candidates.pop();
						face = UINT32_MAX;
					}
				}
				if (face == UINT32_MAX)
					continue; // No candidates for this chart.
				// See if best candidate overall.
				if (cost < lowestCost) {
					lowestCost = cost;
					bestFace = face;
					bestChart = i;
				}
			}
			if (bestFace == UINT32_MAX || lowestCost > threshold)
				break;
			Chart *chart = m_charts[bestChart];
			chart->candidates.pop(); // Pop the selected candidate from the queue.
			if (!addFaceToChart(chart, bestFace))
				chart->failedPlanarRegions.push_back(m_planarCharts.regionIdFromFace(bestFace));
		}
		XA_PROFILE_END(clusteredChartsGrow)
	}

	void resetCharts()
	{
		XA_PROFILE_START(clusteredChartsReset)
		const uint32_t faceCount = m_data.mesh->faceCount();
		for (uint32_t i = 0; i < faceCount; i++) {
			if (m_faceCharts[i] != -1)
				m_data.isFaceInChart.unset(i);
			m_faceCharts[i] = -1;
		}
		m_facesLeft = 0;
		for (uint32_t i = 0; i < faceCount; i++) {
			if (!m_data.isFaceInChart.get(i))
				m_facesLeft++;
		}
		const uint32_t chartCount = m_charts.size();
		for (uint32_t i = 0; i < chartCount; i++) {
			Chart *chart = m_charts[i];
			chart->area = 0.0f;
			chart->boundaryLength = 0.0f;
			chart->basis.normal = Vector3(0.0f);
			chart->basis.tangent = Vector3(0.0f);
			chart->basis.bitangent = Vector3(0.0f);
			chart->centroidSum = Vector3(0.0f);
			chart->centroid = Vector3(0.0f);
			chart->faces.clear();
			chart->candidates.clear();
			chart->failedPlanarRegions.clear();
			addFaceToChart(chart, chart->seed);
		}
		XA_PROFILE_END(clusteredChartsReset)
	}

	bool relocateSeeds()
	{
		XA_PROFILE_START(clusteredChartsRelocateSeeds)
		bool anySeedChanged = false;
		const uint32_t chartCount = m_charts.size();
		for (uint32_t i = 0; i < chartCount; i++) {
			if (relocateSeed(m_charts[i])) {
				anySeedChanged = true;
			}
		}
		XA_PROFILE_END(clusteredChartsRelocateSeeds)
		return anySeedChanged;
	}

	void fillHoles(float threshold)
	{
		XA_PROFILE_START(clusteredChartsFillHoles)
		while (m_facesLeft > 0)
			createChart(threshold);
		XA_PROFILE_END(clusteredChartsFillHoles)
	}

#if XA_MERGE_CHARTS
	void mergeCharts()
	{
		XA_PROFILE_START(clusteredChartsMerge)
		const uint32_t chartCount = m_charts.size();
		// Merge charts progressively until there's none left to merge.
		for (;;) {
			bool merged = false;
			for (int c = chartCount - 1; c >= 0; c--) {
				Chart *chart = m_charts[c];
				if (chart == nullptr)
					continue;
				float externalBoundaryLength = 0.0f;
				m_sharedBoundaryLengths.resize(chartCount);
				m_sharedBoundaryLengths.zeroOutMemory();
				m_sharedBoundaryLengthsNoSeams.resize(chartCount);
				m_sharedBoundaryLengthsNoSeams.zeroOutMemory();
				m_sharedBoundaryEdgeCountNoSeams.resize(chartCount);
				m_sharedBoundaryEdgeCountNoSeams.zeroOutMemory();
				const uint32_t faceCount = chart->faces.size();
				for (uint32_t i = 0; i < faceCount; i++) {
					const uint32_t f = chart->faces[i];
					for (Mesh::FaceEdgeIterator it(m_data.mesh, f); !it.isDone(); it.advance()) {
						const float l = m_data.edgeLengths[it.edge()];
						if (it.isBoundary()) {
							externalBoundaryLength += l;
						} else {
							const int neighborChart = m_faceCharts[it.oppositeFace()];
							if (neighborChart == -1)
								externalBoundaryLength += l;
							else if (m_charts[neighborChart] != chart) {
								if ((it.isSeam() && (isNormalSeam(it.edge()) || it.isTextureSeam()))) {
									externalBoundaryLength += l;
								} else {
									m_sharedBoundaryLengths[neighborChart] += l;
								}
								m_sharedBoundaryLengthsNoSeams[neighborChart] += l;
								m_sharedBoundaryEdgeCountNoSeams[neighborChart]++;
							}
						}
					}
				}
				for (int cc = chartCount - 1; cc >= 0; cc--) {
					if (cc == c)
						continue;
					Chart *chart2 = m_charts[cc];
					if (chart2 == nullptr)
						continue;
					// Must share a boundary.
					if (m_sharedBoundaryLengths[cc] <= 0.0f)
						continue;
					// Compare proxies.
					if (dot(chart2->basis.normal, chart->basis.normal) < XA_MERGE_CHARTS_MIN_NORMAL_DEVIATION)
						continue;
					// Obey max chart area and boundary length.
					if (m_data.options.maxChartArea > 0.0f && chart->area + chart2->area > m_data.options.maxChartArea)
						continue;
					if (m_data.options.maxBoundaryLength > 0.0f && chart->boundaryLength + chart2->boundaryLength - m_sharedBoundaryLengthsNoSeams[cc] > m_data.options.maxBoundaryLength)
						continue;
					// Merge if chart2 has a single face.
					// chart1 must have more than 1 face.
					// chart2 area must be <= 10% of chart1 area.
					if (m_sharedBoundaryLengthsNoSeams[cc] > 0.0f && chart->faces.size() > 1 && chart2->faces.size() == 1 && chart2->area <= chart->area * 0.1f) 
						goto merge;
					// Merge if chart2 has two faces (probably a quad), and chart1 bounds at least 2 of its edges.
					if (chart2->faces.size() == 2 && m_sharedBoundaryEdgeCountNoSeams[cc] >= 2)
						goto merge;
					// Merge if chart2 is wholely inside chart1, ignoring seams.
					if (m_sharedBoundaryLengthsNoSeams[cc] > 0.0f && equal(m_sharedBoundaryLengthsNoSeams[cc], chart2->boundaryLength, kEpsilon))
						goto merge;
					if (m_sharedBoundaryLengths[cc] > 0.2f * max(0.0f, chart->boundaryLength - externalBoundaryLength) || 
						m_sharedBoundaryLengths[cc] > 0.75f * chart2->boundaryLength)
						goto merge;
					continue;
				merge:
					if (!mergeChart(chart, chart2, m_sharedBoundaryLengthsNoSeams[cc]))
						continue;
					merged = true;
					break;
				}
				if (merged)
					break;
			}
			if (!merged)
				break;
		}
		// Remove deleted charts.
		for (int c = 0; c < int32_t(m_charts.size()); /*do not increment if removed*/) {
			if (m_charts[c] == nullptr) {
				m_charts.removeAt(c);
				// Update m_faceCharts.
				const uint32_t faceCount = m_faceCharts.size();
				for (uint32_t i = 0; i < faceCount; i++) {
					XA_DEBUG_ASSERT(m_faceCharts[i] != c);
					XA_DEBUG_ASSERT(m_faceCharts[i] <= int32_t(m_charts.size()));
					if (m_faceCharts[i] > c) {
						m_faceCharts[i]--;
					}
				}
			} else {
				m_charts[c]->id = c;
				c++;
			}
		}
		XA_PROFILE_END(clusteredChartsMerge)
	}
#endif

private:
	void createChart(float threshold)
	{
		Chart *chart = XA_NEW(MemTag::Default, Chart);
		chart->id = (int)m_charts.size();
		m_charts.push_back(chart);
		// Pick a face not used by any chart yet, belonging to the largest planar region.
		chart->seed = 0;
		float largestArea = 0.0f;
		for (uint32_t f = 0; f < m_data.mesh->faceCount(); f++) {
			if (m_data.isFaceInChart.get(f))
				continue;
			const float area = m_planarCharts.regionArea(m_planarCharts.regionIdFromFace(f));
			if (area > largestArea) {
				largestArea = area;
				chart->seed = f;
			}
		}
		addFaceToChart(chart, chart->seed);
		// Grow the chart as much as possible within the given threshold.
		for (;;) {
			if (chart->candidates.count() == 0 || chart->candidates.peekCost() > threshold)
				break;
			const uint32_t f = chart->candidates.pop();
			if (m_data.isFaceInChart.get(f))
				continue;
			if (!addFaceToChart(chart, f)) {
				chart->failedPlanarRegions.push_back(m_planarCharts.regionIdFromFace(f));
				continue;
			}
		}
	}

	bool isChartBoundaryEdge(const Chart *chart, uint32_t edge) const
	{
		const uint32_t oppositeEdge = m_data.mesh->oppositeEdge(edge);
		const uint32_t oppositeFace = meshEdgeFace(oppositeEdge);
		return oppositeEdge == UINT32_MAX || m_faceCharts[oppositeFace] != chart->id;
	}

	bool computeChartBasis(Chart *chart, Basis *basis)
	{
		const uint32_t faceCount = chart->faces.size();
		m_tempPoints.resize(chart->faces.size() * 3);
		for (uint32_t i = 0; i < faceCount; i++) {
			const uint32_t f = chart->faces[i];
			for (uint32_t j = 0; j < 3; j++)
				m_tempPoints[i * 3 + j] = m_data.mesh->position(m_data.mesh->vertexAt(f * 3 + j));
		}
		return Fit::computeBasis(m_tempPoints.data(), m_tempPoints.size(), basis);
	}

	bool isFaceFlipped(uint32_t face) const
	{
		const Vector2 &v1 = m_texcoords[face * 3 + 0];
		const Vector2 &v2 = m_texcoords[face * 3 + 1];
		const Vector2 &v3 = m_texcoords[face * 3 + 2];
		const float parametricArea = ((v2.x - v1.x) * (v3.y - v1.y) - (v3.x - v1.x) * (v2.y - v1.y)) * 0.5f;
		return parametricArea < 0.0f;
	}

	void parameterizeChart(const Chart *chart)
	{
		const uint32_t faceCount = chart->faces.size();
		for (uint32_t i = 0; i < faceCount; i++) {
			const uint32_t face = chart->faces[i];
			for (uint32_t j = 0; j < 3; j++) {
				const uint32_t offset = face * 3 + j;
				const Vector3 &pos = m_data.mesh->position(m_data.mesh->vertexAt(offset));
				m_texcoords[offset] = Vector2(dot(chart->basis.tangent, pos), dot(chart->basis.bitangent, pos));
			}
		}
	}

	// m_faceCharts for the chart faces must be set to the chart ID. Needed to compute boundary edges.
	bool isChartParameterizationValid(const Chart *chart)
	{
		const uint32_t faceCount = chart->faces.size();
		// Check for flipped faces in the parameterization. OK if all are flipped.
		uint32_t flippedFaceCount = 0;
		for (uint32_t i = 0; i < faceCount; i++) {
			if (isFaceFlipped(chart->faces[i]))
				flippedFaceCount++;
		}
		if (flippedFaceCount != 0 && flippedFaceCount != faceCount)
			return false;
		// Check for boundary intersection in the parameterization.
		XA_PROFILE_START(clusteredChartsPlaceSeedsBoundaryIntersection)
		XA_PROFILE_START(clusteredChartsGrowBoundaryIntersection)
		m_boundaryGrid.reset(m_texcoords.data());
		for (uint32_t i = 0; i < faceCount; i++) {
			const uint32_t f = chart->faces[i];
			for (uint32_t j = 0; j < 3; j++) {
				const uint32_t edge = f * 3 + j;
				if (isChartBoundaryEdge(chart, edge))
					m_boundaryGrid.append(edge);
			}
		}
		const bool intersection = m_boundaryGrid.intersect(m_data.mesh->epsilon());
#if XA_PROFILE
		if (m_placingSeeds)
			XA_PROFILE_END(clusteredChartsPlaceSeedsBoundaryIntersection)
		else
			XA_PROFILE_END(clusteredChartsGrowBoundaryIntersection)
#endif
		if (intersection)
			return false;
		return true;
	}

	bool addFaceToChart(Chart *chart, uint32_t face)
	{
		XA_DEBUG_ASSERT(!m_data.isFaceInChart.get(face));
		const uint32_t oldFaceCount = chart->faces.size();
		const bool firstFace = oldFaceCount == 0;
		// Append the face and any coplanar connected faces to the chart faces array.
		chart->faces.push_back(face);
		uint32_t coplanarFace = m_planarCharts.nextRegionFace(face);
		while (coplanarFace != face) { 
			XA_DEBUG_ASSERT(!m_data.isFaceInChart.get(coplanarFace));
			chart->faces.push_back(coplanarFace);
			coplanarFace = m_planarCharts.nextRegionFace(coplanarFace);
		}
		const uint32_t faceCount = chart->faces.size();
		// Compute basis.
		Basis basis;
		if (firstFace) {
			// Use the first face normal.
			// Use any edge as the tangent vector.
			basis.normal = m_data.faceNormals[face];
			basis.tangent = normalize(m_data.mesh->position(m_data.mesh->vertexAt(face * 3 + 0)) - m_data.mesh->position(m_data.mesh->vertexAt(face * 3 + 1)), kEpsilon);
			basis.bitangent = cross(basis.normal, basis.tangent);
		} else {
			// Use best fit normal.
			if (!computeChartBasis(chart, &basis)) {
				chart->faces.resize(oldFaceCount);
				return false;
			}
			if (dot(basis.normal, m_data.faceNormals[face]) < 0.0f) // Flip normal if oriented in the wrong direction.
				basis.normal = -basis.normal;
		}
		if (!firstFace) {
			// Compute orthogonal parameterization and check that it is valid.
			parameterizeChart(chart);
			for (uint32_t i = oldFaceCount; i < faceCount; i++)
				m_faceCharts[chart->faces[i]] = chart->id;
			if (!isChartParameterizationValid(chart)) {
				for (uint32_t i = oldFaceCount; i < faceCount; i++)
					m_faceCharts[chart->faces[i]] = -1;
				chart->faces.resize(oldFaceCount);
				return false;
			}
		}
		// Add face(s) to chart.
		chart->basis = basis;
		chart->area = computeArea(chart, face);
		chart->boundaryLength = computeBoundaryLength(chart, face);
		for (uint32_t i = oldFaceCount; i < faceCount; i++) {
			const uint32_t f = chart->faces[i];
			m_faceCharts[f] = chart->id;
			m_facesLeft--;
			m_data.isFaceInChart.set(f);
			chart->centroidSum += m_data.mesh->computeFaceCenter(f);
		}
		chart->centroid = chart->centroidSum / float(chart->faces.size());
		// Refresh candidates.
		chart->candidates.clear();
		for (uint32_t i = 0; i < faceCount; i++) {
			// Traverse neighboring faces, add the ones that do not belong to any chart yet.
			const uint32_t f = chart->faces[i];
			for (uint32_t j = 0; j < 3; j++) {
				const uint32_t edge = f * 3 + j;
				const uint32_t oedge = m_data.mesh->oppositeEdge(edge);
				if (oedge == UINT32_MAX)
					continue; // Boundary edge.
				const uint32_t oface = meshEdgeFace(oedge);
				if (m_data.isFaceInChart.get(oface))
					continue; // Face belongs to another chart.
				if (chart->failedPlanarRegions.contains(m_planarCharts.regionIdFromFace(oface)))
					continue; // Failed to add this faces planar region to the chart before.
				const float cost = computeCost(chart, oface);
				if (cost < FLT_MAX)
					chart->candidates.push(cost, oface);
			}
		}
		return true;
	}

	// Returns true if the seed has changed.
	bool relocateSeed(Chart *chart)
	{
		// Find the first N triangles that fit the proxy best.
		const uint32_t faceCount = chart->faces.size();
		m_bestTriangles.clear();
		for (uint32_t i = 0; i < faceCount; i++) {
			const float cost = computeNormalDeviationMetric(chart, chart->faces[i]);
			m_bestTriangles.push(cost, chart->faces[i]);
		}
		// Of those, choose the most central triangle.
		uint32_t mostCentral = 0;
		float minDistance = FLT_MAX;
		for (;;) {
			if (m_bestTriangles.count() == 0)
				break;
			const uint32_t face = m_bestTriangles.pop();
			Vector3 faceCentroid = m_data.mesh->computeFaceCenter(face);
			const float distance = length(chart->centroid - faceCentroid);
			if (distance < minDistance) {
				minDistance = distance;
				mostCentral = face;
			}
		}
		XA_DEBUG_ASSERT(minDistance < FLT_MAX);
		if (mostCentral == chart->seed)
			return false;
		chart->seed = mostCentral;
		return true;
	}

	// Cost is combined metrics * weights.
	float computeCost(Chart *chart, uint32_t face) const
	{
		// Estimate boundary length and area:
		const float newChartArea = computeArea(chart, face);
		const float newBoundaryLength = computeBoundaryLength(chart, face);
		// Enforce limits strictly:
		if (m_data.options.maxChartArea > 0.0f && newChartArea > m_data.options.maxChartArea)
			return FLT_MAX;
		if (m_data.options.maxBoundaryLength > 0.0f && newBoundaryLength > m_data.options.maxBoundaryLength)
			return FLT_MAX;
		// Compute metrics.
		float cost = 0.0f;
		const float normalDeviation = computeNormalDeviationMetric(chart, face);
		if (normalDeviation >= 0.707f) // ~75 degrees
			return FLT_MAX;
		cost += m_data.options.normalDeviationWeight * normalDeviation;
		// Penalize faces that cross seams, reward faces that close seams or reach boundaries.
		// Make sure normal seams are fully respected:
		const float normalSeam = computeNormalSeamMetric(chart, face);
		if (m_data.options.normalSeamWeight >= 1000.0f && normalSeam > 0.0f)
			return FLT_MAX;
		cost += m_data.options.normalSeamWeight * normalSeam;
		cost += m_data.options.roundnessWeight * computeRoundnessMetric(chart, newBoundaryLength, newChartArea);
		cost += m_data.options.straightnessWeight * computeStraightnessMetric(chart, face);
		cost += m_data.options.textureSeamWeight * computeTextureSeamMetric(chart, face);
		//float R = evaluateCompletenessMetric(chart, face);
		//float D = evaluateDihedralAngleMetric(chart, face);
		// @@ Add a metric based on local dihedral angle.
		// @@ Tweaking the normal and texture seam metrics.
		// - Cause more impedance. Never cross 90 degree edges.
		XA_DEBUG_ASSERT(isFinite(cost));
		return cost;
	}

	// Returns a value in [0-1].
	// 0 if face normal is coplanar to the chart's best fit normal.
	// 1 if face normal is perpendicular.
	float computeNormalDeviationMetric(Chart *chart, uint32_t face) const
	{
		// All faces in coplanar regions have the same normal, can use any face.
		const Vector3 faceNormal = m_data.faceNormals[face];
		// Use plane fitting metric for now:
		return min(1.0f - dot(faceNormal, chart->basis.normal), 1.0f); // @@ normal deviations should be weighted by face area
	}

	float computeRoundnessMetric(Chart *chart, float newBoundaryLength, float newChartArea) const
	{
		const float oldRoundness = square(chart->boundaryLength) / chart->area;
		const float newRoundness = square(newBoundaryLength) / newChartArea;
		return 1.0f - oldRoundness / newRoundness;
	}

	float computeStraightnessMetric(Chart *chart, uint32_t firstFace) const
	{
		float l_out = 0.0f; // Length of firstFace planar region boundary that doesn't border the chart.
		float l_in = 0.0f; // Length that does border the chart.
		const uint32_t planarRegionId = m_planarCharts.regionIdFromFace(firstFace);
		uint32_t face = firstFace;
		for (;;) { 
			for (Mesh::FaceEdgeIterator it(m_data.mesh, face); !it.isDone(); it.advance()) {
				const float l = m_data.edgeLengths[it.edge()];
				if (it.isBoundary()) {
					l_out += l;
				} else if (m_planarCharts.regionIdFromFace(it.oppositeFace()) != planarRegionId) {
					if (m_faceCharts[it.oppositeFace()] != chart->id)
						l_out += l;
					else
						l_in += l;
				}
			}
			face = m_planarCharts.nextRegionFace(face);
			if (face == firstFace)
				break;
		}
#if 1
		XA_DEBUG_ASSERT(l_in != 0.0f); // Candidate face must be adjacent to chart. @@ This is not true if the input mesh has zero-length edges.
		float ratio = (l_out - l_in) / (l_out + l_in);
		return min(ratio, 0.0f); // Only use the straightness metric to close gaps.
#else
		return 1.0f - l_in / l_out;
#endif
	}

	bool isNormalSeam(uint32_t edge) const
	{
		const uint32_t oppositeEdge = m_data.mesh->oppositeEdge(edge);
		if (oppositeEdge == UINT32_MAX)
			return false; // boundary edge
		if (m_data.mesh->flags() & MeshFlags::HasNormals) {
			const uint32_t v0 = m_data.mesh->vertexAt(meshEdgeIndex0(edge));
			const uint32_t v1 = m_data.mesh->vertexAt(meshEdgeIndex1(edge));
			const uint32_t ov0 = m_data.mesh->vertexAt(meshEdgeIndex0(oppositeEdge));
			const uint32_t ov1 = m_data.mesh->vertexAt(meshEdgeIndex1(oppositeEdge));
			if (v0 == ov1 && v1 == ov0)
				return false;
			return !equal(m_data.mesh->normal(v0), m_data.mesh->normal(ov1), kNormalEpsilon) || !equal(m_data.mesh->normal(v1), m_data.mesh->normal(ov0), kNormalEpsilon);
		}
		const uint32_t f0 = meshEdgeFace(edge);
		const uint32_t f1 = meshEdgeFace(oppositeEdge);
		if (m_planarCharts.regionIdFromFace(f0) == m_planarCharts.regionIdFromFace(f1))
			return false;
		return !equal(m_data.faceNormals[f0], m_data.faceNormals[f1], kNormalEpsilon);
	}

	float computeNormalSeamMetric(Chart *chart, uint32_t firstFace) const
	{
		float seamFactor = 0.0f, totalLength = 0.0f;
		uint32_t face = firstFace;
		for (;;) { 
			for (Mesh::FaceEdgeIterator it(m_data.mesh, face); !it.isDone(); it.advance()) {
				if (it.isBoundary())
					continue;
				if (m_faceCharts[it.oppositeFace()] != chart->id)
					continue;
				float l = m_data.edgeLengths[it.edge()];
				totalLength += l;
				if (!it.isSeam())
					continue;
				// Make sure it's a normal seam.
				if (isNormalSeam(it.edge())) {
					float d;
					if (m_data.mesh->flags() & MeshFlags::HasNormals) {
						const Vector3 &n0 = m_data.mesh->normal(it.vertex0());
						const Vector3 &n1 = m_data.mesh->normal(it.vertex1());
						const Vector3 &on0 = m_data.mesh->normal(m_data.mesh->vertexAt(meshEdgeIndex0(it.oppositeEdge())));
						const Vector3 &on1 = m_data.mesh->normal(m_data.mesh->vertexAt(meshEdgeIndex1(it.oppositeEdge())));
						const float d0 = clamp(dot(n0, on1), 0.0f, 1.0f);
						const float d1 = clamp(dot(n1, on0), 0.0f, 1.0f);
						d = (d0 + d1) * 0.5f;
					} else {
						d = clamp(dot(m_data.faceNormals[face], m_data.faceNormals[meshEdgeFace(it.oppositeEdge())]), 0.0f, 1.0f);
					}
					l *= 1 - d;
					seamFactor += l;
				}
			}
			face = m_planarCharts.nextRegionFace(face);
			if (face == firstFace)
				break;
		}
		if (seamFactor <= 0.0f)
			return 0.0f;
		return seamFactor / totalLength;
	}

	float computeTextureSeamMetric(Chart *chart, uint32_t firstFace) const
	{
		float seamLength = 0.0f, totalLength = 0.0f;
		uint32_t face = firstFace;
		for (;;) { 
			for (Mesh::FaceEdgeIterator it(m_data.mesh, face); !it.isDone(); it.advance()) {
				if (it.isBoundary())
					continue;
				if (m_faceCharts[it.oppositeFace()] != chart->id)
					continue;
				float l = m_data.edgeLengths[it.edge()];
				totalLength += l;
				if (!it.isSeam())
					continue;
				// Make sure it's a texture seam.
				if (it.isTextureSeam())
					seamLength += l;
			}
			face = m_planarCharts.nextRegionFace(face);
			if (face == firstFace)
				break;
		}
		if (seamLength <= 0.0f)
			return 0.0f; // Avoid division by zero.
		return seamLength / totalLength;
	}

	float computeArea(Chart *chart, uint32_t firstFace) const
	{
		float area = chart->area;
		uint32_t face = firstFace;
		for (;;) { 
			area += m_data.faceAreas[face];
			face = m_planarCharts.nextRegionFace(face);
			if (face == firstFace)
				break;
		}
		return area;
	}

	float computeBoundaryLength(Chart *chart, uint32_t firstFace) const
	{
		float boundaryLength = chart->boundaryLength;
		// Add new edges, subtract edges shared with the chart.
		const uint32_t planarRegionId = m_planarCharts.regionIdFromFace(firstFace);
		uint32_t face = firstFace;
		for (;;) { 
			for (Mesh::FaceEdgeIterator it(m_data.mesh, face); !it.isDone(); it.advance()) {
				const float edgeLength = m_data.edgeLengths[it.edge()];
				if (it.isBoundary()) {
					boundaryLength += edgeLength;
				} else if (m_planarCharts.regionIdFromFace(it.oppositeFace()) != planarRegionId) {
					if (m_faceCharts[it.oppositeFace()] != chart->id)
						boundaryLength += edgeLength;
					else
						boundaryLength -= edgeLength;
				}
			}
			face = m_planarCharts.nextRegionFace(face);
			if (face == firstFace)
				break;
		}
		return max(0.0f, boundaryLength);  // @@ Hack!
	}

	bool mergeChart(Chart *owner, Chart *chart, float sharedBoundaryLength)
	{
		const uint32_t oldOwnerFaceCount = owner->faces.size();
		const uint32_t chartFaceCount = chart->faces.size();
		owner->faces.push_back(chart->faces);
		for (uint32_t i = 0; i < chartFaceCount; i++) {
			XA_DEBUG_ASSERT(m_faceCharts[chart->faces[i]] == chart->id);
			m_faceCharts[chart->faces[i]] = owner->id;
		}
		// Compute basis using best fit normal.
		Basis basis;
		if (!computeChartBasis(owner, &basis)) {
			owner->faces.resize(oldOwnerFaceCount);
			for (uint32_t i = 0; i < chartFaceCount; i++)
				m_faceCharts[chart->faces[i]] = chart->id;
			return false;
		}
		if (dot(basis.normal, m_data.faceNormals[owner->faces[0]]) < 0.0f) // Flip normal if oriented in the wrong direction.
			basis.normal = -basis.normal;
		// Compute orthogonal parameterization and check that it is valid.
		parameterizeChart(owner);
		if (!isChartParameterizationValid(owner)) {
			owner->faces.resize(oldOwnerFaceCount);
			for (uint32_t i = 0; i < chartFaceCount; i++)
				m_faceCharts[chart->faces[i]] = chart->id;
			return false;
		}
		// Merge chart.
		owner->basis = basis;
		owner->failedPlanarRegions.push_back(chart->failedPlanarRegions);
		// Update adjacencies?
		owner->area += chart->area;
		owner->boundaryLength += chart->boundaryLength - sharedBoundaryLength;
		// Delete chart.
		m_charts[chart->id] = nullptr;
		chart->~Chart();
		XA_FREE(chart);
		return true;
	}

private:
	AtlasData &m_data;
	const PlanarCharts &m_planarCharts;
	Array<Vector2> m_texcoords;
	uint32_t m_facesLeft;
	Array<int> m_faceCharts;
	Array<Chart *> m_charts;
	CostQueue m_bestTriangles;
	Array<Vector3> m_tempPoints;
	UniformGrid2 m_boundaryGrid;
#if XA_MERGE_CHARTS
	// mergeCharts
	Array<float> m_sharedBoundaryLengths;
	Array<float> m_sharedBoundaryLengthsNoSeams;
	Array<uint32_t> m_sharedBoundaryEdgeCountNoSeams;
#endif
	bool m_placingSeeds;
};

struct Atlas
{
	Atlas() : m_planarCharts(m_data), m_clusteredCharts(m_data, m_planarCharts) {}

	uint32_t chartCount() const
	{
		return m_planarCharts.chartCount() + m_clusteredCharts.chartCount();
	}

	ConstArrayView<uint32_t> chartFaces(uint32_t chartIndex) const
	{
		if (chartIndex < m_planarCharts.chartCount())
			return m_planarCharts.chartFaces(chartIndex);
		chartIndex -= m_planarCharts.chartCount();
		return m_clusteredCharts.chartFaces(chartIndex);
	}

	const Basis &chartBasis(uint32_t chartIndex) const
	{
		if (chartIndex < m_planarCharts.chartCount())
			return m_planarCharts.chartBasis(chartIndex);
		chartIndex -= m_planarCharts.chartCount();
		return m_clusteredCharts.chartBasis(chartIndex);
	}

	void reset(const Mesh *mesh, const ChartOptions &options)
	{
		XA_PROFILE_START(buildAtlasInit)
		m_data.options = options;
		m_data.mesh = mesh;
		m_data.compute();
		XA_PROFILE_END(buildAtlasInit)
	}

	void compute()
	{
		XA_PROFILE_START(planarCharts)
		m_planarCharts.compute();
		XA_PROFILE_END(planarCharts)
		XA_PROFILE_START(clusteredCharts)
		m_clusteredCharts.compute();
		XA_PROFILE_END(clusteredCharts)
	}

private:
	AtlasData m_data;
	PlanarCharts m_planarCharts;
	ClusteredCharts m_clusteredCharts;
};

} // namespace segment

namespace param {

// Fast sweep in 3 directions
static bool findApproximateDiameterVertices(Mesh *mesh, uint32_t *a, uint32_t *b)
{
	XA_DEBUG_ASSERT(a != nullptr);
	XA_DEBUG_ASSERT(b != nullptr);
	const uint32_t vertexCount = mesh->vertexCount();
	uint32_t minVertex[3];
	uint32_t maxVertex[3];
	minVertex[0] = minVertex[1] = minVertex[2] = UINT32_MAX;
	maxVertex[0] = maxVertex[1] = maxVertex[2] = UINT32_MAX;
	for (uint32_t v = 1; v < vertexCount; v++) {
		if (mesh->isBoundaryVertex(v)) {
			minVertex[0] = minVertex[1] = minVertex[2] = v;
			maxVertex[0] = maxVertex[1] = maxVertex[2] = v;
			break;
		}
	}
	if (minVertex[0] == UINT32_MAX) {
		// Input mesh has not boundaries.
		return false;
	}
	for (uint32_t v = 1; v < vertexCount; v++) {
		if (!mesh->isBoundaryVertex(v)) {
			// Skip interior vertices.
			continue;
		}
		const Vector3 &pos = mesh->position(v);
		if (pos.x < mesh->position(minVertex[0]).x)
			minVertex[0] = v;
		else if (pos.x > mesh->position(maxVertex[0]).x)
			maxVertex[0] = v;
		if (pos.y < mesh->position(minVertex[1]).y)
			minVertex[1] = v;
		else if (pos.y > mesh->position(maxVertex[1]).y)
			maxVertex[1] = v;
		if (pos.z < mesh->position(minVertex[2]).z)
			minVertex[2] = v;
		else if (pos.z > mesh->position(maxVertex[2]).z)
			maxVertex[2] = v;
	}
	float lengths[3];
	for (int i = 0; i < 3; i++) {
		lengths[i] = length(mesh->position(minVertex[i]) - mesh->position(maxVertex[i]));
	}
	if (lengths[0] > lengths[1] && lengths[0] > lengths[2]) {
		*a = minVertex[0];
		*b = maxVertex[0];
	} else if (lengths[1] > lengths[2]) {
		*a = minVertex[1];
		*b = maxVertex[1];
	} else {
		*a = minVertex[2];
		*b = maxVertex[2];
	}
	return true;
}

// From OpenNL LSCM example.
// Computes the coordinates of the vertices of a triangle in a local 2D orthonormal basis of the triangle's plane.
static void projectTriangle(Vector3 p0, Vector3 p1, Vector3 p2, Vector2 *z0, Vector2 *z1, Vector2 *z2, float epsilon)
{
	Vector3 X = normalize(p1 - p0, epsilon);
	Vector3 Z = normalize(cross(X, p2 - p0), epsilon);
	Vector3 Y = cross(Z, X);
	Vector3 &O = p0;
	*z0 = Vector2(0, 0);
	*z1 = Vector2(length(p1 - O), 0);
	*z2 = Vector2(dot(p2 - O, X), dot(p2 - O, Y));
}

static bool computeLeastSquaresConformalMap(Mesh *mesh)
{
	uint32_t lockedVertex0, lockedVertex1;
	if (!findApproximateDiameterVertices(mesh, &lockedVertex0, &lockedVertex1)) {
		// Mesh has no boundaries.
		return false;
	}
	const uint32_t vertexCount = mesh->vertexCount();
	opennl::NLContext *context = opennl::nlNewContext();
	opennl::nlSolverParameteri(context, NL_NB_VARIABLES, int(2 * vertexCount));
	opennl::nlSolverParameteri(context, NL_MAX_ITERATIONS, int(5 * vertexCount));
	opennl::nlBegin(context, NL_SYSTEM);
	const Vector2 *texcoords = mesh->texcoords();
	for (uint32_t i = 0; i < vertexCount; i++) {
		opennl::nlSetVariable(context, 2 * i, texcoords[i].x);
		opennl::nlSetVariable(context, 2 * i + 1, texcoords[i].y);
		if (i == lockedVertex0 || i == lockedVertex1) {
			opennl::nlLockVariable(context, 2 * i);
			opennl::nlLockVariable(context, 2 * i + 1);
		} 
	}
	opennl::nlBegin(context, NL_MATRIX);
	const uint32_t faceCount = mesh->faceCount();
	const Vector3 *positions = mesh->positions();
	const uint32_t *indices = mesh->indices();
	for (uint32_t f = 0; f < faceCount; f++) {
		const uint32_t v0 = indices[f * 3 + 0];
		const uint32_t v1 = indices[f * 3 + 1];
		const uint32_t v2 = indices[f * 3 + 2];
		Vector2 z0, z1, z2;
		projectTriangle(positions[v0], positions[v1], positions[v2], &z0, &z1, &z2, mesh->epsilon());
		double a = z1.x - z0.x;
		double b = z1.y - z0.y;
		double c = z2.x - z0.x;
		double d = z2.y - z0.y;
		XA_DEBUG_ASSERT(b == 0.0);
		// Note  : 2*id + 0 --> u
		//         2*id + 1 --> v
		uint32_t u0_id = 2 * v0;
		uint32_t v0_id = 2 * v0 + 1;
		uint32_t u1_id = 2 * v1;
		uint32_t v1_id = 2 * v1 + 1;
		uint32_t u2_id = 2 * v2;
		uint32_t v2_id = 2 * v2 + 1;
		// Note : b = 0
		// Real part
		opennl::nlBegin(context, NL_ROW);
		opennl::nlCoefficient(context, u0_id, -a+c) ;
		opennl::nlCoefficient(context, v0_id, b-d) ;
		opennl::nlCoefficient(context, u1_id, -c) ;
		opennl::nlCoefficient(context, v1_id, d) ;
		opennl::nlCoefficient(context, u2_id, a);
		opennl::nlEnd(context, NL_ROW);
		// Imaginary part
		opennl::nlBegin(context, NL_ROW);
		opennl::nlCoefficient(context, u0_id, -b+d);
		opennl::nlCoefficient(context, v0_id, -a+c);
		opennl::nlCoefficient(context, u1_id, -d);
		opennl::nlCoefficient(context, v1_id, -c);
		opennl::nlCoefficient(context, v2_id, a);
		opennl::nlEnd(context, NL_ROW);
	}
	opennl::nlEnd(context, NL_MATRIX);
	opennl::nlEnd(context, NL_SYSTEM);
	if (!opennl::nlSolve(context)) {
		opennl::nlDeleteContext(context);
		return false;
	}
	for (uint32_t i = 0; i < vertexCount; i++) {
		const double u = opennl::nlGetVariable(context, 2 * i);
		const double v = opennl::nlGetVariable(context, 2 * i + 1);
		mesh->texcoord(i) = Vector2((float)u, (float)v);
		XA_DEBUG_ASSERT(!isNan(mesh->texcoord(i).x));
		XA_DEBUG_ASSERT(!isNan(mesh->texcoord(i).y));
	}
	opennl::nlDeleteContext(context);
	return true;
}

#if XA_RECOMPUTE_CHARTS
struct PiecewiseParam
{
	void reset(const Mesh *mesh, uint32_t faceCount)
	{
		m_mesh = mesh;
		m_faceCount = faceCount;
		const uint32_t vertexCount = m_mesh->vertexCount();
		m_texcoords.resize(vertexCount);
		m_patch.reserve(m_faceCount);
		m_candidates.reserve(m_faceCount);
		m_faceInAnyPatch.resize(m_faceCount);
		m_faceInAnyPatch.zeroOutMemory();
		m_faceInvalid.resize(m_faceCount);
		m_faceInPatch.resize(m_faceCount);
		m_vertexInPatch.resize(vertexCount);
		m_faceToCandidate.resize(m_faceCount);
	}

	ConstArrayView<uint32_t> chartFaces() const { return m_patch; }
	const Vector2 *texcoords() const { return m_texcoords.data(); }

	bool computeChart()
	{
		// Clear per-patch state.
		m_patch.clear();
		m_candidates.clear();
		m_faceToCandidate.zeroOutMemory();
		m_faceInvalid.zeroOutMemory();
		m_faceInPatch.zeroOutMemory();
		m_vertexInPatch.zeroOutMemory();
		// Add the seed face (first unassigned face) to the patch.
		uint32_t seed = UINT32_MAX;
		for (uint32_t f = 0; f < m_faceCount; f++) {
			if (m_faceInAnyPatch.get(f))
				continue;
			seed = f;
			// Add all 3 vertices.
			Vector2 texcoords[3];
			orthoProjectFace(seed, texcoords);
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t vertex = m_mesh->vertexAt(seed * 3 + i);
				m_vertexInPatch.set(vertex);
				m_texcoords[vertex] = texcoords[i];
			}
			addFaceToPatch(seed);
			// Initialize the boundary grid.
			m_boundaryGrid.reset(m_texcoords.data(), m_mesh->indices());
			for (Mesh::FaceEdgeIterator it(m_mesh, seed); !it.isDone(); it.advance())
				m_boundaryGrid.append(it.edge());
			break;
		}
		if (seed == UINT32_MAX)
			return false;
		for (;;) {
			// Find the candidate with the lowest cost.
			float lowestCost = FLT_MAX;
			Candidate *bestCandidate = nullptr;
			for (uint32_t i = 0; i < m_candidates.size(); i++) {
				Candidate *candidate = m_candidates[i];
				if (candidate->maxCost < lowestCost) {
					lowestCost = candidate->maxCost;
					bestCandidate = candidate;
				}
			}
			if (!bestCandidate)
				break;
			XA_DEBUG_ASSERT(!bestCandidate->prev); // Must be head of linked candidates.
			// Compute the position by averaging linked candidates (candidates that share the same free vertex).
			Vector2 position(0.0f);
			uint32_t n = 0;
			for (CandidateIterator it(bestCandidate); !it.isDone(); it.advance()) {
				position += it.current()->position;
				n++;
			}
			position *= 1.0f / (float)n;
			const uint32_t freeVertex = bestCandidate->vertex;
			XA_DEBUG_ASSERT(!isNan(position.x));
			XA_DEBUG_ASSERT(!isNan(position.y));
			m_texcoords[freeVertex] = position;
			// Check for flipped faces. This is also done when candidates are first added, but the averaged position of the free vertex is different now, so check again.
			bool invalid = false;
			for (CandidateIterator it(bestCandidate); !it.isDone(); it.advance()) {
				const uint32_t vertex0 = m_mesh->vertexAt(meshEdgeIndex0(it.current()->patchEdge));
				const uint32_t vertex1 = m_mesh->vertexAt(meshEdgeIndex1(it.current()->patchEdge));
				const float freeVertexOrient = orientToEdge(m_texcoords[vertex0], m_texcoords[vertex1], position);
				if ((it.current()->patchVertexOrient < 0.0f && freeVertexOrient < 0.0f) || (it.current()->patchVertexOrient > 0.0f && freeVertexOrient > 0.0f)) {
					invalid = true;
					break;
				}
			}
			// Check for boundary intersection.
			if (!invalid) {
				XA_PROFILE_START(parameterizeChartsPiecewiseBoundaryIntersection)
				// Test candidate edges that would form part of the new patch boundary.
				// Ignore boundary edges that would become internal if the candidate faces were added to the patch.
				Array<uint32_t> newBoundaryEdges, ignoreEdges;
				for (CandidateIterator candidateIt(bestCandidate); !candidateIt.isDone(); candidateIt.advance()) {
					for (Mesh::FaceEdgeIterator it(m_mesh, candidateIt.current()->face); !it.isDone(); it.advance()) {
						const uint32_t oface = it.oppositeFace();
						if (oface == UINT32_MAX || oface >= m_faceCount || !m_faceInPatch.get(oface))
							newBoundaryEdges.push_back(it.edge());
						if (oface != UINT32_MAX && oface < m_faceCount && m_faceInPatch.get(oface))
							ignoreEdges.push_back(it.oppositeEdge());
					}
				}
				invalid = m_boundaryGrid.intersect(m_mesh->epsilon(), newBoundaryEdges, ignoreEdges);
				XA_PROFILE_END(parameterizeChartsPiecewiseBoundaryIntersection)
			}
			if (invalid) {
				// Mark all faces of linked candidates as invalid.
				for (CandidateIterator it(bestCandidate); !it.isDone(); it.advance())
					m_faceInvalid.set(it.current()->face);
				removeLinkedCandidates(bestCandidate);
			} else {
				// Add vertex to the patch.
				m_vertexInPatch.set(freeVertex);
				// Add faces to the patch.
				for (CandidateIterator it(bestCandidate); !it.isDone(); it.advance())
					addFaceToPatch(it.current()->face);
				// Successfully added candidate face(s) to patch.
				removeLinkedCandidates(bestCandidate);
				// Reset the grid with all edges on the patch boundary.
				XA_PROFILE_START(parameterizeChartsPiecewiseBoundaryIntersection)
				m_boundaryGrid.reset(m_texcoords.data(), m_mesh->indices());
				for (uint32_t i = 0; i < m_patch.size(); i++) {
					for (Mesh::FaceEdgeIterator it(m_mesh, m_patch[i]); !it.isDone(); it.advance()) {
						const uint32_t oface = it.oppositeFace();
						if (oface == UINT32_MAX || oface >= m_faceCount || !m_faceInPatch.get(oface))
							m_boundaryGrid.append(it.edge());
					}
				}
				XA_PROFILE_END(parameterizeChartsPiecewiseBoundaryIntersection)
			}
		}
		return true;
	}

private:
	struct Candidate
	{
		uint32_t face, vertex;
		Candidate *prev, *next; // The previous/next candidate with the same vertex.
		Vector2 position;
		float cost;
		float maxCost; // Of all linked candidates.
		uint32_t patchEdge;
		float patchVertexOrient;
	};

	struct CandidateIterator
	{
		CandidateIterator(Candidate *head) : m_current(head) { XA_DEBUG_ASSERT(!head->prev); }
		void advance() { if (m_current != nullptr) { m_current = m_current->next; } }
		bool isDone() const { return !m_current; }
		Candidate *current() { return m_current; }

	private:
		Candidate *m_current;
	};

	const Mesh *m_mesh;
	uint32_t m_faceCount;
	Array<Vector2> m_texcoords;
	BitArray m_faceInAnyPatch; // Face is in a previous chart patch or the current patch.
	Array<Candidate *> m_candidates; // Incident faces to the patch.
	Array<Candidate *> m_faceToCandidate;
	Array<uint32_t> m_patch; // The current chart patch.
	BitArray m_faceInPatch, m_vertexInPatch; // Face/vertex is in the current patch.
	BitArray m_faceInvalid; // Face cannot be added to the patch - flipped, cost too high or causes boundary intersection.
	UniformGrid2 m_boundaryGrid;

	void addFaceToPatch(uint32_t face)
	{
		XA_DEBUG_ASSERT(!m_faceInPatch.get(face));
		XA_DEBUG_ASSERT(!m_faceInAnyPatch.get(face));
		m_patch.push_back(face);
		m_faceInPatch.set(face);
		m_faceInAnyPatch.set(face);
		// Find new candidate faces on the patch incident to the newly added face.
		for (Mesh::FaceEdgeIterator it(m_mesh, face); !it.isDone(); it.advance()) {
			const uint32_t oface = it.oppositeFace();
			if (oface == UINT32_MAX || oface >= m_faceCount || m_faceInAnyPatch.get(oface) || m_faceToCandidate[oface])
				continue;
			// Found an active edge on the patch front.
			// Find the free vertex (the vertex that isn't on the active edge).
			// Compute the orientation of the other patch face vertex to the active edge.
			uint32_t freeVertex = UINT32_MAX;
			float orient = 0.0f;
			for (uint32_t j = 0; j < 3; j++) {
				const uint32_t vertex = m_mesh->vertexAt(oface * 3 + j);
				if (vertex != it.vertex0() && vertex != it.vertex1()) {
					freeVertex = vertex;
					orient = orientToEdge(m_texcoords[it.vertex0()], m_texcoords[it.vertex1()], m_texcoords[m_mesh->vertexAt(face * 3 + j)]);
					break;
				}
			}
			XA_DEBUG_ASSERT(freeVertex != UINT32_MAX);
			// If the free vertex is already in the patch, the face is enclosed by the patch. Add the face to the patch - don't need to assign texcoords.
			/*if (m_vertexInPatch.get(freeVertex)) {
				freeVertex = UINT32_MAX;
				addFaceToPatch(oface, false);
				continue;
			}*/
			// Check this here rather than above so faces enclosed by the patch are always added.
			if (m_faceInvalid.get(oface))
				continue;
			addCandidateFace(it.edge(), orient, oface, it.oppositeEdge(), freeVertex);
		}
	}

	void addCandidateFace(uint32_t patchEdge, float patchVertexOrient, uint32_t face, uint32_t edge, uint32_t freeVertex)
	{
		XA_DEBUG_ASSERT(!m_faceToCandidate[face]);
		Vector2 texcoords[3];
		orthoProjectFace(face, texcoords);
		// Find corresponding vertices between the patch edge and candidate edge.
		const uint32_t vertex0 = m_mesh->vertexAt(meshEdgeIndex0(patchEdge));
		const uint32_t vertex1 = m_mesh->vertexAt(meshEdgeIndex1(patchEdge));
		uint32_t localVertex0 = UINT32_MAX, localVertex1 = UINT32_MAX, localFreeVertex = UINT32_MAX;
		for (uint32_t i = 0; i < 3; i++) {
			const uint32_t vertex = m_mesh->vertexAt(face * 3 + i);
			if (vertex == m_mesh->vertexAt(meshEdgeIndex1(edge)))
				localVertex0 = i;
			else if (vertex == m_mesh->vertexAt(meshEdgeIndex0(edge)))
				localVertex1 = i;
			else
				localFreeVertex = i;
		}
		// Scale orthogonal projection to match the patch edge.
		const Vector2 patchEdgeVec = m_texcoords[vertex1] - m_texcoords[vertex0];
		const Vector2 localEdgeVec = texcoords[localVertex1] - texcoords[localVertex0];
		const float len1 = length(patchEdgeVec);
		const float len2 = length(localEdgeVec);
		if (len1 <= 0.0f || len2 <= 0.0f)
			return; // Zero length edge.
		const float scale = len1 / len2;
		for (uint32_t i = 0; i < 3; i++)
			texcoords[i] *= scale;
		// Translate to the first vertex on the patch edge.
		const Vector2 translate = m_texcoords[vertex0] - texcoords[localVertex0];
		for (uint32_t i = 0; i < 3; i++)
			texcoords[i] += translate;
		// Compute the angle between the patch edge and the corresponding local edge.
		const float angle = atan2f(patchEdgeVec.y, patchEdgeVec.x) - atan2f(localEdgeVec.y, localEdgeVec.x);
		// Rotate so the patch edge and the corresponding local edge occupy the same space.
		for (uint32_t i = 0; i < 3; i++) {
			if (i == localVertex0)
				continue;
			Vector2 &uv = texcoords[i];
			uv -= texcoords[localVertex0]; // Rotate around the first vertex.
			const float c = cosf(angle);
			const float s = sinf(angle);
			const float x = uv.x * c - uv.y * s;
			const float y = uv.y * c + uv.x * s;
			uv.x = x + texcoords[localVertex0].x;
			uv.y = y + texcoords[localVertex0].y;
		}
		if (isNan(texcoords[localFreeVertex].x) || isNan(texcoords[localFreeVertex].y))
			return;
		// Check for local overlap (flipped triangle).
		// The patch face vertex that isn't on the active edge and the free vertex should be oriented on opposite sides to the active edge.
		const float freeVertexOrient = orientToEdge(m_texcoords[vertex0], m_texcoords[vertex1], texcoords[localFreeVertex]);
		if ((patchVertexOrient < 0.0f && freeVertexOrient < 0.0f) || (patchVertexOrient > 0.0f && freeVertexOrient > 0.0f)) {
			m_faceInvalid.set(face);
			return;
		}
		const float stretch = computeStretch(m_mesh->position(vertex0), m_mesh->position(vertex1), m_mesh->position(freeVertex), texcoords[0], texcoords[1], texcoords[2]);
		if (stretch >= FLT_MAX) {
			m_faceInvalid.set(face);
			return;
		}
		const float cost = fabsf(stretch - 1.0f);
#if 0
		if (cost > 0.25f) {
			m_faceInvalid.set(face);
			return;
		}
#endif
		// Add the candidate.
		Candidate *candidate = XA_ALLOC(MemTag::Default, Candidate);
		candidate->face = face;
		candidate->vertex = freeVertex;
		candidate->position = texcoords[localFreeVertex];
		candidate->prev = candidate->next = nullptr;
		candidate->cost = candidate->maxCost = cost;
		candidate->patchEdge = patchEdge;
		candidate->patchVertexOrient = patchVertexOrient;
		m_candidates.push_back(candidate);
		m_faceToCandidate[face] = candidate;
		// Link with candidates that share the same vertex. Append to tail.
		for (uint32_t i = 0; i < m_candidates.size() - 1; i++) {
			if (m_candidates[i]->vertex == candidate->vertex) {
				Candidate *tail = m_candidates[i];
				for (;;) {
					if (tail->next)
						tail = tail->next;
					else
						break;
				}
				candidate->prev = tail;
				candidate->next = nullptr;
				tail->next = candidate;
				break;
			}
		}
		// Set max cost for linked candidates.
		Candidate *head = linkedCandidateHead(candidate);
		float maxCost = 0.0f;
		for (CandidateIterator it(head); !it.isDone(); it.advance())
			maxCost = max(maxCost, it.current()->cost);
		for (CandidateIterator it(head); !it.isDone(); it.advance())
			it.current()->maxCost = maxCost;
	}

	Candidate *linkedCandidateHead(Candidate *candidate)
	{
		Candidate *current = candidate;
		for (;;) {
			if (!current->prev)
				break;
			current = current->prev;
		}
		return current;
	}

	void removeLinkedCandidates(Candidate *head)
	{
		XA_DEBUG_ASSERT(!head->prev);
		Candidate *current = head;
		while (current) {
			Candidate *next = current->next;
			m_faceToCandidate[current->face] = nullptr;
			for (uint32_t i = 0; i < m_candidates.size(); i++) {
				if (m_candidates[i] == current) {
					m_candidates.removeAt(i);
					break;
				}
			}
			XA_FREE(current);
			current = next;
		}
	}

	void orthoProjectFace(uint32_t face, Vector2 *texcoords) const
	{
		const Vector3 normal = m_mesh->computeFaceNormal(face);
		const Vector3 tangent = normalize(m_mesh->position(m_mesh->vertexAt(face * 3 + 1)) - m_mesh->position(m_mesh->vertexAt(face * 3 + 0)), kEpsilon);
		const Vector3 bitangent = cross(normal, tangent);
		for (uint32_t i = 0; i < 3; i++) {
			const Vector3 &pos = m_mesh->position(m_mesh->vertexAt(face * 3 + i));
			texcoords[i] = Vector2(dot(tangent, pos), dot(bitangent, pos));
		}
	}

	float parametricArea(const Vector2 *texcoords) const
	{
		const Vector2 &v1 = texcoords[0];
		const Vector2 &v2 = texcoords[1];
		const Vector2 &v3 = texcoords[2];
		return ((v2.x - v1.x) * (v3.y - v1.y) - (v3.x - v1.x) * (v2.y - v1.y)) * 0.5f;
	}

	float computeStretch(Vector3 p1, Vector3 p2, Vector3 p3, Vector2 t1, Vector2 t2, Vector2 t3) const
	{
		float parametricArea = ((t2.y - t1.y) * (t3.x - t1.x) - (t3.y - t1.y) * (t2.x - t1.x)) * 0.5f;
		if (isZero(parametricArea, kAreaEpsilon))
			return FLT_MAX;
		if (parametricArea < 0.0f)
			parametricArea = fabsf(parametricArea);
		const float geometricArea = length(cross(p2 - p1, p3 - p1)) * 0.5f;
		if (parametricArea <= geometricArea)
			return parametricArea / geometricArea;
		else
			return geometricArea / parametricArea;
	}

	// Return value is positive if the point is one side of the edge, negative if on the other side.
	float orientToEdge(Vector2 edgeVertex0, Vector2 edgeVertex1, Vector2 point) const
	{
		return (edgeVertex0.x - point.x) * (edgeVertex1.y - point.y) - (edgeVertex0.y - point.y) * (edgeVertex1.x - point.x);
	}
};
#endif

// Estimate quality of existing parameterization.
struct Quality
{
	// computeBoundaryIntersection
	bool boundaryIntersection = false;

	// computeFlippedFaces
	uint32_t totalTriangleCount = 0;
	uint32_t flippedTriangleCount = 0;
	uint32_t zeroAreaTriangleCount = 0;

	// computeMetrics
	float totalParametricArea = 0.0f;
	float totalGeometricArea = 0.0f;
	float stretchMetric = 0.0f;
	float maxStretchMetric = 0.0f;
	float conformalMetric = 0.0f;
	float authalicMetric = 0.0f;

	void computeBoundaryIntersection(const Mesh *mesh, UniformGrid2 &boundaryGrid)
	{
		const Array<uint32_t> &boundaryEdges = mesh->boundaryEdges();
		const uint32_t boundaryEdgeCount = boundaryEdges.size();
		boundaryGrid.reset(mesh->texcoords(), mesh->indices(), boundaryEdgeCount);
		for (uint32_t i = 0; i < boundaryEdgeCount; i++)
			boundaryGrid.append(boundaryEdges[i]);
		boundaryIntersection = boundaryGrid.intersect(mesh->epsilon());
#if XA_DEBUG_EXPORT_BOUNDARY_GRID
		static int exportIndex = 0;
		char filename[256];
		XA_SPRINTF(filename, sizeof(filename), "debug_boundary_grid_%03d.tga", exportIndex);
		boundaryGrid.debugExport(filename);
		exportIndex++;
#endif
	}

	void computeFlippedFaces(const Mesh *mesh, uint32_t faceCount, Array<uint32_t> *flippedFaces)
	{
		totalTriangleCount = flippedTriangleCount = zeroAreaTriangleCount = 0;
		if (flippedFaces)
			flippedFaces->clear();
		for (uint32_t f = 0; f < faceCount; f++) {
			Vector2 texcoord[3];
			for (int i = 0; i < 3; i++) {
				const uint32_t v = mesh->vertexAt(f * 3 + i);
				texcoord[i] = mesh->texcoord(v);
			}
			totalTriangleCount++;
			const float t1 = texcoord[0].x;
			const float s1 = texcoord[0].y;
			const float t2 = texcoord[1].x;
			const float s2 = texcoord[1].y;
			const float t3 = texcoord[2].x;
			const float s3 = texcoord[2].y;
			const float parametricArea = ((s2 - s1) * (t3 - t1) - (s3 - s1) * (t2 - t1)) * 0.5f;
			if (isZero(parametricArea, kAreaEpsilon)) {
				zeroAreaTriangleCount++;
				continue;
			}
			if (parametricArea < 0.0f) {
				// Count flipped triangles.
				flippedTriangleCount++;
				if (flippedFaces)
					flippedFaces->push_back(f);
			}
		}
		if (flippedTriangleCount + zeroAreaTriangleCount == totalTriangleCount) {
			// If all triangles are flipped, then none are.
			if (flippedFaces)
				flippedFaces->clear();
			flippedTriangleCount = 0;
		}
		if (flippedTriangleCount > totalTriangleCount / 2)
		{
			// If more than half the triangles are flipped, reverse the flipped / not flipped classification.
			flippedTriangleCount = totalTriangleCount - flippedTriangleCount;
			if (flippedFaces) {
				Array<uint32_t> temp;
				flippedFaces->copyTo(temp);
				flippedFaces->clear();
				for (uint32_t f = 0; f < faceCount; f++) {
					bool match = false;
					for (uint32_t ff = 0; ff < temp.size(); ff++) {
						if (temp[ff] == f) {
							match = true;
							break;
						}
					}
					if (!match)
						flippedFaces->push_back(f);
				}
			}
		}
	}

	void computeMetrics(const Mesh *mesh, uint32_t faceCount)
	{
		totalGeometricArea = totalParametricArea = 0.0f;
		stretchMetric = maxStretchMetric = conformalMetric = authalicMetric = 0.0f;
		for (uint32_t f = 0; f < faceCount; f++) {
			Vector3 pos[3];
			Vector2 texcoord[3];
			for (int i = 0; i < 3; i++) {
				const uint32_t v = mesh->vertexAt(f * 3 + i);
				pos[i] = mesh->position(v);
				texcoord[i] = mesh->texcoord(v);
			}
			// Evaluate texture stretch metric. See:
			// - "Texture Mapping Progressive Meshes", Sander, Snyder, Gortler & Hoppe
			// - "Mesh Parameterization: Theory and Practice", Siggraph'07 Course Notes, Hormann, Levy & Sheffer.
			const float t1 = texcoord[0].x;
			const float s1 = texcoord[0].y;
			const float t2 = texcoord[1].x;
			const float s2 = texcoord[1].y;
			const float t3 = texcoord[2].x;
			const float s3 = texcoord[2].y;
			float parametricArea = ((s2 - s1) * (t3 - t1) - (s3 - s1) * (t2 - t1)) * 0.5f;
			if (isZero(parametricArea, kAreaEpsilon))
				continue;
			if (parametricArea < 0.0f)
				parametricArea = fabsf(parametricArea);
			const float geometricArea = length(cross(pos[1] - pos[0], pos[2] - pos[0])) / 2;
			const Vector3 Ss = (pos[0] * (t2 - t3) + pos[1] * (t3 - t1) + pos[2] * (t1 - t2)) / (2 * parametricArea);
			const Vector3 St = (pos[0] * (s3 - s2) + pos[1] * (s1 - s3) + pos[2] * (s2 - s1)) / (2 * parametricArea);
			const float a = dot(Ss, Ss); // E
			const float b = dot(Ss, St); // F
			const float c = dot(St, St); // G
										 // Compute eigen-values of the first fundamental form:
			const float sigma1 = sqrtf(0.5f * max(0.0f, a + c - sqrtf(square(a - c) + 4 * square(b)))); // gamma uppercase, min eigenvalue.
			const float sigma2 = sqrtf(0.5f * max(0.0f, a + c + sqrtf(square(a - c) + 4 * square(b)))); // gamma lowercase, max eigenvalue.
			XA_ASSERT(sigma2 > sigma1 || equal(sigma1, sigma2, kEpsilon));
			// isometric: sigma1 = sigma2 = 1
			// conformal: sigma1 / sigma2 = 1
			// authalic: sigma1 * sigma2 = 1
			const float rmsStretch = sqrtf((a + c) * 0.5f);
			const float rmsStretch2 = sqrtf((square(sigma1) + square(sigma2)) * 0.5f);
			XA_DEBUG_ASSERT(equal(rmsStretch, rmsStretch2, 0.01f));
			XA_UNUSED(rmsStretch2);
			stretchMetric += square(rmsStretch) * geometricArea;
			maxStretchMetric = max(maxStretchMetric, sigma2);
			if (!isZero(sigma1, 0.000001f)) {
				// sigma1 is zero when geometricArea is zero.
				conformalMetric += (sigma2 / sigma1) * geometricArea;
			}
			authalicMetric += (sigma1 * sigma2) * geometricArea;
			// Accumulate total areas.
			totalGeometricArea += geometricArea;
			totalParametricArea += parametricArea;
		}
		XA_DEBUG_ASSERT(isFinite(totalParametricArea) && totalParametricArea >= 0);
		XA_DEBUG_ASSERT(isFinite(totalGeometricArea) && totalGeometricArea >= 0);
		XA_DEBUG_ASSERT(isFinite(stretchMetric));
		XA_DEBUG_ASSERT(isFinite(maxStretchMetric));
		XA_DEBUG_ASSERT(isFinite(conformalMetric));
		XA_DEBUG_ASSERT(isFinite(authalicMetric));
		if (totalGeometricArea > 0.0f) {
			const float normFactor = sqrtf(totalParametricArea / totalGeometricArea);
			stretchMetric = sqrtf(stretchMetric / totalGeometricArea) * normFactor;
			maxStretchMetric  *= normFactor;
			conformalMetric = sqrtf(conformalMetric / totalGeometricArea);
			authalicMetric = sqrtf(authalicMetric / totalGeometricArea);
		}
	}
};

struct ChartWarningFlags
{
	enum Enum
	{
		CloseHolesFailed = 1<<1,
		FixTJunctionsDuplicatedEdge = 1<<2,
		FixTJunctionsFailed = 1<<3,
		TriangulateDuplicatedEdge = 1<<4,
	};
};

struct ChartCtorBuffers
{
	Array<uint32_t> chartMeshIndices;
	Array<uint32_t> unifiedMeshIndices;
	Array<uint32_t> boundaryLoops;
};

class Chart
{
public:
	Chart(ChartCtorBuffers &buffers, const ParameterizeOptions &options, const Basis &basis, ConstArrayView<uint32_t> faces, const Mesh *sourceMesh, uint32_t chartGroupId, uint32_t chartId) : m_basis(basis), m_mesh(nullptr), m_unifiedMesh(nullptr), m_unmodifiedUnifiedMesh(nullptr), m_type(ChartType::LSCM), m_warningFlags(0), m_closedHolesCount(0), m_fixedTJunctionsCount(0), m_isInvalid(false)
	{
		XA_UNUSED(chartGroupId);
		XA_UNUSED(chartId);
		m_faceToSourceFaceMap.copyFrom(faces.data, faces.length);
		const uint32_t approxVertexCount = min(faces.length * 3, sourceMesh->vertexCount());
		m_mesh = XA_NEW_ARGS(MemTag::Mesh, Mesh, sourceMesh->epsilon(), approxVertexCount, faces.length);
		m_unifiedMesh = XA_NEW_ARGS(MemTag::Mesh, Mesh, sourceMesh->epsilon(), approxVertexCount, faces.length);
		HashMap<uint32_t, PassthroughHash<uint32_t>> sourceVertexToUnifiedVertexMap(MemTag::Mesh, approxVertexCount), sourceVertexToChartVertexMap(MemTag::Mesh, approxVertexCount);
		// Add vertices.
		const uint32_t faceCount = m_initialFaceCount = faces.length;
		for (uint32_t f = 0; f < faceCount; f++) {
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t sourceVertex = sourceMesh->vertexAt(m_faceToSourceFaceMap[f] * 3 + i);
				const uint32_t sourceUnifiedVertex = sourceMesh->firstColocal(sourceVertex);
				uint32_t unifiedVertex = sourceVertexToUnifiedVertexMap.get(sourceUnifiedVertex);
				if (unifiedVertex == UINT32_MAX) {
					unifiedVertex = sourceVertexToUnifiedVertexMap.add(sourceUnifiedVertex);
					m_unifiedMesh->addVertex(sourceMesh->position(sourceVertex));
				}
				if (sourceVertexToChartVertexMap.get(sourceVertex) == UINT32_MAX) {
					sourceVertexToChartVertexMap.add(sourceVertex);
					m_vertexToSourceVertexMap.push_back(sourceVertex);
					m_chartVertexToUnifiedVertexMap.push_back(unifiedVertex);
					m_mesh->addVertex(sourceMesh->position(sourceVertex), Vector3(0.0f), sourceMesh->texcoord(sourceVertex));
				}
			}
		}
		// Add faces.
		for (uint32_t f = 0; f < faceCount; f++) {
			uint32_t indices[3], unifiedIndices[3];
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t sourceVertex = sourceMesh->vertexAt(m_faceToSourceFaceMap[f] * 3 + i);
				const uint32_t sourceUnifiedVertex = sourceMesh->firstColocal(sourceVertex);
				indices[i] = sourceVertexToChartVertexMap.get(sourceVertex);
				XA_DEBUG_ASSERT(indices[i] != UINT32_MAX);
				unifiedIndices[i] = sourceVertexToUnifiedVertexMap.get(sourceUnifiedVertex);
				XA_DEBUG_ASSERT(unifiedIndices[i] != UINT32_MAX);
			}
			Mesh::AddFaceResult::Enum result = m_mesh->addFace(indices);
			XA_UNUSED(result);
			XA_DEBUG_ASSERT(result == Mesh::AddFaceResult::OK);
#if XA_DEBUG
			// Unifying colocals may create degenerate edges. e.g. if two triangle vertices are colocal.
			for (int i = 0; i < 3; i++) {
				const uint32_t index1 = unifiedIndices[i];
				const uint32_t index2 = unifiedIndices[(i + 1) % 3];
				XA_DEBUG_ASSERT(index1 != index2);
			}
#endif
			result = m_unifiedMesh->addFace(unifiedIndices);
			XA_UNUSED(result);
			XA_DEBUG_ASSERT(result == Mesh::AddFaceResult::OK);
		}
		m_mesh->createBoundaries(); // For AtlasPacker::computeBoundingBox
		m_mesh->destroyEdgeMap(); // Only needed it for createBoundaries.
		m_unifiedMesh->createBoundaries();
		if (meshIsPlanar(*m_unifiedMesh)) {
			m_type = ChartType::Planar;
			return;
		}
		m_unifiedMesh->linkBoundaries();
#if XA_DEBUG_EXPORT_OBJ_BEFORE_FIX_TJUNCTION
		m_unifiedMesh->writeObjFile("debug_before_fix_tjunction.obj");
#endif
		bool duplicatedEdge = false, failed = false;
		if (options.fixTJunctions) {
			XA_PROFILE_START(fixChartMeshTJunctions)
			Mesh *fixedUnifiedMesh = meshFixTJunctions(*m_unifiedMesh, &duplicatedEdge, &failed, &m_fixedTJunctionsCount);
			XA_PROFILE_END(fixChartMeshTJunctions)
			if (fixedUnifiedMesh) {
				if (duplicatedEdge)
					m_warningFlags |= ChartWarningFlags::FixTJunctionsDuplicatedEdge;
				if (failed)
					m_warningFlags |= ChartWarningFlags::FixTJunctionsFailed;
				m_unmodifiedUnifiedMesh = m_unifiedMesh;
				m_unifiedMesh = fixedUnifiedMesh;
				m_unifiedMesh->createBoundaries();
				m_unifiedMesh->linkBoundaries();
				m_initialFaceCount = m_unifiedMesh->faceCount(); // Fixing t-junctions rewrites faces.
			}
		}
		if (options.closeHoles) {
			// See if there are any holes that need closing.
			Array<uint32_t> &boundaryLoops = buffers.boundaryLoops;
			meshGetBoundaryLoops(*m_unifiedMesh, boundaryLoops);
			if (boundaryLoops.size() > 1) {
#if XA_DEBUG_EXPORT_OBJ_CLOSE_HOLES_ERROR
				const uint32_t faceCountBeforeHolesClosed = m_unifiedMesh->faceCount();
#endif
				// Closing the holes is not always the best solution and does not fix all the problems.
				// We need to do some analysis of the holes and the genus to:
				// - Find cuts that reduce genus.
				// - Find cuts to connect holes.
				// - Use minimal spanning trees or seamster.
				XA_PROFILE_START(closeChartMeshHoles)
				uint32_t holeCount = 0;
#if XA_DEBUG_EXPORT_OBJ_CLOSE_HOLES_ERROR
				Array<uint32_t> holeFaceCounts;
				failed = !meshCloseHoles(m_unifiedMesh, boundaryLoops, m_basis.normal, &holeFaceCounts);
#else
				failed = !meshCloseHoles(m_unifiedMesh, boundaryLoops, m_basis.normal, &holeCount, nullptr);
#endif
				XA_PROFILE_END(closeChartMeshHoles)
				m_unifiedMesh->createBoundaries();
				m_unifiedMesh->linkBoundaries();
				meshGetBoundaryLoops(*m_unifiedMesh, boundaryLoops);
				if (failed || boundaryLoops.size() > 1)
					m_warningFlags |= ChartWarningFlags::CloseHolesFailed;
				m_closedHolesCount = holeCount;
#if XA_DEBUG_EXPORT_OBJ_CLOSE_HOLES_ERROR
				if (m_warningFlags & ChartWarningFlags::CloseHolesFailed) {
					char filename[256];
					XA_SPRINTF(filename, sizeof(filename), "debug_mesh_%03u_chartgroup_%03u_chart_%03u_close_holes_error.obj", sourceMesh->id(), chartGroupId, chartId);
					FILE *file;
					XA_FOPEN(file, filename, "w");
					if (file) {
						m_unifiedMesh->writeObjVertices(file);
						fprintf(file, "s off\n");
						fprintf(file, "o object\n");
						for (uint32_t i = 0; i < faceCountBeforeHolesClosed; i++)
							m_unifiedMesh->writeObjFace(file, i);
						uint32_t face = faceCountBeforeHolesClosed;
						for (uint32_t i = 0; i < holeFaceCounts.size(); i++) {
							fprintf(file, "s off\n");
							fprintf(file, "o hole%u\n", i);
							for (uint32_t j = 0; j < holeFaceCounts[i]; j++) {
								m_unifiedMesh->writeObjFace(file, face);
								face++;
							}
						}
						m_unifiedMesh->writeObjBoundaryEges(file);
						m_unifiedMesh->writeObjLinkedBoundaries(file);
						fclose(file);
					}
				}
#endif
			}
		}
	}

#if XA_RECOMPUTE_CHARTS
	Chart(ChartCtorBuffers &buffers, const Chart *parent, const Mesh *parentMesh, ConstArrayView<uint32_t> faces, const Vector2 *texcoords, const Mesh *sourceMesh) : m_mesh(nullptr), m_unifiedMesh(nullptr), m_unmodifiedUnifiedMesh(nullptr), m_type(ChartType::Piecewise), m_warningFlags(0), m_closedHolesCount(0), m_fixedTJunctionsCount(0), m_isInvalid(false)
	{
		const uint32_t faceCount = m_initialFaceCount = faces.length;
		m_faceToSourceFaceMap.resize(faceCount);
		for (uint32_t i = 0; i < faceCount; i++)
			m_faceToSourceFaceMap[i] = parent->m_faceToSourceFaceMap[faces[i]]; // Map faces to parent chart source mesh.
		// Copy face indices.
		m_mesh = XA_NEW_ARGS(MemTag::Mesh, Mesh, sourceMesh->epsilon(), m_faceToSourceFaceMap.size() * 3, m_faceToSourceFaceMap.size());
		Array<uint32_t> &chartMeshIndices = buffers.chartMeshIndices;
		chartMeshIndices.resize(sourceMesh->vertexCount());
		chartMeshIndices.fillBytes(0xff);
		// Add vertices.
		for (uint32_t f = 0; f < faceCount; f++) {
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t vertex = sourceMesh->vertexAt(m_faceToSourceFaceMap[f] * 3 + i);
				const uint32_t parentVertex = parentMesh->vertexAt(faces[f] * 3 + i);
				if (chartMeshIndices[vertex] == (uint32_t)~0) {
					chartMeshIndices[vertex] = m_mesh->vertexCount();
					m_vertexToSourceVertexMap.push_back(vertex);
					m_mesh->addVertex(sourceMesh->position(vertex), Vector3(0.0f), texcoords[parentVertex]);
				}
			}
		}
		// Add faces.
		for (uint32_t f = 0; f < faceCount; f++) {
			uint32_t indices[3];
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t vertex = sourceMesh->vertexAt(m_faceToSourceFaceMap[f] * 3 + i);
				indices[i] = chartMeshIndices[vertex];
			}
			Mesh::AddFaceResult::Enum result = m_mesh->addFace(indices);
			XA_UNUSED(result);
			XA_DEBUG_ASSERT(result == Mesh::AddFaceResult::OK);
		}
		m_mesh->createBoundaries(); // For AtlasPacker::computeBoundingBox
		m_mesh->destroyEdgeMap(); // Only needed it for createBoundaries.
		// Need to store texcoords for backup/restore so packing can be run multiple times.
		backupTexcoords();
	}
#endif

	~Chart()
	{
		if (m_mesh) {
			m_mesh->~Mesh();
			XA_FREE(m_mesh);
		}
		destroyUnifiedMesh();
	}

	bool isInvalid() const { return m_isInvalid; }
	ChartType::Enum type() const { return m_type; }
	uint32_t warningFlags() const { return m_warningFlags; }
	uint32_t closedHolesCount() const { return m_closedHolesCount; }
	uint32_t fixedTJunctionsCount() const { return m_fixedTJunctionsCount; }
	const Quality &quality() const { return m_quality; }
	uint32_t initialFaceCount() const { return m_initialFaceCount; }
#if XA_DEBUG_EXPORT_OBJ_INVALID_PARAMETERIZATION
	const Array<uint32_t> &paramFlippedFaces() const { return m_paramFlippedFaces; }
#endif
	uint32_t mapFaceToSourceFace(uint32_t i) const { return m_faceToSourceFaceMap[i]; }
	uint32_t mapChartVertexToSourceVertex(uint32_t i) const { return m_vertexToSourceVertexMap[i]; }
	const Mesh *mesh() const { return m_mesh; }
	Mesh *mesh() { return m_mesh; }
	const Mesh *unifiedMesh() const { return m_unifiedMesh; }
	const Mesh *unmodifiedUnifiedMesh() const { return m_unmodifiedUnifiedMesh; }

	void parameterize(const ParameterizeOptions &options, UniformGrid2 &boundaryGrid)
	{
		XA_PROFILE_START(parameterizeChartsOrthogonal)
		{
			// Project vertices to plane.
			const uint32_t vertexCount = m_unifiedMesh->vertexCount();
			for (uint32_t i = 0; i < vertexCount; i++)
				m_unifiedMesh->texcoord(i) = Vector2(dot(m_basis.tangent, m_unifiedMesh->position(i)), dot(m_basis.bitangent, m_unifiedMesh->position(i)));
		}
		XA_PROFILE_END(parameterizeChartsOrthogonal)
		// Computing charts checks for flipped triangles and boundary intersection. Don't need to do that again here if chart is planar.
		if (m_type != ChartType::Planar) {
			XA_PROFILE_START(parameterizeChartsEvaluateQuality)
			m_quality.computeBoundaryIntersection(m_unifiedMesh, boundaryGrid);
			m_quality.computeFlippedFaces(m_unifiedMesh, m_initialFaceCount, nullptr);
			m_quality.computeMetrics(m_unifiedMesh, m_initialFaceCount);
			XA_PROFILE_END(parameterizeChartsEvaluateQuality)
			// Use orthogonal parameterization if quality is acceptable.
			if (!m_quality.boundaryIntersection && m_quality.flippedTriangleCount == 0 && m_quality.totalGeometricArea > 0.0f && m_quality.stretchMetric <= 1.1f && m_quality.maxStretchMetric <= 1.25f)
				m_type = ChartType::Ortho;
		}
		if (m_type == ChartType::LSCM) {
			XA_PROFILE_START(parameterizeChartsLSCM)
			if (options.func) {
				options.func(&m_unifiedMesh->position(0).x, &m_unifiedMesh->texcoord(0).x, m_unifiedMesh->vertexCount(), m_unifiedMesh->indices(), m_unifiedMesh->indexCount());
			}
			else
				computeLeastSquaresConformalMap(m_unifiedMesh);
			XA_PROFILE_END(parameterizeChartsLSCM)
			XA_PROFILE_START(parameterizeChartsEvaluateQuality)
			m_quality.computeBoundaryIntersection(m_unifiedMesh, boundaryGrid);
#if XA_DEBUG_EXPORT_OBJ_INVALID_PARAMETERIZATION
			m_quality.computeFlippedFaces(m_unifiedMesh, m_initialFaceCount, &m_paramFlippedFaces);
#else
			m_quality.computeFlippedFaces(m_unifiedMesh, m_initialFaceCount, nullptr);
#endif
			// Don't need to call computeMetrics here, that's only used in evaluateOrthoQuality to determine if quality is acceptable enough to use ortho projection.
			if (m_quality.boundaryIntersection || m_quality.flippedTriangleCount > 0)
				m_isInvalid = true;
			XA_PROFILE_END(parameterizeChartsEvaluateQuality)
		}
#if XA_DEBUG_ALL_CHARTS_INVALID
		m_isInvalid = true;
#endif
		// Transfer parameterization from unified mesh to chart mesh.
		const uint32_t vertexCount = m_mesh->vertexCount();
		for (uint32_t v = 0; v < vertexCount; v++)
			m_mesh->texcoord(v) = m_unifiedMesh->texcoord(m_chartVertexToUnifiedVertexMap[v]);
		// Can destroy unified mesh now.
		// But not if the parameterization is invalid, the unified mesh will be needed for PiecewiseParameterization.
		if (!m_isInvalid)
			destroyUnifiedMesh();
		// Need to store texcoords for backup/restore so packing can be run multiple times.
		backupTexcoords();
	}

	Vector2 computeParametricBounds() const
	{
		Vector2 minCorner(FLT_MAX, FLT_MAX);
		Vector2 maxCorner(-FLT_MAX, -FLT_MAX);
		const uint32_t vertexCount = m_mesh->vertexCount();
		for (uint32_t v = 0; v < vertexCount; v++) {
			minCorner = min(minCorner, m_mesh->texcoord(v));
			maxCorner = max(maxCorner, m_mesh->texcoord(v));
		}
		return (maxCorner - minCorner) * 0.5f;
	}

	void restoreTexcoords()
	{
		memcpy(m_mesh->texcoords(), m_backupTexcoords.data(), m_mesh->vertexCount() * sizeof(Vector2));
	}

private:
	void backupTexcoords()
	{
		m_backupTexcoords.resize(m_mesh->vertexCount());
		memcpy(m_backupTexcoords.data(), m_mesh->texcoords(), m_mesh->vertexCount() * sizeof(Vector2));
	}

	void destroyUnifiedMesh()
	{
		if (m_unifiedMesh) {
			m_unifiedMesh->~Mesh();
			XA_FREE(m_unifiedMesh);
			m_unifiedMesh = nullptr;
		}
		if (m_unmodifiedUnifiedMesh) {
			m_unmodifiedUnifiedMesh->~Mesh();
			XA_FREE(m_unmodifiedUnifiedMesh);
			m_unmodifiedUnifiedMesh = nullptr;
		}
		// Don't need this when unified meshes are destroyed.
		m_chartVertexToUnifiedVertexMap.destroy();
	}

	Basis m_basis;
	Mesh *m_mesh;
	Mesh *m_unifiedMesh;
	Mesh *m_unmodifiedUnifiedMesh; // Unified mesh before fixing t-junctions. Null if no t-junctions were fixed
	ChartType::Enum m_type;
	uint32_t m_warningFlags;
	uint32_t m_initialFaceCount; // Before fixing T-junctions and/or closing holes.
	uint32_t m_closedHolesCount, m_fixedTJunctionsCount;

	// List of faces of the source mesh that belong to this chart.
	Array<uint32_t> m_faceToSourceFaceMap;

	// Map vertices of the chart mesh to vertices of the source mesh.
	Array<uint32_t> m_vertexToSourceVertexMap;

	Array<uint32_t> m_chartVertexToUnifiedVertexMap;

	Array<Vector2> m_backupTexcoords;

	Quality m_quality;
#if XA_DEBUG_EXPORT_OBJ_INVALID_PARAMETERIZATION
	Array<uint32_t> m_paramFlippedFaces;
#endif
	bool m_isInvalid;
};

struct CreateAndParameterizeChartTaskArgs
{
	const Basis *basis;
	ThreadLocal<UniformGrid2> *boundaryGrid;
	Chart *chart; // output
	Array<Chart *> charts; // output (if more than one chart)
	ThreadLocal<ChartCtorBuffers> *chartBuffers;
	const Mesh *mesh;
	const ParameterizeOptions *options;
#if XA_RECOMPUTE_CHARTS
	ThreadLocal<PiecewiseParam> *pp;
#endif
	ConstArrayView<uint32_t> faces;
	uint32_t chartGroupId;
	uint32_t chartId;
};

static void runCreateAndParameterizeChartTask(void *userData)
{
	auto args = (CreateAndParameterizeChartTaskArgs *)userData;
	XA_PROFILE_START(createChartMesh)
	args->chart = XA_NEW_ARGS(MemTag::Default, Chart, args->chartBuffers->get(), *args->options, *args->basis, args->faces, args->mesh, args->chartGroupId, args->chartId);
	XA_PROFILE_END(createChartMesh)
	args->chart->parameterize(*args->options, args->boundaryGrid->get());
#if XA_RECOMPUTE_CHARTS
	if (!args->chart->isInvalid())
		return;
	// Recompute charts with invalid parameterizations.
	XA_PROFILE_START(parameterizeChartsRecompute)
	Chart *invalidChart = args->chart;
	// Fixing t-junctions rewrites unified mesh faces, and we need to map faces back to input mesh. So use the unmodified unified mesh.
	const Mesh *invalidMesh = invalidChart->unmodifiedUnifiedMesh();
	uint32_t faceCount = 0;
	if (invalidMesh) {
		faceCount = invalidMesh->faceCount();
	} else {
		invalidMesh = invalidChart->unifiedMesh();
		faceCount = invalidChart->initialFaceCount(); // Not invalidMesh->faceCount(). Don't want faces added by hole closing.
	}
	PiecewiseParam &pp = args->pp->get();
	pp.reset(invalidMesh, faceCount);
#if XA_DEBUG_EXPORT_OBJ_RECOMPUTED_CHARTS
	char filename[256];
	XA_SPRINTF(filename, sizeof(filename), "debug_mesh_%03u_chartgroup_%03u_chart_%03u_recomputed.obj", args->mesh->id(), args->chartGroupId, args->chartId);
	FILE *file;
	XA_FOPEN(file, filename, "w");
	uint32_t subChartIndex = 0;
#endif
	for (;;) {
		XA_PROFILE_START(parameterizeChartsPiecewise)
		const bool facesRemaining = pp.computeChart();
		XA_PROFILE_END(parameterizeChartsPiecewise)
		if (!facesRemaining)
			break;
		Chart *chart = XA_NEW_ARGS(MemTag::Default, Chart, args->chartBuffers->get(), invalidChart, invalidMesh, pp.chartFaces(), pp.texcoords(), args->mesh);
		args->charts.push_back(chart);
#if XA_DEBUG_EXPORT_OBJ_RECOMPUTED_CHARTS
		if (file) {
			for (uint32_t j = 0; j < invalidMesh->vertexCount(); j++) {
				fprintf(file, "v %g %g %g\n", invalidMesh->position(j).x, invalidMesh->position(j).y, invalidMesh->position(j).z);
				fprintf(file, "vt %g %g\n", pp.texcoords()[j].x, pp.texcoords()[j].y);
			}
			fprintf(file, "o chart%03u\n", subChartIndex);
			fprintf(file, "s off\n");
			for (uint32_t f = 0; f < pp.chartFaces().length; f++) {
				fprintf(file, "f ");
				const uint32_t face = pp.chartFaces()[f];
				for (uint32_t j = 0; j < 3; j++) {
					const uint32_t index = invalidMesh->vertexCount() * subChartIndex + invalidMesh->vertexAt(face * 3 + j) + 1; // 1-indexed
					fprintf(file, "%d/%d/%c", index, index, j == 2 ? '\n' : ' ');
				}
			}
		}
		subChartIndex++;
#endif
	}
#if XA_DEBUG_EXPORT_OBJ_RECOMPUTED_CHARTS
	if (file)
		fclose(file);
#endif
	XA_PROFILE_END(parameterizeChartsRecompute)
#endif // XA_RECOMPUTE_CHARTS
}

// Set of charts corresponding to mesh faces in the same face group.
class ChartGroup
{
public:
	ChartGroup(uint32_t id, const Mesh *sourceMesh, const MeshFaceGroups *sourceMeshFaceGroups, MeshFaceGroups::Handle faceGroup) : m_id(id), m_sourceMesh(sourceMesh), m_sourceMeshFaceGroups(sourceMeshFaceGroups), m_faceGroup(faceGroup), m_faceCount(0), m_paramAddedChartsCount(0), m_paramDeletedChartsCount(0)
	{
	}

	~ChartGroup()
	{
		for (uint32_t i = 0; i < m_charts.size(); i++) {
			m_charts[i]->~Chart();
			XA_FREE(m_charts[i]);
		}
	}

	uint32_t segmentChartCount() const { return m_chartBasis.size(); }
	uint32_t chartCount() const { return m_charts.size(); }
	Chart *chartAt(uint32_t i) const { return m_charts[i]; }
	uint32_t faceCount() const { return m_faceCount; }
	uint32_t paramAddedChartsCount() const { return m_paramAddedChartsCount; }
	uint32_t paramDeletedChartsCount() const { return m_paramDeletedChartsCount; }

	void computeChartFaces(const ChartOptions &options, segment::Atlas &atlas)
	{
		// Create mesh from source mesh, using only the faces in this face group.
		XA_PROFILE_START(createChartGroupMesh)
		Mesh *mesh = createMesh();
		XA_PROFILE_END(createChartGroupMesh)
		// Segment mesh into charts (arrays of faces).
#if XA_DEBUG_SINGLE_CHART
		m_chartBasis.resize(1);
		Fit::computeBasis(&mesh->position(0), mesh->vertexCount(), &m_chartBasis[0]);
		m_chartFaces.resize(1 + mesh->faceCount());
		m_chartFaces[0] = mesh->faceCount();
		for (uint32_t i = 0; i < m_chartFaces.size(); i++)
			m_chartFaces[i + 1] = i;
#else
		XA_PROFILE_START(buildAtlas)
		atlas.reset(mesh, options);
		atlas.compute();
		XA_PROFILE_END(buildAtlas)
#if XA_DEBUG_EXPORT_OBJ_CHARTS
		char filename[256];
		XA_SPRINTF(filename, sizeof(filename), "debug_mesh_%03u_chartgroup_%03u_charts.obj", m_sourceMesh->id(), m_id);
		FILE *file;
		XA_FOPEN(file, filename, "w");
		if (file) {
			mesh->writeObjVertices(file);
			for (uint32_t i = 0; i < atlas.chartCount(); i++) {
				fprintf(file, "o chart_%04d\n", i);
				fprintf(file, "s off\n");
				ConstArrayView<uint32_t> faces = atlas.chartFaces(i);
				for (uint32_t f = 0; f < faces.length; f++)
					mesh->writeObjFace(file, faces[f]);
			}
			mesh->writeObjBoundaryEges(file);
			mesh->writeObjLinkedBoundaries(file);
			fclose(file);
		}
#endif
		// Destroy mesh.
		const uint32_t faceCount = mesh->faceCount();
		mesh->~Mesh();
		XA_FREE(mesh);
		XA_PROFILE_START(copyChartFaces)
		// Copy basis.
		const uint32_t chartCount = atlas.chartCount();
		m_chartBasis.resize(chartCount);
		for (uint32_t i = 0; i < chartCount; i++)
			m_chartBasis[i] = atlas.chartBasis(i);
		// Copy faces from segment::Atlas to m_chartFaces array with <chart 0 face count> <face 0> <face n> <chart 1 face count> etc. encoding.
		// segment::Atlas faces refer to the chart group mesh. Map them to the input mesh instead.
		m_chartFaces.resize(chartCount + faceCount);
		uint32_t offset = 0;
		for (uint32_t i = 0; i < chartCount; i++) {
			ConstArrayView<uint32_t> faces = atlas.chartFaces(i);
			m_chartFaces[offset++] = faces.length;
			for (uint32_t j = 0; j < faces.length; j++)
				m_chartFaces[offset++] = m_faceToSourceFaceMap[faces[j]];
		}
		XA_PROFILE_END(copyChartFaces)
#endif
	}

#if XA_RECOMPUTE_CHARTS
	void parameterizeCharts(TaskScheduler *taskScheduler, const ParameterizeOptions &options, ThreadLocal<UniformGrid2> *boundaryGrid, ThreadLocal<ChartCtorBuffers> *chartBuffers, ThreadLocal<PiecewiseParam> *piecewiseParam)
#else
	void parameterizeCharts(TaskScheduler* taskScheduler, const ParameterizeOptions &options, ThreadLocal<UniformGrid2>* boundaryGrid, ThreadLocal<ChartCtorBuffers>* chartBuffers)
#endif
	{
		// This function may be called multiple times, so destroy existing charts.
		for (uint32_t i = 0; i < m_charts.size(); i++) {
			m_charts[i]->~Chart();
			XA_FREE(m_charts[i]);
		}
		m_paramAddedChartsCount = 0;
		const uint32_t chartCount = m_chartBasis.size();
		Array<CreateAndParameterizeChartTaskArgs> taskArgs;
		taskArgs.resize(chartCount);
		taskArgs.runCtors(); // Has Array member.
		TaskGroupHandle taskGroup = taskScheduler->createTaskGroup(chartCount);
		uint32_t offset = 0;
		for (uint32_t i = 0; i < chartCount; i++) {
			CreateAndParameterizeChartTaskArgs &args = taskArgs[i];
			args.basis = &m_chartBasis[i];
			args.boundaryGrid = boundaryGrid;
			args.chart = nullptr;
			args.chartGroupId = m_id;
			args.chartId = i;
			args.chartBuffers = chartBuffers;
			const uint32_t faceCount = m_chartFaces[offset++];
			args.faces = ConstArrayView<uint32_t>(&m_chartFaces[offset], faceCount);
			offset += faceCount;
			args.mesh = m_sourceMesh;
			args.options = &options;
#if XA_RECOMPUTE_CHARTS
			args.pp = piecewiseParam;
#endif
			Task task;
			task.userData = &args;
			task.func = runCreateAndParameterizeChartTask;
			taskScheduler->run(taskGroup, task);
		}
		taskScheduler->wait(&taskGroup);
#if XA_RECOMPUTE_CHARTS
		// Count charts. Skip invalid ones and include new ones added by recomputing.
		uint32_t newChartCount = 0;
		for (uint32_t i = 0; i < chartCount; i++) {
			if (taskArgs[i].chart->isInvalid())
				newChartCount += taskArgs[i].charts.size();
			else
				newChartCount++;
		}
		m_charts.resize(newChartCount);
		// Add valid charts first. Destroy invalid ones.
		uint32_t current = 0;
		for (uint32_t i = 0; i < chartCount; i++) {
			Chart *chart = taskArgs[i].chart;
			if (chart->isInvalid()) {
				chart->~Chart();
				XA_FREE(chart);
				m_paramDeletedChartsCount++;
				continue;
			}
			m_charts[current++] = chart;
		}
		// Now add new charts.
		for (uint32_t i = 0; i < chartCount; i++) {
			CreateAndParameterizeChartTaskArgs &args = taskArgs[i];
			for (uint32_t j = 0; j < args.charts.size(); j++) {
				m_charts[current++] = args.charts[j];
				m_paramAddedChartsCount++;
			}
		}
#else // XA_RECOMPUTE_CHARTS
		m_charts.resize(chartCount);
		for (uint32_t i = 0; i < chartCount; i++)
			m_charts[i] = taskArgs[i].chart;
#endif // XA_RECOMPUTE_CHARTS
		taskArgs.runDtors(); // Has Array member.
	}

private:
	Mesh *createMesh()
	{
		XA_DEBUG_ASSERT(m_faceGroup != MeshFaceGroups::kInvalid);
		// Create new mesh from the source mesh, using faces that belong to this group.
		m_faceToSourceFaceMap.reserve(m_sourceMeshFaceGroups->faceCount(m_faceGroup));
		for (MeshFaceGroups::Iterator it(m_sourceMeshFaceGroups, m_faceGroup); !it.isDone(); it.advance())
			m_faceToSourceFaceMap.push_back(it.face());
		// Only initial meshes has ignored faces. The only flag we care about is HasNormals.
		const uint32_t faceCount = m_faceCount = m_faceToSourceFaceMap.size();
		XA_DEBUG_ASSERT(faceCount > 0);
		const uint32_t approxVertexCount = min(faceCount * 3, m_sourceMesh->vertexCount());
		Mesh *mesh = XA_NEW_ARGS(MemTag::Mesh, Mesh, m_sourceMesh->epsilon(), approxVertexCount, faceCount, m_sourceMesh->flags() & MeshFlags::HasNormals);
		HashMap<uint32_t, PassthroughHash<uint32_t>> sourceVertexToVertexMap(MemTag::Mesh, approxVertexCount);
		for (uint32_t f = 0; f < faceCount; f++) {
			const uint32_t face = m_faceToSourceFaceMap[f];
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t vertex = m_sourceMesh->vertexAt(face * 3 + i);
				if (sourceVertexToVertexMap.get(vertex) == UINT32_MAX) {
					sourceVertexToVertexMap.add(vertex);
					Vector3 normal(0.0f);
					if (m_sourceMesh->flags() & MeshFlags::HasNormals)
						normal = m_sourceMesh->normal(vertex);
					mesh->addVertex(m_sourceMesh->position(vertex), normal, m_sourceMesh->texcoord(vertex));
				}
			}
		}
		// Add faces.
		for (uint32_t f = 0; f < faceCount; f++) {
			const uint32_t face = m_faceToSourceFaceMap[f];
			XA_DEBUG_ASSERT(!m_sourceMesh->isFaceIgnored(face));
			uint32_t indices[3];
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t vertex = m_sourceMesh->vertexAt(face * 3 + i);
				indices[i] = sourceVertexToVertexMap.get(vertex);
				XA_DEBUG_ASSERT(indices[i] != UINT32_MAX);
			}
			// Don't copy flags - ignored faces aren't used by chart groups, they are handled by InvalidMeshGeometry.
			Mesh::AddFaceResult::Enum result = mesh->addFace(indices);
			XA_UNUSED(result);
			XA_DEBUG_ASSERT(result == Mesh::AddFaceResult::OK);
		}
		XA_PROFILE_START(createChartGroupMeshColocals)
		mesh->createColocals();
		XA_PROFILE_END(createChartGroupMeshColocals)
		XA_PROFILE_START(createChartGroupMeshBoundaries)
		mesh->createBoundaries();
		mesh->destroyEdgeMap(); // Only needed it for createBoundaries.
		XA_PROFILE_END(createChartGroupMeshBoundaries)
#if XA_DEBUG_EXPORT_OBJ_CHART_GROUPS
		char filename[256];
		XA_SPRINTF(filename, sizeof(filename), "debug_mesh_%03u_chartgroup_%03u.obj", m_sourceMesh->id(), m_id);
		mesh->writeObjFile(filename);
#endif
		return mesh;
	}

	const uint32_t m_id;
	const Mesh * const m_sourceMesh;
	const MeshFaceGroups * const m_sourceMeshFaceGroups;
	const MeshFaceGroups::Handle m_faceGroup;
	Array<uint32_t> m_faceToSourceFaceMap; // List of faces of the source mesh that belong to this chart group.
	Array<Basis> m_chartBasis; // Copied from segment::Atlas.
	Array<uint32_t> m_chartFaces; // Copied from segment::Atlas. Encoding: <chart 0 face count> <face 0> <face n> <chart 1 face count> etc.
	Array<Chart *> m_charts;
	uint32_t m_faceCount; // Set by createMesh(). Used for sorting.
	uint32_t m_paramAddedChartsCount; // Number of new charts added by recomputing charts with invalid parameterizations.
	uint32_t m_paramDeletedChartsCount; // Number of charts with invalid parameterizations that were deleted, after charts were recomputed.
};

// References invalid faces and vertices in a mesh.
struct InvalidMeshGeometry
{
	// Invalid faces have the face groups MeshFaceGroups::kInvalid.
	void extract(const Mesh *mesh, const MeshFaceGroups *meshFaceGroups)
	{
		// Copy invalid faces.
		m_faces.clear();
		const uint32_t meshFaceCount = mesh->faceCount();
		for (uint32_t f = 0; f < meshFaceCount; f++) {
			if (meshFaceGroups->groupAt(f) == MeshFaceGroups::kInvalid)
				m_faces.push_back(f);
		}
		// Create *unique* list of vertices of invalid faces.
		const uint32_t faceCount = m_faces.size();
		m_indices.resize(faceCount * 3);
		const uint32_t approxVertexCount = min(faceCount * 3, mesh->vertexCount());
		m_vertexToSourceVertexMap.clear();
		m_vertexToSourceVertexMap.reserve(approxVertexCount);
		HashMap<uint32_t, PassthroughHash<uint32_t>> sourceVertexToVertexMap(MemTag::Mesh, approxVertexCount);
		for (uint32_t f = 0; f < faceCount; f++) {
			const uint32_t face = m_faces[f];
			for (uint32_t i = 0; i < 3; i++) {
				const uint32_t vertex = mesh->vertexAt(face * 3 + i);
				m_indices[f * 3 + i] = m_vertexToSourceVertexMap.size();;
				if (sourceVertexToVertexMap.get(vertex) == UINT32_MAX) {
					sourceVertexToVertexMap.add(vertex);
					m_vertexToSourceVertexMap.push_back(vertex);
				}
			}
		}
	}

	ConstArrayView<uint32_t> faces() const { return m_faces; }
	ConstArrayView<uint32_t> indices() const { return m_indices; }
	ConstArrayView<uint32_t> vertices() const { return m_vertexToSourceVertexMap; }

private:
	Array<uint32_t> m_faces, m_indices;
	Array<uint32_t> m_vertexToSourceVertexMap; // Map face vertices to vertices of the source mesh.
};

struct ChartGroupComputeChartFacesTaskArgs
{
	ThreadLocal<segment::Atlas> *atlas;
	ChartGroup *chartGroup;
	const ChartOptions *options;
	Progress *progress;
};

static void runChartGroupComputeChartFacesJob(void *userData)
{
	auto args = (ChartGroupComputeChartFacesTaskArgs *)userData;
	if (args->progress->cancel)
		return;
	XA_PROFILE_START(chartGroupComputeChartsThread)
	args->chartGroup->computeChartFaces(*args->options, args->atlas->get());
	XA_PROFILE_END(chartGroupComputeChartsThread)
}

struct MeshComputeChartFacesTaskArgs
{
	Array<ChartGroup *> *chartGroups; // output
	InvalidMeshGeometry *invalidMeshGeometry; // output
	ThreadLocal<segment::Atlas> *atlas;
	const ChartOptions *options;
	Progress *progress;
	const Mesh *sourceMesh;
	TaskScheduler *taskScheduler;
};

#if XA_DEBUG_EXPORT_OBJ_FACE_GROUPS
static uint32_t s_faceGroupsCurrentVertex = 0;
#endif

static void runMeshComputeChartFacesJob(void *userData)
{
	auto args = (MeshComputeChartFacesTaskArgs *)userData;
	if (args->progress->cancel)
		return;
	XA_PROFILE_START(computeChartsThread)
	// Create face groups.
	XA_PROFILE_START(createFaceGroups)
	MeshFaceGroups *meshFaceGroups = XA_NEW_ARGS(MemTag::Mesh, MeshFaceGroups, args->sourceMesh);
	meshFaceGroups->compute();
	const uint32_t chartGroupCount = meshFaceGroups->groupCount();
	XA_PROFILE_END(createFaceGroups)
	if (args->progress->cancel)
		goto cleanup;
#if XA_DEBUG_EXPORT_OBJ_FACE_GROUPS
	{
		static std::mutex s_mutex;
		std::lock_guard<std::mutex> lock(s_mutex);
		char filename[256];
		XA_SPRINTF(filename, sizeof(filename), "debug_face_groups.obj");
		FILE *file;
		XA_FOPEN(file, filename, s_faceGroupsCurrentVertex == 0 ? "w" : "a");
		if (file) {
			const Mesh *mesh = args->sourceMesh;
			mesh->writeObjVertices(file);
			// groups
			uint32_t numGroups = 0;
			for (uint32_t i = 0; i < mesh->faceCount(); i++) {
				if (meshFaceGroups->groupAt(i) != MeshFaceGroups::kInvalid)
					numGroups = max(numGroups, meshFaceGroups->groupAt(i) + 1);
			}
			for (uint32_t i = 0; i < numGroups; i++) {
				fprintf(file, "o mesh_%03u_group_%04d\n", mesh->id(), i);
				fprintf(file, "s off\n");
				for (uint32_t f = 0; f < mesh->faceCount(); f++) {
					if (meshFaceGroups->groupAt(f) == i)
						mesh->writeObjFace(file, f, s_faceGroupsCurrentVertex);
				}
			}
			fprintf(file, "o mesh_%03u_group_ignored\n", mesh->id());
			fprintf(file, "s off\n");
			for (uint32_t f = 0; f < mesh->faceCount(); f++) {
				if (meshFaceGroups->groupAt(f) == MeshFaceGroups::kInvalid)
					mesh->writeObjFace(file, f, s_faceGroupsCurrentVertex);
			}
			mesh->writeObjBoundaryEges(file);
			s_faceGroupsCurrentVertex += mesh->vertexCount();
			fclose(file);
		}
	}
#endif
	// Create a chart group for each face group.
	args->chartGroups->resize(chartGroupCount);
	for (uint32_t i = 0; i < chartGroupCount; i++)
		(*args->chartGroups)[i] = XA_NEW_ARGS(MemTag::Default, ChartGroup, i, args->sourceMesh, meshFaceGroups, MeshFaceGroups::Handle(i));
	// Extract invalid geometry via the invalid face group (MeshFaceGroups::kInvalid).
	XA_PROFILE_START(extractInvalidMeshGeometry)
	args->invalidMeshGeometry->extract(args->sourceMesh, meshFaceGroups);
	XA_PROFILE_END(extractInvalidMeshGeometry)
	// One task for each chart group - compute chart faces.
	{
		XA_PROFILE_START(chartGroupComputeChartsReal)
		Array<ChartGroupComputeChartFacesTaskArgs> taskArgs;
		taskArgs.resize(chartGroupCount);
		for (uint32_t i = 0; i < chartGroupCount; i++) {
			taskArgs[i].atlas = args->atlas;
			taskArgs[i].chartGroup = (*args->chartGroups)[i];
			taskArgs[i].options = args->options;
			taskArgs[i].progress = args->progress;
		}
		TaskGroupHandle taskGroup = args->taskScheduler->createTaskGroup(chartGroupCount);
		for (uint32_t i = 0; i < chartGroupCount; i++) {
			Task task;
			task.userData = &taskArgs[i];
			task.func = runChartGroupComputeChartFacesJob;
			args->taskScheduler->run(taskGroup, task);
		}
		args->taskScheduler->wait(&taskGroup);
		XA_PROFILE_END(chartGroupComputeChartsReal)
	}
	XA_PROFILE_END(computeChartsThread)
	args->progress->value++;
	args->progress->update();
cleanup:
	if (meshFaceGroups) {
		meshFaceGroups->~MeshFaceGroups();
		XA_FREE(meshFaceGroups);
	}
}

struct ParameterizeChartsTaskArgs
{
	TaskScheduler *taskScheduler;
	ChartGroup *chartGroup;
	const ParameterizeOptions *options;
	ThreadLocal<UniformGrid2> *boundaryGrid;
	ThreadLocal<ChartCtorBuffers> *chartBuffers;
#if XA_RECOMPUTE_CHARTS
	ThreadLocal<PiecewiseParam> *piecewiseParam;
#endif
	Progress *progress;
};

static void runParameterizeChartsJob(void *userData)
{
	auto args = (ParameterizeChartsTaskArgs *)userData;
	if (args->progress->cancel)
		return;
	XA_PROFILE_START(parameterizeChartsThread)
#if XA_RECOMPUTE_CHARTS
	args->chartGroup->parameterizeCharts(args->taskScheduler, *args->options, args->boundaryGrid, args->chartBuffers, args->piecewiseParam);
#else
	args->chartGroup->parameterizeCharts(args->taskScheduler, *args->options, args->boundaryGrid, args->chartBuffers);
#endif
	XA_PROFILE_END(parameterizeChartsThread)
	args->progress->value++;
	args->progress->update();
}

/// An atlas is a set of chart groups.
class Atlas
{
public:
	Atlas() : m_chartsComputed(false), m_chartsParameterized(false) {}

	~Atlas()
	{
		for (uint32_t i = 0; i < m_meshChartGroups.size(); i++) {
			for (uint32_t j = 0; j < m_meshChartGroups[i].size(); j++) {
				m_meshChartGroups[i][j]->~ChartGroup();
				XA_FREE(m_meshChartGroups[i][j]);
			}
		}
		m_meshChartGroups.runDtors();
		m_invalidMeshGeometry.runDtors();
	}

	uint32_t meshCount() const { return m_meshes.size(); }
	const InvalidMeshGeometry &invalidMeshGeometry(uint32_t meshIndex) const { return m_invalidMeshGeometry[meshIndex]; }
	bool chartsComputed() const { return m_chartsComputed; }
	bool chartsParameterized() const { return m_chartsParameterized; }
	uint32_t chartGroupCount(uint32_t mesh) const { return m_meshChartGroups[mesh].size(); }
	const ChartGroup *chartGroupAt(uint32_t mesh, uint32_t group) const { return m_meshChartGroups[mesh][group]; }

	void addMesh(const Mesh *mesh)
	{
		m_meshes.push_back(mesh);
	}

	bool computeCharts(TaskScheduler *taskScheduler, const ChartOptions &options, ProgressFunc progressFunc, void *progressUserData)
	{
#if XA_DEBUG_EXPORT_OBJ_PLANAR_REGIONS
		segment::s_planarRegionsCurrentRegion = segment::s_planarRegionsCurrentVertex = 0;
#endif
		m_chartsComputed = false;
		m_chartsParameterized = false;
		// Clear chart groups, since this function may be called multiple times.
		if (!m_meshChartGroups.isEmpty()) {
			for (uint32_t i = 0; i < m_meshChartGroups.size(); i++) {
				for (uint32_t j = 0; j < m_meshChartGroups[i].size(); j++) {
					m_meshChartGroups[i][j]->~ChartGroup();
					XA_FREE(m_meshChartGroups[i][j]);
				}
				m_meshChartGroups[i].clear();
			}
			XA_ASSERT(m_meshChartGroups.size() == m_meshes.size()); // The number of meshes shouldn't have changed.
		}
		m_meshChartGroups.resize(m_meshes.size());
		m_meshChartGroups.runCtors();
		m_invalidMeshGeometry.resize(m_meshes.size());
		m_invalidMeshGeometry.runCtors();
		// One task per mesh.
		const uint32_t meshCount = m_meshes.size();
		Progress progress(ProgressCategory::ComputeCharts, progressFunc, progressUserData, meshCount);
		ThreadLocal<segment::Atlas> atlas;
		Array<MeshComputeChartFacesTaskArgs> taskArgs;
		taskArgs.resize(meshCount);
		for (uint32_t i = 0; i < meshCount; i++) {
			MeshComputeChartFacesTaskArgs &args = taskArgs[i];
			args.atlas = &atlas;
			args.chartGroups = &m_meshChartGroups[i];
			args.invalidMeshGeometry = &m_invalidMeshGeometry[i];
			args.options = &options;
			args.progress = &progress;
			args.sourceMesh = m_meshes[i];
			args.taskScheduler = taskScheduler;
		}
		// Sort meshes by indexCount.
		Array<float> meshSortData;
		meshSortData.resize(meshCount);
		for (uint32_t i = 0; i < meshCount; i++)
			meshSortData[i] = (float)m_meshes[i]->indexCount();
		RadixSort meshSort;
		meshSort.sort(meshSortData);
		// Larger meshes are added first to reduce the chance of thread starvation.
		TaskGroupHandle taskGroup = taskScheduler->createTaskGroup(meshCount);
		for (uint32_t i = 0; i < meshCount; i++) {
			Task task;
			task.userData = &taskArgs[meshSort.ranks()[meshCount - i - 1]];
			task.func = runMeshComputeChartFacesJob;
			taskScheduler->run(taskGroup, task);
		}
		taskScheduler->wait(&taskGroup);
		if (progress.cancel)
			return false;
		m_chartsComputed = true;
		return true;
	}

	bool parameterizeCharts(TaskScheduler *taskScheduler, const ParameterizeOptions &options, ProgressFunc progressFunc, void *progressUserData)
	{
		m_chartsParameterized = false;
		uint32_t chartGroupCount = 0;
		for (uint32_t i = 0; i < m_meshChartGroups.size(); i++)
			chartGroupCount += m_meshChartGroups[i].size();
		Progress progress(ProgressCategory::ParameterizeCharts, progressFunc, progressUserData, chartGroupCount);
		ThreadLocal<UniformGrid2> boundaryGrid; // For Quality boundary intersection.
		ThreadLocal<ChartCtorBuffers> chartBuffers;
#if XA_RECOMPUTE_CHARTS
		ThreadLocal<PiecewiseParam> piecewiseParam;
#endif
		Array<ParameterizeChartsTaskArgs> taskArgs;
		taskArgs.resize(chartGroupCount);
		{
			uint32_t k = 0;
			for (uint32_t i = 0; i < m_meshChartGroups.size(); i++) {
				const uint32_t count = m_meshChartGroups[i].size();
				for (uint32_t j = 0; j < count; j++) {
					ParameterizeChartsTaskArgs &args = taskArgs[k];
					args.taskScheduler = taskScheduler;
					args.chartGroup = m_meshChartGroups[i][j];
					args.options = &options;
					args.boundaryGrid = &boundaryGrid;
					args.chartBuffers = &chartBuffers;
#if XA_RECOMPUTE_CHARTS
					args.piecewiseParam = &piecewiseParam;
#endif
					args.progress = &progress;
					k++;
				}
			}
		}
		// Sort chart groups by face count.
		Array<float> chartGroupSortData;
		chartGroupSortData.resize(chartGroupCount);
		{
			uint32_t k = 0;
			for (uint32_t i = 0; i < m_meshChartGroups.size(); i++) {
				const uint32_t count = m_meshChartGroups[i].size();
				for (uint32_t j = 0; j < count; j++) {
					chartGroupSortData[k++] = (float)m_meshChartGroups[i][j]->faceCount();
				}
			}
		}
		RadixSort chartGroupSort;
		chartGroupSort.sort(chartGroupSortData);
		// Larger chart groups are added first to reduce the chance of thread starvation.
		TaskGroupHandle taskGroup = taskScheduler->createTaskGroup(chartGroupCount);
		for (uint32_t i = 0; i < chartGroupCount; i++) {
			Task task;
			task.userData = &taskArgs[chartGroupSort.ranks()[chartGroupCount - i - 1]];
			task.func = runParameterizeChartsJob;
			taskScheduler->run(taskGroup, task);
		}
		taskScheduler->wait(&taskGroup);
		if (progress.cancel)
			return false;
		m_chartsParameterized = true;
		return true;
	}

private:
	Array<const Mesh *> m_meshes;
	Array<InvalidMeshGeometry> m_invalidMeshGeometry; // 1 per mesh.
	Array<Array<ChartGroup *> > m_meshChartGroups;
	bool m_chartsComputed;
	bool m_chartsParameterized;
};

} // namespace param

namespace pack {

class AtlasImage
{
public:
	AtlasImage(uint32_t width, uint32_t height) : m_width(width), m_height(height)
	{
		m_data.resize(m_width * m_height);
		memset(m_data.data(), 0, sizeof(uint32_t) * m_data.size());
	}

	void resize(uint32_t width, uint32_t height)
	{
		Array<uint32_t> data;
		data.resize(width * height);
		memset(data.data(), 0, sizeof(uint32_t) * data.size());
		for (uint32_t y = 0; y < min(m_height, height); y++)
			memcpy(&data[y * width], &m_data[y * m_width], min(m_width, width) * sizeof(uint32_t));
		m_width = width;
		m_height = height;
		data.moveTo(m_data);
	}

	void addChart(uint32_t chartIndex, const BitImage *image, const BitImage *imageBilinear, const BitImage *imagePadding, int atlas_w, int atlas_h, int offset_x, int offset_y)
	{
		const int w = image->width();
		const int h = image->height();
		for (int y = 0; y < h; y++) {
			const int yy = y + offset_y;
			if (yy < 0)
				continue;
			for (int x = 0; x < w; x++) {
				const int xx = x + offset_x;
				if (xx >= 0 && xx < atlas_w && yy < atlas_h) {
					const uint32_t dataOffset = xx + yy * m_width;
					if (image->get(x, y)) {
						XA_DEBUG_ASSERT(m_data[dataOffset] == 0);
						m_data[dataOffset] = chartIndex | kImageHasChartIndexBit;
					} else if (imageBilinear && imageBilinear->get(x, y)) {
						XA_DEBUG_ASSERT(m_data[dataOffset] == 0);
						m_data[dataOffset] = chartIndex | kImageHasChartIndexBit | kImageIsBilinearBit;
					} else if (imagePadding && imagePadding->get(x, y)) {
						XA_DEBUG_ASSERT(m_data[dataOffset] == 0);
						m_data[dataOffset] = chartIndex | kImageHasChartIndexBit | kImageIsPaddingBit;
					}
				}
			}
		}
	}

	void copyTo(uint32_t *dest, uint32_t destWidth, uint32_t destHeight, int padding) const
	{
		for (uint32_t y = 0; y < destHeight; y++)
			memcpy(&dest[y * destWidth], &m_data[padding + (y + padding) * m_width], destWidth * sizeof(uint32_t));
	}

#if XA_DEBUG_EXPORT_ATLAS_IMAGES
	void writeTga(const char *filename, uint32_t width, uint32_t height) const
	{
		Array<uint8_t> image;
		image.resize(width * height * 3);
		for (uint32_t y = 0; y < height; y++) {
			if (y >= m_height)
				continue;
			for (uint32_t x = 0; x < width; x++) {
				if (x >= m_width)
					continue;
				const uint32_t data = m_data[x + y * m_width];
				uint8_t *bgr = &image[(x + y * width) * 3];
				if (data == 0) {
					bgr[0] = bgr[1] = bgr[2] = 0;
					continue;
				}
				const uint32_t chartIndex = data & kImageChartIndexMask;
				if (data & kImageIsPaddingBit) {
					bgr[0] = 0;
					bgr[1] = 0;
					bgr[2] = 255;
				} else if (data & kImageIsBilinearBit) {
					bgr[0] = 0;
					bgr[1] = 255;
					bgr[2] = 0;
				} else {
					const int mix = 192;
					srand((unsigned int)chartIndex);
					bgr[0] = uint8_t((rand() % 255 + mix) * 0.5f);
					bgr[1] = uint8_t((rand() % 255 + mix) * 0.5f);
					bgr[2] = uint8_t((rand() % 255 + mix) * 0.5f);
				}
			}
		}
		WriteTga(filename, image.data(), width, height);
	}
#endif

private:
	uint32_t m_width, m_height;
	Array<uint32_t> m_data;
};

struct Chart
{
	int32_t atlasIndex;
	uint32_t material;
	uint32_t indexCount;
	const uint32_t *indices;
	float parametricArea;
	float surfaceArea;
	Vector2 *vertices;
	uint32_t vertexCount;
	Array<uint32_t> uniqueVertices;
	bool allowRotate;
	// bounding box
	Vector2 majorAxis, minorAxis, minCorner, maxCorner;
	// Mesh only
	const Array<uint32_t> *boundaryEdges;
	// UvMeshChart only
	Array<uint32_t> faces;

	Vector2 &uniqueVertexAt(uint32_t v) { return uniqueVertices.isEmpty() ? vertices[v] : vertices[uniqueVertices[v]]; }
	uint32_t uniqueVertexCount() const { return uniqueVertices.isEmpty() ? vertexCount : uniqueVertices.size(); }
};

struct AddChartTaskArgs
{
	ThreadLocal<BoundingBox2D> *boundingBox;
	param::Chart *paramChart;
	Chart *chart; // out
};

static void runAddChartTask(void *userData)
{
	XA_PROFILE_START(packChartsAddChartsThread)
	auto args = (AddChartTaskArgs *)userData;
	param::Chart *paramChart = args->paramChart;
	XA_PROFILE_START(packChartsAddChartsRestoreTexcoords)
	paramChart->restoreTexcoords();
	XA_PROFILE_END(packChartsAddChartsRestoreTexcoords)
	Mesh *mesh = paramChart->mesh();
	Chart *chart = args->chart = XA_NEW(MemTag::Default, Chart);
	chart->atlasIndex = -1;
	chart->material = 0;
	chart->indexCount = mesh->indexCount();
	chart->indices = mesh->indices();
	chart->parametricArea = mesh->computeParametricArea();
	if (chart->parametricArea < kAreaEpsilon) {
		// When the parametric area is too small we use a rough approximation to prevent divisions by very small numbers.
		const Vector2 bounds = paramChart->computeParametricBounds();
		chart->parametricArea = bounds.x * bounds.y;
	}
	chart->surfaceArea = mesh->computeSurfaceArea();
	chart->vertices = mesh->texcoords();
	chart->vertexCount = mesh->vertexCount();
	chart->allowRotate = true;
	chart->boundaryEdges = &mesh->boundaryEdges();
	// Compute bounding box of chart.
	BoundingBox2D &bb = args->boundingBox->get();
	bb.clear();
	for (uint32_t v = 0; v < chart->vertexCount; v++) {
		if (mesh->isBoundaryVertex(v))
			bb.appendBoundaryVertex(mesh->texcoord(v));
	}
	bb.compute(mesh->texcoords(), mesh->vertexCount());
	chart->majorAxis = bb.majorAxis;
	chart->minorAxis = bb.minorAxis;
	chart->minCorner = bb.minCorner;
	chart->maxCorner = bb.maxCorner;
	XA_PROFILE_END(packChartsAddChartsThread)
}

struct Atlas
{
	~Atlas()
	{
		for (uint32_t i = 0; i < m_atlasImages.size(); i++) {
			m_atlasImages[i]->~AtlasImage();
			XA_FREE(m_atlasImages[i]);
		}
		for (uint32_t i = 0; i < m_bitImages.size(); i++) {
			m_bitImages[i]->~BitImage();
			XA_FREE(m_bitImages[i]);
		}
		for (uint32_t i = 0; i < m_charts.size(); i++) {
			m_charts[i]->~Chart();
			XA_FREE(m_charts[i]);
		}
	}

	uint32_t getWidth() const { return m_width; }
	uint32_t getHeight() const { return m_height; }
	uint32_t getNumAtlases() const { return m_bitImages.size(); }
	float getTexelsPerUnit() const { return m_texelsPerUnit; }
	const Chart *getChart(uint32_t index) const { return m_charts[index]; }
	uint32_t getChartCount() const { return m_charts.size(); }
	const Array<AtlasImage *> &getImages() const { return m_atlasImages; }
	float getUtilization(uint32_t atlas) const { return m_utilization[atlas]; }

	void addCharts(TaskScheduler *taskScheduler, param::Atlas *paramAtlas)
	{
		// Count charts.
		uint32_t chartCount = 0;
		for (uint32_t i = 0; i < paramAtlas->meshCount(); i++) {
			const uint32_t chartGroupsCount = paramAtlas->chartGroupCount(i);
			for (uint32_t j = 0; j < chartGroupsCount; j++) {
				const param::ChartGroup *chartGroup = paramAtlas->chartGroupAt(i, j);
				chartCount += chartGroup->chartCount();
			}
		}
		if (chartCount == 0)
			return;
		// Run one task per chart.
		Array<AddChartTaskArgs> taskArgs;
		taskArgs.resize(chartCount);
		TaskGroupHandle taskGroup = taskScheduler->createTaskGroup(chartCount);
		uint32_t chartIndex = 0;
		ThreadLocal<BoundingBox2D> boundingBox;
		for (uint32_t i = 0; i < paramAtlas->meshCount(); i++) {
			const uint32_t chartGroupsCount = paramAtlas->chartGroupCount(i);
			for (uint32_t j = 0; j < chartGroupsCount; j++) {
				const param::ChartGroup *chartGroup = paramAtlas->chartGroupAt(i, j);
				const uint32_t count = chartGroup->chartCount();
				for (uint32_t k = 0; k < count; k++) {
					AddChartTaskArgs &args = taskArgs[chartIndex];
					args.boundingBox = &boundingBox;
					args.paramChart = chartGroup->chartAt(k);
					Task task;
					task.userData = &taskArgs[chartIndex];
					task.func = runAddChartTask;
					taskScheduler->run(taskGroup, task);
					chartIndex++;
				}
			}
		}
		taskScheduler->wait(&taskGroup);
		// Get task output.
		m_charts.resize(chartCount);
		for (uint32_t i = 0; i < chartCount; i++)
			m_charts[i] = taskArgs[i].chart;
	}

	void addUvMeshCharts(UvMeshInstance *mesh)
	{
		BitArray vertexUsed(mesh->texcoords.size());
		BoundingBox2D boundingBox;
		for (uint32_t c = 0; c < mesh->mesh->charts.size(); c++) {
			UvMeshChart *uvChart = mesh->mesh->charts[c];
			Chart *chart = XA_NEW(MemTag::Default, Chart);
			chart->atlasIndex = -1;
			chart->material = uvChart->material;
			chart->indexCount = uvChart->indices.size();
			chart->indices = uvChart->indices.data();
			chart->vertices = mesh->texcoords.data();
			chart->vertexCount = mesh->texcoords.size();
			chart->allowRotate = mesh->rotateCharts;
			chart->boundaryEdges = nullptr;
			chart->faces.resize(uvChart->faces.size());
			memcpy(chart->faces.data(), uvChart->faces.data(), sizeof(uint32_t) * uvChart->faces.size());
			// Find unique vertices.
			vertexUsed.zeroOutMemory();
			for (uint32_t i = 0; i < chart->indexCount; i++) {
				const uint32_t vertex = chart->indices[i];
				if (!vertexUsed.get(vertex)) {
					vertexUsed.set(vertex);
					chart->uniqueVertices.push_back(vertex);
				}
			}
			// Compute parametric and surface areas.
			chart->parametricArea = 0.0f;
			for (uint32_t f = 0; f < chart->indexCount / 3; f++) {
				const Vector2 &v1 = chart->vertices[chart->indices[f * 3 + 0]];
				const Vector2 &v2 = chart->vertices[chart->indices[f * 3 + 1]];
				const Vector2 &v3 = chart->vertices[chart->indices[f * 3 + 2]];
				chart->parametricArea += fabsf(triangleArea(v1, v2, v3));
			}
			chart->parametricArea *= 0.5f;
			chart->surfaceArea = chart->parametricArea; // Identical for UV meshes.
			if (chart->parametricArea < kAreaEpsilon) {
				// When the parametric area is too small we use a rough approximation to prevent divisions by very small numbers.
				Vector2 minCorner(FLT_MAX, FLT_MAX);
				Vector2 maxCorner(-FLT_MAX, -FLT_MAX);
				for (uint32_t v = 0; v < chart->uniqueVertexCount(); v++) {
					minCorner = min(minCorner, chart->uniqueVertexAt(v));
					maxCorner = max(maxCorner, chart->uniqueVertexAt(v));
				}
				const Vector2 bounds = (maxCorner - minCorner) * 0.5f;
				chart->parametricArea = bounds.x * bounds.y;
			}
			// Compute bounding box of chart.
			// Using all unique vertices for simplicity, can compute real boundaries if this is too slow.
			boundingBox.clear();
			for (uint32_t v = 0; v < chart->uniqueVertexCount(); v++)
				boundingBox.appendBoundaryVertex(chart->uniqueVertexAt(v));
			boundingBox.compute();
			chart->majorAxis = boundingBox.majorAxis;
			chart->minorAxis = boundingBox.minorAxis;
			chart->minCorner = boundingBox.minCorner;
			chart->maxCorner = boundingBox.maxCorner;
			m_charts.push_back(chart);
		}
	}

	// Pack charts in the smallest possible rectangle.
	bool packCharts(const PackOptions &options, ProgressFunc progressFunc, void *progressUserData)
	{
		if (progressFunc) {
			if (!progressFunc(ProgressCategory::PackCharts, 0, progressUserData))
				return false;
		}
		const uint32_t chartCount = m_charts.size();
		XA_PRINT("Packing %u charts\n", chartCount);
		if (chartCount == 0) {
			if (progressFunc) {
				if (!progressFunc(ProgressCategory::PackCharts, 100, progressUserData))
					return false;
			}
			return true;
		}
		// Estimate resolution and/or texels per unit if not specified.
		m_texelsPerUnit = options.texelsPerUnit;
		uint32_t resolution = options.resolution > 0 ? options.resolution + options.padding * 2 : 0;
		const uint32_t maxResolution = m_texelsPerUnit > 0.0f ? resolution : 0;
		if (resolution <= 0 || m_texelsPerUnit <= 0) {
			if (resolution <= 0 && m_texelsPerUnit <= 0)
				resolution = 1024;
			float meshArea = 0;
			for (uint32_t c = 0; c < chartCount; c++)
				meshArea += m_charts[c]->surfaceArea;
			if (resolution <= 0) {
				// Estimate resolution based on the mesh surface area and given texel scale.
				const float texelCount = max(1.0f, meshArea * square(m_texelsPerUnit) / 0.75f); // Assume 75% utilization.
				resolution = max(1u, nextPowerOfTwo(uint32_t(sqrtf(texelCount))));
			}
			if (m_texelsPerUnit <= 0) {
				// Estimate a suitable texelsPerUnit to fit the given resolution.
				const float texelCount = max(1.0f, meshArea / 0.75f); // Assume 75% utilization.
				m_texelsPerUnit = sqrtf((resolution * resolution) / texelCount);
				XA_PRINT("   Estimating texelsPerUnit as %g\n", m_texelsPerUnit);
			}
		}
		Array<float> chartOrderArray;
		chartOrderArray.resize(chartCount);
		Array<Vector2> chartExtents;
		chartExtents.resize(chartCount);
		float minChartPerimeter = FLT_MAX, maxChartPerimeter = 0.0f;
		for (uint32_t c = 0; c < chartCount; c++) {
			Chart *chart = m_charts[c];
			// Compute chart scale
			float scale = 1.0f;
			if (chart->parametricArea != 0.0f) {
				scale = (chart->surfaceArea / chart->parametricArea) * m_texelsPerUnit;
				XA_ASSERT(isFinite(scale));
			}
			// Translate, rotate and scale vertices. Compute extents.
			Vector2 minCorner(FLT_MAX, FLT_MAX);
			if (!chart->allowRotate) {
				for (uint32_t i = 0; i < chart->uniqueVertexCount(); i++)
					minCorner = min(minCorner, chart->uniqueVertexAt(i));
			}
			Vector2 extents(0.0f);
			for (uint32_t i = 0; i < chart->uniqueVertexCount(); i++) {
				Vector2 &texcoord = chart->uniqueVertexAt(i);
				if (chart->allowRotate) {
					const float x = dot(texcoord, chart->majorAxis);
					const float y = dot(texcoord, chart->minorAxis);
					texcoord.x = x;
					texcoord.y = y;
					texcoord -= chart->minCorner;
				} else {
					texcoord -= minCorner;
				}
				texcoord *= scale;
				XA_DEBUG_ASSERT(texcoord.x >= 0.0f && texcoord.y >= 0.0f);
				XA_DEBUG_ASSERT(isFinite(texcoord.x) && isFinite(texcoord.y));
				extents = max(extents, texcoord);
			}
			XA_DEBUG_ASSERT(extents.x >= 0 && extents.y >= 0);
			// Scale the charts to use the entire texel area available. So, if the width is 0.1 we could scale it to 1 without increasing the lightmap usage and making a better use of it. In many cases this also improves the look of the seams, since vertices on the chart boundaries have more chances of being aligned with the texel centers.
			if (extents.x > 0.0f && extents.y > 0.0f) {
				// Block align: align all chart extents to 4x4 blocks, but taking padding and texel center offset into account.
				const int blockAlignSizeOffset = options.padding * 2 + 1;
				int width = ftoi_ceil(extents.x);
				if (options.blockAlign)
					width = align(width + blockAlignSizeOffset, 4) - blockAlignSizeOffset;
				int height = ftoi_ceil(extents.y);
				if (options.blockAlign)
					height = align(height + blockAlignSizeOffset, 4) - blockAlignSizeOffset;
				for (uint32_t v = 0; v < chart->uniqueVertexCount(); v++) {
					Vector2 &texcoord = chart->uniqueVertexAt(v);
					texcoord.x = texcoord.x / extents.x * (float)width;
					texcoord.y = texcoord.y / extents.y * (float)height;
				}
				extents.x = (float)width;
				extents.y = (float)height;
			}
			// Limit chart size, either to PackOptions::maxChartSize or maxResolution (if set), whichever is smaller.
			// If limiting chart size to maxResolution, print a warning, since that may not be desirable to the user.
			uint32_t maxChartSize = options.maxChartSize;
			bool warnChartResized = false;
			if (maxResolution > 0 && (maxChartSize == 0 || maxResolution < maxChartSize)) {
				maxChartSize = maxResolution - options.padding * 2; // Don't include padding.
				warnChartResized = true;
			}
			if (maxChartSize > 0) {
				const float realMaxChartSize = (float)maxChartSize - 1.0f; // Aligning to texel centers increases texel footprint by 1.
				if (extents.x > realMaxChartSize || extents.y > realMaxChartSize) {
					if (warnChartResized)
						XA_PRINT("   Resizing chart %u from %gx%g to %ux%u to fit atlas\n", c, extents.x, extents.y, maxChartSize, maxChartSize);
					scale = realMaxChartSize / max(extents.x, extents.y);
					for (uint32_t i = 0; i < chart->uniqueVertexCount(); i++) {
						Vector2 &texcoord = chart->uniqueVertexAt(i);
						texcoord = min(texcoord * scale, Vector2(realMaxChartSize));
					}
				}
			}
			// Align to texel centers and add padding offset.
			extents.x = extents.y = 0.0f;
			for (uint32_t v = 0; v < chart->uniqueVertexCount(); v++) {
				Vector2 &texcoord = chart->uniqueVertexAt(v);
				texcoord.x += 0.5f + options.padding;
				texcoord.y += 0.5f + options.padding;
				extents = max(extents, texcoord);
			}
			if (extents.x > resolution || extents.y > resolution)
				XA_PRINT("   Chart %u extents are large (%gx%g)\n", c, extents.x, extents.y);
			chartExtents[c] = extents;
			chartOrderArray[c] = extents.x + extents.y; // Use perimeter for chart sort key.
			minChartPerimeter = min(minChartPerimeter, chartOrderArray[c]);
			maxChartPerimeter = max(maxChartPerimeter, chartOrderArray[c]);
		}
		// Sort charts by perimeter.
		m_radix.sort(chartOrderArray);
		const uint32_t *ranks = m_radix.ranks();
		// Divide chart perimeter range into buckets.
		const float chartPerimeterBucketSize = (maxChartPerimeter - minChartPerimeter) / 16.0f;
		uint32_t currentChartBucket = 0;
		Array<Vector2i> chartStartPositions; // per atlas
		chartStartPositions.push_back(Vector2i(0, 0));
		// Pack sorted charts.
#if XA_DEBUG_EXPORT_ATLAS_IMAGES
		const bool createImage = true;
#else
		const bool createImage = options.createImage;
#endif
		// chartImage: result from conservative rasterization
		// chartImageBilinear: chartImage plus any texels that would be sampled by bilinear filtering.
		// chartImagePadding: either chartImage or chartImageBilinear depending on options, with a dilate filter applied options.padding times.
		// Rotated versions swap x and y.
		BitImage chartImage, chartImageBilinear, chartImagePadding;
		BitImage chartImageRotated, chartImageBilinearRotated, chartImagePaddingRotated;
		UniformGrid2 boundaryEdgeGrid;
		Array<Vector2i> atlasSizes;
		atlasSizes.push_back(Vector2i(0, 0));
		int progress = 0;
		for (uint32_t i = 0; i < chartCount; i++) {
			uint32_t c = ranks[chartCount - i - 1]; // largest chart first
			Chart *chart = m_charts[c];
			// @@ Add special cases for dot and line charts. @@ Lightmap rasterizer also needs to handle these special cases.
			// @@ We could also have a special case for chart quads. If the quad surface <= 4 texels, align vertices with texel centers and do not add padding. May be very useful for foliage.
			// @@ In general we could reduce the padding of all charts by one texel by using a rasterizer that takes into account the 2-texel footprint of the tent bilinear filter. For example,
			// if we have a chart that is less than 1 texel wide currently we add one texel to the left and one texel to the right creating a 3-texel-wide bitImage. However, if we know that the
			// chart is only 1 texel wide we could align it so that it only touches the footprint of two texels:
			//      |   |      <- Touches texels 0, 1 and 2.
			//    |   |        <- Only touches texels 0 and 1.
			// \   \ / \ /   /
			//  \   X   X   /
			//   \ / \ / \ /
			//    V   V   V
			//    0   1   2
			XA_PROFILE_START(packChartsRasterize)
			// Resize and clear (discard = true) chart images.
			// Leave room for padding at extents.
			chartImage.resize(ftoi_ceil(chartExtents[c].x) + options.padding, ftoi_ceil(chartExtents[c].y) + options.padding, true);
			if (chart->allowRotate)
				chartImageRotated.resize(chartImage.height(), chartImage.width(), true);
			if (options.bilinear) {
				chartImageBilinear.resize(chartImage.width(), chartImage.height(), true);
				if (chart->allowRotate)
					chartImageBilinearRotated.resize(chartImage.height(), chartImage.width(), true);
			}
			// Rasterize chart faces.
			const uint32_t faceCount = chart->indexCount / 3;
			for (uint32_t f = 0; f < faceCount; f++) {
				Vector2 vertices[3];
				for (uint32_t v = 0; v < 3; v++)
					vertices[v] = chart->vertices[chart->indices[f * 3 + v]];
				DrawTriangleCallbackArgs args;
				args.chartBitImage = &chartImage;
				args.chartBitImageRotated = chart->allowRotate ? &chartImageRotated : nullptr;
				raster::drawTriangle(Vector2((float)chartImage.width(), (float)chartImage.height()), vertices, drawTriangleCallback, &args);
			}
			// Expand chart by pixels sampled by bilinear interpolation.
			if (options.bilinear)
				bilinearExpand(chart, &chartImage, &chartImageBilinear, chart->allowRotate ? &chartImageBilinearRotated : nullptr, boundaryEdgeGrid);
			// Expand chart by padding pixels (dilation).
			if (options.padding > 0) {
				// Copy into the same BitImage instances for every chart to avoid reallocating BitImage buffers (largest chart is packed first).
				XA_PROFILE_START(packChartsDilate)
				if (options.bilinear)
					chartImageBilinear.copyTo(chartImagePadding);
				else
					chartImage.copyTo(chartImagePadding);
				chartImagePadding.dilate(options.padding);
				if (chart->allowRotate) {
					if (options.bilinear)
						chartImageBilinearRotated.copyTo(chartImagePaddingRotated);
					else
						chartImageRotated.copyTo(chartImagePaddingRotated);
					chartImagePaddingRotated.dilate(options.padding);
				}
				XA_PROFILE_END(packChartsDilate)
			}
			XA_PROFILE_END(packChartsRasterize)
			// Update brute force bucketing.
			if (options.bruteForce) {
				if (chartOrderArray[c] > minChartPerimeter && chartOrderArray[c] <= maxChartPerimeter - (chartPerimeterBucketSize * (currentChartBucket + 1))) {
					// Moved to a smaller bucket, reset start location.
					for (uint32_t j = 0; j < chartStartPositions.size(); j++)
						chartStartPositions[j] = Vector2i(0, 0);
					currentChartBucket++;
				}
			}
			// Find a location to place the chart in the atlas.
			BitImage *chartImageToPack, *chartImageToPackRotated;
			if (options.padding > 0) {
				chartImageToPack = &chartImagePadding;
				chartImageToPackRotated = &chartImagePaddingRotated;
			} else if (options.bilinear) {
				chartImageToPack = &chartImageBilinear;
				chartImageToPackRotated = &chartImageBilinearRotated;
			} else {
				chartImageToPack = &chartImage;
				chartImageToPackRotated = &chartImageRotated;
			}
			uint32_t currentAtlas = 0;
			int best_x = 0, best_y = 0;
			int best_cw = 0, best_ch = 0;
			int best_r = 0;
			for (;;)
			{
				bool firstChartInBitImage = false;
				XA_UNUSED(firstChartInBitImage);
				if (currentAtlas + 1 > m_bitImages.size()) {
					// Chart doesn't fit in the current bitImage, create a new one.
					BitImage *bi = XA_NEW_ARGS(MemTag::Default, BitImage, resolution, resolution);
					m_bitImages.push_back(bi);
					atlasSizes.push_back(Vector2i(0, 0));
					firstChartInBitImage = true;
					if (createImage)
						m_atlasImages.push_back(XA_NEW_ARGS(MemTag::Default, AtlasImage, resolution, resolution));
					// Start positions are per-atlas, so create a new one of those too.
					chartStartPositions.push_back(Vector2i(0, 0));
				}
				XA_PROFILE_START(packChartsFindLocation)
				const bool foundLocation = findChartLocation(chartStartPositions[currentAtlas], options.bruteForce, m_bitImages[currentAtlas], chartImageToPack, chartImageToPackRotated, atlasSizes[currentAtlas].x, atlasSizes[currentAtlas].y, &best_x, &best_y, &best_cw, &best_ch, &best_r, options.blockAlign, maxResolution, chart->allowRotate);
				XA_PROFILE_END(packChartsFindLocation)
				XA_DEBUG_ASSERT(!(firstChartInBitImage && !foundLocation)); // Chart doesn't fit in an empty, newly allocated bitImage. Shouldn't happen, since charts are resized if they are too big to fit in the atlas.
				if (maxResolution == 0) {
					XA_DEBUG_ASSERT(foundLocation); // The atlas isn't limited to a fixed resolution, a chart location should be found on the first attempt.
					break;
				}
				if (foundLocation)
					break;
				// Chart doesn't fit in the current bitImage, try the next one.
				currentAtlas++;
			}
			// Update brute force start location.
			if (options.bruteForce) {
				// Reset start location if the chart expanded the atlas.
				if (best_x + best_cw > atlasSizes[currentAtlas].x || best_y + best_ch > atlasSizes[currentAtlas].y) {
					for (uint32_t j = 0; j < chartStartPositions.size(); j++)
						chartStartPositions[j] = Vector2i(0, 0);
				}
				else {
					chartStartPositions[currentAtlas] = Vector2i(best_x, best_y);
				}
			}
			// Update parametric extents.
			atlasSizes[currentAtlas].x = max(atlasSizes[currentAtlas].x, best_x + best_cw);
			atlasSizes[currentAtlas].y = max(atlasSizes[currentAtlas].y, best_y + best_ch);
			// Resize bitImage if necessary.
			// If maxResolution > 0, the bitImage is always set to maxResolutionIncludingPadding on creation and doesn't need to be dynamically resized.
			if (maxResolution == 0) {
				const uint32_t w = (uint32_t)atlasSizes[currentAtlas].x;
				const uint32_t h = (uint32_t)atlasSizes[currentAtlas].y;
				if (w > m_bitImages[0]->width() || h > m_bitImages[0]->height()) {
					m_bitImages[0]->resize(nextPowerOfTwo(w), nextPowerOfTwo(h), false);
					if (createImage)
						m_atlasImages[0]->resize(m_bitImages[0]->width(), m_bitImages[0]->height());
				}
			} else {
				XA_DEBUG_ASSERT(atlasSizes[currentAtlas].x <= (int)maxResolution);
				XA_DEBUG_ASSERT(atlasSizes[currentAtlas].y <= (int)maxResolution);
			}
			XA_PROFILE_START(packChartsBlit)
			addChart(m_bitImages[currentAtlas], chartImageToPack, chartImageToPackRotated, atlasSizes[currentAtlas].x, atlasSizes[currentAtlas].y, best_x, best_y, best_r);
			XA_PROFILE_END(packChartsBlit)
			if (createImage) {
				if (best_r == 0) {
					m_atlasImages[currentAtlas]->addChart(c, &chartImage, options.bilinear ? &chartImageBilinear : nullptr, options.padding > 0 ? &chartImagePadding : nullptr, atlasSizes[currentAtlas].x, atlasSizes[currentAtlas].y, best_x, best_y);
				} else {
					m_atlasImages[currentAtlas]->addChart(c, &chartImageRotated, options.bilinear ? &chartImageBilinearRotated : nullptr, options.padding > 0 ? &chartImagePaddingRotated : nullptr, atlasSizes[currentAtlas].x, atlasSizes[currentAtlas].y, best_x, best_y);
				}
#if XA_DEBUG_EXPORT_ATLAS_IMAGES && XA_DEBUG_EXPORT_ATLAS_IMAGES_PER_CHART
				for (uint32_t j = 0; j < m_atlasImages.size(); j++) {
					char filename[256];
					XA_SPRINTF(filename, sizeof(filename), "debug_atlas_image%02u_chart%04u.tga", j, i);
					m_atlasImages[j]->writeTga(filename, (uint32_t)atlasSizes[j].x, (uint32_t)atlasSizes[j].y);
				}
#endif
			}
			chart->atlasIndex = (int32_t)currentAtlas;
			// Modify texture coordinates:
			//  - rotate if the chart should be rotated
			//  - translate to chart location
			//  - translate to remove padding from top and left atlas edges (unless block aligned)
			for (uint32_t v = 0; v < chart->uniqueVertexCount(); v++) {
				Vector2 &texcoord = chart->uniqueVertexAt(v);
				Vector2 t = texcoord;
				if (best_r) {
					XA_DEBUG_ASSERT(chart->allowRotate);
					swap(t.x, t.y);
				}
				texcoord.x = best_x + t.x;
				texcoord.y = best_y + t.y;
				texcoord.x -= (float)options.padding;
				texcoord.y -= (float)options.padding;
				XA_ASSERT(texcoord.x >= 0 && texcoord.y >= 0);
				XA_ASSERT(isFinite(texcoord.x) && isFinite(texcoord.y));
			}
			if (progressFunc) {
				const int newProgress = int((i + 1) / (float)chartCount * 100.0f);
				if (newProgress != progress) {
					progress = newProgress;
					if (!progressFunc(ProgressCategory::PackCharts, progress, progressUserData))
						return false;
				}
			}
		}
		// Remove padding from outer edges.
		if (maxResolution == 0) {
			m_width = max(0, atlasSizes[0].x - (int)options.padding * 2);
			m_height = max(0, atlasSizes[0].y - (int)options.padding * 2);
		} else {
			m_width = m_height = maxResolution - (int)options.padding * 2;
		}
		XA_PRINT("   %dx%d resolution\n", m_width, m_height);
		m_utilization.resize(m_bitImages.size());
		for (uint32_t i = 0; i < m_utilization.size(); i++) {
			if (m_width == 0 || m_height == 0)
				m_utilization[i] = 0.0f;
			else {
				uint32_t count = 0;
				for (uint32_t y = 0; y < m_height; y++) {
					for (uint32_t x = 0; x < m_width; x++)
						count += m_bitImages[i]->get(x, y);
				}
				m_utilization[i] = float(count) / (m_width * m_height);
			}
			if (m_utilization.size() > 1) {
				XA_PRINT("   %u: %f%% utilization\n", i, m_utilization[i] * 100.0f);
			}
			else {
				XA_PRINT("   %f%% utilization\n", m_utilization[i] * 100.0f);
			}
		}
#if XA_DEBUG_EXPORT_ATLAS_IMAGES
		for (uint32_t i = 0; i < m_atlasImages.size(); i++) {
			char filename[256];
			XA_SPRINTF(filename, sizeof(filename), "debug_atlas_image%02u.tga", i);
			m_atlasImages[i]->writeTga(filename, m_width, m_height);
		}
#endif
		if (progressFunc && progress != 100) {
			if (!progressFunc(ProgressCategory::PackCharts, 100, progressUserData))
				return false;
		}
		return true;
	}

private:
	// IC: Brute force is slow, and random may take too much time to converge. We start inserting large charts in a small atlas. Using brute force is lame, because most of the space
	// is occupied at this point. At the end we have many small charts and a large atlas with sparse holes. Finding those holes randomly is slow. A better approach would be to
	// start stacking large charts as if they were tetris pieces. Once charts get small try to place them randomly. It may be interesting to try a intermediate strategy, first try
	// along one axis and then try exhaustively along that axis.
	bool findChartLocation(const Vector2i &startPosition, bool bruteForce, const BitImage *atlasBitImage, const BitImage *chartBitImage, const BitImage *chartBitImageRotated, int w, int h, int *best_x, int *best_y, int *best_w, int *best_h, int *best_r, bool blockAligned, uint32_t maxResolution, bool allowRotate)
	{
		const int attempts = 4096;
		if (bruteForce || attempts >= w * h)
			return findChartLocation_bruteForce(startPosition, atlasBitImage, chartBitImage, chartBitImageRotated, w, h, best_x, best_y, best_w, best_h, best_r, blockAligned, maxResolution, allowRotate);
		return findChartLocation_random(atlasBitImage, chartBitImage, chartBitImageRotated, w, h, best_x, best_y, best_w, best_h, best_r, attempts, blockAligned, maxResolution, allowRotate);
	}

	bool findChartLocation_bruteForce(const Vector2i &startPosition, const BitImage *atlasBitImage, const BitImage *chartBitImage, const BitImage *chartBitImageRotated, int w, int h, int *best_x, int *best_y, int *best_w, int *best_h, int *best_r, bool blockAligned, uint32_t maxResolution, bool allowRotate)
	{
		const int stepSize = blockAligned ? 4 : 1;
		int best_metric = INT_MAX;
		// Try two different orientations.
		for (int r = 0; r < 2; r++) {
			int cw = chartBitImage->width();
			int ch = chartBitImage->height();
			if (r == 1) {
				if (allowRotate)
					swap(cw, ch);
				else
					break;
			}
			for (int y = startPosition.y; y <= h + stepSize; y += stepSize) {
				if (maxResolution > 0 && y > (int)maxResolution - ch)
					break;
				for (int x = (y == startPosition.y ? startPosition.x : 0); x <= w + stepSize; x += stepSize) {
					if (maxResolution > 0 && x > (int)maxResolution - cw)
						break;
					// Early out if metric is not better.
					const int extentX = max(w, x + cw), extentY = max(h, y + ch);
					const int area = extentX * extentY;
					const int extents = max(extentX, extentY);
					const int metric = extents * extents + area;
					if (metric > best_metric)
						continue;
					// If metric is the same, pick the one closest to the origin.
					if (metric == best_metric && max(x, y) >= max(*best_x, *best_y))
						continue;
					if (!atlasBitImage->canBlit(r == 1 ? *chartBitImageRotated : *chartBitImage, x, y))
						continue;
					best_metric = metric;
					*best_x = x;
					*best_y = y;
					*best_w = cw;
					*best_h = ch;
					*best_r = r;
					if (area == w * h)
						return true; // Chart is completely inside, do not look at any other location.
				}
			}
		}
		return best_metric != INT_MAX;
	}

	bool findChartLocation_random(const BitImage *atlasBitImage, const BitImage *chartBitImage, const BitImage *chartBitImageRotated, int w, int h, int *best_x, int *best_y, int *best_w, int *best_h, int *best_r, int minTrialCount, bool blockAligned, uint32_t maxResolution, bool allowRotate)
	{
		bool result = false;
		const int BLOCK_SIZE = 4;
		int best_metric = INT_MAX;
		for (int i = 0; i < minTrialCount; i++) {
			int cw = chartBitImage->width();
			int ch = chartBitImage->height();
			int r = allowRotate ? m_rand.getRange(1) : 0;
			if (r == 1)
				swap(cw, ch);
			// + 1 to extend atlas in case atlas full. We may want to use a higher number to increase probability of extending atlas.
			int xRange = w + 1;
			int yRange = h + 1;
			// Clamp to max resolution.
			if (maxResolution > 0) {
				xRange = min(xRange, (int)maxResolution - cw);
				yRange = min(yRange, (int)maxResolution - ch);
			}
			int x = m_rand.getRange(xRange);
			int y = m_rand.getRange(yRange);
			if (blockAligned) {
				x = align(x, BLOCK_SIZE);
				y = align(y, BLOCK_SIZE);
				if (maxResolution > 0 && (x > (int)maxResolution - cw || y > (int)maxResolution - ch))
					continue; // Block alignment pushed the chart outside the atlas.
			}
			// Early out.
			int area = max(w, x + cw) * max(h, y + ch);
			//int perimeter = max(w, x+cw) + max(h, y+ch);
			int extents = max(max(w, x + cw), max(h, y + ch));
			int metric = extents * extents + area;
			if (metric > best_metric) {
				continue;
			}
			if (metric == best_metric && min(x, y) > min(*best_x, *best_y)) {
				// If metric is the same, pick the one closest to the origin.
				continue;
			}
			if (atlasBitImage->canBlit(r == 1 ? *chartBitImageRotated : *chartBitImage, x, y)) {
				result = true;
				best_metric = metric;
				*best_x = x;
				*best_y = y;
				*best_w = cw;
				*best_h = ch;
				*best_r = allowRotate ? r : 0;
				if (area == w * h) {
					// Chart is completely inside, do not look at any other location.
					break;
				}
			}
		}
		return result;
	}

	void addChart(BitImage *atlasBitImage, const BitImage *chartBitImage, const BitImage *chartBitImageRotated, int atlas_w, int atlas_h, int offset_x, int offset_y, int r)
	{
		XA_DEBUG_ASSERT(r == 0 || r == 1);
		const BitImage *image = r == 0 ? chartBitImage : chartBitImageRotated;
		const int w = image->width();
		const int h = image->height();
		for (int y = 0; y < h; y++) {
			int yy = y + offset_y;
			if (yy >= 0) {
				for (int x = 0; x < w; x++) {
					int xx = x + offset_x;
					if (xx >= 0) {
						if (image->get(x, y)) {
							if (xx < atlas_w && yy < atlas_h) {
								XA_DEBUG_ASSERT(atlasBitImage->get(xx, yy) == false);
								atlasBitImage->set(xx, yy);
							}
						}
					}
				}
			}
		}
	}

	void bilinearExpand(const Chart *chart, BitImage *source, BitImage *dest, BitImage *destRotated, UniformGrid2 &boundaryEdgeGrid) const
	{
		boundaryEdgeGrid.reset(chart->vertices, chart->indices);
		if (chart->boundaryEdges) {
			const uint32_t edgeCount = chart->boundaryEdges->size();
			for (uint32_t i = 0; i < edgeCount; i++)
				boundaryEdgeGrid.append((*chart->boundaryEdges)[i]);
		} else {
			for (uint32_t i = 0; i < chart->indexCount; i++)
				boundaryEdgeGrid.append(i);
		}
		const int xOffsets[] = { -1, 0, 1, -1, 1, -1, 0, 1 };
		const int yOffsets[] = { -1, -1, -1, 0, 0, 1, 1, 1 };
		for (uint32_t y = 0; y < source->height(); y++) {
			for (uint32_t x = 0; x < source->width(); x++) {
				// Copy pixels from source.
				if (source->get(x, y))
					goto setPixel;
				// Empty pixel. If none of of the surrounding pixels are set, this pixel can't be sampled by bilinear interpolation.
				{
					uint32_t s = 0;
					for (; s < 8; s++) {
						const int sx = (int)x + xOffsets[s];
						const int sy = (int)y + yOffsets[s];
						if (sx < 0 || sy < 0 || sx >= (int)source->width() || sy >= (int)source->height())
							continue;
						if (source->get((uint32_t)sx, (uint32_t)sy))
							break;
					}
					if (s == 8)
						continue;
				}
				{
					// If a 2x2 square centered on the pixels centroid intersects the triangle, this pixel will be sampled by bilinear interpolation.
					// See "Precomputed Global Illumination in Frostbite (GDC 2018)" page 95
					const Vector2 centroid((float)x + 0.5f, (float)y + 0.5f);
					const Vector2 squareVertices[4] = {
						Vector2(centroid.x - 1.0f, centroid.y - 1.0f),
						Vector2(centroid.x + 1.0f, centroid.y - 1.0f),
						Vector2(centroid.x + 1.0f, centroid.y + 1.0f),
						Vector2(centroid.x - 1.0f, centroid.y + 1.0f)
					};
					for (uint32_t j = 0; j < 4; j++) {
						if (boundaryEdgeGrid.intersect(squareVertices[j], squareVertices[(j + 1) % 4], 0.0f))
							goto setPixel;
					}
				}
				continue;
			setPixel:
				dest->set(x, y);
				if (destRotated)
					destRotated->set(y, x);
			}
		}
	}

	struct DrawTriangleCallbackArgs
	{
		BitImage *chartBitImage, *chartBitImageRotated;
	};

	static bool drawTriangleCallback(void *param, int x, int y)
	{
		auto args = (DrawTriangleCallbackArgs *)param;
		args->chartBitImage->set(x, y);
		if (args->chartBitImageRotated)
			args->chartBitImageRotated->set(y, x);
		return true;
	}

	Array<AtlasImage *> m_atlasImages;
	Array<float> m_utilization;
	Array<BitImage *> m_bitImages;
	Array<Chart *> m_charts;
	RadixSort m_radix;
	uint32_t m_width = 0;
	uint32_t m_height = 0;
	float m_texelsPerUnit = 0.0f;
	KISSRng m_rand;
};

} // namespace pack
} // namespace internal

struct Context
{
	Atlas atlas;
	internal::Progress *addMeshProgress = nullptr;
	internal::TaskGroupHandle addMeshTaskGroup;
	internal::param::Atlas paramAtlas;
	ProgressFunc progressFunc = nullptr;
	void *progressUserData = nullptr;
	internal::TaskScheduler *taskScheduler;
	internal::Array<internal::Mesh *> meshes;
	internal::Array<internal::UvMesh *> uvMeshes;
	internal::Array<internal::UvMeshInstance *> uvMeshInstances;
};

Atlas *Create()
{
	Context *ctx = XA_NEW(internal::MemTag::Default, Context);
	memset(&ctx->atlas, 0, sizeof(Atlas));
	ctx->taskScheduler = XA_NEW(internal::MemTag::Default, internal::TaskScheduler);
	return &ctx->atlas;
}

static void DestroyOutputMeshes(Context *ctx)
{
	if (!ctx->atlas.meshes)
		return;
	for (int i = 0; i < (int)ctx->atlas.meshCount; i++) {
		Mesh &mesh = ctx->atlas.meshes[i];
		if (mesh.chartArray) {
			for (uint32_t j = 0; j < mesh.chartCount; j++) {
				if (mesh.chartArray[j].faceArray)
					XA_FREE(mesh.chartArray[j].faceArray);
			}
			XA_FREE(mesh.chartArray);
		}
		if (mesh.vertexArray)
			XA_FREE(mesh.vertexArray);
		if (mesh.indexArray)
			XA_FREE(mesh.indexArray);
	}
	XA_FREE(ctx->atlas.meshes);
	ctx->atlas.meshes = nullptr;
}

void Destroy(Atlas *atlas)
{
	XA_DEBUG_ASSERT(atlas);
	Context *ctx = (Context *)atlas;
	if (atlas->utilization)
		XA_FREE(atlas->utilization);
	if (atlas->image)
		XA_FREE(atlas->image);
	DestroyOutputMeshes(ctx);
	if (ctx->addMeshProgress) {
		ctx->addMeshProgress->cancel = true;
		AddMeshJoin(atlas); // frees addMeshProgress
	}
	ctx->taskScheduler->~TaskScheduler();
	XA_FREE(ctx->taskScheduler);
	for (uint32_t i = 0; i < ctx->meshes.size(); i++) {
		internal::Mesh *mesh = ctx->meshes[i];
		mesh->~Mesh();
		XA_FREE(mesh);
	}
	for (uint32_t i = 0; i < ctx->uvMeshes.size(); i++) {
		internal::UvMesh *mesh = ctx->uvMeshes[i];
		for (uint32_t j = 0; j < mesh->charts.size(); j++) {
			mesh->charts[j]->~UvMeshChart();
			XA_FREE(mesh->charts[j]);
		}
		mesh->~UvMesh();
		XA_FREE(mesh);
	}
	for (uint32_t i = 0; i < ctx->uvMeshInstances.size(); i++) {
		internal::UvMeshInstance *mesh = ctx->uvMeshInstances[i];
		mesh->~UvMeshInstance();
		XA_FREE(mesh);
	}
	ctx->~Context();
	XA_FREE(ctx);
#if XA_DEBUG_HEAP
	internal::ReportLeaks();
#endif
}

struct AddMeshTaskArgs
{
	Context *ctx;
	internal::Mesh *mesh;
};

static void runAddMeshTask(void *userData)
{
	XA_PROFILE_START(addMeshThread)
	auto args = (AddMeshTaskArgs *)userData; // Responsible for freeing this.
	internal::Mesh *mesh = args->mesh;
	internal::Progress *progress = args->ctx->addMeshProgress;
	if (progress->cancel)
		goto cleanup;
	{
		XA_PROFILE_START(addMeshCreateColocals)
		mesh->createColocals();
		XA_PROFILE_END(addMeshCreateColocals)
	}
	if (progress->cancel)
		goto cleanup;
	progress->value++;
	progress->update();
cleanup:
	args->~AddMeshTaskArgs();
	XA_FREE(args);
	XA_PROFILE_END(addMeshThread)
}

static internal::Vector3 DecodePosition(const MeshDecl &meshDecl, uint32_t index)
{
	XA_DEBUG_ASSERT(meshDecl.vertexPositionData);
	XA_DEBUG_ASSERT(meshDecl.vertexPositionStride > 0);
	return *((const internal::Vector3 *)&((const uint8_t *)meshDecl.vertexPositionData)[meshDecl.vertexPositionStride * index]);
}

static internal::Vector3 DecodeNormal(const MeshDecl &meshDecl, uint32_t index)
{
	XA_DEBUG_ASSERT(meshDecl.vertexNormalData);
	XA_DEBUG_ASSERT(meshDecl.vertexNormalStride > 0);
	return *((const internal::Vector3 *)&((const uint8_t *)meshDecl.vertexNormalData)[meshDecl.vertexNormalStride * index]);
}

static internal::Vector2 DecodeUv(const MeshDecl &meshDecl, uint32_t index)
{
	XA_DEBUG_ASSERT(meshDecl.vertexUvData);
	XA_DEBUG_ASSERT(meshDecl.vertexUvStride > 0);
	return *((const internal::Vector2 *)&((const uint8_t *)meshDecl.vertexUvData)[meshDecl.vertexUvStride * index]);
}

static uint32_t DecodeIndex(IndexFormat::Enum format, const void *indexData, int32_t offset, uint32_t i)
{
	XA_DEBUG_ASSERT(indexData);
	if (format == IndexFormat::UInt16)
		return uint16_t((int32_t)((const uint16_t *)indexData)[i] + offset);
	return uint32_t((int32_t)((const uint32_t *)indexData)[i] + offset);
}

AddMeshError::Enum AddMesh(Atlas *atlas, const MeshDecl &meshDecl, uint32_t meshCountHint)
{
	XA_DEBUG_ASSERT(atlas);
	if (!atlas) {
		XA_PRINT_WARNING("AddMesh: atlas is null.\n");
		return AddMeshError::Error;
	}
	Context *ctx = (Context *)atlas;
	if (!ctx->uvMeshes.isEmpty()) {
		XA_PRINT_WARNING("AddMesh: Meshes and UV meshes cannot be added to the same atlas.\n");
		return AddMeshError::Error;
	}
#if XA_PROFILE
	if (ctx->meshes.isEmpty())
		internal::s_profile.addMeshReal = clock();
#endif
	// Don't know how many times AddMesh will be called, so progress needs to adjusted each time.
	if (!ctx->addMeshProgress) {
		ctx->addMeshProgress = XA_NEW_ARGS(internal::MemTag::Default, internal::Progress, ProgressCategory::AddMesh, ctx->progressFunc, ctx->progressUserData, 1);
	}
	else {
		ctx->addMeshProgress->setMaxValue(internal::max(ctx->meshes.size() + 1, meshCountHint));
	}
	XA_PROFILE_START(addMeshCopyData)
	const bool hasIndices = meshDecl.indexCount > 0;
	const uint32_t indexCount = hasIndices ? meshDecl.indexCount : meshDecl.vertexCount;
	XA_PRINT("Adding mesh %d: %u vertices, %u triangles\n", ctx->meshes.size(), meshDecl.vertexCount, indexCount / 3);
	// Expecting triangle faces.
	if ((indexCount % 3) != 0)
		return AddMeshError::InvalidIndexCount;
	if (hasIndices) {
		// Check if any index is out of range.
		for (uint32_t i = 0; i < indexCount; i++) {
			const uint32_t index = DecodeIndex(meshDecl.indexFormat, meshDecl.indexData, meshDecl.indexOffset, i);
			if (index >= meshDecl.vertexCount)
				return AddMeshError::IndexOutOfRange;
		}
	}
	uint32_t meshFlags = internal::MeshFlags::HasIgnoredFaces;
	if (meshDecl.vertexNormalData)
		meshFlags |= internal::MeshFlags::HasNormals;
	internal::Mesh *mesh = XA_NEW_ARGS(internal::MemTag::Mesh, internal::Mesh, meshDecl.epsilon, meshDecl.vertexCount, indexCount / 3, meshFlags, ctx->meshes.size());
	for (uint32_t i = 0; i < meshDecl.vertexCount; i++) {
		internal::Vector3 normal(0.0f);
		internal::Vector2 texcoord(0.0f);
		if (meshDecl.vertexNormalData)
			normal = DecodeNormal(meshDecl, i);
		if (meshDecl.vertexUvData)
			texcoord = DecodeUv(meshDecl, i);
		mesh->addVertex(DecodePosition(meshDecl, i), normal, texcoord);
	}
	const uint32_t kMaxWarnings = 50;
	uint32_t warningCount = 0;
	for (uint32_t i = 0; i < indexCount / 3; i++) {
		uint32_t tri[3];
		for (int j = 0; j < 3; j++)
			tri[j] = hasIndices ? DecodeIndex(meshDecl.indexFormat, meshDecl.indexData, meshDecl.indexOffset, i * 3 + j) : i * 3 + j;
		bool ignore = false;
		// Check for degenerate or zero length edges.
		for (int j = 0; j < 3; j++) {
			const uint32_t index1 = tri[j];
			const uint32_t index2 = tri[(j + 1) % 3];
			if (index1 == index2) {
				ignore = true;
				if (++warningCount <= kMaxWarnings)
					XA_PRINT("   Degenerate edge: index %d, index %d\n", index1, index2);
				break;
			}
			const internal::Vector3 &pos1 = mesh->position(index1);
			const internal::Vector3 &pos2 = mesh->position(index2);
			if (internal::length(pos2 - pos1) <= 0.0f) {
				ignore = true;
				if (++warningCount <= kMaxWarnings)
					XA_PRINT("   Zero length edge: index %d position (%g %g %g), index %d position (%g %g %g)\n", index1, pos1.x, pos1.y, pos1.z, index2, pos2.x, pos2.y, pos2.z);
				break;
			}
		}
		// Ignore faces with any nan vertex attributes.
		if (!ignore) {
			for (int j = 0; j < 3; j++) {
				const internal::Vector3 &pos = mesh->position(tri[j]);
				if (internal::isNan(pos.x) || internal::isNan(pos.y) || internal::isNan(pos.z)) {
					if (++warningCount <= kMaxWarnings)
						XA_PRINT("   NAN position in face: %d\n", i);
					ignore = true;
					break;
				}
				if (meshDecl.vertexNormalData) {
					const internal::Vector3 &normal = mesh->normal(tri[j]);
					if (internal::isNan(normal.x) || internal::isNan(normal.y) || internal::isNan(normal.z)) {
						if (++warningCount <= kMaxWarnings)
							XA_PRINT("   NAN normal in face: %d\n", i);
						ignore = true;
						break;
					}
				}
				if (meshDecl.vertexUvData) {
					const internal::Vector2 &uv = mesh->texcoord(tri[j]);
					if (internal::isNan(uv.x) || internal::isNan(uv.y)) {
						if (++warningCount <= kMaxWarnings)
							XA_PRINT("   NAN texture coordinate in face: %d\n", i);
						ignore = true;
						break;
					}
				}
			}
		}
		const internal::Vector3 &a = mesh->position(tri[0]);
		const internal::Vector3 &b = mesh->position(tri[1]);
		const internal::Vector3 &c = mesh->position(tri[2]);
		// Check for zero area faces.
		float area = 0.0f;
		if (!ignore) {
			area = internal::length(internal::cross(b - a, c - a)) * 0.5f;
			if (area <= internal::kAreaEpsilon) {
				ignore = true;
				if (++warningCount <= kMaxWarnings)
					XA_PRINT("   Zero area face: %d, indices (%d %d %d), area is %f\n", i, tri[0], tri[1], tri[2], area);
			}
		}
		if (!ignore) {
			if (internal::equal(a, b, meshDecl.epsilon) || internal::equal(a, c, meshDecl.epsilon) || internal::equal(b, c, meshDecl.epsilon)) {
				ignore = true;
				if (++warningCount <= kMaxWarnings)
					XA_PRINT("   Degenerate face: %d, area is %f\n", i, area);
			}
		}
		if (meshDecl.faceIgnoreData && meshDecl.faceIgnoreData[i])
			ignore = true;
		mesh->addFace(tri[0], tri[1], tri[2], ignore);
	}
	if (warningCount > kMaxWarnings)
		XA_PRINT("   %u additional warnings truncated\n", warningCount - kMaxWarnings);
	XA_PROFILE_END(addMeshCopyData)
	ctx->meshes.push_back(mesh);
	ctx->paramAtlas.addMesh(mesh);
	if (ctx->addMeshTaskGroup.value == UINT32_MAX)
		ctx->addMeshTaskGroup = ctx->taskScheduler->createTaskGroup();
	AddMeshTaskArgs *taskArgs = XA_NEW(internal::MemTag::Default, AddMeshTaskArgs); // The task frees this.
	taskArgs->ctx = ctx;
	taskArgs->mesh = mesh;
	internal::Task task;
	task.userData = taskArgs;
	task.func = runAddMeshTask;
	ctx->taskScheduler->run(ctx->addMeshTaskGroup, task);
	return AddMeshError::Success;
}

void AddMeshJoin(Atlas *atlas)
{
	XA_DEBUG_ASSERT(atlas);
	if (!atlas) {
		XA_PRINT_WARNING("AddMeshJoin: atlas is null.\n");
		return;
	}
	Context *ctx = (Context *)atlas;
	if (!ctx->addMeshProgress)
		return;
	ctx->taskScheduler->wait(&ctx->addMeshTaskGroup);
	ctx->addMeshProgress->~Progress();
	XA_FREE(ctx->addMeshProgress);
	ctx->addMeshProgress = nullptr;
#if XA_PROFILE
	XA_PRINT("Added %u meshes\n", ctx->meshes.size());
	internal::s_profile.addMeshReal = clock() - internal::s_profile.addMeshReal;
#endif
	XA_PROFILE_PRINT_AND_RESET("   Total (real): ", addMeshReal)
	XA_PROFILE_PRINT_AND_RESET("      Copy data: ", addMeshCopyData)
	XA_PROFILE_PRINT_AND_RESET("   Total (thread): ", addMeshThread)
	XA_PROFILE_PRINT_AND_RESET("      Create colocals: ", addMeshCreateColocals)
#if XA_PROFILE_ALLOC
	XA_PROFILE_PRINT_AND_RESET("   Alloc: ", alloc)
#endif
	XA_PRINT_MEM_USAGE
#if XA_DEBUG_EXPORT_OBJ_FACE_GROUPS
	internal::param::s_faceGroupsCurrentVertex = 0;
#endif
}

struct EdgeKey
{
	EdgeKey() {}
	EdgeKey(const EdgeKey &k) : v0(k.v0), v1(k.v1) {}
	EdgeKey(uint32_t v0, uint32_t v1) : v0(v0), v1(v1) {}
	bool operator==(const EdgeKey &k) const { return v0 == k.v0 && v1 == k.v1; }

	uint32_t v0;
	uint32_t v1;
};

AddMeshError::Enum AddUvMesh(Atlas *atlas, const UvMeshDecl &decl)
{
	XA_DEBUG_ASSERT(atlas);
	if (!atlas) {
		XA_PRINT_WARNING("AddUvMesh: atlas is null.\n");
		return AddMeshError::Error;
	}
	Context *ctx = (Context *)atlas;
	if (!ctx->meshes.isEmpty()) {
		XA_PRINT_WARNING("AddUvMesh: Meshes and UV meshes cannot be added to the same atlas.\n");
		return AddMeshError::Error;
	}
	const bool decoded = (decl.indexCount <= 0);
	const uint32_t indexCount = decoded ? decl.vertexCount : decl.indexCount;
	XA_PRINT("Adding UV mesh %d: %u vertices, %u triangles\n", ctx->uvMeshes.size(), decl.vertexCount, indexCount / 3);
	// Expecting triangle faces.
	if ((indexCount % 3) != 0)
		return AddMeshError::InvalidIndexCount;
	if (!decoded) {
		// Check if any index is out of range.
		for (uint32_t i = 0; i < indexCount; i++) {
			const uint32_t index = DecodeIndex(decl.indexFormat, decl.indexData, decl.indexOffset, i);
			if (index >= decl.vertexCount)
				return AddMeshError::IndexOutOfRange;
		}
	}
	internal::UvMeshInstance *meshInstance = XA_NEW(internal::MemTag::Default, internal::UvMeshInstance);
	meshInstance->texcoords.resize(decl.vertexCount);
	for (uint32_t i = 0; i < decl.vertexCount; i++) {
		internal::Vector2 texcoord = *((const internal::Vector2 *)&((const uint8_t *)decl.vertexUvData)[decl.vertexStride * i]);
		// Set nan values to 0.
		if (internal::isNan(texcoord.x) || internal::isNan(texcoord.y))
			texcoord.x = texcoord.y = 0.0f;
		meshInstance->texcoords[i] = texcoord;
	}
	meshInstance->rotateCharts = decl.rotateCharts;
	// See if this is an instance of an already existing mesh.
	internal::UvMesh *mesh = nullptr;
	for (uint32_t m = 0; m < ctx->uvMeshes.size(); m++) {
		if (memcmp(&ctx->uvMeshes[m]->decl, &decl, sizeof(UvMeshDecl)) == 0) {
			meshInstance->mesh = mesh = ctx->uvMeshes[m];
			break;
		}
	}
	if (!mesh) {
		// Copy geometry to mesh.
		meshInstance->mesh = mesh = XA_NEW(internal::MemTag::Default, internal::UvMesh);
		mesh->decl = decl;
		mesh->indices.resize(decl.indexCount);
		for (uint32_t i = 0; i < indexCount; i++)
			mesh->indices[i] = decoded ? i : DecodeIndex(decl.indexFormat, decl.indexData, decl.indexOffset, i);
		mesh->vertexToChartMap.resize(decl.vertexCount);
		for (uint32_t i = 0; i < mesh->vertexToChartMap.size(); i++)
			mesh->vertexToChartMap[i] = UINT32_MAX;
		// Calculate charts (incident faces).
		internal::HashMap<internal::Vector2> vertexToFaceMap(internal::MemTag::Default, indexCount); // Face is index / 3
		const uint32_t faceCount = indexCount / 3;
		for (uint32_t i = 0; i < indexCount; i++)
			vertexToFaceMap.add(meshInstance->texcoords[mesh->indices[i]]);
		internal::BitArray faceAssigned(faceCount);
		faceAssigned.zeroOutMemory();
		for (uint32_t f = 0; f < faceCount; f++) {
			if (faceAssigned.get(f))
				continue;
			// Found an unassigned face, create a new chart.
			internal::UvMeshChart *chart = XA_NEW(internal::MemTag::Default, internal::UvMeshChart);
			chart->material = decl.faceMaterialData ? decl.faceMaterialData[f] : 0;
			// Walk incident faces and assign them to the chart.
			faceAssigned.set(f);
			chart->faces.push_back(f);
			for (;;) {
				bool newFaceAssigned = false;
				const uint32_t faceCount2 = chart->faces.size();
				for (uint32_t f2 = 0; f2 < faceCount2; f2++) {
					const uint32_t face = chart->faces[f2];
					for (uint32_t i = 0; i < 3; i++) {
						const internal::Vector2 &texcoord = meshInstance->texcoords[meshInstance->mesh->indices[face * 3 + i]];
						uint32_t mapIndex = vertexToFaceMap.get(texcoord);
						while (mapIndex != UINT32_MAX) {
							const uint32_t face2 = mapIndex / 3; // 3 vertices added per face.
							// Materials must match.
							if (!faceAssigned.get(face2) && (!decl.faceMaterialData || decl.faceMaterialData[face] == decl.faceMaterialData[face2])) {
								faceAssigned.set(face2);
								chart->faces.push_back(face2);
								newFaceAssigned = true;
							}
							mapIndex = vertexToFaceMap.getNext(mapIndex);
						}
					}
				}
				if (!newFaceAssigned)
					break;
			}
			for (uint32_t i = 0; i < chart->faces.size(); i++) {
				for (uint32_t j = 0; j < 3; j++) {
					const uint32_t vertex = meshInstance->mesh->indices[chart->faces[i] * 3 + j];
					chart->indices.push_back(vertex);
					mesh->vertexToChartMap[vertex] = mesh->charts.size();
				}
			}
			mesh->charts.push_back(chart);
		}
		ctx->uvMeshes.push_back(mesh);
	} else {
		XA_PRINT("   instance of a previous UV mesh\n");
	}
	XA_PRINT("   %u charts\n", meshInstance->mesh->charts.size());
	ctx->uvMeshInstances.push_back(meshInstance);
	return AddMeshError::Success;
}

void ComputeCharts(Atlas *atlas, ChartOptions options)
{
	if (!atlas) {
		XA_PRINT_WARNING("ComputeCharts: atlas is null.\n");
		return;
	}
	Context *ctx = (Context *)atlas;
	if (!ctx->uvMeshInstances.isEmpty()) {
		XA_PRINT_WARNING("ComputeCharts: This function should not be called with UV meshes.\n");
		return;
	}
	AddMeshJoin(atlas);
	if (ctx->meshes.isEmpty()) {
		XA_PRINT_WARNING("ComputeCharts: No meshes. Call AddMesh first.\n");
		return;
	}
	XA_PRINT("Computing charts\n");
	XA_PROFILE_START(computeChartsReal)
	if (!ctx->paramAtlas.computeCharts(ctx->taskScheduler, options, ctx->progressFunc, ctx->progressUserData)) {
		XA_PRINT("   Cancelled by user\n");
		return;
	}
	XA_PROFILE_END(computeChartsReal)
	// Count charts.
	uint32_t chartCount = 0;
	const uint32_t meshCount = ctx->meshes.size();
	for (uint32_t i = 0; i < meshCount; i++) {
		for (uint32_t j = 0; j < ctx->paramAtlas.chartGroupCount(i); j++) {
			const internal::param::ChartGroup *chartGroup = ctx->paramAtlas.chartGroupAt(i, j);
			chartCount += chartGroup->segmentChartCount();
		}
	}
	XA_PRINT("   %u charts\n", chartCount);
#if XA_PROFILE
	XA_PRINT("   Chart groups\n");
	uint32_t chartGroupCount = 0;
	for (uint32_t i = 0; i < meshCount; i++) {
		XA_PRINT("      Mesh %u: %u chart groups\n", i, ctx->paramAtlas.chartGroupCount(i));
		chartGroupCount += ctx->paramAtlas.chartGroupCount(i);
	}
	XA_PRINT("      %u total\n", chartGroupCount);
#endif
	XA_PROFILE_PRINT_AND_RESET("   Total (real): ", computeChartsReal)
	XA_PROFILE_PRINT_AND_RESET("   Total (thread): ", computeChartsThread)
	XA_PROFILE_PRINT_AND_RESET("      Create face groups: ", createFaceGroups)
	XA_PROFILE_PRINT_AND_RESET("      Extract invalid mesh geometry: ", extractInvalidMeshGeometry)
	XA_PROFILE_PRINT_AND_RESET("      Chart group compute charts (real): ", chartGroupComputeChartsReal)
	XA_PROFILE_PRINT_AND_RESET("      Chart group compute charts (thread): ", chartGroupComputeChartsThread)
	XA_PROFILE_PRINT_AND_RESET("         Create chart group mesh: ", createChartGroupMesh)
	XA_PROFILE_PRINT_AND_RESET("            Create colocals: ", createChartGroupMeshColocals)
	XA_PROFILE_PRINT_AND_RESET("            Create boundaries: ", createChartGroupMeshBoundaries)
	XA_PROFILE_PRINT_AND_RESET("         Build atlas: ", buildAtlas)
	XA_PROFILE_PRINT_AND_RESET("            Init: ", buildAtlasInit)
	XA_PROFILE_PRINT_AND_RESET("            Planar charts: ", planarCharts)
	XA_PROFILE_PRINT_AND_RESET("            Clustered charts: ", clusteredCharts)
	XA_PROFILE_PRINT_AND_RESET("               Place seeds: ", clusteredChartsPlaceSeeds)
	XA_PROFILE_PRINT_AND_RESET("                  Boundary intersection: ", clusteredChartsPlaceSeedsBoundaryIntersection)
	XA_PROFILE_PRINT_AND_RESET("               Relocate seeds: ", clusteredChartsRelocateSeeds)
	XA_PROFILE_PRINT_AND_RESET("               Reset: ", clusteredChartsReset)
	XA_PROFILE_PRINT_AND_RESET("               Grow: ", clusteredChartsGrow)
	XA_PROFILE_PRINT_AND_RESET("                  Boundary intersection: ", clusteredChartsGrowBoundaryIntersection)
	XA_PROFILE_PRINT_AND_RESET("               Merge: ", clusteredChartsMerge)
	XA_PROFILE_PRINT_AND_RESET("               Fill holes: ", clusteredChartsFillHoles)
	XA_PROFILE_PRINT_AND_RESET("         Copy chart faces: ", copyChartFaces)
#if XA_PROFILE_ALLOC
	XA_PROFILE_PRINT_AND_RESET("   Alloc: ", alloc)
#endif
	XA_PRINT_MEM_USAGE
}

void ParameterizeCharts(Atlas *atlas, ParameterizeOptions options)
{
	if (!atlas) {
		XA_PRINT_WARNING("ParameterizeCharts: atlas is null.\n");
		return;
	}
	Context *ctx = (Context *)atlas;
	if (!ctx->uvMeshInstances.isEmpty()) {
		XA_PRINT_WARNING("ParameterizeCharts: This function should not be called with UV meshes.\n");
		return;
	}
	if (!ctx->paramAtlas.chartsComputed()) {
		XA_PRINT_WARNING("ParameterizeCharts: ComputeCharts must be called first.\n");
		return;
	}
	atlas->atlasCount = 0;
	atlas->height = 0;
	atlas->texelsPerUnit = 0;
	atlas->width = 0;
	if (atlas->utilization) {
		XA_FREE(atlas->utilization);
		atlas->utilization = nullptr;
	}
	if (atlas->image) {
		XA_FREE(atlas->image);
		atlas->image = nullptr;
	}
	DestroyOutputMeshes(ctx);
	XA_PRINT("Parameterizing charts\n");
	XA_PROFILE_START(parameterizeChartsReal)
	if (!ctx->paramAtlas.parameterizeCharts(ctx->taskScheduler, options, ctx->progressFunc, ctx->progressUserData)) {
		XA_PRINT("   Cancelled by user\n");
			return;
	}
	XA_PROFILE_END(parameterizeChartsReal)
	const uint32_t meshCount = ctx->meshes.size();
	uint32_t chartCount = 0, chartsWithHolesCount = 0, holesCount = 0, chartsWithTJunctionsCount = 0, tJunctionsCount = 0, orthoChartsCount = 0, planarChartsCount = 0, lscmChartsCount = 0, piecewiseChartsCount = 0, chartsAddedCount = 0, chartsDeletedCount = 0;
	for (uint32_t i = 0; i < meshCount; i++) {
		for (uint32_t j = 0; j < ctx->paramAtlas.chartGroupCount(i); j++) {
			const internal::param::ChartGroup *chartGroup = ctx->paramAtlas.chartGroupAt(i, j);
			for (uint32_t k = 0; k < chartGroup->chartCount(); k++) {
				const internal::param::Chart *chart = chartGroup->chartAt(k);
#if XA_PRINT_CHART_WARNINGS
				if (chart->warningFlags() & internal::param::ChartWarningFlags::CloseHolesFailed)
					XA_PRINT_WARNING("   Chart %u (mesh %u, group %u, id %u): failed to close holes\n", chartCount, i, j, k);
				if (chart->warningFlags() & internal::param::ChartWarningFlags::FixTJunctionsDuplicatedEdge)
					XA_PRINT_WARNING("   Chart %u (mesh %u, group %u, id %u): fixing t-junctions created non-manifold geometry\n", chartCount, i, j, k);
				if (chart->warningFlags() & internal::param::ChartWarningFlags::FixTJunctionsFailed)
					XA_PRINT_WARNING("   Chart %u (mesh %u, group %u, id %u): fixing t-junctions failed\n", chartCount, i, j, k);
				if (chart->warningFlags() & internal::param::ChartWarningFlags::TriangulateDuplicatedEdge)
					XA_PRINT_WARNING("   Chart %u (mesh %u, group %u, id %u): triangulation created non-manifold geometry\n", chartCount, i, j, k);
#endif
				holesCount += chart->closedHolesCount();
				if (chart->closedHolesCount() > 0)
					chartsWithHolesCount++;
				tJunctionsCount += chart->fixedTJunctionsCount();
				if (chart->fixedTJunctionsCount() > 0)
					chartsWithTJunctionsCount++;
				if (chart->type() == ChartType::Planar)
					planarChartsCount++;
				else if (chart->type() == ChartType::Ortho)
					orthoChartsCount++;
				else if (chart->type() == ChartType::LSCM)
					lscmChartsCount++;
				else if (chart->type() == ChartType::Piecewise)
					piecewiseChartsCount++;
			}
			chartCount += chartGroup->chartCount();
			chartsAddedCount += chartGroup->paramAddedChartsCount();
			chartsDeletedCount += chartGroup->paramDeletedChartsCount();
		}
	}
	if (holesCount > 0)
		XA_PRINT("   %u holes closed in %u charts\n", holesCount, chartsWithHolesCount);
	if (tJunctionsCount > 0)
		XA_PRINT("   %u t-junctions fixed in %u charts\n", tJunctionsCount, chartsWithTJunctionsCount);
	XA_PRINT("   %u planar charts, %u ortho charts, %u LSCM charts, %u piecewise charts\n", planarChartsCount, orthoChartsCount, lscmChartsCount, piecewiseChartsCount);
	if (chartsDeletedCount > 0) {
		XA_PRINT("   %u charts with invalid parameterizations replaced with %u new charts\n", chartsDeletedCount, chartsAddedCount);
		XA_PRINT("   %u charts\n", chartCount);
	}
	uint32_t chartIndex = 0, invalidParamCount = 0;
	for (uint32_t i = 0; i < meshCount; i++) {
		for (uint32_t j = 0; j < ctx->paramAtlas.chartGroupCount(i); j++) {
			const internal::param::ChartGroup *chartGroup = ctx->paramAtlas.chartGroupAt(i, j);
			for (uint32_t k = 0; k < chartGroup->chartCount(); k++) {
				internal::param::Chart *chart = chartGroup->chartAt(k);
				const internal::param::Quality &quality = chart->quality();
#if XA_DEBUG_EXPORT_OBJ_CHARTS_AFTER_PARAMETERIZATION
				{
					char filename[256];
					XA_SPRINTF(filename, sizeof(filename), "debug_chart_%03u_after_parameterization.obj", chartIndex);
					chart->unifiedMesh()->writeObjFile(filename);
				}
#endif
				const char *type = "LSCM";
				if (chart->type() == ChartType::Planar)
					type = "planar";
				else if (chart->type() == ChartType::Ortho)
					type = "ortho";
				else if (chart->type() == ChartType::Piecewise)
					type = "piecewise";
				if (chart->isInvalid()) {
					if (quality.boundaryIntersection) {
						XA_PRINT_WARNING("   Chart %u (mesh %u, group %u, id %u) (%s): invalid parameterization, self-intersecting boundary.\n", chartIndex, i, j, k, type);
					}
					if (quality.flippedTriangleCount > 0) {
						XA_PRINT_WARNING("   Chart %u  (mesh %u, group %u, id %u) (%s): invalid parameterization, %u / %u flipped triangles.\n", chartIndex, i, j, k, type, quality.flippedTriangleCount, quality.totalTriangleCount);
					}
					invalidParamCount++;
#if XA_DEBUG_EXPORT_OBJ_INVALID_PARAMETERIZATION
					char filename[256];
					XA_SPRINTF(filename, sizeof(filename), "debug_chart_%03u_invalid_parameterization.obj", chartIndex);
					const internal::Mesh *mesh = chart->unifiedMesh();
					FILE *file;
					XA_FOPEN(file, filename, "w");
					if (file) {
						mesh->writeObjVertices(file);
						fprintf(file, "s off\n");
						fprintf(file, "o object\n");
						for (uint32_t f = 0; f < mesh->faceCount(); f++)
							mesh->writeObjFace(file, f);
						if (!chart->paramFlippedFaces().isEmpty()) {
							fprintf(file, "o flipped_faces\n");
							for (uint32_t f = 0; f < chart->paramFlippedFaces().size(); f++)
								mesh->writeObjFace(file, chart->paramFlippedFaces()[f]);
						}
						mesh->writeObjBoundaryEges(file);
						mesh->writeObjLinkedBoundaries(file);
						fclose(file);
					}
#endif
				}
				chartIndex++;
			}
		}
	}
	if (invalidParamCount > 0)
		XA_PRINT_WARNING("   %u charts with invalid parameterizations\n", invalidParamCount);
	XA_PROFILE_PRINT_AND_RESET("   Total (real): ", parameterizeChartsReal)
	XA_PROFILE_PRINT_AND_RESET("   Total (thread): ", parameterizeChartsThread)
	XA_PROFILE_PRINT_AND_RESET("      Create chart mesh: ", createChartMesh)
	XA_PROFILE_PRINT_AND_RESET("         Fix t-junctions: ", fixChartMeshTJunctions)
	XA_PROFILE_PRINT_AND_RESET("         Close holes: ", closeChartMeshHoles)
	XA_PROFILE_PRINT_AND_RESET("      Orthogonal: ", parameterizeChartsOrthogonal)
	XA_PROFILE_PRINT_AND_RESET("      LSCM: ", parameterizeChartsLSCM)
	XA_PROFILE_PRINT_AND_RESET("      Recompute: ", parameterizeChartsRecompute)
	XA_PROFILE_PRINT_AND_RESET("         Piecewise: ", parameterizeChartsPiecewise)
	XA_PROFILE_PRINT_AND_RESET("            Boundary intersection: ", parameterizeChartsPiecewiseBoundaryIntersection)
	XA_PROFILE_PRINT_AND_RESET("      Evaluate quality: ", parameterizeChartsEvaluateQuality)
#if XA_PROFILE_ALLOC
	XA_PROFILE_PRINT_AND_RESET("   Alloc: ", alloc)
#endif
	XA_PRINT_MEM_USAGE
}

void PackCharts(Atlas *atlas, PackOptions packOptions)
{
	// Validate arguments and context state.
	if (!atlas) {
		XA_PRINT_WARNING("PackCharts: atlas is null.\n");
		return;
	}
	Context *ctx = (Context *)atlas;
	if (ctx->meshes.isEmpty() && ctx->uvMeshInstances.isEmpty()) {
		XA_PRINT_WARNING("PackCharts: No meshes. Call AddMesh or AddUvMesh first.\n");
		return;
	}
	if (ctx->uvMeshInstances.isEmpty()) {
		if (!ctx->paramAtlas.chartsComputed()) {
			XA_PRINT_WARNING("PackCharts: ComputeCharts must be called first.\n");
			return;
		}
		if (!ctx->paramAtlas.chartsParameterized()) {
			XA_PRINT_WARNING("PackCharts: ParameterizeCharts must be called first.\n");
			return;
		}
	}
	if (packOptions.texelsPerUnit < 0.0f) {
		XA_PRINT_WARNING("PackCharts: PackOptions::texelsPerUnit is negative.\n");
		packOptions.texelsPerUnit = 0.0f;
	}
	// Cleanup atlas.
	DestroyOutputMeshes(ctx);
	if (atlas->utilization) {
		XA_FREE(atlas->utilization);
		atlas->utilization = nullptr;
	}
	if (atlas->image) {
		XA_FREE(atlas->image);
		atlas->image = nullptr;
	}
	atlas->meshCount = 0;
	// Pack charts.
	XA_PROFILE_START(packChartsAddCharts)
	internal::pack::Atlas packAtlas;
	if (!ctx->uvMeshInstances.isEmpty()) {
		for (uint32_t i = 0; i < ctx->uvMeshInstances.size(); i++)
			packAtlas.addUvMeshCharts(ctx->uvMeshInstances[i]);
	}
	else
		packAtlas.addCharts(ctx->taskScheduler, &ctx->paramAtlas);
	XA_PROFILE_END(packChartsAddCharts)
	XA_PROFILE_START(packCharts)
	if (!packAtlas.packCharts(packOptions, ctx->progressFunc, ctx->progressUserData))
		return;
	XA_PROFILE_END(packCharts)
	// Populate atlas object with pack results.
	atlas->atlasCount = packAtlas.getNumAtlases();
	atlas->chartCount = packAtlas.getChartCount();
	atlas->width = packAtlas.getWidth();
	atlas->height = packAtlas.getHeight();
	atlas->texelsPerUnit = packAtlas.getTexelsPerUnit();
	if (atlas->atlasCount > 0) {
		atlas->utilization = XA_ALLOC_ARRAY(internal::MemTag::Default, float, atlas->atlasCount);
		for (uint32_t i = 0; i < atlas->atlasCount; i++)
			atlas->utilization[i] = packAtlas.getUtilization(i);
	}
	if (packOptions.createImage) {
		atlas->image = XA_ALLOC_ARRAY(internal::MemTag::Default, uint32_t, atlas->atlasCount * atlas->width * atlas->height);
		for (uint32_t i = 0; i < atlas->atlasCount; i++)
			packAtlas.getImages()[i]->copyTo(&atlas->image[atlas->width * atlas->height * i], atlas->width, atlas->height, packOptions.padding);
	}
	XA_PROFILE_PRINT_AND_RESET("   Total: ", packCharts)
	XA_PROFILE_PRINT_AND_RESET("      Add charts (real): ", packChartsAddCharts)
	XA_PROFILE_PRINT_AND_RESET("      Add charts (thread): ", packChartsAddChartsThread)
	XA_PROFILE_PRINT_AND_RESET("         Restore texcoords: ", packChartsAddChartsRestoreTexcoords)
	XA_PROFILE_PRINT_AND_RESET("      Rasterize: ", packChartsRasterize)
	XA_PROFILE_PRINT_AND_RESET("      Dilate (padding): ", packChartsDilate)
	XA_PROFILE_PRINT_AND_RESET("      Find location: ", packChartsFindLocation)
	XA_PROFILE_PRINT_AND_RESET("      Blit: ", packChartsBlit)
#if XA_PROFILE_ALLOC
	XA_PROFILE_PRINT_AND_RESET("   Alloc: ", alloc)
#endif
	XA_PRINT_MEM_USAGE
	XA_PRINT("Building output meshes\n");
	XA_PROFILE_START(buildOutputMeshes)
	int progress = 0;
	if (ctx->progressFunc) {
		if (!ctx->progressFunc(ProgressCategory::BuildOutputMeshes, 0, ctx->progressUserData))
			return;
	}
	if (ctx->uvMeshInstances.isEmpty())
		atlas->meshCount = ctx->meshes.size();
	else
		atlas->meshCount = ctx->uvMeshInstances.size();
	atlas->meshes = XA_ALLOC_ARRAY(internal::MemTag::Default, Mesh, atlas->meshCount);
	memset(atlas->meshes, 0, sizeof(Mesh) * atlas->meshCount);
	if (ctx->uvMeshInstances.isEmpty()) {
		uint32_t chartIndex = 0;
		for (uint32_t i = 0; i < atlas->meshCount; i++) {
			Mesh &outputMesh = atlas->meshes[i];
			// Count and alloc arrays.
			const internal::param::InvalidMeshGeometry &invalid = ctx->paramAtlas.invalidMeshGeometry(i);
			outputMesh.vertexCount += invalid.vertices().length;
			outputMesh.indexCount += invalid.faces().length * 3;
			for (uint32_t cg = 0; cg < ctx->paramAtlas.chartGroupCount(i); cg++) {
				const internal::param::ChartGroup *chartGroup = ctx->paramAtlas.chartGroupAt(i, cg);
				for (uint32_t c = 0; c < chartGroup->chartCount(); c++) {
					const internal::param::Chart *chart = chartGroup->chartAt(c);
					outputMesh.vertexCount += chart->mesh()->vertexCount();
					outputMesh.indexCount += chart->mesh()->faceCount() * 3;
					outputMesh.chartCount++;
				}
			}
			outputMesh.vertexArray = XA_ALLOC_ARRAY(internal::MemTag::Default, Vertex, outputMesh.vertexCount);
			outputMesh.indexArray = XA_ALLOC_ARRAY(internal::MemTag::Default, uint32_t, outputMesh.indexCount);
			outputMesh.chartArray = XA_ALLOC_ARRAY(internal::MemTag::Default, Chart, outputMesh.chartCount);
			XA_PRINT("   Mesh %u: %u vertices, %u triangles, %u charts\n", i, outputMesh.vertexCount, outputMesh.indexCount / 3, outputMesh.chartCount);
			// Copy mesh data.
			uint32_t firstVertex = 0;
			{
				const internal::param::InvalidMeshGeometry &mesh = ctx->paramAtlas.invalidMeshGeometry(i);
				internal::ConstArrayView<uint32_t> faces = mesh.faces();
				internal::ConstArrayView<uint32_t> indices = mesh.indices();
				internal::ConstArrayView<uint32_t> vertices = mesh.vertices();
				// Vertices.
				for (uint32_t v = 0; v < vertices.length; v++) {
					Vertex &vertex = outputMesh.vertexArray[firstVertex + v];
					vertex.atlasIndex = -1;
					vertex.chartIndex = -1;
					vertex.uv[0] = vertex.uv[1] = 0.0f;
					vertex.xref = vertices[v];
				}
				// Indices.
				for (uint32_t f = 0; f < faces.length; f++) {
					const uint32_t indexOffset = faces[f] * 3;
					for (uint32_t j = 0; j < 3; j++)
						outputMesh.indexArray[indexOffset + j] = firstVertex + indices[f * 3 + j];
				}
				firstVertex += vertices.length;
			}
			uint32_t meshChartIndex = 0;
			for (uint32_t cg = 0; cg < ctx->paramAtlas.chartGroupCount(i); cg++) {
				const internal::param::ChartGroup *chartGroup = ctx->paramAtlas.chartGroupAt(i, cg);
				for (uint32_t c = 0; c < chartGroup->chartCount(); c++) {
					const internal::param::Chart *chart = chartGroup->chartAt(c);
					const internal::Mesh *mesh = chart->mesh();
					// Vertices.
					for (uint32_t v = 0; v < mesh->vertexCount(); v++) {
						Vertex &vertex = outputMesh.vertexArray[firstVertex + v];
						vertex.atlasIndex = packAtlas.getChart(chartIndex)->atlasIndex;
						XA_DEBUG_ASSERT(vertex.atlasIndex >= 0);
						vertex.chartIndex = (int32_t)chartIndex;
						const internal::Vector2 &uv = mesh->texcoord(v);
						vertex.uv[0] = internal::max(0.0f, uv.x);
						vertex.uv[1] = internal::max(0.0f, uv.y);
						vertex.xref = chart->mapChartVertexToSourceVertex(v);
					}
					// Indices.
					for (uint32_t f = 0; f < mesh->faceCount(); f++) {
						const uint32_t indexOffset = chart->mapFaceToSourceFace(f) * 3;
						for (uint32_t j = 0; j < 3; j++)
							outputMesh.indexArray[indexOffset + j] = firstVertex + mesh->vertexAt(f * 3 + j);
					}
					// Charts.
					Chart *outputChart = &outputMesh.chartArray[meshChartIndex];
					const int32_t atlasIndex = packAtlas.getChart(chartIndex)->atlasIndex;
					XA_DEBUG_ASSERT(atlasIndex >= 0);
					outputChart->atlasIndex = (uint32_t)atlasIndex;
					outputChart->type = chart->isInvalid() ? ChartType::Invalid : chart->type();
					outputChart->faceCount = mesh->faceCount();
					outputChart->faceArray = XA_ALLOC_ARRAY(internal::MemTag::Default, uint32_t, outputChart->faceCount);
					for (uint32_t f = 0; f < outputChart->faceCount; f++)
						outputChart->faceArray[f] = chart->mapFaceToSourceFace(f);
					outputChart->material = 0;
					meshChartIndex++;
					chartIndex++;
					firstVertex += mesh->vertexCount();
				}
			}
			XA_DEBUG_ASSERT(outputMesh.vertexCount == firstVertex);
			XA_DEBUG_ASSERT(outputMesh.chartCount == meshChartIndex);
			if (ctx->progressFunc) {
				const int newProgress = int((i + 1) / (float)atlas->meshCount * 100.0f);
				if (newProgress != progress) {
					progress = newProgress;
					if (!ctx->progressFunc(ProgressCategory::BuildOutputMeshes, progress, ctx->progressUserData))
						return;
				}
			}
		}
	} else {
		uint32_t chartIndex = 0;
		for (uint32_t m = 0; m < ctx->uvMeshInstances.size(); m++) {
			Mesh &outputMesh = atlas->meshes[m];
			const internal::UvMeshInstance *mesh = ctx->uvMeshInstances[m];
			// Alloc arrays.
			outputMesh.vertexCount = mesh->texcoords.size();
			outputMesh.indexCount = mesh->mesh->indices.size();
			outputMesh.chartCount = mesh->mesh->charts.size();
			outputMesh.vertexArray = XA_ALLOC_ARRAY(internal::MemTag::Default, Vertex, outputMesh.vertexCount);
			outputMesh.indexArray = XA_ALLOC_ARRAY(internal::MemTag::Default, uint32_t, outputMesh.indexCount);
			outputMesh.chartArray = XA_ALLOC_ARRAY(internal::MemTag::Default, Chart, outputMesh.chartCount);
			XA_PRINT("   UV mesh %u: %u vertices, %u triangles, %u charts\n", m, outputMesh.vertexCount, outputMesh.indexCount / 3, outputMesh.chartCount);
			// Copy mesh data.
			// Vertices.
			for (uint32_t v = 0; v < mesh->texcoords.size(); v++) {
				Vertex &vertex = outputMesh.vertexArray[v];
				vertex.uv[0] = mesh->texcoords[v].x;
				vertex.uv[1] = mesh->texcoords[v].y;
				vertex.xref = v;
				const uint32_t meshChartIndex = mesh->mesh->vertexToChartMap[v];
				if (meshChartIndex == UINT32_MAX) {
					// Vertex doesn't exist in any chart.
					vertex.atlasIndex = -1;
					vertex.chartIndex = -1;
				} else {
					const internal::pack::Chart *chart = packAtlas.getChart(chartIndex + meshChartIndex);
					vertex.atlasIndex = chart->atlasIndex;
					vertex.chartIndex = (int32_t)chartIndex + meshChartIndex;
				}
			}
			// Indices.
			memcpy(outputMesh.indexArray, mesh->mesh->indices.data(), mesh->mesh->indices.size() * sizeof(uint32_t));
			// Charts.
			for (uint32_t c = 0; c < mesh->mesh->charts.size(); c++) {
				Chart *outputChart = &outputMesh.chartArray[c];
				const internal::pack::Chart *chart = packAtlas.getChart(chartIndex);
				XA_DEBUG_ASSERT(chart->atlasIndex >= 0);
				outputChart->atlasIndex = (uint32_t)chart->atlasIndex;
				outputChart->faceCount = chart->faces.size();
				outputChart->faceArray = XA_ALLOC_ARRAY(internal::MemTag::Default, uint32_t, outputChart->faceCount);
				outputChart->material = chart->material;
				for (uint32_t f = 0; f < outputChart->faceCount; f++)
					outputChart->faceArray[f] = chart->faces[f];
				chartIndex++;
			}
			if (ctx->progressFunc) {
				const int newProgress = int((m + 1) / (float)atlas->meshCount * 100.0f);
				if (newProgress != progress) {
					progress = newProgress;
					if (!ctx->progressFunc(ProgressCategory::BuildOutputMeshes, progress, ctx->progressUserData))
						return;
				}
			}
		}
	}
	if (ctx->progressFunc && progress != 100)
		ctx->progressFunc(ProgressCategory::BuildOutputMeshes, 100, ctx->progressUserData);
	XA_PROFILE_END(buildOutputMeshes)
	XA_PROFILE_PRINT_AND_RESET("   Total: ", buildOutputMeshes)
#if XA_PROFILE_ALLOC
	XA_PROFILE_PRINT_AND_RESET("   Alloc: ", alloc)
#endif
	XA_PRINT_MEM_USAGE
}

void Generate(Atlas *atlas, ChartOptions chartOptions, ParameterizeOptions parameterizeOptions, PackOptions packOptions)
{
	if (!atlas) {
		XA_PRINT_WARNING("Generate: atlas is null.\n");
		return;
	}
	Context *ctx = (Context *)atlas;
	if (!ctx->uvMeshInstances.isEmpty()) {
		XA_PRINT_WARNING("Generate: This function should not be called with UV meshes.\n");
		return;
	}
	if (ctx->meshes.isEmpty()) {
		XA_PRINT_WARNING("Generate: No meshes. Call AddMesh first.\n");
		return;
	}
	ComputeCharts(atlas, chartOptions);
	ParameterizeCharts(atlas, parameterizeOptions);
	PackCharts(atlas, packOptions);
}

void SetProgressCallback(Atlas *atlas, ProgressFunc progressFunc, void *progressUserData)
{
	if (!atlas) {
		XA_PRINT_WARNING("SetProgressCallback: atlas is null.\n");
		return;
	}
	Context *ctx = (Context *)atlas;
	ctx->progressFunc = progressFunc;
	ctx->progressUserData = progressUserData;
}

void SetAlloc(ReallocFunc reallocFunc, FreeFunc freeFunc)
{
	internal::s_realloc = reallocFunc;
	internal::s_free = freeFunc;
}

void SetPrint(PrintFunc print, bool verbose)
{
	internal::s_print = print;
	internal::s_printVerbose = verbose;
}

const char *StringForEnum(AddMeshError::Enum error)
{
	if (error == AddMeshError::Error)
		return "Unspecified error";
	if (error == AddMeshError::IndexOutOfRange)
		return "Index out of range";
	if (error == AddMeshError::InvalidIndexCount)
		return "Invalid index count";
	return "Success";
}

const char *StringForEnum(ProgressCategory::Enum category)
{
	if (category == ProgressCategory::AddMesh)
		return "Adding mesh(es)";
	if (category == ProgressCategory::ComputeCharts)
		return "Computing charts";
	if (category == ProgressCategory::ParameterizeCharts)
		return "Parameterizing charts";
	if (category == ProgressCategory::PackCharts)
		return "Packing charts";
	if (category == ProgressCategory::BuildOutputMeshes)
		return "Building output meshes";
	return "";
}

} // namespace xatlas