code: // This file is part of meshoptimizer library; see meshoptimizer.h for version/license details
  #include "meshoptimizer.h"
  
  #include <assert.h>
  #include <math.h>
  #include <string.h>
  
  // This work is based on:
  // Pedro Sander, Diego Nehab and Joshua Barczak. Fast Triangle Reordering for Vertex Locality and Reduced Overdraw. 2007
  namespace meshopt
  {
  
  static void calculateSortData(float* sort_data, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_positions_stride, const unsigned int* clusters, size_t cluster_count)
  {
  	size_t vertex_stride_float = vertex_positions_stride / sizeof(float);
  
  	float mesh_centroid[3] = {};
  
  	for (size_t i = 0; i < index_count; ++i)
  	{
  		const float* p = vertex_positions + vertex_stride_float * indices[i];
  
  		mesh_centroid[0] += p[0];
  		mesh_centroid[1] += p[1];
  		mesh_centroid[2] += p[2];
  	}
  
  	mesh_centroid[0] /= index_count;
  	mesh_centroid[1] /= index_count;
  	mesh_centroid[2] /= index_count;
  
  	for (size_t cluster = 0; cluster < cluster_count; ++cluster)
  	{
  		size_t cluster_begin = clusters[cluster] * 3;
  		size_t cluster_end = (cluster + 1 < cluster_count) ? clusters[cluster + 1] * 3 : index_count;
  		assert(cluster_begin < cluster_end);
  
  		float cluster_area = 0;
  		float cluster_centroid[3] = {};
  		float cluster_normal[3] = {};
  
  		for (size_t i = cluster_begin; i < cluster_end; i += 3)
  		{
  			const float* p0 = vertex_positions + vertex_stride_float * indices[i + 0];
  			const float* p1 = vertex_positions + vertex_stride_float * indices[i + 1];
  			const float* p2 = vertex_positions + vertex_stride_float * indices[i + 2];
  
  			float p10[3] = {p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2]};
  			float p20[3] = {p2[0] - p0[0], p2[1] - p0[1], p2[2] - p0[2]};
  
  			float normalx = p10[1] * p20[2] - p10[2] * p20[1];
  			float normaly = p10[2] * p20[0] - p10[0] * p20[2];
  			float normalz = p10[0] * p20[1] - p10[1] * p20[0];
  
  			float area = sqrtf(normalx * normalx + normaly * normaly + normalz * normalz);
  
  			cluster_centroid[0] += (p0[0] + p1[0] + p2[0]) * (area / 3);
  			cluster_centroid[1] += (p0[1] + p1[1] + p2[1]) * (area / 3);
  			cluster_centroid[2] += (p0[2] + p1[2] + p2[2]) * (area / 3);
  			cluster_normal[0] += normalx;
  			cluster_normal[1] += normaly;
  			cluster_normal[2] += normalz;
  			cluster_area += area;
  		}
  
  		float inv_cluster_area = cluster_area == 0 ? 0 : 1 / cluster_area;
  
  		cluster_centroid[0] *= inv_cluster_area;
  		cluster_centroid[1] *= inv_cluster_area;
  		cluster_centroid[2] *= inv_cluster_area;
  
  		float cluster_normal_length = sqrtf(cluster_normal[0] * cluster_normal[0] + cluster_normal[1] * cluster_normal[1] + cluster_normal[2] * cluster_normal[2]);
  		float inv_cluster_normal_length = cluster_normal_length == 0 ? 0 : 1 / cluster_normal_length;
  
  		cluster_normal[0] *= inv_cluster_normal_length;
  		cluster_normal[1] *= inv_cluster_normal_length;
  		cluster_normal[2] *= inv_cluster_normal_length;
  
  		float centroid_vector[3] = {cluster_centroid[0] - mesh_centroid[0], cluster_centroid[1] - mesh_centroid[1], cluster_centroid[2] - mesh_centroid[2]};
  
  		sort_data[cluster] = centroid_vector[0] * cluster_normal[0] + centroid_vector[1] * cluster_normal[1] + centroid_vector[2] * cluster_normal[2];
  	}
  }
  
  static void calculateSortOrderRadix(unsigned int* sort_order, const float* sort_data, unsigned short* sort_keys, size_t cluster_count)
  {
  	// compute sort data bounds and renormalize, using fixed point snorm
  	float sort_data_max = 1e-3f;
  
  	for (size_t i = 0; i < cluster_count; ++i)
  	{
  		float dpa = fabsf(sort_data[i]);
  
  		sort_data_max = (sort_data_max < dpa) ? dpa : sort_data_max;
  	}
  
  	const int sort_bits = 11;
  
  	for (size_t i = 0; i < cluster_count; ++i)
  	{
  		// note that we flip distribution since high dot product should come first
  		float sort_key = 0.5f - 0.5f * (sort_data[i] / sort_data_max);
  
  		sort_keys[i] = meshopt_quantizeUnorm(sort_key, sort_bits) & ((1 << sort_bits) - 1);
  	}
  
  	// fill histogram for counting sort
  	unsigned int histogram[1 << sort_bits];
  	memset(histogram, 0, sizeof(histogram));
  
  	for (size_t i = 0; i < cluster_count; ++i)
  	{
  		histogram[sort_keys[i]]++;
  	}
  
  	// compute offsets based on histogram data
  	size_t histogram_sum = 0;
  
  	for (size_t i = 0; i < 1 << sort_bits; ++i)
  	{
  		size_t count = histogram[i];
  		histogram[i] = unsigned(histogram_sum);
  		histogram_sum += count;
  	}
  
  	assert(histogram_sum == cluster_count);
  
  	// compute sort order based on offsets
  	for (size_t i = 0; i < cluster_count; ++i)
  	{
  		sort_order[histogram[sort_keys[i]]++] = unsigned(i);
  	}
  }
  
  static unsigned int updateCache(unsigned int a, unsigned int b, unsigned int c, unsigned int cache_size, unsigned int* cache_timestamps, unsigned int& timestamp)
  {
  	unsigned int cache_misses = 0;
  
  	// if vertex is not in cache, put it in cache
  	if (timestamp - cache_timestamps[a] > cache_size)
  	{
  		cache_timestamps[a] = timestamp++;
  		cache_misses++;
  	}
  
  	if (timestamp - cache_timestamps[b] > cache_size)
  	{
  		cache_timestamps[b] = timestamp++;
  		cache_misses++;
  	}
  
  	if (timestamp - cache_timestamps[c] > cache_size)
  	{
  		cache_timestamps[c] = timestamp++;
  		cache_misses++;
  	}
  
  	return cache_misses;
  }
  
  static size_t generateHardBoundaries(unsigned int* destination, const unsigned int* indices, size_t index_count, size_t vertex_count, unsigned int cache_size, unsigned int* cache_timestamps)
  {
  	memset(cache_timestamps, 0, vertex_count * sizeof(unsigned int));
  
  	unsigned int timestamp = cache_size + 1;
  
  	size_t face_count = index_count / 3;
  
  	size_t result = 0;
  
  	for (size_t i = 0; i < face_count; ++i)
  	{
  		unsigned int m = updateCache(indices[i * 3 + 0], indices[i * 3 + 1], indices[i * 3 + 2], cache_size, &cache_timestamps[0], timestamp);
  
  		// when all three vertices are not in the cache it's usually relatively safe to assume that this is a new patch in the mesh
  		// that is disjoint from previous vertices; sometimes it might come back to reference existing vertices but that frequently
  		// suggests an inefficiency in the vertex cache optimization algorithm
  		// usually the first triangle has 3 misses unless it's degenerate - thus we make sure the first cluster always starts with 0
  		if (i == 0 || m == 3)
  		{
  			destination[result++] = unsigned(i);
  		}
  	}
  
  	assert(result <= index_count / 3);
  
  	return result;
  }
  
  static size_t generateSoftBoundaries(unsigned int* destination, const unsigned int* indices, size_t index_count, size_t vertex_count, const unsigned int* clusters, size_t cluster_count, unsigned int cache_size, float threshold, unsigned int* cache_timestamps)
  {
  	memset(cache_timestamps, 0, vertex_count * sizeof(unsigned int));
  
  	unsigned int timestamp = 0;
  
  	size_t result = 0;
  
  	for (size_t it = 0; it < cluster_count; ++it)
  	{
  		size_t start = clusters[it];
  		size_t end = (it + 1 < cluster_count) ? clusters[it + 1] : index_count / 3;
  		assert(start < end);
  
  		// reset cache
  		timestamp += cache_size + 1;
  
  		// measure cluster ACMR
  		unsigned int cluster_misses = 0;
  
  		for (size_t i = start; i < end; ++i)
  		{
  			unsigned int m = updateCache(indices[i * 3 + 0], indices[i * 3 + 1], indices[i * 3 + 2], cache_size, &cache_timestamps[0], timestamp);
  
  			cluster_misses += m;
  		}
  
  		float cluster_threshold = threshold * (float(cluster_misses) / float(end - start));
  
  		// first cluster always starts from the hard cluster boundary
  		destination[result++] = unsigned(start);
  
  		// reset cache
  		timestamp += cache_size + 1;
  
  		unsigned int running_misses = 0;
  		unsigned int running_faces = 0;
  
  		for (size_t i = start; i < end; ++i)
  		{
  			unsigned int m = updateCache(indices[i * 3 + 0], indices[i * 3 + 1], indices[i * 3 + 2], cache_size, &cache_timestamps[0], timestamp);
  
  			running_misses += m;
  			running_faces += 1;
  
  			if (float(running_misses) / float(running_faces) <= cluster_threshold)
  			{
  				// we have reached the target ACMR with the current triangle so we need to start a new cluster on the next one
  				// note that this may mean that we add 'end` to destination for the last triangle, which will imply that the last
  				// cluster is empty; however, the 'pop_back' after the loop will clean it up
  				destination[result++] = unsigned(i + 1);
  
  				// reset cache
  				timestamp += cache_size + 1;
  
  				running_misses = 0;
  				running_faces = 0;
  			}
  		}
  
  		// each time we reach the target ACMR we flush the cluster
  		// this means that the last cluster is by definition not very good - there are frequent cases where we are left with a few triangles
  		// in the last cluster, producing a very bad ACMR and significantly penalizing the overall results
  		// thus we remove the last cluster boundary, merging the last complete cluster with the last incomplete one
  		// there are sometimes cases when the last cluster is actually good enough - in which case the code above would have added 'end'
  		// to the cluster boundary array which we need to remove anyway - this code will do that automatically
  		if (destination[result - 1] != start)
  		{
  			result--;
  		}
  	}
  
  	assert(result >= cluster_count);
  	assert(result <= index_count / 3);
  
  	return result;
  }
  
  } // namespace meshopt
  
  void meshopt_optimizeOverdraw(unsigned int* destination, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, float threshold)
  {
  	using namespace meshopt;
  
  	assert(index_count % 3 == 0);
  	assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
  	assert(vertex_positions_stride % sizeof(float) == 0);
  
  	meshopt_Allocator allocator;
  
  	// guard for empty meshes
  	if (index_count == 0 || vertex_count == 0)
  		return;
  
  	// support in-place optimization
  	if (destination == indices)
  	{
  		unsigned int* indices_copy = allocator.allocate<unsigned int>(index_count);
  		memcpy(indices_copy, indices, index_count * sizeof(unsigned int));
  		indices = indices_copy;
  	}
  
  	unsigned int cache_size = 16;
  
  	unsigned int* cache_timestamps = allocator.allocate<unsigned int>(vertex_count);
  
  	// generate hard boundaries from full-triangle cache misses
  	unsigned int* hard_clusters = allocator.allocate<unsigned int>(index_count / 3);
  	size_t hard_cluster_count = generateHardBoundaries(hard_clusters, indices, index_count, vertex_count, cache_size, cache_timestamps);
  
  	// generate soft boundaries
  	unsigned int* soft_clusters = allocator.allocate<unsigned int>(index_count / 3 + 1);
  	size_t soft_cluster_count = generateSoftBoundaries(soft_clusters, indices, index_count, vertex_count, hard_clusters, hard_cluster_count, cache_size, threshold, cache_timestamps);
  
  	const unsigned int* clusters = soft_clusters;
  	size_t cluster_count = soft_cluster_count;
  
  	// fill sort data
  	float* sort_data = allocator.allocate<float>(cluster_count);
  	calculateSortData(sort_data, indices, index_count, vertex_positions, vertex_positions_stride, clusters, cluster_count);
  
  	// sort clusters using sort data
  	unsigned short* sort_keys = allocator.allocate<unsigned short>(cluster_count);
  	unsigned int* sort_order = allocator.allocate<unsigned int>(cluster_count);
  	calculateSortOrderRadix(sort_order, sort_data, sort_keys, cluster_count);
  
  	// fill output buffer
  	size_t offset = 0;
  
  	for (size_t it = 0; it < cluster_count; ++it)
  	{
  		unsigned int cluster = sort_order[it];
  		assert(cluster < cluster_count);
  
  		size_t cluster_begin = clusters[cluster] * 3;
  		size_t cluster_end = (cluster + 1 < cluster_count) ? clusters[cluster + 1] * 3 : index_count;
  		assert(cluster_begin < cluster_end);
  
  		memcpy(destination + offset, indices + cluster_begin, (cluster_end - cluster_begin) * sizeof(unsigned int));
  		offset += cluster_end - cluster_begin;
  	}
  
  	assert(offset == index_count);
  }
  