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+// This file is part of meshoptimizer library; see meshoptimizer.h for version/license details
+#include "meshoptimizer.h"
+
+#include <assert.h>
+#include <float.h>
+#include <math.h>
+#include <string.h>
+
+// This work is based on:
+// Graham Wihlidal. Optimizing the Graphics Pipeline with Compute. 2016
+// Matthaeus Chajdas. GeometryFX 1.2 - Cluster Culling. 2016
+// Jack Ritter. An Efficient Bounding Sphere. 1990
+namespace meshopt
+{
+
+// This must be <= 255 since index 0xff is used internally to indice a vertex that doesn't belong to a meshlet
+const size_t kMeshletMaxVertices = 255;
+
+// A reasonable limit is around 2*max_vertices or less
+const size_t kMeshletMaxTriangles = 512;
+
+struct TriangleAdjacency2
+{
+ unsigned int* counts;
+ unsigned int* offsets;
+ unsigned int* data;
+};
+
+static void buildTriangleAdjacency(TriangleAdjacency2& adjacency, const unsigned int* indices, size_t index_count, size_t vertex_count, meshopt_Allocator& allocator)
+{
+ size_t face_count = index_count / 3;
+
+ // allocate arrays
+ adjacency.counts = allocator.allocate<unsigned int>(vertex_count);
+ adjacency.offsets = allocator.allocate<unsigned int>(vertex_count);
+ adjacency.data = allocator.allocate<unsigned int>(index_count);
+
+ // fill triangle counts
+ memset(adjacency.counts, 0, vertex_count * sizeof(unsigned int));
+
+ for (size_t i = 0; i < index_count; ++i)
+ {
+ assert(indices[i] < vertex_count);
+
+ adjacency.counts[indices[i]]++;
+ }
+
+ // fill offset table
+ unsigned int offset = 0;
+
+ for (size_t i = 0; i < vertex_count; ++i)
+ {
+ adjacency.offsets[i] = offset;
+ offset += adjacency.counts[i];
+ }
+
+ assert(offset == index_count);
+
+ // fill triangle data
+ for (size_t i = 0; i < face_count; ++i)
+ {
+ unsigned int a = indices[i * 3 + 0], b = indices[i * 3 + 1], c = indices[i * 3 + 2];
+
+ adjacency.data[adjacency.offsets[a]++] = unsigned(i);
+ adjacency.data[adjacency.offsets[b]++] = unsigned(i);
+ adjacency.data[adjacency.offsets[c]++] = unsigned(i);
+ }
+
+ // fix offsets that have been disturbed by the previous pass
+ for (size_t i = 0; i < vertex_count; ++i)
+ {
+ assert(adjacency.offsets[i] >= adjacency.counts[i]);
+
+ adjacency.offsets[i] -= adjacency.counts[i];
+ }
+}
+
+static void computeBoundingSphere(float result[4], const float points[][3], size_t count)
+{
+ assert(count > 0);
+
+ // find extremum points along all 3 axes; for each axis we get a pair of points with min/max coordinates
+ size_t pmin[3] = {0, 0, 0};
+ size_t pmax[3] = {0, 0, 0};
+
+ for (size_t i = 0; i < count; ++i)
+ {
+ const float* p = points[i];
+
+ for (int axis = 0; axis < 3; ++axis)
+ {
+ pmin[axis] = (p[axis] < points[pmin[axis]][axis]) ? i : pmin[axis];
+ pmax[axis] = (p[axis] > points[pmax[axis]][axis]) ? i : pmax[axis];
+ }
+ }
+
+ // find the pair of points with largest distance
+ float paxisd2 = 0;
+ int paxis = 0;
+
+ for (int axis = 0; axis < 3; ++axis)
+ {
+ const float* p1 = points[pmin[axis]];
+ const float* p2 = points[pmax[axis]];
+
+ float d2 = (p2[0] - p1[0]) * (p2[0] - p1[0]) + (p2[1] - p1[1]) * (p2[1] - p1[1]) + (p2[2] - p1[2]) * (p2[2] - p1[2]);
+
+ if (d2 > paxisd2)
+ {
+ paxisd2 = d2;
+ paxis = axis;
+ }
+ }
+
+ // use the longest segment as the initial sphere diameter
+ const float* p1 = points[pmin[paxis]];
+ const float* p2 = points[pmax[paxis]];
+
+ float center[3] = {(p1[0] + p2[0]) / 2, (p1[1] + p2[1]) / 2, (p1[2] + p2[2]) / 2};
+ float radius = sqrtf(paxisd2) / 2;
+
+ // iteratively adjust the sphere up until all points fit
+ for (size_t i = 0; i < count; ++i)
+ {
+ const float* p = points[i];
+ float d2 = (p[0] - center[0]) * (p[0] - center[0]) + (p[1] - center[1]) * (p[1] - center[1]) + (p[2] - center[2]) * (p[2] - center[2]);
+
+ if (d2 > radius * radius)
+ {
+ float d = sqrtf(d2);
+ assert(d > 0);
+
+ float k = 0.5f + (radius / d) / 2;
+
+ center[0] = center[0] * k + p[0] * (1 - k);
+ center[1] = center[1] * k + p[1] * (1 - k);
+ center[2] = center[2] * k + p[2] * (1 - k);
+ radius = (radius + d) / 2;
+ }
+ }
+
+ result[0] = center[0];
+ result[1] = center[1];
+ result[2] = center[2];
+ result[3] = radius;
+}
+
+struct Cone
+{
+ float px, py, pz;
+ float nx, ny, nz;
+};
+
+static float getMeshletScore(float distance2, float spread, float cone_weight, float expected_radius)
+{
+ float cone = 1.f - spread * cone_weight;
+ float cone_clamped = cone < 1e-3f ? 1e-3f : cone;
+
+ return (1 + sqrtf(distance2) / expected_radius * (1 - cone_weight)) * cone_clamped;
+}
+
+static Cone getMeshletCone(const Cone& acc, unsigned int triangle_count)
+{
+ Cone result = acc;
+
+ float center_scale = triangle_count == 0 ? 0.f : 1.f / float(triangle_count);
+
+ result.px *= center_scale;
+ result.py *= center_scale;
+ result.pz *= center_scale;
+
+ float axis_length = result.nx * result.nx + result.ny * result.ny + result.nz * result.nz;
+ float axis_scale = axis_length == 0.f ? 0.f : 1.f / sqrtf(axis_length);
+
+ result.nx *= axis_scale;
+ result.ny *= axis_scale;
+ result.nz *= axis_scale;
+
+ return result;
+}
+
+static float computeTriangleCones(Cone* triangles, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
+{
+ (void)vertex_count;
+
+ size_t vertex_stride_float = vertex_positions_stride / sizeof(float);
+ size_t face_count = index_count / 3;
+
+ float mesh_area = 0;
+
+ for (size_t i = 0; i < face_count; ++i)
+ {
+ unsigned int a = indices[i * 3 + 0], b = indices[i * 3 + 1], c = indices[i * 3 + 2];
+ assert(a < vertex_count && b < vertex_count && c < vertex_count);
+
+ const float* p0 = vertex_positions + vertex_stride_float * a;
+ const float* p1 = vertex_positions + vertex_stride_float * b;
+ const float* p2 = vertex_positions + vertex_stride_float * c;
+
+ 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);
+ float invarea = (area == 0.f) ? 0.f : 1.f / area;
+
+ triangles[i].px = (p0[0] + p1[0] + p2[0]) / 3.f;
+ triangles[i].py = (p0[1] + p1[1] + p2[1]) / 3.f;
+ triangles[i].pz = (p0[2] + p1[2] + p2[2]) / 3.f;
+
+ triangles[i].nx = normalx * invarea;
+ triangles[i].ny = normaly * invarea;
+ triangles[i].nz = normalz * invarea;
+
+ mesh_area += area;
+ }
+
+ return mesh_area;
+}
+
+static void finishMeshlet(meshopt_Meshlet& meshlet, unsigned char* meshlet_triangles)
+{
+ size_t offset = meshlet.triangle_offset + meshlet.triangle_count * 3;
+
+ // fill 4b padding with 0
+ while (offset & 3)
+ meshlet_triangles[offset++] = 0;
+}
+
+static bool appendMeshlet(meshopt_Meshlet& meshlet, unsigned int a, unsigned int b, unsigned int c, unsigned char* used, meshopt_Meshlet* meshlets, unsigned int* meshlet_vertices, unsigned char* meshlet_triangles, size_t meshlet_offset, size_t max_vertices, size_t max_triangles)
+{
+ unsigned char& av = used[a];
+ unsigned char& bv = used[b];
+ unsigned char& cv = used[c];
+
+ bool result = false;
+
+ unsigned int used_extra = (av == 0xff) + (bv == 0xff) + (cv == 0xff);
+
+ if (meshlet.vertex_count + used_extra > max_vertices || meshlet.triangle_count >= max_triangles)
+ {
+ meshlets[meshlet_offset] = meshlet;
+
+ for (size_t j = 0; j < meshlet.vertex_count; ++j)
+ used[meshlet_vertices[meshlet.vertex_offset + j]] = 0xff;
+
+ finishMeshlet(meshlet, meshlet_triangles);
+
+ meshlet.vertex_offset += meshlet.vertex_count;
+ meshlet.triangle_offset += (meshlet.triangle_count * 3 + 3) & ~3; // 4b padding
+ meshlet.vertex_count = 0;
+ meshlet.triangle_count = 0;
+
+ result = true;
+ }
+
+ if (av == 0xff)
+ {
+ av = (unsigned char)meshlet.vertex_count;
+ meshlet_vertices[meshlet.vertex_offset + meshlet.vertex_count++] = a;
+ }
+
+ if (bv == 0xff)
+ {
+ bv = (unsigned char)meshlet.vertex_count;
+ meshlet_vertices[meshlet.vertex_offset + meshlet.vertex_count++] = b;
+ }
+
+ if (cv == 0xff)
+ {
+ cv = (unsigned char)meshlet.vertex_count;
+ meshlet_vertices[meshlet.vertex_offset + meshlet.vertex_count++] = c;
+ }
+
+ meshlet_triangles[meshlet.triangle_offset + meshlet.triangle_count * 3 + 0] = av;
+ meshlet_triangles[meshlet.triangle_offset + meshlet.triangle_count * 3 + 1] = bv;
+ meshlet_triangles[meshlet.triangle_offset + meshlet.triangle_count * 3 + 2] = cv;
+ meshlet.triangle_count++;
+
+ return result;
+}
+
+struct KDNode
+{
+ union
+ {
+ float split;
+ unsigned int index;
+ };
+
+ // leaves: axis = 3, children = number of extra points after this one (0 if 'index' is the only point)
+ // branches: axis != 3, left subtree = skip 1, right subtree = skip 1+children
+ unsigned int axis : 2;
+ unsigned int children : 30;
+};
+
+static size_t kdtreePartition(unsigned int* indices, size_t count, const float* points, size_t stride, unsigned int axis, float pivot)
+{
+ size_t m = 0;
+
+ // invariant: elements in range [0, m) are < pivot, elements in range [m, i) are >= pivot
+ for (size_t i = 0; i < count; ++i)
+ {
+ float v = points[indices[i] * stride + axis];
+
+ // swap(m, i) unconditionally
+ unsigned int t = indices[m];
+ indices[m] = indices[i];
+ indices[i] = t;
+
+ // when v >= pivot, we swap i with m without advancing it, preserving invariants
+ m += v < pivot;
+ }
+
+ return m;
+}
+
+static size_t kdtreeBuildLeaf(size_t offset, KDNode* nodes, size_t node_count, unsigned int* indices, size_t count)
+{
+ assert(offset + count <= node_count);
+ (void)node_count;
+
+ KDNode& result = nodes[offset];
+
+ result.index = indices[0];
+ result.axis = 3;
+ result.children = unsigned(count - 1);
+
+ // all remaining points are stored in nodes immediately following the leaf
+ for (size_t i = 1; i < count; ++i)
+ {
+ KDNode& tail = nodes[offset + i];
+
+ tail.index = indices[i];
+ tail.axis = 3;
+ tail.children = ~0u >> 2; // bogus value to prevent misuse
+ }
+
+ return offset + count;
+}
+
+static size_t kdtreeBuild(size_t offset, KDNode* nodes, size_t node_count, const float* points, size_t stride, unsigned int* indices, size_t count, size_t leaf_size)
+{
+ assert(count > 0);
+ assert(offset < node_count);
+
+ if (count <= leaf_size)
+ return kdtreeBuildLeaf(offset, nodes, node_count, indices, count);
+
+ float mean[3] = {};
+ float vars[3] = {};
+ float runc = 1, runs = 1;
+
+ // gather statistics on the points in the subtree using Welford's algorithm
+ for (size_t i = 0; i < count; ++i, runc += 1.f, runs = 1.f / runc)
+ {
+ const float* point = points + indices[i] * stride;
+
+ for (int k = 0; k < 3; ++k)
+ {
+ float delta = point[k] - mean[k];
+ mean[k] += delta * runs;
+ vars[k] += delta * (point[k] - mean[k]);
+ }
+ }
+
+ // split axis is one where the variance is largest
+ unsigned int axis = vars[0] >= vars[1] && vars[0] >= vars[2] ? 0 : vars[1] >= vars[2] ? 1
+ : 2;
+
+ float split = mean[axis];
+ size_t middle = kdtreePartition(indices, count, points, stride, axis, split);
+
+ // when the partition is degenerate simply consolidate the points into a single node
+ if (middle <= leaf_size / 2 || middle >= count - leaf_size / 2)
+ return kdtreeBuildLeaf(offset, nodes, node_count, indices, count);
+
+ KDNode& result = nodes[offset];
+
+ result.split = split;
+ result.axis = axis;
+
+ // left subtree is right after our node
+ size_t next_offset = kdtreeBuild(offset + 1, nodes, node_count, points, stride, indices, middle, leaf_size);
+
+ // distance to the right subtree is represented explicitly
+ result.children = unsigned(next_offset - offset - 1);
+
+ return kdtreeBuild(next_offset, nodes, node_count, points, stride, indices + middle, count - middle, leaf_size);
+}
+
+static void kdtreeNearest(KDNode* nodes, unsigned int root, const float* points, size_t stride, const unsigned char* emitted_flags, const float* position, unsigned int& result, float& limit)
+{
+ const KDNode& node = nodes[root];
+
+ if (node.axis == 3)
+ {
+ // leaf
+ for (unsigned int i = 0; i <= node.children; ++i)
+ {
+ unsigned int index = nodes[root + i].index;
+
+ if (emitted_flags[index])
+ continue;
+
+ const float* point = points + index * stride;
+
+ float distance2 =
+ (point[0] - position[0]) * (point[0] - position[0]) +
+ (point[1] - position[1]) * (point[1] - position[1]) +
+ (point[2] - position[2]) * (point[2] - position[2]);
+ float distance = sqrtf(distance2);
+
+ if (distance < limit)
+ {
+ result = index;
+ limit = distance;
+ }
+ }
+ }
+ else
+ {
+ // branch; we order recursion to process the node that search position is in first
+ float delta = position[node.axis] - node.split;
+ unsigned int first = (delta <= 0) ? 0 : node.children;
+ unsigned int second = first ^ node.children;
+
+ kdtreeNearest(nodes, root + 1 + first, points, stride, emitted_flags, position, result, limit);
+
+ // only process the other node if it can have a match based on closest distance so far
+ if (fabsf(delta) <= limit)
+ kdtreeNearest(nodes, root + 1 + second, points, stride, emitted_flags, position, result, limit);
+ }
+}
+
+} // namespace meshopt
+
+size_t meshopt_buildMeshletsBound(size_t index_count, size_t max_vertices, size_t max_triangles)
+{
+ using namespace meshopt;
+
+ assert(index_count % 3 == 0);
+ assert(max_vertices >= 3 && max_vertices <= kMeshletMaxVertices);
+ assert(max_triangles >= 1 && max_triangles <= kMeshletMaxTriangles);
+ assert(max_triangles % 4 == 0); // ensures the caller will compute output space properly as index data is 4b aligned
+
+ (void)kMeshletMaxVertices;
+ (void)kMeshletMaxTriangles;
+
+ // meshlet construction is limited by max vertices and max triangles per meshlet
+ // the worst case is that the input is an unindexed stream since this equally stresses both limits
+ // note that we assume that in the worst case, we leave 2 vertices unpacked in each meshlet - if we have space for 3 we can pack any triangle
+ size_t max_vertices_conservative = max_vertices - 2;
+ size_t meshlet_limit_vertices = (index_count + max_vertices_conservative - 1) / max_vertices_conservative;
+ size_t meshlet_limit_triangles = (index_count / 3 + max_triangles - 1) / max_triangles;
+
+ return meshlet_limit_vertices > meshlet_limit_triangles ? meshlet_limit_vertices : meshlet_limit_triangles;
+}
+
+size_t meshopt_buildMeshlets(meshopt_Meshlet* meshlets, unsigned int* meshlet_vertices, unsigned char* meshlet_triangles, const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride, size_t max_vertices, size_t max_triangles, float cone_weight)
+{
+ using namespace meshopt;
+
+ assert(index_count % 3 == 0);
+ assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
+ assert(vertex_positions_stride % sizeof(float) == 0);
+
+ assert(max_vertices >= 3 && max_vertices <= kMeshletMaxVertices);
+ assert(max_triangles >= 1 && max_triangles <= kMeshletMaxTriangles);
+ assert(max_triangles % 4 == 0); // ensures the caller will compute output space properly as index data is 4b aligned
+
+ meshopt_Allocator allocator;
+
+ TriangleAdjacency2 adjacency = {};
+ buildTriangleAdjacency(adjacency, indices, index_count, vertex_count, allocator);
+
+ unsigned int* live_triangles = allocator.allocate<unsigned int>(vertex_count);
+ memcpy(live_triangles, adjacency.counts, vertex_count * sizeof(unsigned int));
+
+ size_t face_count = index_count / 3;
+
+ unsigned char* emitted_flags = allocator.allocate<unsigned char>(face_count);
+ memset(emitted_flags, 0, face_count);
+
+ // for each triangle, precompute centroid & normal to use for scoring
+ Cone* triangles = allocator.allocate<Cone>(face_count);
+ float mesh_area = computeTriangleCones(triangles, indices, index_count, vertex_positions, vertex_count, vertex_positions_stride);
+
+ // assuming each meshlet is a square patch, expected radius is sqrt(expected area)
+ float triangle_area_avg = face_count == 0 ? 0.f : mesh_area / float(face_count) * 0.5f;
+ float meshlet_expected_radius = sqrtf(triangle_area_avg * max_triangles) * 0.5f;
+
+ // build a kd-tree for nearest neighbor lookup
+ unsigned int* kdindices = allocator.allocate<unsigned int>(face_count);
+ for (size_t i = 0; i < face_count; ++i)
+ kdindices[i] = unsigned(i);
+
+ KDNode* nodes = allocator.allocate<KDNode>(face_count * 2);
+ kdtreeBuild(0, nodes, face_count * 2, &triangles[0].px, sizeof(Cone) / sizeof(float), kdindices, face_count, /* leaf_size= */ 8);
+
+ // index of the vertex in the meshlet, 0xff if the vertex isn't used
+ unsigned char* used = allocator.allocate<unsigned char>(vertex_count);
+ memset(used, -1, vertex_count);
+
+ meshopt_Meshlet meshlet = {};
+ size_t meshlet_offset = 0;
+
+ Cone meshlet_cone_acc = {};
+
+ for (;;)
+ {
+ unsigned int best_triangle = ~0u;
+ unsigned int best_extra = 5;
+ float best_score = FLT_MAX;
+
+ Cone meshlet_cone = getMeshletCone(meshlet_cone_acc, meshlet.triangle_count);
+
+ for (size_t i = 0; i < meshlet.vertex_count; ++i)
+ {
+ unsigned int index = meshlet_vertices[meshlet.vertex_offset + i];
+
+ unsigned int* neighbours = &adjacency.data[0] + adjacency.offsets[index];
+ size_t neighbours_size = adjacency.counts[index];
+
+ for (size_t j = 0; j < neighbours_size; ++j)
+ {
+ unsigned int triangle = neighbours[j];
+ assert(!emitted_flags[triangle]);
+
+ unsigned int a = indices[triangle * 3 + 0], b = indices[triangle * 3 + 1], c = indices[triangle * 3 + 2];
+ assert(a < vertex_count && b < vertex_count && c < vertex_count);
+
+ unsigned int extra = (used[a] == 0xff) + (used[b] == 0xff) + (used[c] == 0xff);
+
+ // triangles that don't add new vertices to meshlets are max. priority
+ if (extra != 0)
+ {
+ // artificially increase the priority of dangling triangles as they're expensive to add to new meshlets
+ if (live_triangles[a] == 1 || live_triangles[b] == 1 || live_triangles[c] == 1)
+ extra = 0;
+
+ extra++;
+ }
+
+ // since topology-based priority is always more important than the score, we can skip scoring in some cases
+ if (extra > best_extra)
+ continue;
+
+ const Cone& tri_cone = triangles[triangle];
+
+ float distance2 =
+ (tri_cone.px - meshlet_cone.px) * (tri_cone.px - meshlet_cone.px) +
+ (tri_cone.py - meshlet_cone.py) * (tri_cone.py - meshlet_cone.py) +
+ (tri_cone.pz - meshlet_cone.pz) * (tri_cone.pz - meshlet_cone.pz);
+
+ float spread = tri_cone.nx * meshlet_cone.nx + tri_cone.ny * meshlet_cone.ny + tri_cone.nz * meshlet_cone.nz;
+
+ float score = getMeshletScore(distance2, spread, cone_weight, meshlet_expected_radius);
+
+ // note that topology-based priority is always more important than the score
+ // this helps maintain reasonable effectiveness of meshlet data and reduces scoring cost
+ if (extra < best_extra || score < best_score)
+ {
+ best_triangle = triangle;
+ best_extra = extra;
+ best_score = score;
+ }
+ }
+ }
+
+ if (best_triangle == ~0u)
+ {
+ float position[3] = {meshlet_cone.px, meshlet_cone.py, meshlet_cone.pz};
+ unsigned int index = ~0u;
+ float limit = FLT_MAX;
+
+ kdtreeNearest(nodes, 0, &triangles[0].px, sizeof(Cone) / sizeof(float), emitted_flags, position, index, limit);
+
+ best_triangle = index;
+ }
+
+ if (best_triangle == ~0u)
+ break;
+
+ unsigned int a = indices[best_triangle * 3 + 0], b = indices[best_triangle * 3 + 1], c = indices[best_triangle * 3 + 2];
+ assert(a < vertex_count && b < vertex_count && c < vertex_count);
+
+ // add meshlet to the output; when the current meshlet is full we reset the accumulated bounds
+ if (appendMeshlet(meshlet, a, b, c, used, meshlets, meshlet_vertices, meshlet_triangles, meshlet_offset, max_vertices, max_triangles))
+ {
+ meshlet_offset++;
+ memset(&meshlet_cone_acc, 0, sizeof(meshlet_cone_acc));
+ }
+
+ live_triangles[a]--;
+ live_triangles[b]--;
+ live_triangles[c]--;
+
+ // remove emitted triangle from adjacency data
+ // this makes sure that we spend less time traversing these lists on subsequent iterations
+ for (size_t k = 0; k < 3; ++k)
+ {
+ unsigned int index = indices[best_triangle * 3 + k];
+
+ unsigned int* neighbours = &adjacency.data[0] + adjacency.offsets[index];
+ size_t neighbours_size = adjacency.counts[index];
+
+ for (size_t i = 0; i < neighbours_size; ++i)
+ {
+ unsigned int tri = neighbours[i];
+
+ if (tri == best_triangle)
+ {
+ neighbours[i] = neighbours[neighbours_size - 1];
+ adjacency.counts[index]--;
+ break;
+ }
+ }
+ }
+
+ // update aggregated meshlet cone data for scoring subsequent triangles
+ meshlet_cone_acc.px += triangles[best_triangle].px;
+ meshlet_cone_acc.py += triangles[best_triangle].py;
+ meshlet_cone_acc.pz += triangles[best_triangle].pz;
+ meshlet_cone_acc.nx += triangles[best_triangle].nx;
+ meshlet_cone_acc.ny += triangles[best_triangle].ny;
+ meshlet_cone_acc.nz += triangles[best_triangle].nz;
+
+ emitted_flags[best_triangle] = 1;
+ }
+
+ if (meshlet.triangle_count)
+ {
+ finishMeshlet(meshlet, meshlet_triangles);
+
+ meshlets[meshlet_offset++] = meshlet;
+ }
+
+ assert(meshlet_offset <= meshopt_buildMeshletsBound(index_count, max_vertices, max_triangles));
+ return meshlet_offset;
+}
+
+size_t meshopt_buildMeshletsScan(meshopt_Meshlet* meshlets, unsigned int* meshlet_vertices, unsigned char* meshlet_triangles, const unsigned int* indices, size_t index_count, size_t vertex_count, size_t max_vertices, size_t max_triangles)
+{
+ using namespace meshopt;
+
+ assert(index_count % 3 == 0);
+
+ assert(max_vertices >= 3 && max_vertices <= kMeshletMaxVertices);
+ assert(max_triangles >= 1 && max_triangles <= kMeshletMaxTriangles);
+ assert(max_triangles % 4 == 0); // ensures the caller will compute output space properly as index data is 4b aligned
+
+ meshopt_Allocator allocator;
+
+ // index of the vertex in the meshlet, 0xff if the vertex isn't used
+ unsigned char* used = allocator.allocate<unsigned char>(vertex_count);
+ memset(used, -1, vertex_count);
+
+ meshopt_Meshlet meshlet = {};
+ size_t meshlet_offset = 0;
+
+ for (size_t i = 0; i < index_count; i += 3)
+ {
+ unsigned int a = indices[i + 0], b = indices[i + 1], c = indices[i + 2];
+ assert(a < vertex_count && b < vertex_count && c < vertex_count);
+
+ // appends triangle to the meshlet and writes previous meshlet to the output if full
+ meshlet_offset += appendMeshlet(meshlet, a, b, c, used, meshlets, meshlet_vertices, meshlet_triangles, meshlet_offset, max_vertices, max_triangles);
+ }
+
+ if (meshlet.triangle_count)
+ {
+ finishMeshlet(meshlet, meshlet_triangles);
+
+ meshlets[meshlet_offset++] = meshlet;
+ }
+
+ assert(meshlet_offset <= meshopt_buildMeshletsBound(index_count, max_vertices, max_triangles));
+ return meshlet_offset;
+}
+
+meshopt_Bounds meshopt_computeClusterBounds(const unsigned int* indices, size_t index_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
+{
+ using namespace meshopt;
+
+ assert(index_count % 3 == 0);
+ assert(index_count / 3 <= kMeshletMaxTriangles);
+ assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
+ assert(vertex_positions_stride % sizeof(float) == 0);
+
+ (void)vertex_count;
+
+ size_t vertex_stride_float = vertex_positions_stride / sizeof(float);
+
+ // compute triangle normals and gather triangle corners
+ float normals[kMeshletMaxTriangles][3];
+ float corners[kMeshletMaxTriangles][3][3];
+ size_t triangles = 0;
+
+ for (size_t i = 0; i < index_count; i += 3)
+ {
+ unsigned int a = indices[i + 0], b = indices[i + 1], c = indices[i + 2];
+ assert(a < vertex_count && b < vertex_count && c < vertex_count);
+
+ const float* p0 = vertex_positions + vertex_stride_float * a;
+ const float* p1 = vertex_positions + vertex_stride_float * b;
+ const float* p2 = vertex_positions + vertex_stride_float * c;
+
+ 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);
+
+ // no need to include degenerate triangles - they will be invisible anyway
+ if (area == 0.f)
+ continue;
+
+ // record triangle normals & corners for future use; normal and corner 0 define a plane equation
+ normals[triangles][0] = normalx / area;
+ normals[triangles][1] = normaly / area;
+ normals[triangles][2] = normalz / area;
+ memcpy(corners[triangles][0], p0, 3 * sizeof(float));
+ memcpy(corners[triangles][1], p1, 3 * sizeof(float));
+ memcpy(corners[triangles][2], p2, 3 * sizeof(float));
+ triangles++;
+ }
+
+ meshopt_Bounds bounds = {};
+
+ // degenerate cluster, no valid triangles => trivial reject (cone data is 0)
+ if (triangles == 0)
+ return bounds;
+
+ // compute cluster bounding sphere; we'll use the center to determine normal cone apex as well
+ float psphere[4] = {};
+ computeBoundingSphere(psphere, corners[0], triangles * 3);
+
+ float center[3] = {psphere[0], psphere[1], psphere[2]};
+
+ // treating triangle normals as points, find the bounding sphere - the sphere center determines the optimal cone axis
+ float nsphere[4] = {};
+ computeBoundingSphere(nsphere, normals, triangles);
+
+ float axis[3] = {nsphere[0], nsphere[1], nsphere[2]};
+ float axislength = sqrtf(axis[0] * axis[0] + axis[1] * axis[1] + axis[2] * axis[2]);
+ float invaxislength = axislength == 0.f ? 0.f : 1.f / axislength;
+
+ axis[0] *= invaxislength;
+ axis[1] *= invaxislength;
+ axis[2] *= invaxislength;
+
+ // compute a tight cone around all normals, mindp = cos(angle/2)
+ float mindp = 1.f;
+
+ for (size_t i = 0; i < triangles; ++i)
+ {
+ float dp = normals[i][0] * axis[0] + normals[i][1] * axis[1] + normals[i][2] * axis[2];
+
+ mindp = (dp < mindp) ? dp : mindp;
+ }
+
+ // fill bounding sphere info; note that below we can return bounds without cone information for degenerate cones
+ bounds.center[0] = center[0];
+ bounds.center[1] = center[1];
+ bounds.center[2] = center[2];
+ bounds.radius = psphere[3];
+
+ // degenerate cluster, normal cone is larger than a hemisphere => trivial accept
+ // note that if mindp is positive but close to 0, the triangle intersection code below gets less stable
+ // we arbitrarily decide that if a normal cone is ~168 degrees wide or more, the cone isn't useful
+ if (mindp <= 0.1f)
+ {
+ bounds.cone_cutoff = 1;
+ bounds.cone_cutoff_s8 = 127;
+ return bounds;
+ }
+
+ float maxt = 0;
+
+ // we need to find the point on center-t*axis ray that lies in negative half-space of all triangles
+ for (size_t i = 0; i < triangles; ++i)
+ {
+ // dot(center-t*axis-corner, trinormal) = 0
+ // dot(center-corner, trinormal) - t * dot(axis, trinormal) = 0
+ float cx = center[0] - corners[i][0][0];
+ float cy = center[1] - corners[i][0][1];
+ float cz = center[2] - corners[i][0][2];
+
+ float dc = cx * normals[i][0] + cy * normals[i][1] + cz * normals[i][2];
+ float dn = axis[0] * normals[i][0] + axis[1] * normals[i][1] + axis[2] * normals[i][2];
+
+ // dn should be larger than mindp cutoff above
+ assert(dn > 0.f);
+ float t = dc / dn;
+
+ maxt = (t > maxt) ? t : maxt;
+ }
+
+ // cone apex should be in the negative half-space of all cluster triangles by construction
+ bounds.cone_apex[0] = center[0] - axis[0] * maxt;
+ bounds.cone_apex[1] = center[1] - axis[1] * maxt;
+ bounds.cone_apex[2] = center[2] - axis[2] * maxt;
+
+ // note: this axis is the axis of the normal cone, but our test for perspective camera effectively negates the axis
+ bounds.cone_axis[0] = axis[0];
+ bounds.cone_axis[1] = axis[1];
+ bounds.cone_axis[2] = axis[2];
+
+ // cos(a) for normal cone is mindp; we need to add 90 degrees on both sides and invert the cone
+ // which gives us -cos(a+90) = -(-sin(a)) = sin(a) = sqrt(1 - cos^2(a))
+ bounds.cone_cutoff = sqrtf(1 - mindp * mindp);
+
+ // quantize axis & cutoff to 8-bit SNORM format
+ bounds.cone_axis_s8[0] = (signed char)(meshopt_quantizeSnorm(bounds.cone_axis[0], 8));
+ bounds.cone_axis_s8[1] = (signed char)(meshopt_quantizeSnorm(bounds.cone_axis[1], 8));
+ bounds.cone_axis_s8[2] = (signed char)(meshopt_quantizeSnorm(bounds.cone_axis[2], 8));
+
+ // for the 8-bit test to be conservative, we need to adjust the cutoff by measuring the max. error
+ float cone_axis_s8_e0 = fabsf(bounds.cone_axis_s8[0] / 127.f - bounds.cone_axis[0]);
+ float cone_axis_s8_e1 = fabsf(bounds.cone_axis_s8[1] / 127.f - bounds.cone_axis[1]);
+ float cone_axis_s8_e2 = fabsf(bounds.cone_axis_s8[2] / 127.f - bounds.cone_axis[2]);
+
+ // note that we need to round this up instead of rounding to nearest, hence +1
+ int cone_cutoff_s8 = int(127 * (bounds.cone_cutoff + cone_axis_s8_e0 + cone_axis_s8_e1 + cone_axis_s8_e2) + 1);
+
+ bounds.cone_cutoff_s8 = (cone_cutoff_s8 > 127) ? 127 : (signed char)(cone_cutoff_s8);
+
+ return bounds;
+}
+
+meshopt_Bounds meshopt_computeMeshletBounds(const unsigned int* meshlet_vertices, const unsigned char* meshlet_triangles, size_t triangle_count, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
+{
+ using namespace meshopt;
+
+ assert(triangle_count <= kMeshletMaxTriangles);
+ assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
+ assert(vertex_positions_stride % sizeof(float) == 0);
+
+ unsigned int indices[kMeshletMaxTriangles * 3];
+
+ for (size_t i = 0; i < triangle_count * 3; ++i)
+ {
+ unsigned int index = meshlet_vertices[meshlet_triangles[i]];
+ assert(index < vertex_count);
+
+ indices[i] = index;
+ }
+
+ return meshopt_computeClusterBounds(indices, triangle_count * 3, vertex_positions, vertex_count, vertex_positions_stride);
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-12-28 22:50:28 +0000