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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 <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
+{
+
+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;
+}
+
+} // namespace meshopt
+
+size_t meshopt_buildMeshletsBound(size_t index_count, size_t max_vertices, size_t max_triangles)
+{
+ assert(index_count % 3 == 0);
+ assert(max_vertices >= 3);
+ assert(max_triangles >= 1);
+
+ // 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* destination, const unsigned int* indices, size_t index_count, size_t vertex_count, size_t max_vertices, size_t max_triangles)
+{
+ assert(index_count % 3 == 0);
+ assert(max_vertices >= 3);
+ assert(max_triangles >= 1);
+
+ meshopt_Allocator allocator;
+
+ meshopt_Meshlet meshlet;
+ memset(&meshlet, 0, sizeof(meshlet));
+
+ assert(max_vertices <= sizeof(meshlet.vertices) / sizeof(meshlet.vertices[0]));
+ assert(max_triangles <= sizeof(meshlet.indices) / 3);
+
+ // 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);
+
+ size_t 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);
+
+ unsigned char& av = used[a];
+ unsigned char& bv = used[b];
+ unsigned char& cv = used[c];
+
+ unsigned int used_extra = (av == 0xff) + (bv == 0xff) + (cv == 0xff);
+
+ if (meshlet.vertex_count + used_extra > max_vertices || meshlet.triangle_count >= max_triangles)
+ {
+ destination[offset++] = meshlet;
+
+ for (size_t j = 0; j < meshlet.vertex_count; ++j)
+ used[meshlet.vertices[j]] = 0xff;
+
+ memset(&meshlet, 0, sizeof(meshlet));
+ }
+
+ if (av == 0xff)
+ {
+ av = meshlet.vertex_count;
+ meshlet.vertices[meshlet.vertex_count++] = a;
+ }
+
+ if (bv == 0xff)
+ {
+ bv = meshlet.vertex_count;
+ meshlet.vertices[meshlet.vertex_count++] = b;
+ }
+
+ if (cv == 0xff)
+ {
+ cv = meshlet.vertex_count;
+ meshlet.vertices[meshlet.vertex_count++] = c;
+ }
+
+ meshlet.indices[meshlet.triangle_count][0] = av;
+ meshlet.indices[meshlet.triangle_count][1] = bv;
+ meshlet.indices[meshlet.triangle_count][2] = cv;
+ meshlet.triangle_count++;
+ }
+
+ if (meshlet.triangle_count)
+ destination[offset++] = meshlet;
+
+ assert(offset <= meshopt_buildMeshletsBound(index_count, max_vertices, max_triangles));
+
+ return 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(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
+ assert(vertex_positions_stride % sizeof(float) == 0);
+
+ assert(index_count / 3 <= 256);
+
+ (void)vertex_count;
+
+ size_t vertex_stride_float = vertex_positions_stride / sizeof(float);
+
+ // compute triangle normals and gather triangle corners
+ float normals[256][3];
+ float corners[256][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 meshopt_Meshlet* meshlet, const float* vertex_positions, size_t vertex_count, size_t vertex_positions_stride)
+{
+ assert(vertex_positions_stride > 0 && vertex_positions_stride <= 256);
+ assert(vertex_positions_stride % sizeof(float) == 0);
+
+ unsigned int indices[sizeof(meshlet->indices) / sizeof(meshlet->indices[0][0])];
+
+ for (size_t i = 0; i < meshlet->triangle_count; ++i)
+ {
+ unsigned int a = meshlet->vertices[meshlet->indices[i][0]];
+ unsigned int b = meshlet->vertices[meshlet->indices[i][1]];
+ unsigned int c = meshlet->vertices[meshlet->indices[i][2]];
+
+ assert(a < vertex_count && b < vertex_count && c < vertex_count);
+
+ indices[i * 3 + 0] = a;
+ indices[i * 3 + 1] = b;
+ indices[i * 3 + 2] = c;
+ }
+
+ return meshopt_computeClusterBounds(indices, meshlet->triangle_count * 3, vertex_positions, vertex_count, vertex_positions_stride);
+}