// This file is part of meshoptimizer library; see meshoptimizer.h for version/license details #include "meshoptimizer.h" #include #include #include // 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(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); }