// This file is part of meshoptimizer library; see meshoptimizer.h for version/license details #include "meshoptimizer.h" #include <assert.h> #include <float.h> #include <string.h> // This work is based on: // Nicolas Capens. Advanced Rasterization. 2004 namespace meshopt { const int kViewport = 256; struct OverdrawBuffer { float z[kViewport][kViewport][2]; unsigned int overdraw[kViewport][kViewport][2]; }; #ifndef min #define min(a, b) ((a) < (b) ? (a) : (b)) #endif #ifndef max #define max(a, b) ((a) > (b) ? (a) : (b)) #endif static float computeDepthGradients(float& dzdx, float& dzdy, float x1, float y1, float z1, float x2, float y2, float z2, float x3, float y3, float z3) { // z2 = z1 + dzdx * (x2 - x1) + dzdy * (y2 - y1) // z3 = z1 + dzdx * (x3 - x1) + dzdy * (y3 - y1) // (x2-x1 y2-y1)(dzdx) = (z2-z1) // (x3-x1 y3-y1)(dzdy) (z3-z1) // we'll solve it with Cramer's rule float det = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1); float invdet = (det == 0) ? 0 : 1 / det; dzdx = (z2 - z1) * (y3 - y1) - (y2 - y1) * (z3 - z1) * invdet; dzdy = (x2 - x1) * (z3 - z1) - (z2 - z1) * (x3 - x1) * invdet; return det; } // half-space fixed point triangle rasterizer static void rasterize(OverdrawBuffer* buffer, float v1x, float v1y, float v1z, float v2x, float v2y, float v2z, float v3x, float v3y, float v3z) { // compute depth gradients float DZx, DZy; float det = computeDepthGradients(DZx, DZy, v1x, v1y, v1z, v2x, v2y, v2z, v3x, v3y, v3z); int sign = det > 0; // flip backfacing triangles to simplify rasterization logic if (sign) { // flipping v2 & v3 preserves depth gradients since they're based on v1 float t; t = v2x, v2x = v3x, v3x = t; t = v2y, v2y = v3y, v3y = t; t = v2z, v2z = v3z, v3z = t; // flip depth since we rasterize backfacing triangles to second buffer with reverse Z; only v1z is used below v1z = kViewport - v1z; DZx = -DZx; DZy = -DZy; } // coordinates, 28.4 fixed point int X1 = int(16.0f * v1x + 0.5f); int X2 = int(16.0f * v2x + 0.5f); int X3 = int(16.0f * v3x + 0.5f); int Y1 = int(16.0f * v1y + 0.5f); int Y2 = int(16.0f * v2y + 0.5f); int Y3 = int(16.0f * v3y + 0.5f); // bounding rectangle, clipped against viewport // since we rasterize pixels with covered centers, min >0.5 should round up // as for max, due to top-left filling convention we will never rasterize right/bottom edges // so max >= 0.5 should round down int minx = max((min(X1, min(X2, X3)) + 7) >> 4, 0); int maxx = min((max(X1, max(X2, X3)) + 7) >> 4, kViewport); int miny = max((min(Y1, min(Y2, Y3)) + 7) >> 4, 0); int maxy = min((max(Y1, max(Y2, Y3)) + 7) >> 4, kViewport); // deltas, 28.4 fixed point int DX12 = X1 - X2; int DX23 = X2 - X3; int DX31 = X3 - X1; int DY12 = Y1 - Y2; int DY23 = Y2 - Y3; int DY31 = Y3 - Y1; // fill convention correction int TL1 = DY12 < 0 || (DY12 == 0 && DX12 > 0); int TL2 = DY23 < 0 || (DY23 == 0 && DX23 > 0); int TL3 = DY31 < 0 || (DY31 == 0 && DX31 > 0); // half edge equations, 24.8 fixed point // note that we offset minx/miny by half pixel since we want to rasterize pixels with covered centers int FX = (minx << 4) + 8; int FY = (miny << 4) + 8; int CY1 = DX12 * (FY - Y1) - DY12 * (FX - X1) + TL1 - 1; int CY2 = DX23 * (FY - Y2) - DY23 * (FX - X2) + TL2 - 1; int CY3 = DX31 * (FY - Y3) - DY31 * (FX - X3) + TL3 - 1; float ZY = v1z + (DZx * float(FX - X1) + DZy * float(FY - Y1)) * (1 / 16.f); for (int y = miny; y < maxy; y++) { int CX1 = CY1; int CX2 = CY2; int CX3 = CY3; float ZX = ZY; for (int x = minx; x < maxx; x++) { // check if all CXn are non-negative if ((CX1 | CX2 | CX3) >= 0) { if (ZX >= buffer->z[y][x][sign]) { buffer->z[y][x][sign] = ZX; buffer->overdraw[y][x][sign]++; } } // signed left shift is UB for negative numbers so use unsigned-signed casts CX1 -= int(unsigned(DY12) << 4); CX2 -= int(unsigned(DY23) << 4); CX3 -= int(unsigned(DY31) << 4); ZX += DZx; } // signed left shift is UB for negative numbers so use unsigned-signed casts CY1 += int(unsigned(DX12) << 4); CY2 += int(unsigned(DX23) << 4); CY3 += int(unsigned(DX31) << 4); ZY += DZy; } } } // namespace meshopt meshopt_OverdrawStatistics meshopt_analyzeOverdraw(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); meshopt_Allocator allocator; size_t vertex_stride_float = vertex_positions_stride / sizeof(float); meshopt_OverdrawStatistics result = {}; float minv[3] = {FLT_MAX, FLT_MAX, FLT_MAX}; float maxv[3] = {-FLT_MAX, -FLT_MAX, -FLT_MAX}; for (size_t i = 0; i < vertex_count; ++i) { const float* v = vertex_positions + i * vertex_stride_float; for (int j = 0; j < 3; ++j) { minv[j] = min(minv[j], v[j]); maxv[j] = max(maxv[j], v[j]); } } float extent = max(maxv[0] - minv[0], max(maxv[1] - minv[1], maxv[2] - minv[2])); float scale = kViewport / extent; float* triangles = allocator.allocate<float>(index_count * 3); for (size_t i = 0; i < index_count; ++i) { unsigned int index = indices[i]; assert(index < vertex_count); const float* v = vertex_positions + index * vertex_stride_float; triangles[i * 3 + 0] = (v[0] - minv[0]) * scale; triangles[i * 3 + 1] = (v[1] - minv[1]) * scale; triangles[i * 3 + 2] = (v[2] - minv[2]) * scale; } OverdrawBuffer* buffer = allocator.allocate<OverdrawBuffer>(1); for (int axis = 0; axis < 3; ++axis) { memset(buffer, 0, sizeof(OverdrawBuffer)); for (size_t i = 0; i < index_count; i += 3) { const float* vn0 = &triangles[3 * (i + 0)]; const float* vn1 = &triangles[3 * (i + 1)]; const float* vn2 = &triangles[3 * (i + 2)]; switch (axis) { case 0: rasterize(buffer, vn0[2], vn0[1], vn0[0], vn1[2], vn1[1], vn1[0], vn2[2], vn2[1], vn2[0]); break; case 1: rasterize(buffer, vn0[0], vn0[2], vn0[1], vn1[0], vn1[2], vn1[1], vn2[0], vn2[2], vn2[1]); break; case 2: rasterize(buffer, vn0[1], vn0[0], vn0[2], vn1[1], vn1[0], vn1[2], vn2[1], vn2[0], vn2[2]); break; } } for (int y = 0; y < kViewport; ++y) for (int x = 0; x < kViewport; ++x) for (int s = 0; s < 2; ++s) { unsigned int overdraw = buffer->overdraw[y][x][s]; result.pixels_covered += overdraw > 0; result.pixels_shaded += overdraw; } } result.overdraw = result.pixels_covered ? float(result.pixels_shaded) / float(result.pixels_covered) : 0.f; return result; }