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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 <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;
}
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