// This code is in the public domain -- castanyo@yahoo.es /** @file Raster.cpp * @brief Triangle rasterization library using affine interpolation. Not * specially optimized, but enough for my purposes. **/ #include "nvmesh.h" // pch #include "Raster.h" #include "ClippedTriangle.h" #include "nvcore/Utils.h" // min, max #include "nvmath/Vector.inl" #include "nvmath/ftoi.h" #define RA_EPSILON 0.00001f using namespace nv; using namespace nv::Raster; namespace { static inline float delta(float bot, float top, float ih) { return (bot - top) * ih; } static inline Vector2 delta(Vector2::Arg bot, Vector2::Arg top, float ih) { return (bot - top) * ih; } static inline Vector3 delta(Vector3::Arg bot, Vector3::Arg top, float ih) { return (bot - top) * ih; } // @@ The implementation in nvmath.h should be equivalent. static inline int iround(float f) { // @@ Optimize this. return int(floorf(f+0.5f)); //return int(round(f)); //return int(f); } /// A triangle vertex. struct Vertex { Vector2 pos; // Position. Vector3 tex; // Texcoord. (Barycentric coordinate) }; /// A triangle for rasterization. struct Triangle { Triangle(Vector2::Arg v0, Vector2::Arg v1, Vector2::Arg v2, Vector3::Arg t0, Vector3::Arg t1, Vector3::Arg t2); bool computeDeltas(); bool draw(const Vector2 & extents, bool enableScissors, SamplingCallback cb, void * param); bool drawAA(const Vector2 & extents, bool enableScissors, SamplingCallback cb, void * param); bool drawC(const Vector2 & extents, bool enableScissors, SamplingCallback cb, void * param); void flipBackface(); void computeUnitInwardNormals(); // Vertices. Vector2 v1, v2, v3; Vector2 n1, n2, n3; // unit inward normals Vector3 t1, t2, t3; // Deltas. Vector3 dx, dy; float sign; bool valid; }; /// Triangle ctor. Triangle::Triangle(Vector2::Arg v0, Vector2::Arg v1, Vector2::Arg v2, Vector3::Arg t0, Vector3::Arg t1, Vector3::Arg t2) { // Init vertices. this->v1 = v0; this->v2 = v2; this->v3 = v1; // Set barycentric coordinates. this->t1 = t0; this->t2 = t2; this->t3 = t1; // make sure every triangle is front facing. flipBackface(); // Compute deltas. valid = computeDeltas(); computeUnitInwardNormals(); } /// Compute texture space deltas. /// This method takes two edge vectors that form a basis, determines the /// coordinates of the canonic vectors in that basis, and computes the /// texture gradient that corresponds to those vectors. bool Triangle::computeDeltas() { Vector2 e0 = v3 - v1; Vector2 e1 = v2 - v1; Vector3 de0 = t3 - t1; Vector3 de1 = t2 - t1; float denom = 1.0f / (e0.y * e1.x - e1.y * e0.x); if (!isFinite(denom)) { return false; } float lambda1 = - e1.y * denom; float lambda2 = e0.y * denom; float lambda3 = e1.x * denom; float lambda4 = - e0.x * denom; dx = de0 * lambda1 + de1 * lambda2; dy = de0 * lambda3 + de1 * lambda4; return true; } // compute unit inward normals for each edge. void Triangle::computeUnitInwardNormals() { n1 = v1 - v2; n1 = Vector2(-n1.y, n1.x); n1 = n1 * (1.0f/sqrtf(n1.x*n1.x + n1.y*n1.y)); n2 = v2 - v3; n2 = Vector2(-n2.y, n2.x); n2 = n2 * (1.0f/sqrtf(n2.x*n2.x + n2.y*n2.y)); n3 = v3 - v1; n3 = Vector2(-n3.y, n3.x); n3 = n3 * (1.0f/sqrtf(n3.x*n3.x + n3.y*n3.y)); } void Triangle::flipBackface() { // check if triangle is backfacing, if so, swap two vertices if ( ((v3.x-v1.x)*(v2.y-v1.y) - (v3.y-v1.y)*(v2.x-v1.x)) < 0 ) { Vector2 hv=v1; v1=v2; v2=hv; // swap pos Vector3 ht=t1; t1=t2; t2=ht; // swap tex } } bool Triangle::draw(const Vector2 & extents, bool enableScissors, SamplingCallback cb, void * param) { // 28.4 fixed-point coordinates const int Y1 = iround(16.0f * v1.y); const int Y2 = iround(16.0f * v2.y); const int Y3 = iround(16.0f * v3.y); const int X1 = iround(16.0f * v1.x); const int X2 = iround(16.0f * v2.x); const int X3 = iround(16.0f * v3.x); // Deltas const int DX12 = X1 - X2; const int DX23 = X2 - X3; const int DX31 = X3 - X1; const int DY12 = Y1 - Y2; const int DY23 = Y2 - Y3; const int DY31 = Y3 - Y1; // Fixed-point deltas const int FDX12 = DX12 << 4; const int FDX23 = DX23 << 4; const int FDX31 = DX31 << 4; const int FDY12 = DY12 << 4; const int FDY23 = DY23 << 4; const int FDY31 = DY31 << 4; int minx, miny, maxx, maxy; if (enableScissors) { int frustumX0 = 0 << 4; int frustumY0 = 0 << 4; int frustumX1 = (int)extents.x << 4; int frustumY1 = (int)extents.y << 4; // Bounding rectangle minx = (nv::max(min3(X1, X2, X3), frustumX0) + 0xF) >> 4; miny = (nv::max(min3(Y1, Y2, Y3), frustumY0) + 0xF) >> 4; maxx = (nv::min(max3(X1, X2, X3), frustumX1) + 0xF) >> 4; maxy = (nv::min(max3(Y1, Y2, Y3), frustumY1) + 0xF) >> 4; } else { // Bounding rectangle minx = (min3(X1, X2, X3) + 0xF) >> 4; miny = (min3(Y1, Y2, Y3) + 0xF) >> 4; maxx = (max3(X1, X2, X3) + 0xF) >> 4; maxy = (max3(Y1, Y2, Y3) + 0xF) >> 4; } // Block size, standard 8x8 (must be power of two) const int q = 8; // @@ This won't work when minx,miny are negative. This code path is not used. Leaving as is for now. nvCheck(minx >= 0); nvCheck(miny >= 0); // Start in corner of 8x8 block minx &= ~(q - 1); miny &= ~(q - 1); // Half-edge constants int C1 = DY12 * X1 - DX12 * Y1; int C2 = DY23 * X2 - DX23 * Y2; int C3 = DY31 * X3 - DX31 * Y3; // Correct for fill convention if(DY12 < 0 || (DY12 == 0 && DX12 > 0)) C1++; if(DY23 < 0 || (DY23 == 0 && DX23 > 0)) C2++; if(DY31 < 0 || (DY31 == 0 && DX31 > 0)) C3++; // Loop through blocks for(int y = miny; y < maxy; y += q) { for(int x = minx; x < maxx; x += q) { // Corners of block int x0 = x << 4; int x1 = (x + q - 1) << 4; int y0 = y << 4; int y1 = (y + q - 1) << 4; // Evaluate half-space functions bool a00 = C1 + DX12 * y0 - DY12 * x0 > 0; bool a10 = C1 + DX12 * y0 - DY12 * x1 > 0; bool a01 = C1 + DX12 * y1 - DY12 * x0 > 0; bool a11 = C1 + DX12 * y1 - DY12 * x1 > 0; int a = (a00 << 0) | (a10 << 1) | (a01 << 2) | (a11 << 3); bool b00 = C2 + DX23 * y0 - DY23 * x0 > 0; bool b10 = C2 + DX23 * y0 - DY23 * x1 > 0; bool b01 = C2 + DX23 * y1 - DY23 * x0 > 0; bool b11 = C2 + DX23 * y1 - DY23 * x1 > 0; int b = (b00 << 0) | (b10 << 1) | (b01 << 2) | (b11 << 3); bool c00 = C3 + DX31 * y0 - DY31 * x0 > 0; bool c10 = C3 + DX31 * y0 - DY31 * x1 > 0; bool c01 = C3 + DX31 * y1 - DY31 * x0 > 0; bool c11 = C3 + DX31 * y1 - DY31 * x1 > 0; int c = (c00 << 0) | (c10 << 1) | (c01 << 2) | (c11 << 3); // Skip block when outside an edge if(a == 0x0 || b == 0x0 || c == 0x0) continue; // Accept whole block when totally covered if(a == 0xF && b == 0xF && c == 0xF) { Vector3 texRow = t1 + dy*(y0 - v1.y) + dx*(x0 - v1.x); for(int iy = y; iy < y + q; iy++) { Vector3 tex = texRow; for(int ix = x; ix < x + q; ix++) { //Vector3 tex = t1 + dx * (ix - v1.x) + dy * (iy - v1.y); if (!cb(param, ix, iy, tex, dx, dy, 1.0)) { // early out. return false; } tex += dx; } texRow += dy; } } else // Partially covered block { int CY1 = C1 + DX12 * y0 - DY12 * x0; int CY2 = C2 + DX23 * y0 - DY23 * x0; int CY3 = C3 + DX31 * y0 - DY31 * x0; Vector3 texRow = t1 + dy*(y0 - v1.y) + dx*(x0 - v1.x); for(int iy = y; iy < y + q; iy++) { int CX1 = CY1; int CX2 = CY2; int CX3 = CY3; Vector3 tex = texRow; for(int ix = x; ix < x + q; ix++) { if(CX1 > 0 && CX2 > 0 && CX3 > 0) { if (!cb(param, ix, iy, tex, dx, dy, 1.0)) { // early out. return false; } } CX1 -= FDY12; CX2 -= FDY23; CX3 -= FDY31; tex += dx; } CY1 += FDX12; CY2 += FDX23; CY3 += FDX31; texRow += dy; } } } } return true; } #define PX_INSIDE 1.0f/sqrt(2.0f) #define PX_OUTSIDE -1.0f/sqrt(2.0f) #define BK_SIZE 8 #define BK_INSIDE sqrt(BK_SIZE*BK_SIZE/2.0f) #define BK_OUTSIDE -sqrt(BK_SIZE*BK_SIZE/2.0f) // extents has to be multiple of BK_SIZE!! bool Triangle::drawAA(const Vector2 & extents, bool enableScissors, SamplingCallback cb, void * param) { float minx, miny, maxx, maxy; if (enableScissors) { // Bounding rectangle minx = floorf(max(min3(v1.x, v2.x, v3.x), 0.0f)); miny = floorf(max(min3(v1.y, v2.y, v3.y), 0.0f)); maxx = ceilf( min(max3(v1.x, v2.x, v3.x), extents.x-1.0f)); maxy = ceilf( min(max3(v1.y, v2.y, v3.y), extents.y-1.0f)); } else { // Bounding rectangle minx = floorf(min3(v1.x, v2.x, v3.x)); miny = floorf(min3(v1.y, v2.y, v3.y)); maxx = ceilf( max3(v1.x, v2.x, v3.x)); maxy = ceilf( max3(v1.y, v2.y, v3.y)); } // There's no reason to align the blocks to the viewport, instead we align them to the origin of the triangle bounds. minx = floorf(minx); miny = floorf(miny); //minx = (float)(((int)minx) & (~((int)BK_SIZE - 1))); // align to blocksize (we don't need to worry about blocks partially out of viewport) //miny = (float)(((int)miny) & (~((int)BK_SIZE - 1))); minx += 0.5; miny +=0.5; // sampling at texel centers! maxx += 0.5; maxy +=0.5; // Half-edge constants float C1 = n1.x * (-v1.x) + n1.y * (-v1.y); float C2 = n2.x * (-v2.x) + n2.y * (-v2.y); float C3 = n3.x * (-v3.x) + n3.y * (-v3.y); // Loop through blocks for(float y0 = miny; y0 <= maxy; y0 += BK_SIZE) { for(float x0 = minx; x0 <= maxx; x0 += BK_SIZE) { // Corners of block float xc = (x0 + (BK_SIZE-1)/2.0f); float yc = (y0 + (BK_SIZE-1)/2.0f); // Evaluate half-space functions float aC = C1 + n1.x * xc + n1.y * yc; float bC = C2 + n2.x * xc + n2.y * yc; float cC = C3 + n3.x * xc + n3.y * yc; // Skip block when outside an edge if( (aC <= BK_OUTSIDE) || (bC <= BK_OUTSIDE) || (cC <= BK_OUTSIDE) ) continue; // Accept whole block when totally covered if( (aC >= BK_INSIDE) && (bC >= BK_INSIDE) && (cC >= BK_INSIDE) ) { Vector3 texRow = t1 + dy*(y0 - v1.y) + dx*(x0 - v1.x); for (float y = y0; y < y0 + BK_SIZE; y++) { Vector3 tex = texRow; for(float x = x0; x < x0 + BK_SIZE; x++) { if (!cb(param, (int)x, (int)y, tex, dx, dy, 1.0f)) { return false; } tex += dx; } texRow += dy; } } else // Partially covered block { float CY1 = C1 + n1.x * x0 + n1.y * y0; float CY2 = C2 + n2.x * x0 + n2.y * y0; float CY3 = C3 + n3.x * x0 + n3.y * y0; Vector3 texRow = t1 + dy*(y0 - v1.y) + dx*(x0 - v1.x); for(float y = y0; y < y0 + BK_SIZE; y++) // @@ This is not clipping to scissor rectangle correctly. { float CX1 = CY1; float CX2 = CY2; float CX3 = CY3; Vector3 tex = texRow; for (float x = x0; x < x0 + BK_SIZE; x++) // @@ This is not clipping to scissor rectangle correctly. { if (CX1 >= PX_INSIDE && CX2 >= PX_INSIDE && CX3 >= PX_INSIDE) { // pixel completely covered Vector3 tex = t1 + dx * (x - v1.x) + dy * (y - v1.y); if (!cb(param, (int)x, (int)y, tex, dx, dy, 1.0f)) { return false; } } else if ((CX1 >= PX_OUTSIDE) && (CX2 >= PX_OUTSIDE) && (CX3 >= PX_OUTSIDE)) { // triangle partially covers pixel. do clipping. ClippedTriangle ct(v1-Vector2(x,y), v2-Vector2(x,y), v3-Vector2(x,y)); ct.clipAABox(-0.5, -0.5, 0.5, 0.5); Vector2 centroid = ct.centroid(); float area = ct.area(); if (area > 0.0f) { Vector3 texCent = tex - dx*centroid.x - dy*centroid.y; //nvCheck(texCent.x >= -0.1f && texCent.x <= 1.1f); // @@ Centroid is not very exact... //nvCheck(texCent.y >= -0.1f && texCent.y <= 1.1f); //nvCheck(texCent.z >= -0.1f && texCent.z <= 1.1f); //Vector3 texCent2 = t1 + dx * (x - v1.x) + dy * (y - v1.y); if (!cb(param, (int)x, (int)y, texCent, dx, dy, area)) { return false; } } } CX1 += n1.x; CX2 += n2.x; CX3 += n3.x; tex += dx; } CY1 += n1.y; CY2 += n2.y; CY3 += n3.y; texRow += dy; } } } } return true; } } // namespace /// Process the given triangle. bool nv::Raster::drawTriangle(Mode mode, Vector2::Arg extents, bool enableScissors, const Vector2 v[3], SamplingCallback cb, void * param) { Triangle tri(v[0], v[1], v[2], Vector3(1, 0, 0), Vector3(0, 1, 0), Vector3(0, 0, 1)); // @@ It would be nice to have a conservative drawing mode that enlarges the triangle extents by one texel and is able to handle degenerate triangles. // @@ Maybe the simplest thing to do would be raster triangle edges. if (tri.valid) { if (mode == Mode_Antialiased) { return tri.drawAA(extents, enableScissors, cb, param); } if (mode == Mode_Nearest) { return tri.draw(extents, enableScissors, cb, param); } } return true; } inline static float triangleArea(Vector2::Arg v1, Vector2::Arg v2, Vector2::Arg v3) { return 0.5f * (v3.x * v1.y + v1.x * v2.y + v2.x * v3.y - v2.x * v1.y - v3.x * v2.y - v1.x * v3.y); } /// Process the given quad. bool nv::Raster::drawQuad(Mode mode, Vector2::Arg extents, bool enableScissors, const Vector2 v[4], SamplingCallback cb, void * param) { bool sign0 = triangleArea(v[0], v[1], v[2]) > 0.0f; bool sign1 = triangleArea(v[0], v[2], v[3]) > 0.0f; // Divide the quad into two non overlapping triangles. if (sign0 == sign1) { Triangle tri0(v[0], v[1], v[2], Vector3(0,0,0), Vector3(1,0,0), Vector3(1,1,0)); Triangle tri1(v[0], v[2], v[3], Vector3(0,0,0), Vector3(1,1,0), Vector3(0,1,0)); if (tri0.valid && tri1.valid) { if (mode == Mode_Antialiased) { return tri0.drawAA(extents, enableScissors, cb, param) && tri1.drawAA(extents, enableScissors, cb, param); } else { return tri0.draw(extents, enableScissors, cb, param) && tri1.draw(extents, enableScissors, cb, param); } } } else { Triangle tri0(v[0], v[1], v[3], Vector3(0,0,0), Vector3(1,0,0), Vector3(0,1,0)); Triangle tri1(v[1], v[2], v[3], Vector3(1,0,0), Vector3(1,1,0), Vector3(0,1,0)); if (tri0.valid && tri1.valid) { if (mode == Mode_Antialiased) { return tri0.drawAA(extents, enableScissors, cb, param) && tri1.drawAA(extents, enableScissors, cb, param); } else { return tri0.draw(extents, enableScissors, cb, param) && tri1.draw(extents, enableScissors, cb, param); } } } return true; } static bool drawPoint(const Vector2 & p, const Vector2 v[2], LineSamplingCallback cb, void * param) { int x = ftoi_round(p.x); int y = ftoi_round(p.y); Vector2 ip = Vector2(float(x) + 0.5f, float(y) + 0.5f); float t; // Return minimum distance between line segment vw and point p Vector2 dv = v[1] - v[0]; const float l2 = nv::lengthSquared(dv); // i.e. |w-v|^2 - avoid a sqrt if (l2 == 0.0) { t = 0; // v0 == v1 case } else { // Consider the line extending the segment, parameterized as v + t (w - v). // We find projection of point p onto the line. // It falls where t = [(p-v) . (w-v)] / |w-v|^2 t = dot(ip - v[0], dv) / l2; if (t < 0.0) { t = 0; // Beyond the 'v0' end of the segment } else if (t > 1.0) { t = 1; // Beyond the 'v1' end of the segment } } Vector2 projection = v[0] + t * dv; // Projection falls on the segment float d = distance(ip, projection); return cb(param, x, y, t, saturate(1-d)); } void nv::Raster::drawLine(bool antialias, Vector2::Arg extents, bool enableScissors, const Vector2 v[2], LineSamplingCallback cb, void * param) { nvCheck(antialias == true); // @@ Not implemented. //nvCheck(enableScissors == false); // @@ Not implemented. // Very crappy DDA implementation. Vector2 p = v[0]; Vector2 dp, dpdy; float dx = v[1].x - v[0].x; float dy = v[1].y - v[0].y; int n; // Degenerate line. if (dx == 0 && dy == 0) return; if (fabsf(dx) >= fabsf(dy)) { n = iround(fabsf(dx)); dp.x = dx / fabsf(dx); dp.y = dy / fabsf(dx); nvDebugCheck(fabsf(dp.y) <= 1.0f); dpdy.x = 0; dpdy.y = 1; } else { n = iround(fabs(dy)); dp.x = dx / fabsf(dy); dp.y = dy / fabsf(dy); nvDebugCheck(fabsf(dp.x) <= 1.0f); dpdy.x = 1; dpdy.y = 0; } for (int i = 0; i <= n; i++) { drawPoint(p, v, cb, param); drawPoint(p + dpdy, v, cb, param); drawPoint(p - dpdy, v, cb, param); p += dp; } } // Draw vertical or horizontal segments. For degenerate triangles. /*bool nv::Raster::drawSegment(Vector2::Arg extents, bool enableScissors, const Vector2 v[2], LineSamplingCallback cb, void * param) { nvCheck(enableScissors == false); if (v[0].x == v[1].x) { // Vertical segment. } else if (v[0].y == v[1].y) { // Horizontal segment. int y = ftoi_round(v[0].y); int x0 = ftoi_floor(v[0].x); int x1 = ftoi_floor(v[0].x); for (int x = x0; x <= x1; x++) { cb(param, x, y, t, } } return false; // Not a valid segment. } */