blob: 113adb2ba23e9dc53a5a2febcb8006803074c20e [file] [log] [blame]
 // Graphite-specific vertex shader code // Wang's formula gives the minimum number of evenly spaced (in the parametric sense) line segments // that a bezier curve must be chopped into in order to guarantee all lines stay within a distance // of "1/precision" pixels from the true curve. Its definition for a bezier curve of degree "n" is // as follows: // // maxLength = max([length(p[i+2] - 2p[i+1] + p[i]) for (0 <= i <= n-2)]) // numParametricSegments = sqrt(maxLength * precision * n*(n - 1)/8) // // (Goldman, Ron. (2003). 5.6.3 Wang's Formula. "Pyramid Algorithms: A Dynamic Programming Approach // to Curves and Surfaces for Geometric Modeling". Morgan Kaufmann Publishers.) const float \$Degree = 3; const float \$Precision = 1; const float \$LengthTerm = (\$Degree * (\$Degree - 1) / 8.0) * \$Precision; const float \$LengthTermPow2 = ((\$Degree * \$Degree) * ((\$Degree - 1) * (\$Degree - 1)) / 64.0) * (\$Precision * \$Precision); // Returns the length squared of the largest forward difference from Wang's cubic formula. float wangs_formula_max_fdiff_pow2(float2 p0, float2 p1, float2 p2, float2 p3, float2x2 matrix) { float2 d0 = matrix * (fma(float2(-2), p1, p2) + p0); float2 d1 = matrix * (fma(float2(-2), p2, p3) + p1); return max(dot(d0,d0), dot(d1,d1)); } float wangs_formula_cubic(float _precision_, float2 p0, float2 p1, float2 p2, float2 p3, float2x2 matrix) { float m = wangs_formula_max_fdiff_pow2(p0, p1, p2, p3, matrix); return max(ceil(sqrt(\$LengthTerm * _precision_ * sqrt(m))), 1.0); } float wangs_formula_cubic_log2(float _precision_, float2 p0, float2 p1, float2 p2, float2 p3, float2x2 matrix) { float m = wangs_formula_max_fdiff_pow2(p0, p1, p2, p3, matrix); return ceil(log2(max(\$LengthTermPow2 * _precision_ * _precision_ * m, 1.0)) * .25); } float wangs_formula_conic_pow2(float _precision_, float2 p0, float2 p1, float2 p2, float w) { // Translate the bounding box center to the origin. float2 C = (min(min(p0, p1), p2) + max(max(p0, p1), p2)) * 0.5; p0 -= C; p1 -= C; p2 -= C; // Compute max length. float m = sqrt(max(max(dot(p0,p0), dot(p1,p1)), dot(p2,p2))); // Compute forward differences. float2 dp = fma(float2(-2.0 * w), p1, p0) + p2; float dw = abs(fma(-2.0, w, 2.0)); // Compute numerator and denominator for parametric step size of linearization. Here, the // epsilon referenced from the cited paper is 1/precision. float rp_minus_1 = max(0.0, fma(m, _precision_, -1.0)); float numer = length(dp) * _precision_ + rp_minus_1 * dw; float denom = 4 * min(w, 1.0); return numer/denom; } float wangs_formula_conic(float _precision_, float2 p0, float2 p1, float2 p2, float w) { float n2 = wangs_formula_conic_pow2(_precision_, p0, p1, p2, w); return max(ceil(sqrt(n2)), 1.0); } float wangs_formula_conic_log2(float _precision_, float2 p0, float2 p1, float2 p2, float w) { float n2 = wangs_formula_conic_pow2(_precision_, p0, p1, p2, w); return ceil(log2(max(n2, 1.0)) * .5); } float2 middle_out_curve(float resolveLevel, float idxInResolveLevel, float4 p01, float4 p23) { float2 localcoord; if (isinf(p23.z)) { // This patch is an exact triangle. localcoord = (resolveLevel != 0) ? p01.zw : (idxInResolveLevel != 0) ? p23.xy : p01.xy; } else { float2 p0=p01.xy, p1=p01.zw, p2=p23.xy, p3=p23.zw; float w = -1; // w < 0 tells us to treat the instance as an integral cubic. float maxResolveLevel; if (isinf(p23.w)) { // Conics are 3 points, with the weight in p3. w = p3.x; maxResolveLevel = wangs_formula_conic_log2(4, p0, p1, p2, w); p1 *= w; // Unproject p1. p3 = p2; // Duplicate the endpoint for shared code that also runs on cubics. } else { // The patch is an integral cubic. maxResolveLevel = wangs_formula_cubic_log2(4, p0, p1, p2, p3, float2x2(1.0)); } if (resolveLevel > maxResolveLevel) { // This vertex is at a higher resolve level than we need. Demote to a lower // resolveLevel, which will produce a degenerate triangle. idxInResolveLevel = floor(ldexp(idxInResolveLevel, int(maxResolveLevel - resolveLevel))); resolveLevel = maxResolveLevel; } // Promote our location to a discrete position in the maximum fixed resolve level. // This is extra paranoia to ensure we get the exact same fp32 coordinates for // colocated points from different resolve levels (e.g., the vertices T=3/4 and // T=6/8 should be exactly colocated). float fixedVertexID = floor(.5 + ldexp(idxInResolveLevel, int(5 - resolveLevel))); if (0 < fixedVertexID && fixedVertexID < 32) { float T = fixedVertexID * (1 / 32.0); // Evaluate at T. Use De Casteljau's for its accuracy and stability. float2 ab = mix(p0, p1, T); float2 bc = mix(p1, p2, T); float2 cd = mix(p2, p3, T); float2 abc = mix(ab, bc, T); float2 bcd = mix(bc, cd, T); float2 abcd = mix(abc, bcd, T); // Evaluate the conic weight at T. float u = mix(1.0, w, T); float v = w + 1 - u; // == mix(w, 1, T) float uv = mix(u, v, T); localcoord = (w < 0) ? /*cubic*/ abcd : /*conic*/ abc/uv; } else { localcoord = (fixedVertexID == 0) ? p0.xy : p3.xy; } } return localcoord; } float2 middle_out_wedge(float resolveLevel, float idxInResolveLevel, float4 p01, float4 p23, float2 fanPointAttrib) { if (resolveLevel < 0) { // A negative resolve level means this is the fan point. return fanPointAttrib; } else { return middle_out_curve(resolveLevel, idxInResolveLevel, p01, p23); } }