blob: 96725d1f8ad7651e9304a9676600e836db820cf7 [file] [log] [blame]
 // Graphite-specific vertex shader code const float \$PI = 3.141592653589793238; // 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 = 4; // Must match skgpu::tess::kPrecision 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_p2(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(float2 p0, float2 p1, float2 p2, float2 p3, float2x2 matrix) { float m = wangs_formula_max_fdiff_p2(p0, p1, p2, p3, matrix); return max(ceil(sqrt(\$LengthTerm * sqrt(m))), 1.0); } float wangs_formula_cubic_log2(float2 p0, float2 p1, float2 p2, float2 p3, float2x2 matrix) { float m = wangs_formula_max_fdiff_p2(p0, p1, p2, p3, matrix); return ceil(log2(max(\$LengthTermPow2 * m, 1.0)) * .25); } float wangs_formula_conic_p2(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(float2 p0, float2 p1, float2 p2, float w) { float n2 = wangs_formula_conic_p2(p0, p1, p2, w); return max(ceil(sqrt(n2)), 1.0); } float wangs_formula_conic_log2(float2 p0, float2 p1, float2 p2, float w) { float n2 = wangs_formula_conic_p2(p0, p1, p2, w); return ceil(log2(max(n2, 1.0)) * .5); } // Returns the normalized difference between a and b, i.e. normalize(a - b), with care taken for // if 'a' and/or 'b' have large coordinates. float2 robust_normalize_diff(float2 a, float2 b) { float2 diff = a - b; if (diff == float2(0.0)) { return float2(0.0); } else { float invMag = 1.0 / max(abs(diff.x), abs(diff.y)); return normalize(invMag * diff); } } // Returns the cosine of the angle between a and b, assuming a and b are unit vectors already. // Guaranteed to be between [-1, 1]. float cosine_between_unit_vectors(float2 a, float2 b) { // Since a and b are assumed to be normalized, the cosine is equal to the dot product, although // we clamp that to ensure it falls within the expected range of [-1, 1]. return clamp(dot(a, b), -1.0, 1.0); } // Extends the middle radius to either the miter point, or the bevel edge if we surpassed the // miter limit and need to revert to a bevel join. float miter_extent(float cosTheta, float miterLimit) { float x = fma(cosTheta, .5, .5); return (x * miterLimit * miterLimit >= 1.0) ? inversesqrt(x) : sqrt(x); } // Returns the number of radial segments required for each radian of rotation, in order for the // curve to appear "smooth" as defined by the approximate device-space stroke radius. float num_radial_segments_per_radian(float approxDevStrokeRadius) { return .5 / acos(max(1.0 - (1.0 / \$Precision) / approxDevStrokeRadius, -1.0)); } // Unlike mix(), this does not return b when t==1. But it otherwise seems to get better // precision than "a*(1 - t) + b*t" for things like chopping cubics on exact cusp points. // We override this result anyway when t==1 so it shouldn't be a problem. float unchecked_mix(float a, float b, float T) { return fma(b - a, T, a); } float2 unchecked_mix(float2 a, float2 b, float T) { return fma(b - a, float2(T), a); } float4 unchecked_mix(float4 a, float4 b, float4 T) { return fma(b - a, T, a); } // Compute a vertex position for the curve described by p01 and p23 packed control points, // tessellated to the given resolve level, and assuming it will be drawn as a filled curve. float2 tessellate_filled_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(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(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; } // Like tessellate_filled_curve but assumes the output vertex will be used for filled wedges, where // a negative resolve level maps to the interior wedge point stored in 'fanPointAttrib'. float2 tessellate_filled_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 tessellate_filled_curve(resolveLevel, idxInResolveLevel, p01, p23); } } float2 tessellate_stroked_curve(float edgeID, float maxEdges, float2x2 affineMatrix, float2 translate, float maxScale /* derived from affineMatrix */, float4 p01, float4 p23, float2 lastControlPoint, float2 strokeParams) { float2 p0=p01.xy, p1=p01.zw, p2=p23.xy, p3=p23.zw; float w = -1; // w<0 means the curve is an integral cubic. if (isinf(p23.w)) { // Conics are 3 points, with the weight in p3. w = p3.x; p3 = p2; // Setting p3 equal to p2 works for the remaining rotational logic. } // Call Wang's formula to determine parametric segments before transform points for hairlines // so that it is consistent with how the CPU tested the control points for chopping. float numParametricSegments; if (w < 0) { if (p0 == p1 && p2 == p3) { numParametricSegments = 1; // a line } else { numParametricSegments = wangs_formula_cubic(p0, p1, p2, p3, affineMatrix); } } else { numParametricSegments = wangs_formula_conic(affineMatrix * p0, affineMatrix * p1, affineMatrix * p2, w); } // Matches skgpu::tess::StrokeParams float strokeRadius = strokeParams.x; float joinType = strokeParams.y; // <0 = round join, ==0 = bevel join, >0 encodes miter limit bool isHairline = strokeParams.x == 0.0; float numRadialSegmentsPerRadian; if (isHairline) { numRadialSegmentsPerRadian = num_radial_segments_per_radian(1.0); strokeRadius = 0.5; } else { numRadialSegmentsPerRadian = num_radial_segments_per_radian(maxScale * strokeParams.x); } if (isHairline) { // Hairline case. Transform the points before tessellation. We can still hold off on the // translate until the end; we just need to perform the scale and skew right now. p0 = affineMatrix * p0; p1 = affineMatrix * p1; p2 = affineMatrix * p2; p3 = affineMatrix * p3; lastControlPoint = affineMatrix * lastControlPoint; } // Find the starting and ending tangents. float2 tan0 = robust_normalize_diff((p0 == p1) ? ((p1 == p2) ? p3 : p2) : p1, p0); float2 tan1 = robust_normalize_diff(p3, (p3 == p2) ? ((p2 == p1) ? p0 : p1) : p2); if (tan0 == float2(0)) { // The stroke is a point. This special case tells us to draw a stroke-width circle as a // 180 degree point stroke instead. tan0 = float2(1,0); tan1 = float2(-1,0); } // Determine how many edges to give to the join. We emit the first and final edges // of the join twice: once full width and once restricted to half width. This guarantees // perfect seaming by matching the vertices from the join as well as from the strokes on // either side. float numEdgesInJoin; if (joinType >= 0 /*Is the join not a round type?*/) { // Bevel(0) and miter(+) joins get 1 and 2 segments respectively. // +2 because we emit the beginning and ending edges twice (see above comments). numEdgesInJoin = sign(joinType) + 1 + 2; } else { float2 prevTan = robust_normalize_diff(p0, lastControlPoint); float joinRads = acos(cosine_between_unit_vectors(prevTan, tan0)); float numRadialSegmentsInJoin = max(ceil(joinRads * numRadialSegmentsPerRadian), 1); // +2 because we emit the beginning and ending edges twice (see above comment). numEdgesInJoin = numRadialSegmentsInJoin + 2; // The stroke section needs at least two edges. Don't assign more to the join than // "maxEdges - 2". (This is only relevant when the ideal max edge count calculated // on the CPU had to be limited to maxEdges in the draw call). numEdgesInJoin = min(numEdgesInJoin, maxEdges - 2); } // Find which direction the curve turns. // NOTE: Since the curve is not allowed to inflect, we can just check F'(.5) x F''(.5). // NOTE: F'(.5) x F''(.5) has the same sign as (P2 - P0) x (P3 - P1) float turn = cross_length_2d(p2 - p0, p3 - p1); float combinedEdgeID = abs(edgeID) - numEdgesInJoin; if (combinedEdgeID < 0) { tan1 = tan0; // Don't let tan0 become zero. The code as-is isn't built to handle that case. tan0=0 // means the join is disabled, and to disable it with the existing code we can leave // tan0 equal to tan1. if (lastControlPoint != p0) { tan0 = robust_normalize_diff(p0, lastControlPoint); } turn = cross_length_2d(tan0, tan1); } // Calculate the curve's starting angle and rotation. float cosTheta = cosine_between_unit_vectors(tan0, tan1); float rotation = acos(cosTheta); if (turn < 0) { // Adjust sign of rotation to match the direction the curve turns. rotation = -rotation; } float numRadialSegments; float strokeOutset = sign(edgeID); if (combinedEdgeID < 0) { // We belong to the preceding join. The first and final edges get duplicated, so we only // have "numEdgesInJoin - 2" segments. numRadialSegments = numEdgesInJoin - 2; numParametricSegments = 1; // Joins don't have parametric segments. p3 = p2 = p1 = p0; // Colocate all points on the junction point. // Shift combinedEdgeID to the range [-1, numRadialSegments]. This duplicates the first // edge and lands one edge at the very end of the join. (The duplicated final edge will // actually come from the section of our strip that belongs to the stroke.) combinedEdgeID += numRadialSegments + 1; // We normally restrict the join on one side of the junction, but if the tangents are // nearly equivalent this could theoretically result in bad seaming and/or cracks on the // side we don't put it on. If the tangents are nearly equivalent then we leave the join // double-sided. float sinEpsilon = 1e-2; // ~= sin(180deg / 3000) bool tangentsNearlyParallel = (abs(turn) * inversesqrt(dot(tan0, tan0) * dot(tan1, tan1))) < sinEpsilon; if (!tangentsNearlyParallel || dot(tan0, tan1) < 0) { // There are two edges colocated at the beginning. Leave the first one double sided // for seaming with the previous stroke. (The double sided edge at the end will // actually come from the section of our strip that belongs to the stroke.) if (combinedEdgeID >= 0) { strokeOutset = (turn < 0) ? min(strokeOutset, 0) : max(strokeOutset, 0); } } combinedEdgeID = max(combinedEdgeID, 0); } else { // We belong to the stroke. Unless numRadialSegmentsPerRadian is incredibly high, // clamping to maxCombinedSegments will be a no-op because the draw call was invoked with // sufficient vertices to cover the worst case scenario of 180 degree rotation. float maxCombinedSegments = maxEdges - numEdgesInJoin - 1; numRadialSegments = max(ceil(abs(rotation) * numRadialSegmentsPerRadian), 1); numRadialSegments = min(numRadialSegments, maxCombinedSegments); numParametricSegments = min(numParametricSegments, maxCombinedSegments - numRadialSegments + 1); } // Additional parameters for final tessellation evaluation. float radsPerSegment = rotation / numRadialSegments; float numCombinedSegments = numParametricSegments + numRadialSegments - 1; bool isFinalEdge = (combinedEdgeID >= numCombinedSegments); if (combinedEdgeID > numCombinedSegments) { strokeOutset = 0; // The strip has more edges than we need. Drop this one. } // Edge #2 extends to the miter point. if (abs(edgeID) == 2 && joinType > 0/*Is the join a miter type?*/) { strokeOutset *= miter_extent(cosTheta, joinType/*miterLimit*/); } float2 tangent, strokeCoord; if (combinedEdgeID != 0 && !isFinalEdge) { // Compute the location and tangent direction of the stroke edge with the integral id // "combinedEdgeID", where combinedEdgeID is the sorted-order index of parametric and radial // edges. Start by finding the tangent function's power basis coefficients. These define a // tangent direction (scaled by some uniform value) as: // |T^2| // Tangent_Direction(T) = dx,dy = |A 2B C| * |T | // |. . .| |1 | float2 A, B, C = p1 - p0; float2 D = p3 - p0; if (w >= 0.0) { // P0..P2 represent a conic and P3==P2. The derivative of a conic has a cumbersome // order-4 denominator. However, this isn't necessary if we are only interested in a // vector in the same *direction* as a given tangent line. Since the denominator scales // dx and dy uniformly, we can throw it out completely after evaluating the derivative // with the standard quotient rule. This leaves us with a simpler quadratic function // that we use to find a tangent. C *= w; B = .5*D - C; A = (w - 1.0) * D; p1 *= w; } else { float2 E = p2 - p1; B = E - C; A = fma(float2(-3), E, D); } // FIXME(crbug.com/800804,skbug.com/11268): Consider normalizing the exponents in A,B,C at // this point in order to prevent fp32 overflow. // Now find the coefficients that give a tangent direction from a parametric edge ID: // // |parametricEdgeID^2| // Tangent_Direction(parametricEdgeID) = dx,dy = |A B_ C_| * |parametricEdgeID | // |. . .| |1 | // float2 B_ = B * (numParametricSegments * 2.0); float2 C_ = C * (numParametricSegments * numParametricSegments); // Run a binary search to determine the highest parametric edge that is located on or before // the combinedEdgeID. A combined ID is determined by the sum of complete parametric and // radial segments behind it. i.e., find the highest parametric edge where: // // parametricEdgeID + floor(numRadialSegmentsAtParametricT) <= combinedEdgeID // float lastParametricEdgeID = 0.0; float maxParametricEdgeID = min(numParametricSegments - 1.0, combinedEdgeID); float negAbsRadsPerSegment = -abs(radsPerSegment); float maxRotation0 = (1.0 + combinedEdgeID) * abs(radsPerSegment); for (int exp = 5 /*max resolve level*/ - 1; exp >= 0; --exp) { // Test the parametric edge at lastParametricEdgeID + 2^exp. float testParametricID = lastParametricEdgeID + exp2(float(exp)); if (testParametricID <= maxParametricEdgeID) { float2 testTan = fma(float2(testParametricID), A, B_); testTan = fma(float2(testParametricID), testTan, C_); float cosRotation = dot(normalize(testTan), tan0); float maxRotation = fma(testParametricID, negAbsRadsPerSegment, maxRotation0); maxRotation = min(maxRotation, \$PI); // Is rotation <= maxRotation? (i.e., is the number of complete radial segments // behind testT, + testParametricID <= combinedEdgeID?) if (cosRotation >= cos(maxRotation)) { // testParametricID is on or before the combinedEdgeID. Keep it! lastParametricEdgeID = testParametricID; } } } // Find the T value of the parametric edge at lastParametricEdgeID. float parametricT = lastParametricEdgeID / numParametricSegments; // Now that we've identified the highest parametric edge on or before the // combinedEdgeID, the highest radial edge is easy: float lastRadialEdgeID = combinedEdgeID - lastParametricEdgeID; // Find the angle of tan0, i.e. the angle between tan0 and the positive x axis. float angle0 = acos(clamp(tan0.x, -1.0, 1.0)); angle0 = tan0.y >= 0.0 ? angle0 : -angle0; // Find the tangent vector on the edge at lastRadialEdgeID. By construction it is already // normalized. float radialAngle = fma(lastRadialEdgeID, radsPerSegment, angle0); tangent = float2(cos(radialAngle), sin(radialAngle)); float2 norm = float2(-tangent.y, tangent.x); // Find the T value where the tangent is orthogonal to norm. This is a quadratic: // // dot(norm, Tangent_Direction(T)) == 0 // // |T^2| // norm * |A 2B C| * |T | == 0 // |. . .| |1 | // float a=dot(norm,A), b_over_2=dot(norm,B), c=dot(norm,C); float discr_over_4 = max(b_over_2*b_over_2 - a*c, 0.0); float q = sqrt(discr_over_4); if (b_over_2 > 0.0) { q = -q; } q -= b_over_2; // Roots are q/a and c/q. Since each curve section does not inflect or rotate more than 180 // degrees, there can only be one tangent orthogonal to "norm" inside 0..1. Pick the root // nearest .5. float _5qa = -.5*q*a; float2 root = (abs(fma(q,q,_5qa)) < abs(fma(a,c,_5qa))) ? float2(q,a) : float2(c,q); float radialT = (root.t != 0.0) ? root.s / root.t : 0.0; radialT = clamp(radialT, 0.0, 1.0); if (lastRadialEdgeID == 0.0) { // The root finder above can become unstable when lastRadialEdgeID == 0 (e.g., if // there are roots at exatly 0 and 1 both). radialT should always == 0 in this case. radialT = 0.0; } // Now that we've identified the T values of the last parametric and radial edges, our final // T value for combinedEdgeID is whichever is larger. float T = max(parametricT, radialT); // Evaluate the cubic at T. Use De Casteljau's for its accuracy and stability. float2 ab = unchecked_mix(p0, p1, T); float2 bc = unchecked_mix(p1, p2, T); float2 cd = unchecked_mix(p2, p3, T); float2 abc = unchecked_mix(ab, bc, T); float2 bcd = unchecked_mix(bc, cd, T); float2 abcd = unchecked_mix(abc, bcd, T); // Evaluate the conic weight at T. float u = unchecked_mix(1.0, w, T); float v = w + 1 - u; // == mix(w, 1, T) float uv = unchecked_mix(u, v, T); // If we went with T=parametricT, then update the tangent. Otherwise leave it at the radial // tangent found previously. (In the event that parametricT == radialT, we keep the radial // tangent.) if (T != radialT) { // We must re-normalize here because the tangent is determined by the curve coefficients tangent = w >= 0.0 ? robust_normalize_diff(bc*u, ab*v) : robust_normalize_diff(bcd, abc); } strokeCoord = (w >= 0.0) ? abc/uv : abcd; } else { // Edges at the beginning and end of the strip use exact endpoints and tangents. This // ensures crack-free seaming between instances. tangent = (combinedEdgeID == 0) ? tan0 : tan1; strokeCoord = (combinedEdgeID == 0) ? p0 : p3; } // At this point 'tangent' is normalized, so the orthogonal vector is also normalized. float2 ortho = float2(tangent.y, -tangent.x); strokeCoord += ortho * (strokeRadius * strokeOutset); if (isHairline) { // Hairline case. The scale and skew already happened before tessellation. return strokeCoord + translate; } else { // Normal case. Do the transform after tessellation. return affineMatrix * strokeCoord + translate; } }