| // 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; |
| } |
| } |
