| /* | |
| * Copyright 2011 Google Inc. | |
| * | |
| * Use of this source code is governed by a BSD-style license that can be | |
| * found in the LICENSE file. | |
| */ | |
| #include "src/gpu/geometry/GrPathUtils.h" | |
| #include "include/gpu/GrTypes.h" | |
| #include "src/core/SkMathPriv.h" | |
| #include "src/core/SkPointPriv.h" | |
| #include "src/core/SkUtils.h" | |
| #include "src/gpu/geometry/GrWangsFormula.h" | |
| static const SkScalar kMinCurveTol = 0.0001f; | |
| static float tolerance_to_wangs_precision(float srcTol) { | |
| // You should have called scaleToleranceToSrc, which guarantees this | |
| SkASSERT(srcTol >= kMinCurveTol); | |
| // The GrPathUtil API defines tolerance as the max distance the linear segment can be from | |
| // the real curve. Wang's formula guarantees the linear segments will be within 1/precision | |
| // of the true curve, so precision = 1/srcTol | |
| return 1.f / srcTol; | |
| } | |
| uint32_t max_bezier_vertices(uint32_t chopCount) { | |
| static constexpr uint32_t kMaxChopsPerCurve = 10; | |
| static_assert((1 << kMaxChopsPerCurve) == GrPathUtils::kMaxPointsPerCurve); | |
| return 1 << std::min(chopCount, kMaxChopsPerCurve); | |
| } | |
| SkScalar GrPathUtils::scaleToleranceToSrc(SkScalar devTol, | |
| const SkMatrix& viewM, | |
| const SkRect& pathBounds) { | |
| // In order to tesselate the path we get a bound on how much the matrix can | |
| // scale when mapping to screen coordinates. | |
| SkScalar stretch = viewM.getMaxScale(); | |
| if (stretch < 0) { | |
| // take worst case mapRadius amoung four corners. | |
| // (less than perfect) | |
| for (int i = 0; i < 4; ++i) { | |
| SkMatrix mat; | |
| mat.setTranslate((i % 2) ? pathBounds.fLeft : pathBounds.fRight, | |
| (i < 2) ? pathBounds.fTop : pathBounds.fBottom); | |
| mat.postConcat(viewM); | |
| stretch = std::max(stretch, mat.mapRadius(SK_Scalar1)); | |
| } | |
| } | |
| SkScalar srcTol = 0; | |
| if (stretch <= 0) { | |
| // We have degenerate bounds or some degenerate matrix. Thus we set the tolerance to be the | |
| // max of the path pathBounds width and height. | |
| srcTol = std::max(pathBounds.width(), pathBounds.height()); | |
| } else { | |
| srcTol = devTol / stretch; | |
| } | |
| if (srcTol < kMinCurveTol) { | |
| srcTol = kMinCurveTol; | |
| } | |
| return srcTol; | |
| } | |
| uint32_t GrPathUtils::quadraticPointCount(const SkPoint points[], SkScalar tol) { | |
| return max_bezier_vertices(GrWangsFormula::quadratic_log2( | |
| tolerance_to_wangs_precision(tol), points)); | |
| } | |
| uint32_t GrPathUtils::generateQuadraticPoints(const SkPoint& p0, | |
| const SkPoint& p1, | |
| const SkPoint& p2, | |
| SkScalar tolSqd, | |
| SkPoint** points, | |
| uint32_t pointsLeft) { | |
| if (pointsLeft < 2 || | |
| (SkPointPriv::DistanceToLineSegmentBetweenSqd(p1, p0, p2)) < tolSqd) { | |
| (*points)[0] = p2; | |
| *points += 1; | |
| return 1; | |
| } | |
| SkPoint q[] = { | |
| { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, | |
| { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, | |
| }; | |
| SkPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }; | |
| pointsLeft >>= 1; | |
| uint32_t a = generateQuadraticPoints(p0, q[0], r, tolSqd, points, pointsLeft); | |
| uint32_t b = generateQuadraticPoints(r, q[1], p2, tolSqd, points, pointsLeft); | |
| return a + b; | |
| } | |
| uint32_t GrPathUtils::cubicPointCount(const SkPoint points[], SkScalar tol) { | |
| return max_bezier_vertices(GrWangsFormula::cubic_log2( | |
| tolerance_to_wangs_precision(tol), points)); | |
| } | |
| uint32_t GrPathUtils::generateCubicPoints(const SkPoint& p0, | |
| const SkPoint& p1, | |
| const SkPoint& p2, | |
| const SkPoint& p3, | |
| SkScalar tolSqd, | |
| SkPoint** points, | |
| uint32_t pointsLeft) { | |
| if (pointsLeft < 2 || | |
| (SkPointPriv::DistanceToLineSegmentBetweenSqd(p1, p0, p3) < tolSqd && | |
| SkPointPriv::DistanceToLineSegmentBetweenSqd(p2, p0, p3) < tolSqd)) { | |
| (*points)[0] = p3; | |
| *points += 1; | |
| return 1; | |
| } | |
| SkPoint q[] = { | |
| { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) }, | |
| { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) }, | |
| { SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) } | |
| }; | |
| SkPoint r[] = { | |
| { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) }, | |
| { SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) } | |
| }; | |
| SkPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) }; | |
| pointsLeft >>= 1; | |
| uint32_t a = generateCubicPoints(p0, q[0], r[0], s, tolSqd, points, pointsLeft); | |
| uint32_t b = generateCubicPoints(s, r[1], q[2], p3, tolSqd, points, pointsLeft); | |
| return a + b; | |
| } | |
| void GrPathUtils::QuadUVMatrix::set(const SkPoint qPts[3]) { | |
| SkMatrix m; | |
| // We want M such that M * xy_pt = uv_pt | |
| // We know M * control_pts = [0 1/2 1] | |
| // [0 0 1] | |
| // [1 1 1] | |
| // And control_pts = [x0 x1 x2] | |
| // [y0 y1 y2] | |
| // [1 1 1 ] | |
| // We invert the control pt matrix and post concat to both sides to get M. | |
| // Using the known form of the control point matrix and the result, we can | |
| // optimize and improve precision. | |
| double x0 = qPts[0].fX; | |
| double y0 = qPts[0].fY; | |
| double x1 = qPts[1].fX; | |
| double y1 = qPts[1].fY; | |
| double x2 = qPts[2].fX; | |
| double y2 = qPts[2].fY; | |
| double det = x0*y1 - y0*x1 + x2*y0 - y2*x0 + x1*y2 - y1*x2; | |
| if (!sk_float_isfinite(det) | |
| || SkScalarNearlyZero((float)det, SK_ScalarNearlyZero * SK_ScalarNearlyZero)) { | |
| // The quad is degenerate. Hopefully this is rare. Find the pts that are | |
| // farthest apart to compute a line (unless it is really a pt). | |
| SkScalar maxD = SkPointPriv::DistanceToSqd(qPts[0], qPts[1]); | |
| int maxEdge = 0; | |
| SkScalar d = SkPointPriv::DistanceToSqd(qPts[1], qPts[2]); | |
| if (d > maxD) { | |
| maxD = d; | |
| maxEdge = 1; | |
| } | |
| d = SkPointPriv::DistanceToSqd(qPts[2], qPts[0]); | |
| if (d > maxD) { | |
| maxD = d; | |
| maxEdge = 2; | |
| } | |
| // We could have a tolerance here, not sure if it would improve anything | |
| if (maxD > 0) { | |
| // Set the matrix to give (u = 0, v = distance_to_line) | |
| SkVector lineVec = qPts[(maxEdge + 1)%3] - qPts[maxEdge]; | |
| // when looking from the point 0 down the line we want positive | |
| // distances to be to the left. This matches the non-degenerate | |
| // case. | |
| lineVec = SkPointPriv::MakeOrthog(lineVec, SkPointPriv::kLeft_Side); | |
| // first row | |
| fM[0] = 0; | |
| fM[1] = 0; | |
| fM[2] = 0; | |
| // second row | |
| fM[3] = lineVec.fX; | |
| fM[4] = lineVec.fY; | |
| fM[5] = -lineVec.dot(qPts[maxEdge]); | |
| } else { | |
| // It's a point. It should cover zero area. Just set the matrix such | |
| // that (u, v) will always be far away from the quad. | |
| fM[0] = 0; fM[1] = 0; fM[2] = 100.f; | |
| fM[3] = 0; fM[4] = 0; fM[5] = 100.f; | |
| } | |
| } else { | |
| double scale = 1.0/det; | |
| // compute adjugate matrix | |
| double a2, a3, a4, a5, a6, a7, a8; | |
| a2 = x1*y2-x2*y1; | |
| a3 = y2-y0; | |
| a4 = x0-x2; | |
| a5 = x2*y0-x0*y2; | |
| a6 = y0-y1; | |
| a7 = x1-x0; | |
| a8 = x0*y1-x1*y0; | |
| // this performs the uv_pts*adjugate(control_pts) multiply, | |
| // then does the scale by 1/det afterwards to improve precision | |
| m[SkMatrix::kMScaleX] = (float)((0.5*a3 + a6)*scale); | |
| m[SkMatrix::kMSkewX] = (float)((0.5*a4 + a7)*scale); | |
| m[SkMatrix::kMTransX] = (float)((0.5*a5 + a8)*scale); | |
| m[SkMatrix::kMSkewY] = (float)(a6*scale); | |
| m[SkMatrix::kMScaleY] = (float)(a7*scale); | |
| m[SkMatrix::kMTransY] = (float)(a8*scale); | |
| // kMPersp0 & kMPersp1 should algebraically be zero | |
| m[SkMatrix::kMPersp0] = 0.0f; | |
| m[SkMatrix::kMPersp1] = 0.0f; | |
| m[SkMatrix::kMPersp2] = (float)((a2 + a5 + a8)*scale); | |
| // It may not be normalized to have 1.0 in the bottom right | |
| float m33 = m.get(SkMatrix::kMPersp2); | |
| if (1.f != m33) { | |
| m33 = 1.f / m33; | |
| fM[0] = m33 * m.get(SkMatrix::kMScaleX); | |
| fM[1] = m33 * m.get(SkMatrix::kMSkewX); | |
| fM[2] = m33 * m.get(SkMatrix::kMTransX); | |
| fM[3] = m33 * m.get(SkMatrix::kMSkewY); | |
| fM[4] = m33 * m.get(SkMatrix::kMScaleY); | |
| fM[5] = m33 * m.get(SkMatrix::kMTransY); | |
| } else { | |
| fM[0] = m.get(SkMatrix::kMScaleX); | |
| fM[1] = m.get(SkMatrix::kMSkewX); | |
| fM[2] = m.get(SkMatrix::kMTransX); | |
| fM[3] = m.get(SkMatrix::kMSkewY); | |
| fM[4] = m.get(SkMatrix::kMScaleY); | |
| fM[5] = m.get(SkMatrix::kMTransY); | |
| } | |
| } | |
| } | |
| //////////////////////////////////////////////////////////////////////////////// | |
| // k = (y2 - y0, x0 - x2, x2*y0 - x0*y2) | |
| // l = (y1 - y0, x0 - x1, x1*y0 - x0*y1) * 2*w | |
| // m = (y2 - y1, x1 - x2, x2*y1 - x1*y2) * 2*w | |
| void GrPathUtils::getConicKLM(const SkPoint p[3], const SkScalar weight, SkMatrix* out) { | |
| SkMatrix& klm = *out; | |
| const SkScalar w2 = 2.f * weight; | |
| klm[0] = p[2].fY - p[0].fY; | |
| klm[1] = p[0].fX - p[2].fX; | |
| klm[2] = p[2].fX * p[0].fY - p[0].fX * p[2].fY; | |
| klm[3] = w2 * (p[1].fY - p[0].fY); | |
| klm[4] = w2 * (p[0].fX - p[1].fX); | |
| klm[5] = w2 * (p[1].fX * p[0].fY - p[0].fX * p[1].fY); | |
| klm[6] = w2 * (p[2].fY - p[1].fY); | |
| klm[7] = w2 * (p[1].fX - p[2].fX); | |
| klm[8] = w2 * (p[2].fX * p[1].fY - p[1].fX * p[2].fY); | |
| // scale the max absolute value of coeffs to 10 | |
| SkScalar scale = 0.f; | |
| for (int i = 0; i < 9; ++i) { | |
| scale = std::max(scale, SkScalarAbs(klm[i])); | |
| } | |
| SkASSERT(scale > 0.f); | |
| scale = 10.f / scale; | |
| for (int i = 0; i < 9; ++i) { | |
| klm[i] *= scale; | |
| } | |
| } | |
| //////////////////////////////////////////////////////////////////////////////// | |
| namespace { | |
| // a is the first control point of the cubic. | |
| // ab is the vector from a to the second control point. | |
| // dc is the vector from the fourth to the third control point. | |
| // d is the fourth control point. | |
| // p is the candidate quadratic control point. | |
| // this assumes that the cubic doesn't inflect and is simple | |
| bool is_point_within_cubic_tangents(const SkPoint& a, | |
| const SkVector& ab, | |
| const SkVector& dc, | |
| const SkPoint& d, | |
| SkPathFirstDirection dir, | |
| const SkPoint p) { | |
| SkVector ap = p - a; | |
| SkScalar apXab = ap.cross(ab); | |
| if (SkPathFirstDirection::kCW == dir) { | |
| if (apXab > 0) { | |
| return false; | |
| } | |
| } else { | |
| SkASSERT(SkPathFirstDirection::kCCW == dir); | |
| if (apXab < 0) { | |
| return false; | |
| } | |
| } | |
| SkVector dp = p - d; | |
| SkScalar dpXdc = dp.cross(dc); | |
| if (SkPathFirstDirection::kCW == dir) { | |
| if (dpXdc < 0) { | |
| return false; | |
| } | |
| } else { | |
| SkASSERT(SkPathFirstDirection::kCCW == dir); | |
| if (dpXdc > 0) { | |
| return false; | |
| } | |
| } | |
| return true; | |
| } | |
| void convert_noninflect_cubic_to_quads(const SkPoint p[4], | |
| SkScalar toleranceSqd, | |
| SkTArray<SkPoint, true>* quads, | |
| int sublevel = 0, | |
| bool preserveFirstTangent = true, | |
| bool preserveLastTangent = true) { | |
| // Notation: Point a is always p[0]. Point b is p[1] unless p[1] == p[0], in which case it is | |
| // p[2]. Point d is always p[3]. Point c is p[2] unless p[2] == p[3], in which case it is p[1]. | |
| SkVector ab = p[1] - p[0]; | |
| SkVector dc = p[2] - p[3]; | |
| if (SkPointPriv::LengthSqd(ab) < SK_ScalarNearlyZero) { | |
| if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) { | |
| SkPoint* degQuad = quads->push_back_n(3); | |
| degQuad[0] = p[0]; | |
| degQuad[1] = p[0]; | |
| degQuad[2] = p[3]; | |
| return; | |
| } | |
| ab = p[2] - p[0]; | |
| } | |
| if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) { | |
| dc = p[1] - p[3]; | |
| } | |
| static const SkScalar kLengthScale = 3 * SK_Scalar1 / 2; | |
| static const int kMaxSubdivs = 10; | |
| ab.scale(kLengthScale); | |
| dc.scale(kLengthScale); | |
| // c0 and c1 are extrapolations along vectors ab and dc. | |
| SkPoint c0 = p[0] + ab; | |
| SkPoint c1 = p[3] + dc; | |
| SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : SkPointPriv::DistanceToSqd(c0, c1); | |
| if (dSqd < toleranceSqd) { | |
| SkPoint newC; | |
| if (preserveFirstTangent == preserveLastTangent) { | |
| // We used to force a split when both tangents need to be preserved and c0 != c1. | |
| // This introduced a large performance regression for tiny paths for no noticeable | |
| // quality improvement. However, we aren't quite fulfilling our contract of guaranteeing | |
| // the two tangent vectors and this could introduce a missed pixel in | |
| // GrAAHairlinePathRenderer. | |
| newC = (c0 + c1) * 0.5f; | |
| } else if (preserveFirstTangent) { | |
| newC = c0; | |
| } else { | |
| newC = c1; | |
| } | |
| SkPoint* pts = quads->push_back_n(3); | |
| pts[0] = p[0]; | |
| pts[1] = newC; | |
| pts[2] = p[3]; | |
| return; | |
| } | |
| SkPoint choppedPts[7]; | |
| SkChopCubicAtHalf(p, choppedPts); | |
| convert_noninflect_cubic_to_quads( | |
| choppedPts + 0, toleranceSqd, quads, sublevel + 1, preserveFirstTangent, false); | |
| convert_noninflect_cubic_to_quads( | |
| choppedPts + 3, toleranceSqd, quads, sublevel + 1, false, preserveLastTangent); | |
| } | |
| void convert_noninflect_cubic_to_quads_with_constraint(const SkPoint p[4], | |
| SkScalar toleranceSqd, | |
| SkPathFirstDirection dir, | |
| SkTArray<SkPoint, true>* quads, | |
| int sublevel = 0) { | |
| // Notation: Point a is always p[0]. Point b is p[1] unless p[1] == p[0], in which case it is | |
| // p[2]. Point d is always p[3]. Point c is p[2] unless p[2] == p[3], in which case it is p[1]. | |
| SkVector ab = p[1] - p[0]; | |
| SkVector dc = p[2] - p[3]; | |
| if (SkPointPriv::LengthSqd(ab) < SK_ScalarNearlyZero) { | |
| if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) { | |
| SkPoint* degQuad = quads->push_back_n(3); | |
| degQuad[0] = p[0]; | |
| degQuad[1] = p[0]; | |
| degQuad[2] = p[3]; | |
| return; | |
| } | |
| ab = p[2] - p[0]; | |
| } | |
| if (SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero) { | |
| dc = p[1] - p[3]; | |
| } | |
| // When the ab and cd tangents are degenerate or nearly parallel with vector from d to a the | |
| // constraint that the quad point falls between the tangents becomes hard to enforce and we are | |
| // likely to hit the max subdivision count. However, in this case the cubic is approaching a | |
| // line and the accuracy of the quad point isn't so important. We check if the two middle cubic | |
| // control points are very close to the baseline vector. If so then we just pick quadratic | |
| // points on the control polygon. | |
| SkVector da = p[0] - p[3]; | |
| bool doQuads = SkPointPriv::LengthSqd(dc) < SK_ScalarNearlyZero || | |
| SkPointPriv::LengthSqd(ab) < SK_ScalarNearlyZero; | |
| if (!doQuads) { | |
| SkScalar invDALengthSqd = SkPointPriv::LengthSqd(da); | |
| if (invDALengthSqd > SK_ScalarNearlyZero) { | |
| invDALengthSqd = SkScalarInvert(invDALengthSqd); | |
| // cross(ab, da)^2/length(da)^2 == sqd distance from b to line from d to a. | |
| // same goes for point c using vector cd. | |
| SkScalar detABSqd = ab.cross(da); | |
| detABSqd = SkScalarSquare(detABSqd); | |
| SkScalar detDCSqd = dc.cross(da); | |
| detDCSqd = SkScalarSquare(detDCSqd); | |
| if (detABSqd * invDALengthSqd < toleranceSqd && | |
| detDCSqd * invDALengthSqd < toleranceSqd) { | |
| doQuads = true; | |
| } | |
| } | |
| } | |
| if (doQuads) { | |
| SkPoint b = p[0] + ab; | |
| SkPoint c = p[3] + dc; | |
| SkPoint mid = b + c; | |
| mid.scale(SK_ScalarHalf); | |
| // Insert two quadratics to cover the case when ab points away from d and/or dc | |
| // points away from a. | |
| if (SkVector::DotProduct(da, dc) < 0 || SkVector::DotProduct(ab, da) > 0) { | |
| SkPoint* qpts = quads->push_back_n(6); | |
| qpts[0] = p[0]; | |
| qpts[1] = b; | |
| qpts[2] = mid; | |
| qpts[3] = mid; | |
| qpts[4] = c; | |
| qpts[5] = p[3]; | |
| } else { | |
| SkPoint* qpts = quads->push_back_n(3); | |
| qpts[0] = p[0]; | |
| qpts[1] = mid; | |
| qpts[2] = p[3]; | |
| } | |
| return; | |
| } | |
| static const SkScalar kLengthScale = 3 * SK_Scalar1 / 2; | |
| static const int kMaxSubdivs = 10; | |
| ab.scale(kLengthScale); | |
| dc.scale(kLengthScale); | |
| // c0 and c1 are extrapolations along vectors ab and dc. | |
| SkVector c0 = p[0] + ab; | |
| SkVector c1 = p[3] + dc; | |
| SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : SkPointPriv::DistanceToSqd(c0, c1); | |
| if (dSqd < toleranceSqd) { | |
| SkPoint cAvg = (c0 + c1) * 0.5f; | |
| bool subdivide = false; | |
| if (!is_point_within_cubic_tangents(p[0], ab, dc, p[3], dir, cAvg)) { | |
| // choose a new cAvg that is the intersection of the two tangent lines. | |
| ab = SkPointPriv::MakeOrthog(ab); | |
| SkScalar z0 = -ab.dot(p[0]); | |
| dc = SkPointPriv::MakeOrthog(dc); | |
| SkScalar z1 = -dc.dot(p[3]); | |
| cAvg.fX = ab.fY * z1 - z0 * dc.fY; | |
| cAvg.fY = z0 * dc.fX - ab.fX * z1; | |
| SkScalar z = ab.fX * dc.fY - ab.fY * dc.fX; | |
| z = SkScalarInvert(z); | |
| cAvg.fX *= z; | |
| cAvg.fY *= z; | |
| if (sublevel <= kMaxSubdivs) { | |
| SkScalar d0Sqd = SkPointPriv::DistanceToSqd(c0, cAvg); | |
| SkScalar d1Sqd = SkPointPriv::DistanceToSqd(c1, cAvg); | |
| // We need to subdivide if d0 + d1 > tolerance but we have the sqd values. We know | |
| // the distances and tolerance can't be negative. | |
| // (d0 + d1)^2 > toleranceSqd | |
| // d0Sqd + 2*d0*d1 + d1Sqd > toleranceSqd | |
| SkScalar d0d1 = SkScalarSqrt(d0Sqd * d1Sqd); | |
| subdivide = 2 * d0d1 + d0Sqd + d1Sqd > toleranceSqd; | |
| } | |
| } | |
| if (!subdivide) { | |
| SkPoint* pts = quads->push_back_n(3); | |
| pts[0] = p[0]; | |
| pts[1] = cAvg; | |
| pts[2] = p[3]; | |
| return; | |
| } | |
| } | |
| SkPoint choppedPts[7]; | |
| SkChopCubicAtHalf(p, choppedPts); | |
| convert_noninflect_cubic_to_quads_with_constraint( | |
| choppedPts + 0, toleranceSqd, dir, quads, sublevel + 1); | |
| convert_noninflect_cubic_to_quads_with_constraint( | |
| choppedPts + 3, toleranceSqd, dir, quads, sublevel + 1); | |
| } | |
| } // namespace | |
| void GrPathUtils::convertCubicToQuads(const SkPoint p[4], | |
| SkScalar tolScale, | |
| SkTArray<SkPoint, true>* quads) { | |
| if (!p[0].isFinite() || !p[1].isFinite() || !p[2].isFinite() || !p[3].isFinite()) { | |
| return; | |
| } | |
| if (!SkScalarIsFinite(tolScale)) { | |
| return; | |
| } | |
| SkPoint chopped[10]; | |
| int count = SkChopCubicAtInflections(p, chopped); | |
| const SkScalar tolSqd = SkScalarSquare(tolScale); | |
| for (int i = 0; i < count; ++i) { | |
| SkPoint* cubic = chopped + 3*i; | |
| convert_noninflect_cubic_to_quads(cubic, tolSqd, quads); | |
| } | |
| } | |
| void GrPathUtils::convertCubicToQuadsConstrainToTangents(const SkPoint p[4], | |
| SkScalar tolScale, | |
| SkPathFirstDirection dir, | |
| SkTArray<SkPoint, true>* quads) { | |
| if (!p[0].isFinite() || !p[1].isFinite() || !p[2].isFinite() || !p[3].isFinite()) { | |
| return; | |
| } | |
| if (!SkScalarIsFinite(tolScale)) { | |
| return; | |
| } | |
| SkPoint chopped[10]; | |
| int count = SkChopCubicAtInflections(p, chopped); | |
| const SkScalar tolSqd = SkScalarSquare(tolScale); | |
| for (int i = 0; i < count; ++i) { | |
| SkPoint* cubic = chopped + 3*i; | |
| convert_noninflect_cubic_to_quads_with_constraint(cubic, tolSqd, dir, quads); | |
| } | |
| } | |
| int GrPathUtils::findCubicConvex180Chops(const SkPoint pts[], float T[2], bool* areCusps) { | |
| using grvx::float2; | |
| SkASSERT(pts); | |
| SkASSERT(T); | |
| SkASSERT(areCusps); | |
| // If a chop falls within a distance of "kEpsilon" from 0 or 1, throw it out. Tangents become | |
| // unstable when we chop too close to the boundary. This works out because the tessellation | |
| // shaders don't allow more than 2^10 parametric segments, and they snap the beginning and | |
| // ending edges at 0 and 1. So if we overstep an inflection or point of 180-degree rotation by a | |
| // fraction of a tessellation segment, it just gets snapped. | |
| constexpr static float kEpsilon = 1.f / (1 << 11); | |
| // Floating-point representation of "1 - 2*kEpsilon". | |
| constexpr static uint32_t kIEEE_one_minus_2_epsilon = (127 << 23) - 2 * (1 << (24 - 11)); | |
| // Unfortunately we don't have a way to static_assert this, but we can runtime assert that the | |
| // kIEEE_one_minus_2_epsilon bits are correct. | |
| SkASSERT(sk_bit_cast<float>(kIEEE_one_minus_2_epsilon) == 1 - 2*kEpsilon); | |
| float2 p0 = skvx::bit_pun<float2>(pts[0]); | |
| float2 p1 = skvx::bit_pun<float2>(pts[1]); | |
| float2 p2 = skvx::bit_pun<float2>(pts[2]); | |
| float2 p3 = skvx::bit_pun<float2>(pts[3]); | |
| // Find the cubic's power basis coefficients. These define the bezier curve as: | |
| // | |
| // |T^3| | |
| // Cubic(T) = x,y = |A 3B 3C| * |T^2| + P0 | |
| // |. . .| |T | | |
| // | |
| // And the tangent direction (scaled by a uniform 1/3) will be: | |
| // | |
| // |T^2| | |
| // Tangent_Direction(T) = dx,dy = |A 2B C| * |T | | |
| // |. . .| |1 | | |
| // | |
| float2 C = p1 - p0; | |
| float2 D = p2 - p1; | |
| float2 E = p3 - p0; | |
| float2 B = D - C; | |
| float2 A = grvx::fast_madd<2>(-3,D,E); | |
| // Now find the cubic's inflection function. There are inflections where F' x F'' == 0. | |
| // We formulate this as a quadratic equation: F' x F'' == aT^2 + bT + c == 0. | |
| // See: https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf | |
| // NOTE: We only need the roots, so a uniform scale factor does not affect the solution. | |
| float a = grvx::cross(A,B); | |
| float b = grvx::cross(A,C); | |
| float c = grvx::cross(B,C); | |
| float b_over_minus_2 = -.5f * b; | |
| float discr_over_4 = b_over_minus_2*b_over_minus_2 - a*c; | |
| // If -cuspThreshold <= discr_over_4 <= cuspThreshold, it means the two roots are within | |
| // kEpsilon of one another (in parametric space). This is close enough for our purposes to | |
| // consider them a single cusp. | |
| float cuspThreshold = a * (kEpsilon/2); | |
| cuspThreshold *= cuspThreshold; | |
| if (discr_over_4 < -cuspThreshold) { | |
| // The curve does not inflect or cusp. This means it might rotate more than 180 degrees | |
| // instead. Chop were rotation == 180 deg. (This is the 2nd root where the tangent is | |
| // parallel to tan0.) | |
| // | |
| // Tangent_Direction(T) x tan0 == 0 | |
| // (AT^2 x tan0) + (2BT x tan0) + (C x tan0) == 0 | |
| // (A x C)T^2 + (2B x C)T + (C x C) == 0 [[because tan0 == P1 - P0 == C]] | |
| // bT^2 + 2cT + 0 == 0 [[because A x C == b, B x C == c]] | |
| // T = [0, -2c/b] | |
| // | |
| // NOTE: if C == 0, then C != tan0. But this is fine because the curve is definitely | |
| // convex-180 if any points are colocated, and T[0] will equal NaN which returns 0 chops. | |
| *areCusps = false; | |
| float root = sk_ieee_float_divide(c, b_over_minus_2); | |
| // Is "root" inside the range [kEpsilon, 1 - kEpsilon)? | |
| if (sk_bit_cast<uint32_t>(root - kEpsilon) < kIEEE_one_minus_2_epsilon) { | |
| T[0] = root; | |
| return 1; | |
| } | |
| return 0; | |
| } | |
| *areCusps = (discr_over_4 <= cuspThreshold); | |
| if (*areCusps) { | |
| // The two roots are close enough that we can consider them a single cusp. | |
| if (a != 0 || b_over_minus_2 != 0 || c != 0) { | |
| // Pick the average of both roots. | |
| float root = sk_ieee_float_divide(b_over_minus_2, a); | |
| // Is "root" inside the range [kEpsilon, 1 - kEpsilon)? | |
| if (sk_bit_cast<uint32_t>(root - kEpsilon) < kIEEE_one_minus_2_epsilon) { | |
| T[0] = root; | |
| return 1; | |
| } | |
| return 0; | |
| } | |
| // The curve is a flat line. The standard inflection function doesn't detect cusps from flat | |
| // lines. Find cusps by searching instead for points where the tangent is perpendicular to | |
| // tan0. This will find any cusp point. | |
| // | |
| // dot(tan0, Tangent_Direction(T)) == 0 | |
| // | |
| // |T^2| | |
| // tan0 * |A 2B C| * |T | == 0 | |
| // |. . .| |1 | | |
| // | |
| float2 tan0 = skvx::if_then_else(C != 0, C, p2 - p0); | |
| a = grvx::dot(tan0, A); | |
| b_over_minus_2 = -grvx::dot(tan0, B); | |
| c = grvx::dot(tan0, C); | |
| discr_over_4 = std::max(b_over_minus_2*b_over_minus_2 - a*c, 0.f); | |
| } | |
| // Solve our quadratic equation to find where to chop. See the quadratic formula from | |
| // Numerical Recipes in C. | |
| float q = sqrtf(discr_over_4); | |
| q = copysignf(q, b_over_minus_2); | |
| q = q + b_over_minus_2; | |
| float2 roots = float2{q,c} / float2{a,q}; | |
| auto inside = (roots > kEpsilon) & (roots < (1 - kEpsilon)); | |
| if (inside[0]) { | |
| if (inside[1] && roots[0] != roots[1]) { | |
| if (roots[0] > roots[1]) { | |
| roots = skvx::shuffle<1,0>(roots); // Sort. | |
| } | |
| roots.store(T); | |
| return 2; | |
| } | |
| T[0] = roots[0]; | |
| return 1; | |
| } | |
| if (inside[1]) { | |
| T[0] = roots[1]; | |
| return 1; | |
| } | |
| return 0; | |
| } |