| /* |
| * 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" |
| |
| static const SkScalar gMinCurveTol = 0.0001f; |
| |
| 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 < gMinCurveTol) { |
| srcTol = gMinCurveTol; |
| } |
| return srcTol; |
| } |
| |
| uint32_t GrPathUtils::quadraticPointCount(const SkPoint points[], SkScalar tol) { |
| // You should have called scaleToleranceToSrc, which guarantees this |
| SkASSERT(tol >= gMinCurveTol); |
| |
| SkScalar d = SkPointPriv::DistanceToLineSegmentBetween(points[1], points[0], points[2]); |
| if (!SkScalarIsFinite(d)) { |
| return kMaxPointsPerCurve; |
| } else if (d <= tol) { |
| return 1; |
| } else { |
| // Each time we subdivide, d should be cut in 4. So we need to |
| // subdivide x = log4(d/tol) times. x subdivisions creates 2^(x) |
| // points. |
| // 2^(log4(x)) = sqrt(x); |
| SkScalar divSqrt = SkScalarSqrt(d / tol); |
| if (((SkScalar)SK_MaxS32) <= divSqrt) { |
| return kMaxPointsPerCurve; |
| } else { |
| int temp = SkScalarCeilToInt(divSqrt); |
| int pow2 = GrNextPow2(temp); |
| // Because of NaNs & INFs we can wind up with a degenerate temp |
| // such that pow2 comes out negative. Also, our point generator |
| // will always output at least one pt. |
| if (pow2 < 1) { |
| pow2 = 1; |
| } |
| return std::min(pow2, kMaxPointsPerCurve); |
| } |
| } |
| } |
| |
| 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) { |
| // You should have called scaleToleranceToSrc, which guarantees this |
| SkASSERT(tol >= gMinCurveTol); |
| |
| SkScalar d = std::max( |
| SkPointPriv::DistanceToLineSegmentBetweenSqd(points[1], points[0], points[3]), |
| SkPointPriv::DistanceToLineSegmentBetweenSqd(points[2], points[0], points[3])); |
| d = SkScalarSqrt(d); |
| if (!SkScalarIsFinite(d)) { |
| return kMaxPointsPerCurve; |
| } else if (d <= tol) { |
| return 1; |
| } else { |
| SkScalar divSqrt = SkScalarSqrt(d / tol); |
| if (((SkScalar)SK_MaxS32) <= divSqrt) { |
| return kMaxPointsPerCurve; |
| } else { |
| int temp = SkScalarCeilToInt(SkScalarSqrt(d / tol)); |
| int pow2 = GrNextPow2(temp); |
| // Because of NaNs & INFs we can wind up with a degenerate temp |
| // such that pow2 comes out negative. Also, our point generator |
| // will always output at least one pt. |
| if (pow2 < 1) { |
| pow2 = 1; |
| } |
| return std::min(pow2, kMaxPointsPerCurve); |
| } |
| } |
| } |
| |
| 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; |
| } |
