| /* | |
| * 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/ganesh/geometry/GrPathUtils.h" | |
| #include "include/core/SkMatrix.h" | |
| #include "include/core/SkRect.h" | |
| #include "include/private/base/SkAssert.h" | |
| #include "include/private/base/SkFloatingPoint.h" | |
| #include "include/private/base/SkPoint_impl.h" | |
| #include "src/core/SkGeometry.h" | |
| #include "src/core/SkPathEnums.h" | |
| #include "src/core/SkPointPriv.h" | |
| #include "src/gpu/tessellate/WangsFormula.h" | |
| #include <algorithm> | |
| using namespace skia_private; | |
| 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(skgpu::wangs_formula::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[] = { | |
| { sk_float_midpoint(p0.fX, p1.fX), sk_float_midpoint(p0.fY, p1.fY) }, | |
| { sk_float_midpoint(p1.fX, p2.fX), sk_float_midpoint(p1.fY, p2.fY) }, | |
| }; | |
| SkPoint r = { sk_float_midpoint(q[0].fX, q[1].fX), sk_float_midpoint(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(skgpu::wangs_formula::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[] = { | |
| { sk_float_midpoint(p0.fX, p1.fX), sk_float_midpoint(p0.fY, p1.fY) }, | |
| { sk_float_midpoint(p1.fX, p2.fX), sk_float_midpoint(p1.fY, p2.fY) }, | |
| { sk_float_midpoint(p2.fX, p3.fX), sk_float_midpoint(p2.fY, p3.fY) } | |
| }; | |
| SkPoint r[] = { | |
| { sk_float_midpoint(q[0].fX, q[1].fX), sk_float_midpoint(q[0].fY, q[1].fY) }, | |
| { sk_float_midpoint(q[1].fX, q[2].fX), sk_float_midpoint(q[1].fY, q[2].fY) } | |
| }; | |
| SkPoint s = { sk_float_midpoint(r[0].fX, r[1].fX), sk_float_midpoint(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]) { | |
| // 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; | |
| // pre-calculate some adjugate matrix factors for determinant | |
| double a2 = x1*y2-x2*y1; | |
| double a5 = x2*y0-x0*y2; | |
| double a8 = x0*y1-x1*y0; | |
| double det = a2 + a5 + a8; | |
| if (!SkIsFinite(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 a3, a4, a6, a7; | |
| a3 = y2-y0; | |
| a4 = x0-x2; | |
| a6 = y0-y1; | |
| a7 = x1-x0; | |
| // this performs the uv_pts*adjugate(control_pts) multiply, | |
| // then does the scale by 1/det afterwards to improve precision | |
| fM[0] = (float)((0.5*a3 + a6)*scale); | |
| fM[1] = (float)((0.5*a4 + a7)*scale); | |
| fM[2] = (float)((0.5*a5 + a8)*scale); | |
| fM[3] = (float)(a6*scale); | |
| fM[4] = (float)(a7*scale); | |
| fM[5] = (float)(a8*scale); | |
| } | |
| } | |
| //////////////////////////////////////////////////////////////////////////////// | |
| // 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, | |
| TArray<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 | |
| // AAHairlinePathRenderer. | |
| 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, | |
| TArray<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 = sk_ieee_float_divide(1.0f, 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, | |
| TArray<SkPoint, true>* quads) { | |
| if (!p[0].isFinite() || !p[1].isFinite() || !p[2].isFinite() || !p[3].isFinite()) { | |
| return; | |
| } | |
| if (!SkIsFinite(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, | |
| TArray<SkPoint, true>* quads) { | |
| if (!p[0].isFinite() || !p[1].isFinite() || !p[2].isFinite() || !p[3].isFinite()) { | |
| return; | |
| } | |
| if (!SkIsFinite(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); | |
| } | |
| } |