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- /*
- * 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"
- 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 = SkMaxScalar(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 = SkTMax(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 SkTMin(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 = SkTMax(
- 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 SkTMin(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;
- }
- int GrPathUtils::worstCasePointCount(const SkPath& path, int* subpaths, SkScalar tol) {
- // You should have called scaleToleranceToSrc, which guarantees this
- SkASSERT(tol >= gMinCurveTol);
- int pointCount = 0;
- *subpaths = 1;
- bool first = true;
- SkPath::Iter iter(path, false);
- SkPath::Verb verb;
- SkPoint pts[4];
- while ((verb = iter.next(pts, false)) != SkPath::kDone_Verb) {
- switch (verb) {
- case SkPath::kLine_Verb:
- pointCount += 1;
- break;
- case SkPath::kConic_Verb: {
- SkScalar weight = iter.conicWeight();
- SkAutoConicToQuads converter;
- const SkPoint* quadPts = converter.computeQuads(pts, weight, tol);
- for (int i = 0; i < converter.countQuads(); ++i) {
- pointCount += quadraticPointCount(quadPts + 2*i, tol);
- }
- }
- case SkPath::kQuad_Verb:
- pointCount += quadraticPointCount(pts, tol);
- break;
- case SkPath::kCubic_Verb:
- pointCount += cubicPointCount(pts, tol);
- break;
- case SkPath::kMove_Verb:
- pointCount += 1;
- if (!first) {
- ++(*subpaths);
- }
- break;
- default:
- break;
- }
- first = false;
- }
- return pointCount;
- }
- 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 = SkMaxScalar(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,
- SkPathPriv::FirstDirection dir,
- const SkPoint p) {
- SkVector ap = p - a;
- SkScalar apXab = ap.cross(ab);
- if (SkPathPriv::kCW_FirstDirection == dir) {
- if (apXab > 0) {
- return false;
- }
- } else {
- SkASSERT(SkPathPriv::kCCW_FirstDirection == dir);
- if (apXab < 0) {
- return false;
- }
- }
- SkVector dp = p - d;
- SkScalar dpXdc = dp.cross(dc);
- if (SkPathPriv::kCW_FirstDirection == dir) {
- if (dpXdc < 0) {
- return false;
- }
- } else {
- SkASSERT(SkPathPriv::kCCW_FirstDirection == 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,
- SkPathPriv::FirstDirection 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);
- }
- }
- 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,
- SkPathPriv::FirstDirection 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);
- }
- }
- ////////////////////////////////////////////////////////////////////////////////
- using ExcludedTerm = GrPathUtils::ExcludedTerm;
- ExcludedTerm GrPathUtils::calcCubicInverseTransposePowerBasisMatrix(const SkPoint p[4],
- SkMatrix* out) {
- GR_STATIC_ASSERT(SK_SCALAR_IS_FLOAT);
- // First convert the bezier coordinates p[0..3] to power basis coefficients X,Y(,W=[0 0 0 1]).
- // M3 is the matrix that does this conversion. The homogeneous equation for the cubic becomes:
- //
- // | X Y 0 |
- // C(t,s) = [t^3 t^2*s t*s^2 s^3] * | . . 0 |
- // | . . 0 |
- // | . . 1 |
- //
- const Sk4f M3[3] = {Sk4f(-1, 3, -3, 1),
- Sk4f(3, -6, 3, 0),
- Sk4f(-3, 3, 0, 0)};
- // 4th col of M3 = Sk4f(1, 0, 0, 0)};
- Sk4f X(p[3].x(), 0, 0, 0);
- Sk4f Y(p[3].y(), 0, 0, 0);
- for (int i = 2; i >= 0; --i) {
- X += M3[i] * p[i].x();
- Y += M3[i] * p[i].y();
- }
- // The matrix is 3x4. In order to invert it, we first need to make it square by throwing out one
- // of the middle two rows. We toss the row that leaves us with the largest absolute determinant.
- // Since the right column will be [0 0 1], the respective determinants reduce to x0*y2 - y0*x2
- // and x0*y1 - y0*x1.
- SkScalar dets[4];
- Sk4f D = SkNx_shuffle<0,0,2,1>(X) * SkNx_shuffle<2,1,0,0>(Y);
- D -= SkNx_shuffle<2,3,0,1>(D);
- D.store(dets);
- ExcludedTerm skipTerm = SkScalarAbs(dets[0]) > SkScalarAbs(dets[1]) ?
- ExcludedTerm::kQuadraticTerm : ExcludedTerm::kLinearTerm;
- SkScalar det = dets[ExcludedTerm::kQuadraticTerm == skipTerm ? 0 : 1];
- if (0 == det) {
- return ExcludedTerm::kNonInvertible;
- }
- SkScalar rdet = 1 / det;
- // Compute the inverse-transpose of the power basis matrix with the 'skipRow'th row removed.
- // Since W=[0 0 0 1], it follows that our corresponding solution will be equal to:
- //
- // | y1 -x1 x1*y2 - y1*x2 |
- // 1/det * | -y0 x0 -x0*y2 + y0*x2 |
- // | 0 0 det |
- //
- SkScalar x[4], y[4], z[4];
- X.store(x);
- Y.store(y);
- (X * SkNx_shuffle<3,3,3,3>(Y) - Y * SkNx_shuffle<3,3,3,3>(X)).store(z);
- int middleRow = ExcludedTerm::kQuadraticTerm == skipTerm ? 2 : 1;
- out->setAll( y[middleRow] * rdet, -x[middleRow] * rdet, z[middleRow] * rdet,
- -y[0] * rdet, x[0] * rdet, -z[0] * rdet,
- 0, 0, 1);
- return skipTerm;
- }
- inline static void calc_serp_kcoeffs(SkScalar tl, SkScalar sl, SkScalar tm, SkScalar sm,
- ExcludedTerm skipTerm, SkScalar outCoeffs[3]) {
- SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
- outCoeffs[0] = 0;
- outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? sl*sm : -tl*sm - tm*sl;
- outCoeffs[2] = tl*tm;
- }
- inline static void calc_serp_lmcoeffs(SkScalar t, SkScalar s, ExcludedTerm skipTerm,
- SkScalar outCoeffs[3]) {
- SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
- outCoeffs[0] = -s*s*s;
- outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? 3*s*s*t : -3*s*t*t;
- outCoeffs[2] = t*t*t;
- }
- inline static void calc_loop_kcoeffs(SkScalar td, SkScalar sd, SkScalar te, SkScalar se,
- SkScalar tdse, SkScalar tesd, ExcludedTerm skipTerm,
- SkScalar outCoeffs[3]) {
- SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
- outCoeffs[0] = 0;
- outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? sd*se : -tdse - tesd;
- outCoeffs[2] = td*te;
- }
- inline static void calc_loop_lmcoeffs(SkScalar t2, SkScalar s2, SkScalar t1, SkScalar s1,
- SkScalar t2s1, SkScalar t1s2, ExcludedTerm skipTerm,
- SkScalar outCoeffs[3]) {
- SkASSERT(ExcludedTerm::kQuadraticTerm == skipTerm || ExcludedTerm::kLinearTerm == skipTerm);
- outCoeffs[0] = -s2*s2*s1;
- outCoeffs[1] = (ExcludedTerm::kLinearTerm == skipTerm) ? s2 * (2*t2s1 + t1s2)
- : -t2 * (t2s1 + 2*t1s2);
- outCoeffs[2] = t2*t2*t1;
- }
- // For the case when a cubic bezier is actually a quadratic. We duplicate k in l so that the
- // implicit becomes:
- //
- // k^3 - l*m == k^3 - l*k == k * (k^2 - l)
- //
- // In the quadratic case we can simply assign fixed values at each control point:
- //
- // | ..K.. | | pts[0] pts[1] pts[2] pts[3] | | 0 1/3 2/3 1 |
- // | ..L.. | * | . . . . | == | 0 0 1/3 1 |
- // | ..K.. | | 1 1 1 1 | | 0 1/3 2/3 1 |
- //
- static void calc_quadratic_klm(const SkPoint pts[4], double d3, SkMatrix* klm) {
- SkMatrix klmAtPts;
- klmAtPts.setAll(0, 1.f/3, 1,
- 0, 0, 1,
- 0, 1.f/3, 1);
- SkMatrix inversePts;
- inversePts.setAll(pts[0].x(), pts[1].x(), pts[3].x(),
- pts[0].y(), pts[1].y(), pts[3].y(),
- 1, 1, 1);
- SkAssertResult(inversePts.invert(&inversePts));
- klm->setConcat(klmAtPts, inversePts);
- // If d3 > 0 we need to flip the orientation of our curve
- // This is done by negating the k and l values
- if (d3 > 0) {
- klm->postScale(-1, -1);
- }
- }
- // For the case when a cubic bezier is actually a line. We set K=0, L=1, M=-line, which results in
- // the following implicit:
- //
- // k^3 - l*m == 0^3 - 1*(-line) == -(-line) == line
- //
- static void calc_line_klm(const SkPoint pts[4], SkMatrix* klm) {
- SkScalar ny = pts[0].x() - pts[3].x();
- SkScalar nx = pts[3].y() - pts[0].y();
- SkScalar k = nx * pts[0].x() + ny * pts[0].y();
- klm->setAll( 0, 0, 0,
- 0, 0, 1,
- -nx, -ny, k);
- }
- SkCubicType GrPathUtils::getCubicKLM(const SkPoint src[4], SkMatrix* klm, double tt[2],
- double ss[2]) {
- double d[4];
- SkCubicType type = SkClassifyCubic(src, tt, ss, d);
- if (SkCubicType::kLineOrPoint == type) {
- calc_line_klm(src, klm);
- return SkCubicType::kLineOrPoint;
- }
- if (SkCubicType::kQuadratic == type) {
- calc_quadratic_klm(src, d[3], klm);
- return SkCubicType::kQuadratic;
- }
- SkMatrix CIT;
- ExcludedTerm skipTerm = calcCubicInverseTransposePowerBasisMatrix(src, &CIT);
- if (ExcludedTerm::kNonInvertible == skipTerm) {
- // This could technically also happen if the curve were quadratic, but SkClassifyCubic
- // should have detected that case already with tolerance.
- calc_line_klm(src, klm);
- return SkCubicType::kLineOrPoint;
- }
- const SkScalar t0 = static_cast<SkScalar>(tt[0]), t1 = static_cast<SkScalar>(tt[1]),
- s0 = static_cast<SkScalar>(ss[0]), s1 = static_cast<SkScalar>(ss[1]);
- SkMatrix klmCoeffs;
- switch (type) {
- case SkCubicType::kCuspAtInfinity:
- SkASSERT(1 == t1 && 0 == s1); // Infinity.
- // fallthru.
- case SkCubicType::kLocalCusp:
- case SkCubicType::kSerpentine:
- calc_serp_kcoeffs(t0, s0, t1, s1, skipTerm, &klmCoeffs[0]);
- calc_serp_lmcoeffs(t0, s0, skipTerm, &klmCoeffs[3]);
- calc_serp_lmcoeffs(t1, s1, skipTerm, &klmCoeffs[6]);
- break;
- case SkCubicType::kLoop: {
- const SkScalar tdse = t0 * s1;
- const SkScalar tesd = t1 * s0;
- calc_loop_kcoeffs(t0, s0, t1, s1, tdse, tesd, skipTerm, &klmCoeffs[0]);
- calc_loop_lmcoeffs(t0, s0, t1, s1, tdse, tesd, skipTerm, &klmCoeffs[3]);
- calc_loop_lmcoeffs(t1, s1, t0, s0, tesd, tdse, skipTerm, &klmCoeffs[6]);
- break;
- }
- default:
- SK_ABORT("Unexpected cubic type.");
- break;
- }
- klm->setConcat(klmCoeffs, CIT);
- return type;
- }
- int GrPathUtils::chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10], SkMatrix* klm,
- int* loopIndex) {
- SkSTArray<2, SkScalar> chops;
- *loopIndex = -1;
- double t[2], s[2];
- if (SkCubicType::kLoop == GrPathUtils::getCubicKLM(src, klm, t, s)) {
- SkScalar t0 = static_cast<SkScalar>(t[0] / s[0]);
- SkScalar t1 = static_cast<SkScalar>(t[1] / s[1]);
- SkASSERT(t0 <= t1); // Technically t0 != t1 in a loop, but there may be FP error.
- if (t0 < 1 && t1 > 0) {
- *loopIndex = 0;
- if (t0 > 0) {
- chops.push_back(t0);
- *loopIndex = 1;
- }
- if (t1 < 1) {
- chops.push_back(t1);
- *loopIndex = chops.count() - 1;
- }
- }
- }
- SkChopCubicAt(src, dst, chops.begin(), chops.count());
- return chops.count() + 1;
- }
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