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-rw-r--r--gfx/skia/skia/src/gpu/GrPathUtils.cpp826
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diff --git a/gfx/skia/skia/src/gpu/GrPathUtils.cpp b/gfx/skia/skia/src/gpu/GrPathUtils.cpp
new file mode 100644
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+++ b/gfx/skia/skia/src/gpu/GrPathUtils.cpp
@@ -0,0 +1,826 @@
+/*
+ * 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 "GrPathUtils.h"
+
+#include "GrTypes.h"
+#include "SkGeometry.h"
+#include "SkMathPriv.h"
+
+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();
+ SkScalar srcTol = devTol;
+
+ 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));
+ }
+ }
+ return srcTol / stretch;
+}
+
+static const int MAX_POINTS_PER_CURVE = 1 << 10;
+static const SkScalar gMinCurveTol = 0.0001f;
+
+uint32_t GrPathUtils::quadraticPointCount(const SkPoint points[],
+ SkScalar tol) {
+ if (tol < gMinCurveTol) {
+ tol = gMinCurveTol;
+ }
+ SkASSERT(tol > 0);
+
+ SkScalar d = points[1].distanceToLineSegmentBetween(points[0], points[2]);
+ if (!SkScalarIsFinite(d)) {
+ return MAX_POINTS_PER_CURVE;
+ } 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 MAX_POINTS_PER_CURVE;
+ } 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, MAX_POINTS_PER_CURVE);
+ }
+ }
+}
+
+uint32_t GrPathUtils::generateQuadraticPoints(const SkPoint& p0,
+ const SkPoint& p1,
+ const SkPoint& p2,
+ SkScalar tolSqd,
+ SkPoint** points,
+ uint32_t pointsLeft) {
+ if (pointsLeft < 2 ||
+ (p1.distanceToLineSegmentBetweenSqd(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) {
+ if (tol < gMinCurveTol) {
+ tol = gMinCurveTol;
+ }
+ SkASSERT(tol > 0);
+
+ SkScalar d = SkTMax(
+ points[1].distanceToLineSegmentBetweenSqd(points[0], points[3]),
+ points[2].distanceToLineSegmentBetweenSqd(points[0], points[3]));
+ d = SkScalarSqrt(d);
+ if (!SkScalarIsFinite(d)) {
+ return MAX_POINTS_PER_CURVE;
+ } else if (d <= tol) {
+ return 1;
+ } else {
+ SkScalar divSqrt = SkScalarSqrt(d / tol);
+ if (((SkScalar)SK_MaxS32) <= divSqrt) {
+ return MAX_POINTS_PER_CURVE;
+ } 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, MAX_POINTS_PER_CURVE);
+ }
+ }
+}
+
+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 ||
+ (p1.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd &&
+ p2.distanceToLineSegmentBetweenSqd(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) {
+ if (tol < gMinCurveTol) {
+ tol = gMinCurveTol;
+ }
+ SkASSERT(tol > 0);
+
+ int pointCount = 0;
+ *subpaths = 1;
+
+ bool first = true;
+
+ SkPath::Iter iter(path, false);
+ SkPath::Verb verb;
+
+ SkPoint pts[4];
+ while ((verb = iter.next(pts)) != 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, 0.25f);
+ 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 = qPts[0].distanceToSqd(qPts[1]);
+ int maxEdge = 0;
+ SkScalar d = qPts[1].distanceToSqd(qPts[2]);
+ if (d > maxD) {
+ maxD = d;
+ maxEdge = 1;
+ }
+ d = qPts[2].distanceToSqd(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.setOrthog(lineVec, SkPoint::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 - x0)*y0 - (y2 - y0)*x0 )
+// l = (2*w * (y1 - y0), 2*w * (x0 - x1), 2*w * (x1*y0 - x0*y1))
+// m = (2*w * (y2 - y1), 2*w * (x1 - x2), 2*w * (x2*y1 - x1*y2))
+void GrPathUtils::getConicKLM(const SkPoint p[3], const SkScalar weight, SkScalar klm[9]) {
+ 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].fX) * p[0].fY - (p[2].fY - p[0].fY) * p[0].fX;
+
+ 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,
+ bool constrainWithinTangents,
+ 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 (ab.lengthSqd() < SK_ScalarNearlyZero) {
+ if (dc.lengthSqd() < 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 (dc.lengthSqd() < 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.
+
+ if (constrainWithinTangents) {
+ SkVector da = p[0] - p[3];
+ bool doQuads = dc.lengthSqd() < SK_ScalarNearlyZero ||
+ ab.lengthSqd() < SK_ScalarNearlyZero;
+ if (!doQuads) {
+ SkScalar invDALengthSqd = da.lengthSqd();
+ 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 (SkScalarMul(detABSqd, invDALengthSqd) < toleranceSqd &&
+ SkScalarMul(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);
+
+ // e0 and e1 are extrapolations along vectors ab and dc.
+ SkVector c0 = p[0];
+ c0 += ab;
+ SkVector c1 = p[3];
+ c1 += dc;
+
+ SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : c0.distanceToSqd(c1);
+ if (dSqd < toleranceSqd) {
+ SkPoint cAvg = c0;
+ cAvg += c1;
+ cAvg.scale(SK_ScalarHalf);
+
+ bool subdivide = false;
+
+ if (constrainWithinTangents &&
+ !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.setOrthog(ab);
+ SkScalar z0 = -ab.dot(p[0]);
+ dc.setOrthog(dc);
+ SkScalar z1 = -dc.dot(p[3]);
+ cAvg.fX = SkScalarMul(ab.fY, z1) - SkScalarMul(z0, dc.fY);
+ cAvg.fY = SkScalarMul(z0, dc.fX) - SkScalarMul(ab.fX, z1);
+ SkScalar z = SkScalarMul(ab.fX, dc.fY) - SkScalarMul(ab.fY, dc.fX);
+ z = SkScalarInvert(z);
+ cAvg.fX *= z;
+ cAvg.fY *= z;
+ if (sublevel <= kMaxSubdivs) {
+ SkScalar d0Sqd = c0.distanceToSqd(cAvg);
+ SkScalar d1Sqd = c1.distanceToSqd(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(SkScalarMul(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(choppedPts + 0,
+ toleranceSqd,
+ constrainWithinTangents,
+ dir,
+ quads,
+ sublevel + 1);
+ convert_noninflect_cubic_to_quads(choppedPts + 3,
+ toleranceSqd,
+ constrainWithinTangents,
+ dir,
+ quads,
+ sublevel + 1);
+}
+}
+
+void GrPathUtils::convertCubicToQuads(const SkPoint p[4],
+ SkScalar tolScale,
+ SkTArray<SkPoint, true>* quads) {
+ 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;
+ // The direction param is ignored if the third param is false.
+ convert_noninflect_cubic_to_quads(cubic, tolSqd, false,
+ SkPathPriv::kCCW_FirstDirection, quads);
+ }
+}
+
+void GrPathUtils::convertCubicToQuadsConstrainToTangents(const SkPoint p[4],
+ SkScalar tolScale,
+ SkPathPriv::FirstDirection dir,
+ SkTArray<SkPoint, true>* quads) {
+ 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, true, dir, quads);
+ }
+}
+
+////////////////////////////////////////////////////////////////////////////////
+
+// Solves linear system to extract klm
+// P.K = k (similarly for l, m)
+// Where P is matrix of control points
+// K is coefficients for the line K
+// k is vector of values of K evaluated at the control points
+// Solving for K, thus K = P^(-1) . k
+static void calc_cubic_klm(const SkPoint p[4], const SkScalar controlK[4],
+ const SkScalar controlL[4], const SkScalar controlM[4],
+ SkScalar k[3], SkScalar l[3], SkScalar m[3]) {
+ SkMatrix matrix;
+ matrix.setAll(p[0].fX, p[0].fY, 1.f,
+ p[1].fX, p[1].fY, 1.f,
+ p[2].fX, p[2].fY, 1.f);
+ SkMatrix inverse;
+ if (matrix.invert(&inverse)) {
+ inverse.mapHomogeneousPoints(k, controlK, 1);
+ inverse.mapHomogeneousPoints(l, controlL, 1);
+ inverse.mapHomogeneousPoints(m, controlM, 1);
+ }
+
+}
+
+static void set_serp_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ SkScalar tempSqrt = SkScalarSqrt(9.f * d[1] * d[1] - 12.f * d[0] * d[2]);
+ SkScalar ls = 3.f * d[1] - tempSqrt;
+ SkScalar lt = 6.f * d[0];
+ SkScalar ms = 3.f * d[1] + tempSqrt;
+ SkScalar mt = 6.f * d[0];
+
+ k[0] = ls * ms;
+ k[1] = (3.f * ls * ms - ls * mt - lt * ms) / 3.f;
+ k[2] = (lt * (mt - 2.f * ms) + ls * (3.f * ms - 2.f * mt)) / 3.f;
+ k[3] = (lt - ls) * (mt - ms);
+
+ l[0] = ls * ls * ls;
+ const SkScalar lt_ls = lt - ls;
+ l[1] = ls * ls * lt_ls * -1.f;
+ l[2] = lt_ls * lt_ls * ls;
+ l[3] = -1.f * lt_ls * lt_ls * lt_ls;
+
+ m[0] = ms * ms * ms;
+ const SkScalar mt_ms = mt - ms;
+ m[1] = ms * ms * mt_ms * -1.f;
+ m[2] = mt_ms * mt_ms * ms;
+ m[3] = -1.f * mt_ms * mt_ms * mt_ms;
+
+ // If d0 < 0 we need to flip the orientation of our curve
+ // This is done by negating the k and l values
+ // We want negative distance values to be on the inside
+ if ( d[0] > 0) {
+ for (int i = 0; i < 4; ++i) {
+ k[i] = -k[i];
+ l[i] = -l[i];
+ }
+ }
+}
+
+static void set_loop_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ SkScalar tempSqrt = SkScalarSqrt(4.f * d[0] * d[2] - 3.f * d[1] * d[1]);
+ SkScalar ls = d[1] - tempSqrt;
+ SkScalar lt = 2.f * d[0];
+ SkScalar ms = d[1] + tempSqrt;
+ SkScalar mt = 2.f * d[0];
+
+ k[0] = ls * ms;
+ k[1] = (3.f * ls*ms - ls * mt - lt * ms) / 3.f;
+ k[2] = (lt * (mt - 2.f * ms) + ls * (3.f * ms - 2.f * mt)) / 3.f;
+ k[3] = (lt - ls) * (mt - ms);
+
+ l[0] = ls * ls * ms;
+ l[1] = (ls * (ls * (mt - 3.f * ms) + 2.f * lt * ms))/-3.f;
+ l[2] = ((lt - ls) * (ls * (2.f * mt - 3.f * ms) + lt * ms))/3.f;
+ l[3] = -1.f * (lt - ls) * (lt - ls) * (mt - ms);
+
+ m[0] = ls * ms * ms;
+ m[1] = (ms * (ls * (2.f * mt - 3.f * ms) + lt * ms))/-3.f;
+ m[2] = ((mt - ms) * (ls * (mt - 3.f * ms) + 2.f * lt * ms))/3.f;
+ m[3] = -1.f * (lt - ls) * (mt - ms) * (mt - ms);
+
+
+ // If (d0 < 0 && sign(k1) > 0) || (d0 > 0 && sign(k1) < 0),
+ // we need to flip the orientation of our curve.
+ // This is done by negating the k and l values
+ if ( (d[0] < 0 && k[1] > 0) || (d[0] > 0 && k[1] < 0)) {
+ for (int i = 0; i < 4; ++i) {
+ k[i] = -k[i];
+ l[i] = -l[i];
+ }
+ }
+}
+
+static void set_cusp_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ const SkScalar ls = d[2];
+ const SkScalar lt = 3.f * d[1];
+
+ k[0] = ls;
+ k[1] = ls - lt / 3.f;
+ k[2] = ls - 2.f * lt / 3.f;
+ k[3] = ls - lt;
+
+ l[0] = ls * ls * ls;
+ const SkScalar ls_lt = ls - lt;
+ l[1] = ls * ls * ls_lt;
+ l[2] = ls_lt * ls_lt * ls;
+ l[3] = ls_lt * ls_lt * ls_lt;
+
+ m[0] = 1.f;
+ m[1] = 1.f;
+ m[2] = 1.f;
+ m[3] = 1.f;
+}
+
+// For the case when a cubic is actually a quadratic
+// M =
+// 0 0 0
+// 1/3 0 1/3
+// 2/3 1/3 2/3
+// 1 1 1
+static void set_quadratic_klm(const SkScalar d[3], SkScalar k[4], SkScalar l[4], SkScalar m[4]) {
+ k[0] = 0.f;
+ k[1] = 1.f/3.f;
+ k[2] = 2.f/3.f;
+ k[3] = 1.f;
+
+ l[0] = 0.f;
+ l[1] = 0.f;
+ l[2] = 1.f/3.f;
+ l[3] = 1.f;
+
+ m[0] = 0.f;
+ m[1] = 1.f/3.f;
+ m[2] = 2.f/3.f;
+ m[3] = 1.f;
+
+ // If d2 < 0 we need to flip the orientation of our curve
+ // This is done by negating the k and l values
+ if ( d[2] > 0) {
+ for (int i = 0; i < 4; ++i) {
+ k[i] = -k[i];
+ l[i] = -l[i];
+ }
+ }
+}
+
+int GrPathUtils::chopCubicAtLoopIntersection(const SkPoint src[4], SkPoint dst[10], SkScalar klm[9],
+ SkScalar klm_rev[3]) {
+ // Variable to store the two parametric values at the loop double point
+ SkScalar smallS = 0.f;
+ SkScalar largeS = 0.f;
+
+ SkScalar d[3];
+ SkCubicType cType = SkClassifyCubic(src, d);
+
+ int chop_count = 0;
+ if (kLoop_SkCubicType == cType) {
+ SkScalar tempSqrt = SkScalarSqrt(4.f * d[0] * d[2] - 3.f * d[1] * d[1]);
+ SkScalar ls = d[1] - tempSqrt;
+ SkScalar lt = 2.f * d[0];
+ SkScalar ms = d[1] + tempSqrt;
+ SkScalar mt = 2.f * d[0];
+ ls = ls / lt;
+ ms = ms / mt;
+ // need to have t values sorted since this is what is expected by SkChopCubicAt
+ if (ls <= ms) {
+ smallS = ls;
+ largeS = ms;
+ } else {
+ smallS = ms;
+ largeS = ls;
+ }
+
+ SkScalar chop_ts[2];
+ if (smallS > 0.f && smallS < 1.f) {
+ chop_ts[chop_count++] = smallS;
+ }
+ if (largeS > 0.f && largeS < 1.f) {
+ chop_ts[chop_count++] = largeS;
+ }
+ if(dst) {
+ SkChopCubicAt(src, dst, chop_ts, chop_count);
+ }
+ } else {
+ if (dst) {
+ memcpy(dst, src, sizeof(SkPoint) * 4);
+ }
+ }
+
+ if (klm && klm_rev) {
+ // Set klm_rev to to match the sub_section of cubic that needs to have its orientation
+ // flipped. This will always be the section that is the "loop"
+ if (2 == chop_count) {
+ klm_rev[0] = 1.f;
+ klm_rev[1] = -1.f;
+ klm_rev[2] = 1.f;
+ } else if (1 == chop_count) {
+ if (smallS < 0.f) {
+ klm_rev[0] = -1.f;
+ klm_rev[1] = 1.f;
+ } else {
+ klm_rev[0] = 1.f;
+ klm_rev[1] = -1.f;
+ }
+ } else {
+ if (smallS < 0.f && largeS > 1.f) {
+ klm_rev[0] = -1.f;
+ } else {
+ klm_rev[0] = 1.f;
+ }
+ }
+ SkScalar controlK[4];
+ SkScalar controlL[4];
+ SkScalar controlM[4];
+
+ if (kSerpentine_SkCubicType == cType || (kCusp_SkCubicType == cType && 0.f != d[0])) {
+ set_serp_klm(d, controlK, controlL, controlM);
+ } else if (kLoop_SkCubicType == cType) {
+ set_loop_klm(d, controlK, controlL, controlM);
+ } else if (kCusp_SkCubicType == cType) {
+ SkASSERT(0.f == d[0]);
+ set_cusp_klm(d, controlK, controlL, controlM);
+ } else if (kQuadratic_SkCubicType == cType) {
+ set_quadratic_klm(d, controlK, controlL, controlM);
+ }
+
+ calc_cubic_klm(src, controlK, controlL, controlM, klm, &klm[3], &klm[6]);
+ }
+ return chop_count + 1;
+}
+
+void GrPathUtils::getCubicKLM(const SkPoint p[4], SkScalar klm[9]) {
+ SkScalar d[3];
+ SkCubicType cType = SkClassifyCubic(p, d);
+
+ SkScalar controlK[4];
+ SkScalar controlL[4];
+ SkScalar controlM[4];
+
+ if (kSerpentine_SkCubicType == cType || (kCusp_SkCubicType == cType && 0.f != d[0])) {
+ set_serp_klm(d, controlK, controlL, controlM);
+ } else if (kLoop_SkCubicType == cType) {
+ set_loop_klm(d, controlK, controlL, controlM);
+ } else if (kCusp_SkCubicType == cType) {
+ SkASSERT(0.f == d[0]);
+ set_cusp_klm(d, controlK, controlL, controlM);
+ } else if (kQuadratic_SkCubicType == cType) {
+ set_quadratic_klm(d, controlK, controlL, controlM);
+ }
+
+ calc_cubic_klm(p, controlK, controlL, controlM, klm, &klm[3], &klm[6]);
+}
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