Move GrPathUtils, GrRect, and GrShape into src/gpu/geometry/
Change-Id: I864d3c2452f3affdc744bf8b11ed3b3e37d6d922
Reviewed-on: https://skia-review.googlesource.com/c/skia/+/216602
Commit-Queue: Michael Ludwig <michaelludwig@google.com>
Reviewed-by: Robert Phillips <robertphillips@google.com>
diff --git a/src/gpu/geometry/GrPathUtils.cpp b/src/gpu/geometry/GrPathUtils.cpp
new file mode 100644
index 0000000..3da6e13
--- /dev/null
+++ b/src/gpu/geometry/GrPathUtils.cpp
@@ -0,0 +1,859 @@
+/*
+ * 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;
+}