The Tor Browser: gfx/skia/trunk/src/gpu/GrPathUtils.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/gpu/GrPathUtils.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/gpu/GrPathUtils.cpp

Sat, 03 Jan 2015 20:18:00 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Sat, 03 Jan 2015 20:18:00 +0100
branch: TOR_BUG_3246
changeset 7: 129ffea94266
permissions: -rw-r--r--

Conditionally enable double key logic according to:
private browsing mode or privacy.thirdparty.isolate preference and
implement in GetCookieStringCommon and FindCookie where it counts...
With some reservations of how to convince FindCookie users to test
condition and pass a nullptr when disabling double key logic.

 /*
  * 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 "GrPoint.h"
 #include "SkGeometry.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
     // stretch when mapping to screen coordinates.
     SkScalar stretch = viewM.getMaxStretch();
     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));
         }
     }
     srcTol = SkScalarDiv(srcTol, stretch);
     return srcTol;
 }
 static const int MAX_POINTS_PER_CURVE = 1 << 10;
 static const SkScalar gMinCurveTol = 0.0001f;
 uint32_t GrPathUtils::quadraticPointCount(const GrPoint points[],
                                           SkScalar tol) {
     if (tol < gMinCurveTol) {
         tol = gMinCurveTol;
     }
     SkASSERT(tol > 0);
     SkScalar d = points[1].distanceToLineSegmentBetween(points[0], points[2]);
     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);
         int temp = SkScalarCeilToInt(SkScalarSqrt(SkScalarDiv(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 GrMin(pow2, MAX_POINTS_PER_CURVE);
     }
 }
 uint32_t GrPathUtils::generateQuadraticPoints(const GrPoint& p0,
                                               const GrPoint& p1,
                                               const GrPoint& p2,
                                               SkScalar tolSqd,
                                               GrPoint** points,
                                               uint32_t pointsLeft) {
     if (pointsLeft < 2 ||
         (p1.distanceToLineSegmentBetweenSqd(p0, p2)) < tolSqd) {
         (*points)[0] = p2;
         *points += 1;
         return 1;
     }
     GrPoint q[] = {
         { SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
         { SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
     };
     GrPoint 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 GrPoint points[],
                                            SkScalar tol) {
     if (tol < gMinCurveTol) {
         tol = gMinCurveTol;
     }
     SkASSERT(tol > 0);
     SkScalar d = GrMax(
         points[1].distanceToLineSegmentBetweenSqd(points[0], points[3]),
         points[2].distanceToLineSegmentBetweenSqd(points[0], points[3]));
     d = SkScalarSqrt(d);
     if (d <= tol) {
         return 1;
     } else {
         int temp = SkScalarCeilToInt(SkScalarSqrt(SkScalarDiv(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 GrMin(pow2, MAX_POINTS_PER_CURVE);
     }
 }
 uint32_t GrPathUtils::generateCubicPoints(const GrPoint& p0,
                                           const GrPoint& p1,
                                           const GrPoint& p2,
                                           const GrPoint& p3,
                                           SkScalar tolSqd,
                                           GrPoint** points,
                                           uint32_t pointsLeft) {
     if (pointsLeft < 2 ||
         (p1.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd &&
          p2.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd)) {
             (*points)[0] = p3;
             *points += 1;
             return 1;
         }
     GrPoint 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) }
     };
     GrPoint 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) }
     };
     GrPoint 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;
     GrPoint pts[4];
     while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
         switch (verb) {
             case SkPath::kLine_Verb:
                 pointCount += 1;
                 break;
             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 GrPoint 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)
             GrVec 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, GrPoint::kLeft_Side);
             lineVec.dot(qPts[0]);
             // 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 a0, a1, a2, a3, a4, a5, a6, a7, a8;
         a0 = y1-y2;
         a1 = x2-x1;
         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);
         m[SkMatrix::kMPersp0] = (float)((a0 + a3 + a6)*scale);
         m[SkMatrix::kMPersp1] = (float)((a1 + a4 + a7)*scale);
         m[SkMatrix::kMPersp2] = (float)((a2 + a5 + a8)*scale);
         // The matrix should not have perspective.
         SkDEBUGCODE(static const SkScalar gTOL = 1.f / 100.f);
         SkASSERT(SkScalarAbs(m.get(SkMatrix::kMPersp0)) < gTOL);
         SkASSERT(SkScalarAbs(m.get(SkMatrix::kMPersp1)) < gTOL);
         // 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,
                                     SkPath::Direction dir,
                                     const SkPoint p) {
     SkVector ap = p - a;
     SkScalar apXab = ap.cross(ab);
     if (SkPath::kCW_Direction == dir) {
         if (apXab > 0) {
             return false;
         }
     } else {
         SkASSERT(SkPath::kCCW_Direction == dir);
         if (apXab < 0) {
             return false;
         }
     }
     SkVector dp = p - d;
     SkScalar dpXdc = dp.cross(dc);
     if (SkPath::kCW_Direction == dir) {
         if (dpXdc < 0) {
             return false;
         }
     } else {
         SkASSERT(SkPath::kCCW_Direction == dir);
         if (dpXdc > 0) {
             return false;
         }
     }
     return true;
 }
 void convert_noninflect_cubic_to_quads(const SkPoint p[4],
                                        SkScalar toleranceSqd,
                                        bool constrainWithinTangents,
                                        SkPath::Direction 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.isZero()) {
         if (dc.isZero()) {
             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.isZero()) {
         dc = p[1] - p[3];
     }
     // When the ab and cd tangents are 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];
         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 goed 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) {
                 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 GrPoint p[4],
                                       SkScalar tolScale,
                                       bool constrainWithinTangents,
                                       SkPath::Direction dir,
                                       SkTArray<SkPoint, true>* quads) {
     SkPoint chopped[10];
     int count = SkChopCubicAtInflections(p, chopped);
     // base tolerance is 1 pixel.
     static const SkScalar kTolerance = SK_Scalar1;
     const SkScalar tolSqd = SkScalarSquare(SkScalarMul(tolScale, kTolerance));
     for (int i = 0; i < count; ++i) {
         SkPoint* cubic = chopped + 3*i;
         convert_noninflect_cubic_to_quads(cubic, tolSqd, constrainWithinTangents, dir, quads);
     }
 }
 ////////////////////////////////////////////////////////////////////////////////
 enum CubicType {
     kSerpentine_CubicType,
     kCusp_CubicType,
     kLoop_CubicType,
     kQuadratic_CubicType,
     kLine_CubicType,
     kPoint_CubicType
 };
 // discr(I) = d0^2 * (3*d1^2 - 4*d0*d2)
 // Classification:
 // discr(I) > 0        Serpentine
 // discr(I) = 0        Cusp
 // discr(I) < 0        Loop
 // d0 = d1 = 0         Quadratic
 // d0 = d1 = d2 = 0    Line
 // p0 = p1 = p2 = p3   Point
 static CubicType classify_cubic(const SkPoint p[4], const SkScalar d[3]) {
     if (p[0] == p[1] && p[0] == p[2] && p[0] == p[3]) {
         return kPoint_CubicType;
     }
     const SkScalar discr = d[0] * d[0] * (3.f * d[1] * d[1] - 4.f * d[0] * d[2]);
     if (discr > SK_ScalarNearlyZero) {
         return kSerpentine_CubicType;
     } else if (discr < -SK_ScalarNearlyZero) {
         return kLoop_CubicType;
     } else {
         if (0.f == d[0] && 0.f == d[1]) {
             return (0.f == d[2] ? kLine_CubicType : kQuadratic_CubicType);
         } else {
             return kCusp_CubicType;
         }
     }
 }
 // Assumes the third component of points is 1.
 // Calcs p0 . (p1 x p2)
 static SkScalar calc_dot_cross_cubic(const SkPoint& p0, const SkPoint& p1, const SkPoint& p2) {
     const SkScalar xComp = p0.fX * (p1.fY - p2.fY);
     const SkScalar yComp = p0.fY * (p2.fX - p1.fX);
     const SkScalar wComp = p1.fX * p2.fY - p1.fY * p2.fX;
     return (xComp + yComp + wComp);
 }
 // 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];
         }
     }
 }
 // Calc coefficients of I(s,t) where roots of I are inflection points of curve
 // I(s,t) = t*(3*d0*s^2 - 3*d1*s*t + d2*t^2)
 // d0 = a1 - 2*a2+3*a3
 // d1 = -a2 + 3*a3
 // d2 = 3*a3
 // a1 = p0 . (p3 x p2)
 // a2 = p1 . (p0 x p3)
 // a3 = p2 . (p1 x p0)
 // Places the values of d1, d2, d3 in array d passed in
 static void calc_cubic_inflection_func(const SkPoint p[4], SkScalar d[3]) {
     SkScalar a1 = calc_dot_cross_cubic(p[0], p[3], p[2]);
     SkScalar a2 = calc_dot_cross_cubic(p[1], p[0], p[3]);
     SkScalar a3 = calc_dot_cross_cubic(p[2], p[1], p[0]);
     // need to scale a's or values in later calculations will grow to high
     SkScalar max = SkScalarAbs(a1);
     max = SkMaxScalar(max, SkScalarAbs(a2));
     max = SkMaxScalar(max, SkScalarAbs(a3));
     max = 1.f/max;
     a1 = a1 * max;
     a2 = a2 * max;
     a3 = a3 * max;
     d[2] = 3.f * a3;
     d[1] = d[2] - a2;
     d[0] = d[1] - a2 + a1;
 }
 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];
     calc_cubic_inflection_func(src, d);
     CubicType cType = classify_cubic(src, d);
     int chop_count = 0;
     if (kLoop_CubicType == 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_CubicType == cType || (kCusp_CubicType == cType && 0.f != d[0])) {
             set_serp_klm(d, controlK, controlL, controlM);
         } else if (kLoop_CubicType == cType) {
             set_loop_klm(d, controlK, controlL, controlM);
         } else if (kCusp_CubicType == cType) {
             SkASSERT(0.f == d[0]);
             set_cusp_klm(d, controlK, controlL, controlM);
         } else if (kQuadratic_CubicType == 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];
     calc_cubic_inflection_func(p, d);
     CubicType cType = classify_cubic(p, d);
     SkScalar controlK[4];
     SkScalar controlL[4];
     SkScalar controlM[4];
     if (kSerpentine_CubicType == cType || (kCusp_CubicType == cType && 0.f != d[0])) {
         set_serp_klm(d, controlK, controlL, controlM);
     } else if (kLoop_CubicType == cType) {
         set_loop_klm(d, controlK, controlL, controlM);
     } else if (kCusp_CubicType == cType) {
         SkASSERT(0.f == d[0]);
         set_cusp_klm(d, controlK, controlL, controlM);
     } else if (kQuadratic_CubicType == cType) {
         set_quadratic_klm(d, controlK, controlL, controlM);
     }
     calc_cubic_klm(p, controlK, controlL, controlM, klm, &klm[3], &klm[6]);
 }

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gfx/skia/trunk/src/gpu/GrPathUtils.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/gpu/GrPathUtils.cpp