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

gfx/skia/trunk/src/pathops/SkPathOpsCubic.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/pathops/SkPathOpsCubic.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 2012 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 #include "SkLineParameters.h"
 #include "SkPathOpsCubic.h"
 #include "SkPathOpsLine.h"
 #include "SkPathOpsQuad.h"
 #include "SkPathOpsRect.h"
 const int SkDCubic::gPrecisionUnit = 256;  // FIXME: test different values in test framework
 // FIXME: cache keep the bounds and/or precision with the caller?
 double SkDCubic::calcPrecision() const {
     SkDRect dRect;
     dRect.setBounds(*this);  // OPTIMIZATION: just use setRawBounds ?
     double width = dRect.fRight - dRect.fLeft;
     double height = dRect.fBottom - dRect.fTop;
     return (width > height ? width : height) / gPrecisionUnit;
 }
 bool SkDCubic::clockwise() const {
     double sum = (fPts[0].fX - fPts[3].fX) * (fPts[0].fY + fPts[3].fY);
     for (int idx = 0; idx < 3; ++idx) {
         sum += (fPts[idx + 1].fX - fPts[idx].fX) * (fPts[idx + 1].fY + fPts[idx].fY);
     }
     return sum <= 0;
 }
 void SkDCubic::Coefficients(const double* src, double* A, double* B, double* C, double* D) {
     *A = src[6];  // d
     *B = src[4] * 3;  // 3*c
     *C = src[2] * 3;  // 3*b
     *D = src[0];  // a
     *A -= *D - *C + *B;     // A =   -a + 3*b - 3*c + d
     *B += 3 * *D - 2 * *C;  // B =  3*a - 6*b + 3*c
     *C -= 3 * *D;           // C = -3*a + 3*b
 }
 bool SkDCubic::controlsContainedByEnds() const {
     SkDVector startTan = fPts[1] - fPts[0];
     if (startTan.fX == 0 && startTan.fY == 0) {
         startTan = fPts[2] - fPts[0];
     }
     SkDVector endTan = fPts[2] - fPts[3];
     if (endTan.fX == 0 && endTan.fY == 0) {
         endTan = fPts[1] - fPts[3];
     }
     if (startTan.dot(endTan) >= 0) {
         return false;
     }
     SkDLine startEdge = {{fPts[0], fPts[0]}};
     startEdge[1].fX -= startTan.fY;
     startEdge[1].fY += startTan.fX;
     SkDLine endEdge = {{fPts[3], fPts[3]}};
     endEdge[1].fX -= endTan.fY;
     endEdge[1].fY += endTan.fX;
     double leftStart1 = startEdge.isLeft(fPts[1]);
     if (leftStart1 * startEdge.isLeft(fPts[2]) < 0) {
         return false;
     }
     double leftEnd1 = endEdge.isLeft(fPts[1]);
     if (leftEnd1 * endEdge.isLeft(fPts[2]) < 0) {
         return false;
     }
     return leftStart1 * leftEnd1 >= 0;
 }
 bool SkDCubic::endsAreExtremaInXOrY() const {
     return (between(fPts[0].fX, fPts[1].fX, fPts[3].fX)
             && between(fPts[0].fX, fPts[2].fX, fPts[3].fX))
             || (between(fPts[0].fY, fPts[1].fY, fPts[3].fY)
             && between(fPts[0].fY, fPts[2].fY, fPts[3].fY));
 }
 bool SkDCubic::isLinear(int startIndex, int endIndex) const {
     SkLineParameters lineParameters;
     lineParameters.cubicEndPoints(*this, startIndex, endIndex);
     // FIXME: maybe it's possible to avoid this and compare non-normalized
     lineParameters.normalize();
     double distance = lineParameters.controlPtDistance(*this, 1);
     if (!approximately_zero(distance)) {
         return false;
     }
     distance = lineParameters.controlPtDistance(*this, 2);
     return approximately_zero(distance);
 }
 bool SkDCubic::monotonicInY() const {
     return between(fPts[0].fY, fPts[1].fY, fPts[3].fY)
             && between(fPts[0].fY, fPts[2].fY, fPts[3].fY);
 }
 bool SkDCubic::serpentine() const {
     if (!controlsContainedByEnds()) {
         return false;
     }
     double wiggle = (fPts[0].fX - fPts[2].fX) * (fPts[0].fY + fPts[2].fY);
     for (int idx = 0; idx < 2; ++idx) {
         wiggle += (fPts[idx + 1].fX - fPts[idx].fX) * (fPts[idx + 1].fY + fPts[idx].fY);
     }
     double waggle = (fPts[1].fX - fPts[3].fX) * (fPts[1].fY + fPts[3].fY);
     for (int idx = 1; idx < 3; ++idx) {
         waggle += (fPts[idx + 1].fX - fPts[idx].fX) * (fPts[idx + 1].fY + fPts[idx].fY);
     }
     return wiggle * waggle < 0;
 }
 // cubic roots
 static const double PI = 3.141592653589793;
 // from SkGeometry.cpp (and Numeric Solutions, 5.6)
 int SkDCubic::RootsValidT(double A, double B, double C, double D, double t[3]) {
     double s[3];
     int realRoots = RootsReal(A, B, C, D, s);
     int foundRoots = SkDQuad::AddValidTs(s, realRoots, t);
     return foundRoots;
 }
 int SkDCubic::RootsReal(double A, double B, double C, double D, double s[3]) {
 #ifdef SK_DEBUG
     // create a string mathematica understands
     // GDB set print repe 15 # if repeated digits is a bother
     //     set print elements 400 # if line doesn't fit
     char str[1024];
     sk_bzero(str, sizeof(str));
     SK_SNPRINTF(str, sizeof(str), "Solve[%1.19g x^3 + %1.19g x^2 + %1.19g x + %1.19g == 0, x]",
             A, B, C, D);
     SkPathOpsDebug::MathematicaIze(str, sizeof(str));
 #if ONE_OFF_DEBUG && ONE_OFF_DEBUG_MATHEMATICA
     SkDebugf("%s\n", str);
 #endif
 #endif
     if (approximately_zero(A)
             && approximately_zero_when_compared_to(A, B)
             && approximately_zero_when_compared_to(A, C)
             && approximately_zero_when_compared_to(A, D)) {  // we're just a quadratic
         return SkDQuad::RootsReal(B, C, D, s);
     }
     if (approximately_zero_when_compared_to(D, A)
             && approximately_zero_when_compared_to(D, B)
             && approximately_zero_when_compared_to(D, C)) {  // 0 is one root
         int num = SkDQuad::RootsReal(A, B, C, s);
         for (int i = 0; i < num; ++i) {
             if (approximately_zero(s[i])) {
                 return num;
             }
         }
         s[num++] = 0;
         return num;
     }
     if (approximately_zero(A + B + C + D)) {  // 1 is one root
         int num = SkDQuad::RootsReal(A, A + B, -D, s);
         for (int i = 0; i < num; ++i) {
             if (AlmostDequalUlps(s[i], 1)) {
                 return num;
             }
         }
         s[num++] = 1;
         return num;
     }
     double a, b, c;
     {
         double invA = 1 / A;
         a = B * invA;
         b = C * invA;
         c = D * invA;
     }
     double a2 = a * a;
     double Q = (a2 - b * 3) / 9;
     double R = (2 * a2 * a - 9 * a * b + 27 * c) / 54;
     double R2 = R * R;
     double Q3 = Q * Q * Q;
     double R2MinusQ3 = R2 - Q3;
     double adiv3 = a / 3;
     double r;
     double* roots = s;
     if (R2MinusQ3 < 0) {   // we have 3 real roots
         double theta = acos(R / sqrt(Q3));
         double neg2RootQ = -2 * sqrt(Q);
         r = neg2RootQ * cos(theta / 3) - adiv3;
         *roots++ = r;
         r = neg2RootQ * cos((theta + 2 * PI) / 3) - adiv3;
         if (!AlmostDequalUlps(s[0], r)) {
             *roots++ = r;
         }
         r = neg2RootQ * cos((theta - 2 * PI) / 3) - adiv3;
         if (!AlmostDequalUlps(s[0], r) && (roots - s == 1 || !AlmostDequalUlps(s[1], r))) {
             *roots++ = r;
         }
     } else {  // we have 1 real root
         double sqrtR2MinusQ3 = sqrt(R2MinusQ3);
         double A = fabs(R) + sqrtR2MinusQ3;
         A = SkDCubeRoot(A);
         if (R > 0) {
             A = -A;
         }
         if (A != 0) {
             A += Q / A;
         }
         r = A - adiv3;
         *roots++ = r;
         if (AlmostDequalUlps(R2, Q3)) {
             r = -A / 2 - adiv3;
             if (!AlmostDequalUlps(s[0], r)) {
                 *roots++ = r;
             }
         }
     }
     return static_cast<int>(roots - s);
 }
 // from http://www.cs.sunysb.edu/~qin/courses/geometry/4.pdf
 // c(t)  = a(1-t)^3 + 3bt(1-t)^2 + 3c(1-t)t^2 + dt^3
 // c'(t) = -3a(1-t)^2 + 3b((1-t)^2 - 2t(1-t)) + 3c(2t(1-t) - t^2) + 3dt^2
 //       = 3(b-a)(1-t)^2 + 6(c-b)t(1-t) + 3(d-c)t^2
 static double derivative_at_t(const double* src, double t) {
     double one_t = 1 - t;
     double a = src[0];
     double b = src[2];
     double c = src[4];
     double d = src[6];
     return 3 * ((b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t);
 }
 // OPTIMIZE? compute t^2, t(1-t), and (1-t)^2 and pass them to another version of derivative at t?
 SkDVector SkDCubic::dxdyAtT(double t) const {
     SkDVector result = { derivative_at_t(&fPts[0].fX, t), derivative_at_t(&fPts[0].fY, t) };
     return result;
 }
 // OPTIMIZE? share code with formulate_F1DotF2
 int SkDCubic::findInflections(double tValues[]) const {
     double Ax = fPts[1].fX - fPts[0].fX;
     double Ay = fPts[1].fY - fPts[0].fY;
     double Bx = fPts[2].fX - 2 * fPts[1].fX + fPts[0].fX;
     double By = fPts[2].fY - 2 * fPts[1].fY + fPts[0].fY;
     double Cx = fPts[3].fX + 3 * (fPts[1].fX - fPts[2].fX) - fPts[0].fX;
     double Cy = fPts[3].fY + 3 * (fPts[1].fY - fPts[2].fY) - fPts[0].fY;
     return SkDQuad::RootsValidT(Bx * Cy - By * Cx, Ax * Cy - Ay * Cx, Ax * By - Ay * Bx, tValues);
 }
 static void formulate_F1DotF2(const double src[], double coeff[4]) {
     double a = src[2] - src[0];
     double b = src[4] - 2 * src[2] + src[0];
     double c = src[6] + 3 * (src[2] - src[4]) - src[0];
     coeff[0] = c * c;
     coeff[1] = 3 * b * c;
     coeff[2] = 2 * b * b + c * a;
     coeff[3] = a * b;
 }
 /** SkDCubic'(t) = At^2 + Bt + C, where
     A = 3(-a + 3(b - c) + d)
     B = 6(a - 2b + c)
     C = 3(b - a)
     Solve for t, keeping only those that fit between 0 < t < 1
 */
 int SkDCubic::FindExtrema(double a, double b, double c, double d, double tValues[2]) {
     // we divide A,B,C by 3 to simplify
     double A = d - a + 3*(b - c);
     double B = 2*(a - b - b + c);
     double C = b - a;
     return SkDQuad::RootsValidT(A, B, C, tValues);
 }
 /*  from SkGeometry.cpp
     Looking for F' dot F'' == 0
     A = b - a
     B = c - 2b + a
     C = d - 3c + 3b - a
     F' = 3Ct^2 + 6Bt + 3A
     F'' = 6Ct + 6B
     F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB
 */
 int SkDCubic::findMaxCurvature(double tValues[]) const {
     double coeffX[4], coeffY[4];
     int i;
     formulate_F1DotF2(&fPts[0].fX, coeffX);
     formulate_F1DotF2(&fPts[0].fY, coeffY);
     for (i = 0; i < 4; i++) {
         coeffX[i] = coeffX[i] + coeffY[i];
     }
     return RootsValidT(coeffX[0], coeffX[1], coeffX[2], coeffX[3], tValues);
 }
 SkDPoint SkDCubic::top(double startT, double endT) const {
     SkDCubic sub = subDivide(startT, endT);
     SkDPoint topPt = sub[0];
     if (topPt.fY > sub[3].fY || (topPt.fY == sub[3].fY && topPt.fX > sub[3].fX)) {
         topPt = sub[3];
     }
     double extremeTs[2];
     if (!sub.monotonicInY()) {
         int roots = FindExtrema(sub[0].fY, sub[1].fY, sub[2].fY, sub[3].fY, extremeTs);
         for (int index = 0; index < roots; ++index) {
             double t = startT + (endT - startT) * extremeTs[index];
             SkDPoint mid = ptAtT(t);
             if (topPt.fY > mid.fY || (topPt.fY == mid.fY && topPt.fX > mid.fX)) {
                 topPt = mid;
             }
         }
     }
     return topPt;
 }
 SkDPoint SkDCubic::ptAtT(double t) const {
     if (0 == t) {
         return fPts[0];
     }
     if (1 == t) {
         return fPts[3];
     }
     double one_t = 1 - t;
     double one_t2 = one_t * one_t;
     double a = one_t2 * one_t;
     double b = 3 * one_t2 * t;
     double t2 = t * t;
     double c = 3 * one_t * t2;
     double d = t2 * t;
     SkDPoint result = {a * fPts[0].fX + b * fPts[1].fX + c * fPts[2].fX + d * fPts[3].fX,
             a * fPts[0].fY + b * fPts[1].fY + c * fPts[2].fY + d * fPts[3].fY};
     return result;
 }
 /*
  Given a cubic c, t1, and t2, find a small cubic segment.
  The new cubic is defined as points A, B, C, and D, where
  s1 = 1 - t1
  s2 = 1 - t2
  A = c[0]*s1*s1*s1 + 3*c[1]*s1*s1*t1 + 3*c[2]*s1*t1*t1 + c[3]*t1*t1*t1
  D = c[0]*s2*s2*s2 + 3*c[1]*s2*s2*t2 + 3*c[2]*s2*t2*t2 + c[3]*t2*t2*t2
  We don't have B or C. So We define two equations to isolate them.
  First, compute two reference T values 1/3 and 2/3 from t1 to t2:
  c(at (2*t1 + t2)/3) == E
  c(at (t1 + 2*t2)/3) == F
  Next, compute where those values must be if we know the values of B and C:
  _12   =  A*2/3 + B*1/3
 _   =  A*1/3 + B*2/3
  _23   =  B*2/3 + C*1/3
 _   =  B*1/3 + C*2/3
  _34   =  C*2/3 + D*1/3
 _   =  C*1/3 + D*2/3
  _123  = (A*2/3 + B*1/3)*2/3 + (B*2/3 + C*1/3)*1/3 = A*4/9 + B*4/9 + C*1/9
 _  = (A*1/3 + B*2/3)*1/3 + (B*1/3 + C*2/3)*2/3 = A*1/9 + B*4/9 + C*4/9
  _234  = (B*2/3 + C*1/3)*2/3 + (C*2/3 + D*1/3)*1/3 = B*4/9 + C*4/9 + D*1/9
 _  = (B*1/3 + C*2/3)*1/3 + (C*1/3 + D*2/3)*2/3 = B*1/9 + C*4/9 + D*4/9
  _1234 = (A*4/9 + B*4/9 + C*1/9)*2/3 + (B*4/9 + C*4/9 + D*1/9)*1/3
        =  A*8/27 + B*12/27 + C*6/27 + D*1/27
        =  E
 _ = (A*1/9 + B*4/9 + C*4/9)*1/3 + (B*1/9 + C*4/9 + D*4/9)*2/3
        =  A*1/27 + B*6/27 + C*12/27 + D*8/27
        =  F
  E*27  =  A*8    + B*12   + C*6     + D
  F*27  =  A      + B*6    + C*12    + D*8
 Group the known values on one side:
  M       = E*27 - A*8 - D     = B*12 + C* 6
  N       = F*27 - A   - D*8   = B* 6 + C*12
  M*2 - N = B*18
  N*2 - M = C*18
  B       = (M*2 - N)/18
  C       = (N*2 - M)/18
  */
 static double interp_cubic_coords(const double* src, double t) {
     double ab = SkDInterp(src[0], src[2], t);
     double bc = SkDInterp(src[2], src[4], t);
     double cd = SkDInterp(src[4], src[6], t);
     double abc = SkDInterp(ab, bc, t);
     double bcd = SkDInterp(bc, cd, t);
     double abcd = SkDInterp(abc, bcd, t);
     return abcd;
 }
 SkDCubic SkDCubic::subDivide(double t1, double t2) const {
     if (t1 == 0 || t2 == 1) {
         if (t1 == 0 && t2 == 1) {
             return *this;
         }
         SkDCubicPair pair = chopAt(t1 == 0 ? t2 : t1);
         SkDCubic dst = t1 == 0 ? pair.first() : pair.second();
         return dst;
     }
     SkDCubic dst;
     double ax = dst[0].fX = interp_cubic_coords(&fPts[0].fX, t1);
     double ay = dst[0].fY = interp_cubic_coords(&fPts[0].fY, t1);
     double ex = interp_cubic_coords(&fPts[0].fX, (t1*2+t2)/3);
     double ey = interp_cubic_coords(&fPts[0].fY, (t1*2+t2)/3);
     double fx = interp_cubic_coords(&fPts[0].fX, (t1+t2*2)/3);
     double fy = interp_cubic_coords(&fPts[0].fY, (t1+t2*2)/3);
     double dx = dst[3].fX = interp_cubic_coords(&fPts[0].fX, t2);
     double dy = dst[3].fY = interp_cubic_coords(&fPts[0].fY, t2);
     double mx = ex * 27 - ax * 8 - dx;
     double my = ey * 27 - ay * 8 - dy;
     double nx = fx * 27 - ax - dx * 8;
     double ny = fy * 27 - ay - dy * 8;
     /* bx = */ dst[1].fX = (mx * 2 - nx) / 18;
     /* by = */ dst[1].fY = (my * 2 - ny) / 18;
     /* cx = */ dst[2].fX = (nx * 2 - mx) / 18;
     /* cy = */ dst[2].fY = (ny * 2 - my) / 18;
     // FIXME: call align() ?
     return dst;
 }
 void SkDCubic::align(int endIndex, int ctrlIndex, SkDPoint* dstPt) const {
     if (fPts[endIndex].fX == fPts[ctrlIndex].fX) {
         dstPt->fX = fPts[endIndex].fX;
     }
     if (fPts[endIndex].fY == fPts[ctrlIndex].fY) {
         dstPt->fY = fPts[endIndex].fY;
     }
 }
 void SkDCubic::subDivide(const SkDPoint& a, const SkDPoint& d,
                          double t1, double t2, SkDPoint dst[2]) const {
     SkASSERT(t1 != t2);
 #if 0
     double ex = interp_cubic_coords(&fPts[0].fX, (t1 * 2 + t2) / 3);
     double ey = interp_cubic_coords(&fPts[0].fY, (t1 * 2 + t2) / 3);
     double fx = interp_cubic_coords(&fPts[0].fX, (t1 + t2 * 2) / 3);
     double fy = interp_cubic_coords(&fPts[0].fY, (t1 + t2 * 2) / 3);
     double mx = ex * 27 - a.fX * 8 - d.fX;
     double my = ey * 27 - a.fY * 8 - d.fY;
     double nx = fx * 27 - a.fX - d.fX * 8;
     double ny = fy * 27 - a.fY - d.fY * 8;
     /* bx = */ dst[0].fX = (mx * 2 - nx) / 18;
     /* by = */ dst[0].fY = (my * 2 - ny) / 18;
     /* cx = */ dst[1].fX = (nx * 2 - mx) / 18;
     /* cy = */ dst[1].fY = (ny * 2 - my) / 18;
 #else
     // this approach assumes that the control points computed directly are accurate enough
     SkDCubic sub = subDivide(t1, t2);
     dst[0] = sub[1] + (a - sub[0]);
     dst[1] = sub[2] + (d - sub[3]);
 #endif
     if (t1 == 0 || t2 == 0) {
         align(0, 1, t1 == 0 ? &dst[0] : &dst[1]);
     }
     if (t1 == 1 || t2 == 1) {
         align(3, 2, t1 == 1 ? &dst[0] : &dst[1]);
     }
     if (precisely_subdivide_equal(dst[0].fX, a.fX)) {
         dst[0].fX = a.fX;
     }
     if (precisely_subdivide_equal(dst[0].fY, a.fY)) {
         dst[0].fY = a.fY;
     }
     if (precisely_subdivide_equal(dst[1].fX, d.fX)) {
         dst[1].fX = d.fX;
     }
     if (precisely_subdivide_equal(dst[1].fY, d.fY)) {
         dst[1].fY = d.fY;
     }
 }
 /* classic one t subdivision */
 static void interp_cubic_coords(const double* src, double* dst, double t) {
     double ab = SkDInterp(src[0], src[2], t);
     double bc = SkDInterp(src[2], src[4], t);
     double cd = SkDInterp(src[4], src[6], t);
     double abc = SkDInterp(ab, bc, t);
     double bcd = SkDInterp(bc, cd, t);
     double abcd = SkDInterp(abc, bcd, t);
     dst[0] = src[0];
     dst[2] = ab;
     dst[4] = abc;
     dst[6] = abcd;
     dst[8] = bcd;
     dst[10] = cd;
     dst[12] = src[6];
 }
 SkDCubicPair SkDCubic::chopAt(double t) const {
     SkDCubicPair dst;
     if (t == 0.5) {
         dst.pts[0] = fPts[0];
         dst.pts[1].fX = (fPts[0].fX + fPts[1].fX) / 2;
         dst.pts[1].fY = (fPts[0].fY + fPts[1].fY) / 2;
         dst.pts[2].fX = (fPts[0].fX + 2 * fPts[1].fX + fPts[2].fX) / 4;
         dst.pts[2].fY = (fPts[0].fY + 2 * fPts[1].fY + fPts[2].fY) / 4;
         dst.pts[3].fX = (fPts[0].fX + 3 * (fPts[1].fX + fPts[2].fX) + fPts[3].fX) / 8;
         dst.pts[3].fY = (fPts[0].fY + 3 * (fPts[1].fY + fPts[2].fY) + fPts[3].fY) / 8;
         dst.pts[4].fX = (fPts[1].fX + 2 * fPts[2].fX + fPts[3].fX) / 4;
         dst.pts[4].fY = (fPts[1].fY + 2 * fPts[2].fY + fPts[3].fY) / 4;
         dst.pts[5].fX = (fPts[2].fX + fPts[3].fX) / 2;
         dst.pts[5].fY = (fPts[2].fY + fPts[3].fY) / 2;
         dst.pts[6] = fPts[3];
         return dst;
     }
     interp_cubic_coords(&fPts[0].fX, &dst.pts[0].fX, t);
     interp_cubic_coords(&fPts[0].fY, &dst.pts[0].fY, t);
     return dst;
 }
 #ifdef SK_DEBUG
 void SkDCubic::dump() {
     SkDebugf("{{");
     int index = 0;
     do {
         fPts[index].dump();
         SkDebugf(", ");
     } while (++index < 3);
     fPts[index].dump();
     SkDebugf("}}\n");
 }
 #endif

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gfx/skia/trunk/src/pathops/SkPathOpsCubic.cpp@129ffea94266 (annotated)

gfx/skia/trunk/src/pathops/SkPathOpsCubic.cpp