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

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

gfx/skia/trunk/src/pathops/SkDCubicLineIntersection.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 "SkIntersections.h"
 #include "SkPathOpsCubic.h"
 #include "SkPathOpsLine.h"
 /*
 Find the interection of a line and cubic by solving for valid t values.
 Analogous to line-quadratic intersection, solve line-cubic intersection by
 representing the cubic as:
   x = a(1-t)^3 + 2b(1-t)^2t + c(1-t)t^2 + dt^3
   y = e(1-t)^3 + 2f(1-t)^2t + g(1-t)t^2 + ht^3
 and the line as:
   y = i*x + j  (if the line is more horizontal)
 or:
   x = i*y + j  (if the line is more vertical)
 Then using Mathematica, solve for the values of t where the cubic intersects the
 line:
   (in) Resultant[
         a*(1 - t)^3 + 3*b*(1 - t)^2*t + 3*c*(1 - t)*t^2 + d*t^3 - x,
         e*(1 - t)^3 + 3*f*(1 - t)^2*t + 3*g*(1 - t)*t^2 + h*t^3 - i*x - j, x]
   (out) -e     +   j     +
 e t   - 3 f t   -
 e t^2 + 6 f t^2 - 3 g t^2 +
          e t^3 - 3 f t^3 + 3 g t^3 - h t^3 +
      i ( a     -
 a t + 3 b t +
 a t^2 - 6 b t^2 + 3 c t^2 -
          a t^3 + 3 b t^3 - 3 c t^3 + d t^3 )
 if i goes to infinity, we can rewrite the line in terms of x. Mathematica:
   (in) Resultant[
         a*(1 - t)^3 + 3*b*(1 - t)^2*t + 3*c*(1 - t)*t^2 + d*t^3 - i*y - j,
         e*(1 - t)^3 + 3*f*(1 - t)^2*t + 3*g*(1 - t)*t^2 + h*t^3 - y,       y]
   (out)  a     -   j     -
 a t   + 3 b t   +
 a t^2 - 6 b t^2 + 3 c t^2 -
          a t^3 + 3 b t^3 - 3 c t^3 + d t^3 -
      i ( e     -
 e t   + 3 f t   +
 e t^2 - 6 f t^2 + 3 g t^2 -
          e t^3 + 3 f t^3 - 3 g t^3 + h t^3 )
 Solving this with Mathematica produces an expression with hundreds of terms;
 instead, use Numeric Solutions recipe to solve the cubic.
 The near-horizontal case, in terms of:  Ax^3 + Bx^2 + Cx + D == 0
     A =   (-(-e + 3*f - 3*g + h) + i*(-a + 3*b - 3*c + d)     )
     B = 3*(-( e - 2*f +   g    ) + i*( a - 2*b +   c    )     )
     C = 3*(-(-e +   f          ) + i*(-a +   b          )     )
     D =   (-( e                ) + i*( a                ) + j )
 The near-vertical case, in terms of:  Ax^3 + Bx^2 + Cx + D == 0
     A =   ( (-a + 3*b - 3*c + d) - i*(-e + 3*f - 3*g + h)     )
     B = 3*( ( a - 2*b +   c    ) - i*( e - 2*f +   g    )     )
     C = 3*( (-a +   b          ) - i*(-e +   f          )     )
     D =   ( ( a                ) - i*( e                ) - j )
 For horizontal lines:
 (in) Resultant[
       a*(1 - t)^3 + 3*b*(1 - t)^2*t + 3*c*(1 - t)*t^2 + d*t^3 - j,
       e*(1 - t)^3 + 3*f*(1 - t)^2*t + 3*g*(1 - t)*t^2 + h*t^3 - y, y]
 (out)  e     -   j     -
 e t   + 3 f t   +
 e t^2 - 6 f t^2 + 3 g t^2 -
        e t^3 + 3 f t^3 - 3 g t^3 + h t^3
  */
 class LineCubicIntersections {
 public:
     enum PinTPoint {
         kPointUninitialized,
         kPointInitialized
     };
     LineCubicIntersections(const SkDCubic& c, const SkDLine& l, SkIntersections* i)
         : fCubic(c)
         , fLine(l)
         , fIntersections(i)
         , fAllowNear(true) {
         i->setMax(3);
     }
     void allowNear(bool allow) {
         fAllowNear = allow;
     }
     // see parallel routine in line quadratic intersections
     int intersectRay(double roots[3]) {
         double adj = fLine[1].fX - fLine[0].fX;
         double opp = fLine[1].fY - fLine[0].fY;
         SkDCubic r;
         for (int n = 0; n < 4; ++n) {
             r[n].fX = (fCubic[n].fY - fLine[0].fY) * adj - (fCubic[n].fX - fLine[0].fX) * opp;
         }
         double A, B, C, D;
         SkDCubic::Coefficients(&r[0].fX, &A, &B, &C, &D);
         return SkDCubic::RootsValidT(A, B, C, D, roots);
     }
     int intersect() {
         addExactEndPoints();
         if (fAllowNear) {
             addNearEndPoints();
         }
         double rootVals[3];
         int roots = intersectRay(rootVals);
         for (int index = 0; index < roots; ++index) {
             double cubicT = rootVals[index];
             double lineT = findLineT(cubicT);
             SkDPoint pt;
             if (pinTs(&cubicT, &lineT, &pt, kPointUninitialized)) {
     #if ONE_OFF_DEBUG
                 SkDPoint cPt = fCubic.ptAtT(cubicT);
                 SkDebugf("%s pt=(%1.9g,%1.9g) cPt=(%1.9g,%1.9g)\n", __FUNCTION__, pt.fX, pt.fY,
                         cPt.fX, cPt.fY);
     #endif
                 for (int inner = 0; inner < fIntersections->used(); ++inner) {
                     if (fIntersections->pt(inner) != pt) {
                         continue;
                     }
                     double existingCubicT = (*fIntersections)[0][inner];
                     if (cubicT == existingCubicT) {
                         goto skipInsert;
                     }
                     // check if midway on cubic is also same point. If so, discard this
                     double cubicMidT = (existingCubicT + cubicT) / 2;
                     SkDPoint cubicMidPt = fCubic.ptAtT(cubicMidT);
                     if (cubicMidPt.approximatelyEqual(pt)) {
                         goto skipInsert;
                     }
                 }
                 fIntersections->insert(cubicT, lineT, pt);
         skipInsert:
                 ;
             }
         }
         return fIntersections->used();
     }
     int horizontalIntersect(double axisIntercept, double roots[3]) {
         double A, B, C, D;
         SkDCubic::Coefficients(&fCubic[0].fY, &A, &B, &C, &D);
         D -= axisIntercept;
         return SkDCubic::RootsValidT(A, B, C, D, roots);
     }
     int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) {
         addExactHorizontalEndPoints(left, right, axisIntercept);
         if (fAllowNear) {
             addNearHorizontalEndPoints(left, right, axisIntercept);
         }
         double rootVals[3];
         int roots = horizontalIntersect(axisIntercept, rootVals);
         for (int index = 0; index < roots; ++index) {
             double cubicT = rootVals[index];
             SkDPoint pt = fCubic.ptAtT(cubicT);
             double lineT = (pt.fX - left) / (right - left);
             if (pinTs(&cubicT, &lineT, &pt, kPointInitialized)) {
                 fIntersections->insert(cubicT, lineT, pt);
             }
         }
         if (flipped) {
             fIntersections->flip();
         }
         return fIntersections->used();
     }
     int verticalIntersect(double axisIntercept, double roots[3]) {
         double A, B, C, D;
         SkDCubic::Coefficients(&fCubic[0].fX, &A, &B, &C, &D);
         D -= axisIntercept;
         return SkDCubic::RootsValidT(A, B, C, D, roots);
     }
     int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) {
         addExactVerticalEndPoints(top, bottom, axisIntercept);
         if (fAllowNear) {
             addNearVerticalEndPoints(top, bottom, axisIntercept);
         }
         double rootVals[3];
         int roots = verticalIntersect(axisIntercept, rootVals);
         for (int index = 0; index < roots; ++index) {
             double cubicT = rootVals[index];
             SkDPoint pt = fCubic.ptAtT(cubicT);
             double lineT = (pt.fY - top) / (bottom - top);
             if (pinTs(&cubicT, &lineT, &pt, kPointInitialized)) {
                 fIntersections->insert(cubicT, lineT, pt);
             }
         }
         if (flipped) {
             fIntersections->flip();
         }
         return fIntersections->used();
     }
     protected:
     void addExactEndPoints() {
         for (int cIndex = 0; cIndex < 4; cIndex += 3) {
             double lineT = fLine.exactPoint(fCubic[cIndex]);
             if (lineT < 0) {
                 continue;
             }
             double cubicT = (double) (cIndex >> 1);
             fIntersections->insert(cubicT, lineT, fCubic[cIndex]);
         }
     }
     /* Note that this does not look for endpoints of the line that are near the cubic.
        These points are found later when check ends looks for missing points */
     void addNearEndPoints() {
         for (int cIndex = 0; cIndex < 4; cIndex += 3) {
             double cubicT = (double) (cIndex >> 1);
             if (fIntersections->hasT(cubicT)) {
                 continue;
             }
             double lineT = fLine.nearPoint(fCubic[cIndex]);
             if (lineT < 0) {
                 continue;
             }
             fIntersections->insert(cubicT, lineT, fCubic[cIndex]);
         }
     }
     void addExactHorizontalEndPoints(double left, double right, double y) {
         for (int cIndex = 0; cIndex < 4; cIndex += 3) {
             double lineT = SkDLine::ExactPointH(fCubic[cIndex], left, right, y);
             if (lineT < 0) {
                 continue;
             }
             double cubicT = (double) (cIndex >> 1);
             fIntersections->insert(cubicT, lineT, fCubic[cIndex]);
         }
     }
     void addNearHorizontalEndPoints(double left, double right, double y) {
         for (int cIndex = 0; cIndex < 4; cIndex += 3) {
             double cubicT = (double) (cIndex >> 1);
             if (fIntersections->hasT(cubicT)) {
                 continue;
             }
             double lineT = SkDLine::NearPointH(fCubic[cIndex], left, right, y);
             if (lineT < 0) {
                 continue;
             }
             fIntersections->insert(cubicT, lineT, fCubic[cIndex]);
         }
         // FIXME: see if line end is nearly on cubic
     }
     void addExactVerticalEndPoints(double top, double bottom, double x) {
         for (int cIndex = 0; cIndex < 4; cIndex += 3) {
             double lineT = SkDLine::ExactPointV(fCubic[cIndex], top, bottom, x);
             if (lineT < 0) {
                 continue;
             }
             double cubicT = (double) (cIndex >> 1);
             fIntersections->insert(cubicT, lineT, fCubic[cIndex]);
         }
     }
     void addNearVerticalEndPoints(double top, double bottom, double x) {
         for (int cIndex = 0; cIndex < 4; cIndex += 3) {
             double cubicT = (double) (cIndex >> 1);
             if (fIntersections->hasT(cubicT)) {
                 continue;
             }
             double lineT = SkDLine::NearPointV(fCubic[cIndex], top, bottom, x);
             if (lineT < 0) {
                 continue;
             }
             fIntersections->insert(cubicT, lineT, fCubic[cIndex]);
         }
         // FIXME: see if line end is nearly on cubic
     }
     double findLineT(double t) {
         SkDPoint xy = fCubic.ptAtT(t);
         double dx = fLine[1].fX - fLine[0].fX;
         double dy = fLine[1].fY - fLine[0].fY;
         if (fabs(dx) > fabs(dy)) {
             return (xy.fX - fLine[0].fX) / dx;
         }
         return (xy.fY - fLine[0].fY) / dy;
     }
     bool pinTs(double* cubicT, double* lineT, SkDPoint* pt, PinTPoint ptSet) {
         if (!approximately_one_or_less(*lineT)) {
             return false;
         }
         if (!approximately_zero_or_more(*lineT)) {
             return false;
         }
         double cT = *cubicT = SkPinT(*cubicT);
         double lT = *lineT = SkPinT(*lineT);
         if (lT == 0 || lT == 1 || (ptSet == kPointUninitialized && cT != 0 && cT != 1)) {
             *pt = fLine.ptAtT(lT);
         } else if (ptSet == kPointUninitialized) {
             *pt = fCubic.ptAtT(cT);
         }
         SkPoint gridPt = pt->asSkPoint();
         if (gridPt == fLine[0].asSkPoint()) {
             *lineT = 0;
         } else if (gridPt == fLine[1].asSkPoint()) {
             *lineT = 1;
         }
         if (gridPt == fCubic[0].asSkPoint() && approximately_equal(*cubicT, 0)) {
             *cubicT = 0;
         } else if (gridPt == fCubic[3].asSkPoint() && approximately_equal(*cubicT, 1)) {
             *cubicT = 1;
         }
         return true;
     }
 private:
     const SkDCubic& fCubic;
     const SkDLine& fLine;
     SkIntersections* fIntersections;
     bool fAllowNear;
 };
 int SkIntersections::horizontal(const SkDCubic& cubic, double left, double right, double y,
         bool flipped) {
     SkDLine line = {{{ left, y }, { right, y }}};
     LineCubicIntersections c(cubic, line, this);
     return c.horizontalIntersect(y, left, right, flipped);
 }
 int SkIntersections::vertical(const SkDCubic& cubic, double top, double bottom, double x,
         bool flipped) {
     SkDLine line = {{{ x, top }, { x, bottom }}};
     LineCubicIntersections c(cubic, line, this);
     return c.verticalIntersect(x, top, bottom, flipped);
 }
 int SkIntersections::intersect(const SkDCubic& cubic, const SkDLine& line) {
     LineCubicIntersections c(cubic, line, this);
     c.allowNear(fAllowNear);
     return c.intersect();
 }
 int SkIntersections::intersectRay(const SkDCubic& cubic, const SkDLine& line) {
     LineCubicIntersections c(cubic, line, this);
     fUsed = c.intersectRay(fT[0]);
     for (int index = 0; index < fUsed; ++index) {
         fPt[index] = cubic.ptAtT(fT[0][index]);
     }
     return fUsed;
 }

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

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