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

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

gfx/skia/trunk/src/pathops/SkDQuadLineIntersection.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 "SkPathOpsLine.h"
 #include "SkPathOpsQuad.h"
 /*
 Find the interection of a line and quadratic by solving for valid t values.
 From http://stackoverflow.com/questions/1853637/how-to-find-the-mathematical-function-defining-a-bezier-curve
 "A Bezier curve is a parametric function. A quadratic Bezier curve (i.e. three
 control points) can be expressed as: F(t) = A(1 - t)^2 + B(1 - t)t + Ct^2 where
 A, B and C are points and t goes from zero to one.
 This will give you two equations:
   x = a(1 - t)^2 + b(1 - t)t + ct^2
   y = d(1 - t)^2 + e(1 - t)t + ft^2
 If you add for instance the line equation (y = kx + m) to that, you'll end up
 with three equations and three unknowns (x, y and t)."
 Similar to above, the quadratic is represented as
   x = a(1-t)^2 + 2b(1-t)t + ct^2
   y = d(1-t)^2 + 2e(1-t)t + ft^2
 and the line as
   y = g*x + h
 Using Mathematica, solve for the values of t where the quadratic intersects the
 line:
   (in)  t1 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - x,
                        d*(1 - t)^2 + 2*e*(1 - t)*t  + f*t^2 - g*x - h, x]
   (out) -d + h + 2 d t - 2 e t - d t^2 + 2 e t^2 - f t^2 +
          g  (a - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2)
   (in)  Solve[t1 == 0, t]
   (out) {
     {t -> (-2 d + 2 e +   2 a g - 2 b g    -
       Sqrt[(2 d - 2 e -   2 a g + 2 b g)^2 -
 (-d + 2 e - f + a g - 2 b g    + c g) (-d + a g + h)]) /
          (2 (-d + 2 e - f + a g - 2 b g    + c g))
          },
     {t -> (-2 d + 2 e +   2 a g - 2 b g    +
       Sqrt[(2 d - 2 e -   2 a g + 2 b g)^2 -
 (-d + 2 e - f + a g - 2 b g    + c g) (-d + a g + h)]) /
          (2 (-d + 2 e - f + a g - 2 b g    + c g))
          }
         }
 Using the results above (when the line tends towards horizontal)
        A =   (-(d - 2*e + f) + g*(a - 2*b + c)     )
        B = 2*( (d -   e    ) - g*(a -   b    )     )
        C =   (-(d          ) + g*(a          ) + h )
 If g goes to infinity, we can rewrite the line in terms of x.
   x = g'*y + h'
 And solve accordingly in Mathematica:
   (in)  t2 = Resultant[a*(1 - t)^2 + 2*b*(1 - t)*t + c*t^2 - g'*y - h',
                        d*(1 - t)^2 + 2*e*(1 - t)*t  + f*t^2 - y, y]
   (out)  a - h' - 2 a t + 2 b t + a t^2 - 2 b t^2 + c t^2 -
          g'  (d - 2 d t + 2 e t + d t^2 - 2 e t^2 + f t^2)
   (in)  Solve[t2 == 0, t]
   (out) {
     {t -> (2 a - 2 b -   2 d g' + 2 e g'    -
     Sqrt[(-2 a + 2 b +   2 d g' - 2 e g')^2 -
 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')]) /
          (2 (a - 2 b + c - d g' + 2 e g' - f g'))
          },
     {t -> (2 a - 2 b -   2 d g' + 2 e g'    +
     Sqrt[(-2 a + 2 b +   2 d g' - 2 e g')^2 -
 (a - 2 b + c - d g' + 2 e g' - f g') (a - d g' - h')])/
          (2 (a - 2 b + c - d g' + 2 e g' - f g'))
          }
         }
 Thus, if the slope of the line tends towards vertical, we use:
        A =   ( (a - 2*b + c) - g'*(d  - 2*e + f)      )
        B = 2*(-(a -   b    ) + g'*(d  -   e    )      )
        C =   ( (a          ) - g'*(d           ) - h' )
  */
 class LineQuadraticIntersections {
 public:
     enum PinTPoint {
         kPointUninitialized,
         kPointInitialized
     };
     LineQuadraticIntersections(const SkDQuad& q, const SkDLine& l, SkIntersections* i)
         : fQuad(q)
         , fLine(l)
         , fIntersections(i)
         , fAllowNear(true) {
         i->setMax(2);
     }
     void allowNear(bool allow) {
         fAllowNear = allow;
     }
     int intersectRay(double roots[2]) {
     /*
         solve by rotating line+quad so line is horizontal, then finding the roots
         set up matrix to rotate quad to x-axis
         |cos(a) -sin(a)|
         |sin(a)  cos(a)|
         note that cos(a) = A(djacent) / Hypoteneuse
                   sin(a) = O(pposite) / Hypoteneuse
         since we are computing Ts, we can ignore hypoteneuse, the scale factor:
         |  A     -O    |
         |  O      A    |
         A = line[1].fX - line[0].fX (adjacent side of the right triangle)
         O = line[1].fY - line[0].fY (opposite side of the right triangle)
         for each of the three points (e.g. n = 0 to 2)
         quad[n].fY' = (quad[n].fY - line[0].fY) * A - (quad[n].fX - line[0].fX) * O
     */
         double adj = fLine[1].fX - fLine[0].fX;
         double opp = fLine[1].fY - fLine[0].fY;
         double r[3];
         for (int n = 0; n < 3; ++n) {
             r[n] = (fQuad[n].fY - fLine[0].fY) * adj - (fQuad[n].fX - fLine[0].fX) * opp;
         }
         double A = r[2];
         double B = r[1];
         double C = r[0];
         A += C - 2 * B;  // A = a - 2*b + c
         B -= C;  // B = -(b - c)
         return SkDQuad::RootsValidT(A, 2 * B, C, roots);
     }
     int intersect() {
         addExactEndPoints();
         if (fAllowNear) {
             addNearEndPoints();
         }
         if (fIntersections->used() == 2) {
             // FIXME : need sharable code that turns spans into coincident if middle point is on
         } else {
             double rootVals[2];
             int roots = intersectRay(rootVals);
             for (int index = 0; index < roots; ++index) {
                 double quadT = rootVals[index];
                 double lineT = findLineT(quadT);
                 SkDPoint pt;
                 if (pinTs(&quadT, &lineT, &pt, kPointUninitialized)) {
                     fIntersections->insert(quadT, lineT, pt);
                 }
             }
         }
         return fIntersections->used();
     }
     int horizontalIntersect(double axisIntercept, double roots[2]) {
         double D = fQuad[2].fY;  // f
         double E = fQuad[1].fY;  // e
         double F = fQuad[0].fY;  // d
         D += F - 2 * E;         // D = d - 2*e + f
         E -= F;                 // E = -(d - e)
         F -= axisIntercept;
         return SkDQuad::RootsValidT(D, 2 * E, F, roots);
     }
     int horizontalIntersect(double axisIntercept, double left, double right, bool flipped) {
         addExactHorizontalEndPoints(left, right, axisIntercept);
         if (fAllowNear) {
             addNearHorizontalEndPoints(left, right, axisIntercept);
         }
         double rootVals[2];
         int roots = horizontalIntersect(axisIntercept, rootVals);
         for (int index = 0; index < roots; ++index) {
             double quadT = rootVals[index];
             SkDPoint pt = fQuad.ptAtT(quadT);
             double lineT = (pt.fX - left) / (right - left);
             if (pinTs(&quadT, &lineT, &pt, kPointInitialized)) {
                 fIntersections->insert(quadT, lineT, pt);
             }
         }
         if (flipped) {
             fIntersections->flip();
         }
         return fIntersections->used();
     }
     int verticalIntersect(double axisIntercept, double roots[2]) {
         double D = fQuad[2].fX;  // f
         double E = fQuad[1].fX;  // e
         double F = fQuad[0].fX;  // d
         D += F - 2 * E;         // D = d - 2*e + f
         E -= F;                 // E = -(d - e)
         F -= axisIntercept;
         return SkDQuad::RootsValidT(D, 2 * E, F, roots);
     }
     int verticalIntersect(double axisIntercept, double top, double bottom, bool flipped) {
         addExactVerticalEndPoints(top, bottom, axisIntercept);
         if (fAllowNear) {
             addNearVerticalEndPoints(top, bottom, axisIntercept);
         }
         double rootVals[2];
         int roots = verticalIntersect(axisIntercept, rootVals);
         for (int index = 0; index < roots; ++index) {
             double quadT = rootVals[index];
             SkDPoint pt = fQuad.ptAtT(quadT);
             double lineT = (pt.fY - top) / (bottom - top);
             if (pinTs(&quadT, &lineT, &pt, kPointInitialized)) {
                 fIntersections->insert(quadT, lineT, pt);
             }
         }
         if (flipped) {
             fIntersections->flip();
         }
         return fIntersections->used();
     }
 protected:
     // add endpoints first to get zero and one t values exactly
     void addExactEndPoints() {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
             double lineT = fLine.exactPoint(fQuad[qIndex]);
             if (lineT < 0) {
                 continue;
             }
             double quadT = (double) (qIndex >> 1);
             fIntersections->insert(quadT, lineT, fQuad[qIndex]);
         }
     }
     void addNearEndPoints() {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
             double quadT = (double) (qIndex >> 1);
             if (fIntersections->hasT(quadT)) {
                 continue;
             }
             double lineT = fLine.nearPoint(fQuad[qIndex]);
             if (lineT < 0) {
                 continue;
             }
             fIntersections->insert(quadT, lineT, fQuad[qIndex]);
         }
         // FIXME: see if line end is nearly on quad
     }
     void addExactHorizontalEndPoints(double left, double right, double y) {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
             double lineT = SkDLine::ExactPointH(fQuad[qIndex], left, right, y);
             if (lineT < 0) {
                 continue;
             }
             double quadT = (double) (qIndex >> 1);
             fIntersections->insert(quadT, lineT, fQuad[qIndex]);
         }
     }
     void addNearHorizontalEndPoints(double left, double right, double y) {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
             double quadT = (double) (qIndex >> 1);
             if (fIntersections->hasT(quadT)) {
                 continue;
             }
             double lineT = SkDLine::NearPointH(fQuad[qIndex], left, right, y);
             if (lineT < 0) {
                 continue;
             }
             fIntersections->insert(quadT, lineT, fQuad[qIndex]);
         }
         // FIXME: see if line end is nearly on quad
     }
     void addExactVerticalEndPoints(double top, double bottom, double x) {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
             double lineT = SkDLine::ExactPointV(fQuad[qIndex], top, bottom, x);
             if (lineT < 0) {
                 continue;
             }
             double quadT = (double) (qIndex >> 1);
             fIntersections->insert(quadT, lineT, fQuad[qIndex]);
         }
     }
     void addNearVerticalEndPoints(double top, double bottom, double x) {
         for (int qIndex = 0; qIndex < 3; qIndex += 2) {
             double quadT = (double) (qIndex >> 1);
             if (fIntersections->hasT(quadT)) {
                 continue;
             }
             double lineT = SkDLine::NearPointV(fQuad[qIndex], top, bottom, x);
             if (lineT < 0) {
                 continue;
             }
             fIntersections->insert(quadT, lineT, fQuad[qIndex]);
         }
         // FIXME: see if line end is nearly on quad
     }
     double findLineT(double t) {
         SkDPoint xy = fQuad.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* quadT, double* lineT, SkDPoint* pt, PinTPoint ptSet) {
         if (!approximately_one_or_less(*lineT)) {
             return false;
         }
         if (!approximately_zero_or_more(*lineT)) {
             return false;
         }
         double qT = *quadT = SkPinT(*quadT);
         double lT = *lineT = SkPinT(*lineT);
         if (lT == 0 || lT == 1 || (ptSet == kPointUninitialized && qT != 0 && qT != 1)) {
             *pt = fLine.ptAtT(lT);
         } else if (ptSet == kPointUninitialized) {
             *pt = fQuad.ptAtT(qT);
         }
         SkPoint gridPt = pt->asSkPoint();
         if (gridPt == fLine[0].asSkPoint()) {
             *lineT = 0;
         } else if (gridPt == fLine[1].asSkPoint()) {
             *lineT = 1;
         }
         if (gridPt == fQuad[0].asSkPoint()) {
             *quadT = 0;
         } else if (gridPt == fQuad[2].asSkPoint()) {
             *quadT = 1;
         }
         return true;
     }
 private:
     const SkDQuad& fQuad;
     const SkDLine& fLine;
     SkIntersections* fIntersections;
     bool fAllowNear;
 };
 // utility for pairs of coincident quads
 static double horizontalIntersect(const SkDQuad& quad, const SkDPoint& pt) {
     LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)),
             static_cast<SkIntersections*>(0));
     double rootVals[2];
     int roots = q.horizontalIntersect(pt.fY, rootVals);
     for (int index = 0; index < roots; ++index) {
         double t = rootVals[index];
         SkDPoint qPt = quad.ptAtT(t);
         if (AlmostEqualUlps(qPt.fX, pt.fX)) {
             return t;
         }
     }
     return -1;
 }
 static double verticalIntersect(const SkDQuad& quad, const SkDPoint& pt) {
     LineQuadraticIntersections q(quad, *(static_cast<SkDLine*>(0)),
             static_cast<SkIntersections*>(0));
     double rootVals[2];
     int roots = q.verticalIntersect(pt.fX, rootVals);
     for (int index = 0; index < roots; ++index) {
         double t = rootVals[index];
         SkDPoint qPt = quad.ptAtT(t);
         if (AlmostEqualUlps(qPt.fY, pt.fY)) {
             return t;
         }
     }
     return -1;
 }
 double SkIntersections::Axial(const SkDQuad& q1, const SkDPoint& p, bool vertical) {
     if (vertical) {
         return verticalIntersect(q1, p);
     }
     return horizontalIntersect(q1, p);
 }
 int SkIntersections::horizontal(const SkDQuad& quad, double left, double right, double y,
                                 bool flipped) {
     SkDLine line = {{{ left, y }, { right, y }}};
     LineQuadraticIntersections q(quad, line, this);
     return q.horizontalIntersect(y, left, right, flipped);
 }
 int SkIntersections::vertical(const SkDQuad& quad, double top, double bottom, double x,
                               bool flipped) {
     SkDLine line = {{{ x, top }, { x, bottom }}};
     LineQuadraticIntersections q(quad, line, this);
     return q.verticalIntersect(x, top, bottom, flipped);
 }
 int SkIntersections::intersect(const SkDQuad& quad, const SkDLine& line) {
     LineQuadraticIntersections q(quad, line, this);
     q.allowNear(fAllowNear);
     return q.intersect();
 }
 int SkIntersections::intersectRay(const SkDQuad& quad, const SkDLine& line) {
     LineQuadraticIntersections q(quad, line, this);
     fUsed = q.intersectRay(fT[0]);
     for (int index = 0; index < fUsed; ++index) {
         fPt[index] = quad.ptAtT(fT[0][index]);
     }
     return fUsed;
 }

The Tor Browser / annotate

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

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