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

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

gfx/skia/trunk/src/pathops/SkDQuadIntersection.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.

 // Another approach is to start with the implicit form of one curve and solve
 // (seek implicit coefficients in QuadraticParameter.cpp
 // by substituting in the parametric form of the other.
 // The downside of this approach is that early rejects are difficult to come by.
 // http://planetmath.org/encyclopedia/GaloisTheoreticDerivationOfTheQuarticFormula.html#step
 #include "SkDQuadImplicit.h"
 #include "SkIntersections.h"
 #include "SkPathOpsLine.h"
 #include "SkQuarticRoot.h"
 #include "SkTArray.h"
 #include "SkTSort.h"
 /* given the implicit form 0 = Ax^2 + Bxy + Cy^2 + Dx + Ey + F
  * and given x = at^2 + bt + c  (the parameterized form)
  *           y = dt^2 + et + f
  * then
  * 0 = A(at^2+bt+c)(at^2+bt+c)+B(at^2+bt+c)(dt^2+et+f)+C(dt^2+et+f)(dt^2+et+f)+D(at^2+bt+c)+E(dt^2+et+f)+F
  */
 static int findRoots(const SkDQuadImplicit& i, const SkDQuad& quad, double roots[4],
         bool oneHint, bool flip, int firstCubicRoot) {
     SkDQuad flipped;
     const SkDQuad& q = flip ? (flipped = quad.flip()) : quad;
     double a, b, c;
     SkDQuad::SetABC(&q[0].fX, &a, &b, &c);
     double d, e, f;
     SkDQuad::SetABC(&q[0].fY, &d, &e, &f);
     const double t4 =     i.x2() *  a * a
                     +     i.xy() *  a * d
                     +     i.y2() *  d * d;
     const double t3 = 2 * i.x2() *  a * b
                     +     i.xy() * (a * e +     b * d)
                     + 2 * i.y2() *  d * e;
     const double t2 =     i.x2() * (b * b + 2 * a * c)
                     +     i.xy() * (c * d +     b * e + a * f)
                     +     i.y2() * (e * e + 2 * d * f)
                     +     i.x()  *  a
                     +     i.y()  *  d;
     const double t1 = 2 * i.x2() *  b * c
                     +     i.xy() * (c * e + b * f)
                     + 2 * i.y2() *  e * f
                     +     i.x()  *  b
                     +     i.y()  *  e;
     const double t0 =     i.x2() *  c * c
                     +     i.xy() *  c * f
                     +     i.y2() *  f * f
                     +     i.x()  *  c
                     +     i.y()  *  f
                     +     i.c();
     int rootCount = SkReducedQuarticRoots(t4, t3, t2, t1, t0, oneHint, roots);
     if (rootCount < 0) {
         rootCount = SkQuarticRootsReal(firstCubicRoot, t4, t3, t2, t1, t0, roots);
     }
     if (flip) {
         for (int index = 0; index < rootCount; ++index) {
             roots[index] = 1 - roots[index];
         }
     }
     return rootCount;
 }
 static int addValidRoots(const double roots[4], const int count, double valid[4]) {
     int result = 0;
     int index;
     for (index = 0; index < count; ++index) {
         if (!approximately_zero_or_more(roots[index]) || !approximately_one_or_less(roots[index])) {
             continue;
         }
         double t = 1 - roots[index];
         if (approximately_less_than_zero(t)) {
             t = 0;
         } else if (approximately_greater_than_one(t)) {
             t = 1;
         }
         valid[result++] = t;
     }
     return result;
 }
 static bool only_end_pts_in_common(const SkDQuad& q1, const SkDQuad& q2) {
 // the idea here is to see at minimum do a quick reject by rotating all points
 // to either side of the line formed by connecting the endpoints
 // if the opposite curves points are on the line or on the other side, the
 // curves at most intersect at the endpoints
     for (int oddMan = 0; oddMan < 3; ++oddMan) {
         const SkDPoint* endPt[2];
         for (int opp = 1; opp < 3; ++opp) {
             int end = oddMan ^ opp;  // choose a value not equal to oddMan
             if (3 == end) {  // and correct so that largest value is 1 or 2
                 end = opp;
             }
             endPt[opp - 1] = &q1[end];
         }
         double origX = endPt[0]->fX;
         double origY = endPt[0]->fY;
         double adj = endPt[1]->fX - origX;
         double opp = endPt[1]->fY - origY;
         double sign = (q1[oddMan].fY - origY) * adj - (q1[oddMan].fX - origX) * opp;
         if (approximately_zero(sign)) {
             goto tryNextHalfPlane;
         }
         for (int n = 0; n < 3; ++n) {
             double test = (q2[n].fY - origY) * adj - (q2[n].fX - origX) * opp;
             if (test * sign > 0 && !precisely_zero(test)) {
                 goto tryNextHalfPlane;
             }
         }
         return true;
 tryNextHalfPlane:
         ;
     }
     return false;
 }
 // returns false if there's more than one intercept or the intercept doesn't match the point
 // returns true if the intercept was successfully added or if the
 // original quads need to be subdivided
 static bool add_intercept(const SkDQuad& q1, const SkDQuad& q2, double tMin, double tMax,
                           SkIntersections* i, bool* subDivide) {
     double tMid = (tMin + tMax) / 2;
     SkDPoint mid = q2.ptAtT(tMid);
     SkDLine line;
     line[0] = line[1] = mid;
     SkDVector dxdy = q2.dxdyAtT(tMid);
     line[0] -= dxdy;
     line[1] += dxdy;
     SkIntersections rootTs;
     rootTs.allowNear(false);
     int roots = rootTs.intersect(q1, line);
     if (roots == 0) {
         if (subDivide) {
             *subDivide = true;
         }
         return true;
     }
     if (roots == 2) {
         return false;
     }
     SkDPoint pt2 = q1.ptAtT(rootTs[0][0]);
     if (!pt2.approximatelyEqual(mid)) {
         return false;
     }
     i->insertSwap(rootTs[0][0], tMid, pt2);
     return true;
 }
 static bool is_linear_inner(const SkDQuad& q1, double t1s, double t1e, const SkDQuad& q2,
                             double t2s, double t2e, SkIntersections* i, bool* subDivide) {
     SkDQuad hull = q1.subDivide(t1s, t1e);
     SkDLine line = {{hull[2], hull[0]}};
     const SkDLine* testLines[] = { &line, (const SkDLine*) &hull[0], (const SkDLine*) &hull[1] };
     const size_t kTestCount = SK_ARRAY_COUNT(testLines);
     SkSTArray<kTestCount * 2, double, true> tsFound;
     for (size_t index = 0; index < kTestCount; ++index) {
         SkIntersections rootTs;
         rootTs.allowNear(false);
         int roots = rootTs.intersect(q2, *testLines[index]);
         for (int idx2 = 0; idx2 < roots; ++idx2) {
             double t = rootTs[0][idx2];
 #ifdef SK_DEBUG
             SkDPoint qPt = q2.ptAtT(t);
             SkDPoint lPt = testLines[index]->ptAtT(rootTs[1][idx2]);
             SkASSERT(qPt.approximatelyPEqual(lPt));
 #endif
             if (approximately_negative(t - t2s) || approximately_positive(t - t2e)) {
                 continue;
             }
             tsFound.push_back(rootTs[0][idx2]);
         }
     }
     int tCount = tsFound.count();
     if (tCount <= 0) {
         return true;
     }
     double tMin, tMax;
     if (tCount == 1) {
         tMin = tMax = tsFound[0];
     } else {
         SkASSERT(tCount > 1);
         SkTQSort<double>(tsFound.begin(), tsFound.end() - 1);
         tMin = tsFound[0];
         tMax = tsFound[tsFound.count() - 1];
     }
     SkDPoint end = q2.ptAtT(t2s);
     bool startInTriangle = hull.pointInHull(end);
     if (startInTriangle) {
         tMin = t2s;
     }
     end = q2.ptAtT(t2e);
     bool endInTriangle = hull.pointInHull(end);
     if (endInTriangle) {
         tMax = t2e;
     }
     int split = 0;
     SkDVector dxy1, dxy2;
     if (tMin != tMax || tCount > 2) {
         dxy2 = q2.dxdyAtT(tMin);
         for (int index = 1; index < tCount; ++index) {
             dxy1 = dxy2;
             dxy2 = q2.dxdyAtT(tsFound[index]);
             double dot = dxy1.dot(dxy2);
             if (dot < 0) {
                 split = index - 1;
                 break;
             }
         }
     }
     if (split == 0) {  // there's one point
         if (add_intercept(q1, q2, tMin, tMax, i, subDivide)) {
             return true;
         }
         i->swap();
         return is_linear_inner(q2, tMin, tMax, q1, t1s, t1e, i, subDivide);
     }
     // At this point, we have two ranges of t values -- treat each separately at the split
     bool result;
     if (add_intercept(q1, q2, tMin, tsFound[split - 1], i, subDivide)) {
         result = true;
     } else {
         i->swap();
         result = is_linear_inner(q2, tMin, tsFound[split - 1], q1, t1s, t1e, i, subDivide);
     }
     if (add_intercept(q1, q2, tsFound[split], tMax, i, subDivide)) {
         result = true;
     } else {
         i->swap();
         result |= is_linear_inner(q2, tsFound[split], tMax, q1, t1s, t1e, i, subDivide);
     }
     return result;
 }
 static double flat_measure(const SkDQuad& q) {
     SkDVector mid = q[1] - q[0];
     SkDVector dxy = q[2] - q[0];
     double length = dxy.length();  // OPTIMIZE: get rid of sqrt
     return fabs(mid.cross(dxy) / length);
 }
 // FIXME ? should this measure both and then use the quad that is the flattest as the line?
 static bool is_linear(const SkDQuad& q1, const SkDQuad& q2, SkIntersections* i) {
     double measure = flat_measure(q1);
     // OPTIMIZE: (get rid of sqrt) use approximately_zero
     if (!approximately_zero_sqrt(measure)) {
         return false;
     }
     return is_linear_inner(q1, 0, 1, q2, 0, 1, i, NULL);
 }
 // FIXME: if flat measure is sufficiently large, then probably the quartic solution failed
 // avoid imprecision incurred with chopAt
 static void relaxed_is_linear(const SkDQuad* q1, double s1, double e1, const SkDQuad* q2,
         double s2, double e2, SkIntersections* i) {
     double m1 = flat_measure(*q1);
     double m2 = flat_measure(*q2);
     i->reset();
     const SkDQuad* rounder, *flatter;
     double sf, midf, ef, sr, er;
     if (m2 < m1) {
         rounder = q1;
         sr = s1;
         er = e1;
         flatter = q2;
         sf = s2;
         midf = (s2 + e2) / 2;
         ef = e2;
     } else {
         rounder = q2;
         sr = s2;
         er = e2;
         flatter = q1;
         sf = s1;
         midf = (s1 + e1) / 2;
         ef = e1;
     }
     bool subDivide = false;
     is_linear_inner(*flatter, sf, ef, *rounder, sr, er, i, &subDivide);
     if (subDivide) {
         relaxed_is_linear(flatter, sf, midf, rounder, sr, er, i);
         relaxed_is_linear(flatter, midf, ef, rounder, sr, er, i);
     }
     if (m2 < m1) {
         i->swapPts();
     }
 }
 // each time through the loop, this computes values it had from the last loop
 // if i == j == 1, the center values are still good
 // otherwise, for i != 1 or j != 1, four of the values are still good
 // and if i == 1 ^ j == 1, an additional value is good
 static bool binary_search(const SkDQuad& quad1, const SkDQuad& quad2, double* t1Seed,
                           double* t2Seed, SkDPoint* pt) {
     double tStep = ROUGH_EPSILON;
     SkDPoint t1[3], t2[3];
     int calcMask = ~0;
     do {
         if (calcMask & (1 << 1)) t1[1] = quad1.ptAtT(*t1Seed);
         if (calcMask & (1 << 4)) t2[1] = quad2.ptAtT(*t2Seed);
         if (t1[1].approximatelyEqual(t2[1])) {
             *pt = t1[1];
     #if ONE_OFF_DEBUG
             SkDebugf("%s t1=%1.9g t2=%1.9g (%1.9g,%1.9g) == (%1.9g,%1.9g)\n", __FUNCTION__,
                     t1Seed, t2Seed, t1[1].fX, t1[1].fY, t2[1].fX, t2[1].fY);
     #endif
             return true;
         }
         if (calcMask & (1 << 0)) t1[0] = quad1.ptAtT(*t1Seed - tStep);
         if (calcMask & (1 << 2)) t1[2] = quad1.ptAtT(*t1Seed + tStep);
         if (calcMask & (1 << 3)) t2[0] = quad2.ptAtT(*t2Seed - tStep);
         if (calcMask & (1 << 5)) t2[2] = quad2.ptAtT(*t2Seed + tStep);
         double dist[3][3];
         // OPTIMIZE: using calcMask value permits skipping some distance calcuations
         //   if prior loop's results are moved to correct slot for reuse
         dist[1][1] = t1[1].distanceSquared(t2[1]);
         int best_i = 1, best_j = 1;
         for (int i = 0; i < 3; ++i) {
             for (int j = 0; j < 3; ++j) {
                 if (i == 1 && j == 1) {
                     continue;
                 }
                 dist[i][j] = t1[i].distanceSquared(t2[j]);
                 if (dist[best_i][best_j] > dist[i][j]) {
                     best_i = i;
                     best_j = j;
                 }
             }
         }
         if (best_i == 1 && best_j == 1) {
             tStep /= 2;
             if (tStep < FLT_EPSILON_HALF) {
                 break;
             }
             calcMask = (1 << 0) | (1 << 2) | (1 << 3) | (1 << 5);
             continue;
         }
         if (best_i == 0) {
             *t1Seed -= tStep;
             t1[2] = t1[1];
             t1[1] = t1[0];
             calcMask = 1 << 0;
         } else if (best_i == 2) {
             *t1Seed += tStep;
             t1[0] = t1[1];
             t1[1] = t1[2];
             calcMask = 1 << 2;
         } else {
             calcMask = 0;
         }
         if (best_j == 0) {
             *t2Seed -= tStep;
             t2[2] = t2[1];
             t2[1] = t2[0];
             calcMask |= 1 << 3;
         } else if (best_j == 2) {
             *t2Seed += tStep;
             t2[0] = t2[1];
             t2[1] = t2[2];
             calcMask |= 1 << 5;
         }
     } while (true);
 #if ONE_OFF_DEBUG
     SkDebugf("%s t1=%1.9g t2=%1.9g (%1.9g,%1.9g) != (%1.9g,%1.9g) %s\n", __FUNCTION__,
         t1Seed, t2Seed, t1[1].fX, t1[1].fY, t1[2].fX, t1[2].fY);
 #endif
     return false;
 }
 static void lookNearEnd(const SkDQuad& q1, const SkDQuad& q2, int testT,
         const SkIntersections& orig, bool swap, SkIntersections* i) {
     if (orig.used() == 1 && orig[!swap][0] == testT) {
         return;
     }
     if (orig.used() == 2 && orig[!swap][1] == testT) {
         return;
     }
     SkDLine tmpLine;
     int testTIndex = testT << 1;
     tmpLine[0] = tmpLine[1] = q2[testTIndex];
     tmpLine[1].fX += q2[1].fY - q2[testTIndex].fY;
     tmpLine[1].fY -= q2[1].fX - q2[testTIndex].fX;
     SkIntersections impTs;
     impTs.intersectRay(q1, tmpLine);
     for (int index = 0; index < impTs.used(); ++index) {
         SkDPoint realPt = impTs.pt(index);
         if (!tmpLine[0].approximatelyEqual(realPt)) {
             continue;
         }
         if (swap) {
             i->insert(testT, impTs[0][index], tmpLine[0]);
         } else {
             i->insert(impTs[0][index], testT, tmpLine[0]);
         }
     }
 }
 int SkIntersections::intersect(const SkDQuad& q1, const SkDQuad& q2) {
     fMax = 4;
     // if the quads share an end point, check to see if they overlap
     for (int i1 = 0; i1 < 3; i1 += 2) {
         for (int i2 = 0; i2 < 3; i2 += 2) {
             if (q1[i1].asSkPoint() == q2[i2].asSkPoint()) {
                 insert(i1 >> 1, i2 >> 1, q1[i1]);
             }
         }
     }
     SkASSERT(fUsed < 3);
     if (only_end_pts_in_common(q1, q2)) {
         return fUsed;
     }
     if (only_end_pts_in_common(q2, q1)) {
         return fUsed;
     }
     // see if either quad is really a line
     // FIXME: figure out why reduce step didn't find this earlier
     if (is_linear(q1, q2, this)) {
         return fUsed;
     }
     SkIntersections swapped;
     swapped.setMax(fMax);
     if (is_linear(q2, q1, &swapped)) {
         swapped.swapPts();
         set(swapped);
         return fUsed;
     }
     SkIntersections copyI(*this);
     lookNearEnd(q1, q2, 0, *this, false, &copyI);
     lookNearEnd(q1, q2, 1, *this, false, &copyI);
     lookNearEnd(q2, q1, 0, *this, true, &copyI);
     lookNearEnd(q2, q1, 1, *this, true, &copyI);
     int innerEqual = 0;
     if (copyI.fUsed >= 2) {
         SkASSERT(copyI.fUsed <= 4);
         double width = copyI[0][1] - copyI[0][0];
         int midEnd = 1;
         for (int index = 2; index < copyI.fUsed; ++index) {
             double testWidth = copyI[0][index] - copyI[0][index - 1];
             if (testWidth <= width) {
                 continue;
             }
             midEnd = index;
         }
         for (int index = 0; index < 2; ++index) {
             double testT = (copyI[0][midEnd] * (index + 1)
                     + copyI[0][midEnd - 1] * (2 - index)) / 3;
             SkDPoint testPt1 = q1.ptAtT(testT);
             testT = (copyI[1][midEnd] * (index + 1) + copyI[1][midEnd - 1] * (2 - index)) / 3;
             SkDPoint testPt2 = q2.ptAtT(testT);
             innerEqual += testPt1.approximatelyEqual(testPt2);
         }
     }
     bool expectCoincident = copyI.fUsed >= 2 && innerEqual == 2;
     if (expectCoincident) {
         reset();
         insertCoincident(copyI[0][0], copyI[1][0], copyI.fPt[0]);
         int last = copyI.fUsed - 1;
         insertCoincident(copyI[0][last], copyI[1][last], copyI.fPt[last]);
         return fUsed;
     }
     SkDQuadImplicit i1(q1);
     SkDQuadImplicit i2(q2);
     int index;
     bool flip1 = q1[2] == q2[0];
     bool flip2 = q1[0] == q2[2];
     bool useCubic = q1[0] == q2[0];
     double roots1[4];
     int rootCount = findRoots(i2, q1, roots1, useCubic, flip1, 0);
     // OPTIMIZATION: could short circuit here if all roots are < 0 or > 1
     double roots1Copy[4];
     int r1Count = addValidRoots(roots1, rootCount, roots1Copy);
     SkDPoint pts1[4];
     for (index = 0; index < r1Count; ++index) {
         pts1[index] = q1.ptAtT(roots1Copy[index]);
     }
     double roots2[4];
     int rootCount2 = findRoots(i1, q2, roots2, useCubic, flip2, 0);
     double roots2Copy[4];
     int r2Count = addValidRoots(roots2, rootCount2, roots2Copy);
     SkDPoint pts2[4];
     for (index = 0; index < r2Count; ++index) {
         pts2[index] = q2.ptAtT(roots2Copy[index]);
     }
     if (r1Count == r2Count && r1Count <= 1) {
         if (r1Count == 1 && used() == 0) {
             if (pts1[0].approximatelyEqual(pts2[0])) {
                 insert(roots1Copy[0], roots2Copy[0], pts1[0]);
             } else if (pts1[0].moreRoughlyEqual(pts2[0])) {
                 // experiment: try to find intersection by chasing t
                 if (binary_search(q1, q2, roots1Copy, roots2Copy, pts1)) {
                     insert(roots1Copy[0], roots2Copy[0], pts1[0]);
                 }
             }
         }
         return fUsed;
     }
     int closest[4];
     double dist[4];
     bool foundSomething = false;
     for (index = 0; index < r1Count; ++index) {
         dist[index] = DBL_MAX;
         closest[index] = -1;
         for (int ndex2 = 0; ndex2 < r2Count; ++ndex2) {
             if (!pts2[ndex2].approximatelyEqual(pts1[index])) {
                 continue;
             }
             double dx = pts2[ndex2].fX - pts1[index].fX;
             double dy = pts2[ndex2].fY - pts1[index].fY;
             double distance = dx * dx + dy * dy;
             if (dist[index] <= distance) {
                 continue;
             }
             for (int outer = 0; outer < index; ++outer) {
                 if (closest[outer] != ndex2) {
                     continue;
                 }
                 if (dist[outer] < distance) {
                     goto next;
                 }
                 closest[outer] = -1;
             }
             dist[index] = distance;
             closest[index] = ndex2;
             foundSomething = true;
         next:
             ;
         }
     }
     if (r1Count && r2Count && !foundSomething) {
         relaxed_is_linear(&q1, 0, 1, &q2, 0, 1, this);
         return fUsed;
     }
     int used = 0;
     do {
         double lowest = DBL_MAX;
         int lowestIndex = -1;
         for (index = 0; index < r1Count; ++index) {
             if (closest[index] < 0) {
                 continue;
             }
             if (roots1Copy[index] < lowest) {
                 lowestIndex = index;
                 lowest = roots1Copy[index];
             }
         }
         if (lowestIndex < 0) {
             break;
         }
         insert(roots1Copy[lowestIndex], roots2Copy[closest[lowestIndex]],
                 pts1[lowestIndex]);
         closest[lowestIndex] = -1;
     } while (++used < r1Count);
     return fUsed;
 }

The Tor Browser / annotate

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

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