The Tor Browser: gfx/skia/trunk/src/pathops/SkDCubicIntersection.cpp@b8a032363ba2 (annotated)

gfx/skia/trunk/src/pathops/SkDCubicIntersection.cpp@b8a032363ba2 (annotated)

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

Thu, 22 Jan 2015 13:21:57 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Thu, 22 Jan 2015 13:21:57 +0100
branch: TOR_BUG_9701
changeset 15: b8a032363ba2
permissions: -rw-r--r--

Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6

 /*
  * 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"
 #include "SkPathOpsPoint.h"
 #include "SkPathOpsQuad.h"
 #include "SkPathOpsRect.h"
 #include "SkReduceOrder.h"
 #include "SkTSort.h"
 #if ONE_OFF_DEBUG
 static const double tLimits1[2][2] = {{0.3, 0.4}, {0.8, 0.9}};
 static const double tLimits2[2][2] = {{-0.8, -0.9}, {-0.8, -0.9}};
 #endif
 #define DEBUG_QUAD_PART ONE_OFF_DEBUG && 1
 #define DEBUG_QUAD_PART_SHOW_SIMPLE DEBUG_QUAD_PART && 0
 #define SWAP_TOP_DEBUG 0
 static const int kCubicToQuadSubdivisionDepth = 8; // slots reserved for cubic to quads subdivision
 static int quadPart(const SkDCubic& cubic, double tStart, double tEnd, SkReduceOrder* reducer) {
     SkDCubic part = cubic.subDivide(tStart, tEnd);
     SkDQuad quad = part.toQuad();
     // FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an
     // extremely shallow quadratic?
     int order = reducer->reduce(quad);
 #if DEBUG_QUAD_PART
     SkDebugf("%s cubic=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
             " t=(%1.9g,%1.9g)\n", __FUNCTION__, cubic[0].fX, cubic[0].fY,
             cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY,
             cubic[3].fX, cubic[3].fY, tStart, tEnd);
     SkDebugf("  {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n"
              "  {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
             part[0].fX, part[0].fY, part[1].fX, part[1].fY, part[2].fX, part[2].fY,
             part[3].fX, part[3].fY, quad[0].fX, quad[0].fY,
             quad[1].fX, quad[1].fY, quad[2].fX, quad[2].fY);
 #if DEBUG_QUAD_PART_SHOW_SIMPLE
     SkDebugf("%s simple=(%1.9g,%1.9g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY);
     if (order > 1) {
         SkDebugf(" %1.9g,%1.9g", reducer->fQuad[1].fX, reducer->fQuad[1].fY);
     }
     if (order > 2) {
         SkDebugf(" %1.9g,%1.9g", reducer->fQuad[2].fX, reducer->fQuad[2].fY);
     }
     SkDebugf(")\n");
     SkASSERT(order < 4 && order > 0);
 #endif
 #endif
     return order;
 }
 static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2,
         int order2, SkIntersections& i) {
     if (order1 == 3 && order2 == 3) {
         i.intersect(simple1, simple2);
     } else if (order1 <= 2 && order2 <= 2) {
         i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2);
     } else if (order1 == 3 && order2 <= 2) {
         i.intersect(simple1, (const SkDLine&) simple2);
     } else {
         SkASSERT(order1 <= 2 && order2 == 3);
         i.intersect(simple2, (const SkDLine&) simple1);
         i.swapPts();
     }
 }
 // this flavor centers potential intersections recursively. In contrast, '2' may inadvertently
 // chase intersections near quadratic ends, requiring odd hacks to find them.
 static void intersect(const SkDCubic& cubic1, double t1s, double t1e, const SkDCubic& cubic2,
         double t2s, double t2e, double precisionScale, SkIntersections& i) {
     i.upDepth();
     SkDCubic c1 = cubic1.subDivide(t1s, t1e);
     SkDCubic c2 = cubic2.subDivide(t2s, t2e);
     SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts1;
     // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection)
     c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1);
     SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts2;
     c2.toQuadraticTs(c2.calcPrecision() * precisionScale, &ts2);
     double t1Start = t1s;
     int ts1Count = ts1.count();
     for (int i1 = 0; i1 <= ts1Count; ++i1) {
         const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1;
         const double t1 = t1s + (t1e - t1s) * tEnd1;
         SkReduceOrder s1;
         int o1 = quadPart(cubic1, t1Start, t1, &s1);
         double t2Start = t2s;
         int ts2Count = ts2.count();
         for (int i2 = 0; i2 <= ts2Count; ++i2) {
             const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1;
             const double t2 = t2s + (t2e - t2s) * tEnd2;
             if (&cubic1 == &cubic2 && t1Start >= t2Start) {
                 t2Start = t2;
                 continue;
             }
             SkReduceOrder s2;
             int o2 = quadPart(cubic2, t2Start, t2, &s2);
         #if ONE_OFF_DEBUG
             char tab[] = "                  ";
             if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1
                     && tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) {
                 SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab,
                         __FUNCTION__, t1Start, t1, t2Start, t2);
                 SkIntersections xlocals;
                 xlocals.allowNear(false);
                 intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals);
                 SkDebugf(" xlocals.fUsed=%d\n", xlocals.used());
             }
         #endif
             SkIntersections locals;
             locals.allowNear(false);
             intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals);
             int tCount = locals.used();
             for (int tIdx = 0; tIdx < tCount; ++tIdx) {
                 double to1 = t1Start + (t1 - t1Start) * locals[0][tIdx];
                 double to2 = t2Start + (t2 - t2Start) * locals[1][tIdx];
     // if the computed t is not sufficiently precise, iterate
                 SkDPoint p1 = cubic1.ptAtT(to1);
                 SkDPoint p2 = cubic2.ptAtT(to2);
                 if (p1.approximatelyEqual(p2)) {
     // FIXME: local edge may be coincident -- experiment with not propagating coincidence to caller
 //                    SkASSERT(!locals.isCoincident(tIdx));
                     if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) {
                         if (i.swapped()) {  //  FIXME: insert should respect swap
                             i.insert(to2, to1, p1);
                         } else {
                             i.insert(to1, to2, p1);
                         }
                     }
                 } else {
                     double offset = precisionScale / 16;  // FIME: const is arbitrary: test, refine
                     double c1Bottom = tIdx == 0 ? 0 :
                             (t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2;
                     double c1Min = SkTMax(c1Bottom, to1 - offset);
                     double c1Top = tIdx == tCount - 1 ? 1 :
                             (t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2;
                     double c1Max = SkTMin(c1Top, to1 + offset);
                     double c2Min = SkTMax(0., to2 - offset);
                     double c2Max = SkTMin(1., to2 + offset);
                 #if ONE_OFF_DEBUG
                     SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
                             __FUNCTION__,
                             c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
                          && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
                             to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
                          && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
                             c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
                          && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
                             to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
                          && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
                     SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
                             " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
                             i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1.,
                             to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
                     SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
                             " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
                             c1Max, c2Min, c2Max);
                 #endif
                     intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                 #if ONE_OFF_DEBUG
                     SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
                             i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
                 #endif
                     if (tCount > 1) {
                         c1Min = SkTMax(0., to1 - offset);
                         c1Max = SkTMin(1., to1 + offset);
                         double c2Bottom = tIdx == 0 ? to2 :
                                 (t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2;
                         double c2Top = tIdx == tCount - 1 ? to2 :
                                 (t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2;
                         if (c2Bottom > c2Top) {
                             SkTSwap(c2Bottom, c2Top);
                         }
                         if (c2Bottom == to2) {
                             c2Bottom = 0;
                         }
                         if (c2Top == to2) {
                             c2Top = 1;
                         }
                         c2Min = SkTMax(c2Bottom, to2 - offset);
                         c2Max = SkTMin(c2Top, to2 + offset);
                     #if ONE_OFF_DEBUG
                         SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
                             __FUNCTION__,
                             c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
                          && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
                             to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
                          && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
                             c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
                          && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
                             to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
                          && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
                         SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
                                 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
                                 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
                                 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
                         SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
                                 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
                                 c1Max, c2Min, c2Max);
                     #endif
                         intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                 #if ONE_OFF_DEBUG
                     SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
                             i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
                 #endif
                         c1Min = SkTMax(c1Bottom, to1 - offset);
                         c1Max = SkTMin(c1Top, to1 + offset);
                     #if ONE_OFF_DEBUG
                         SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
                         __FUNCTION__,
                             c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
                          && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
                             to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
                          && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
                             c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
                          && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
                             to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
                          && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
                         SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
                                 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
                                 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
                                 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
                         SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
                                 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
                                 c1Max, c2Min, c2Max);
                     #endif
                         intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                 #if ONE_OFF_DEBUG
                     SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
                             i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
                 #endif
                     }
           //          intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
                     // FIXME: if no intersection is found, either quadratics intersected where
                     // cubics did not, or the intersection was missed. In the former case, expect
                     // the quadratics to be nearly parallel at the point of intersection, and check
                     // for that.
                 }
             }
             t2Start = t2;
         }
         t1Start = t1;
     }
     i.downDepth();
 }
     // if two ends intersect, check middle for coincidence
 bool SkIntersections::cubicCheckCoincidence(const SkDCubic& c1, const SkDCubic& c2) {
     if (fUsed < 2) {
         return false;
     }
     int last = fUsed - 1;
     double tRange1 = fT[0][last] - fT[0][0];
     double tRange2 = fT[1][last] - fT[1][0];
     for (int index = 1; index < 5; ++index) {
         double testT1 = fT[0][0] + tRange1 * index / 5;
         double testT2 = fT[1][0] + tRange2 * index / 5;
         SkDPoint testPt1 = c1.ptAtT(testT1);
         SkDPoint testPt2 = c2.ptAtT(testT2);
         if (!testPt1.approximatelyEqual(testPt2)) {
             return false;
         }
     }
     if (fUsed > 2) {
         fPt[1] = fPt[last];
         fT[0][1] = fT[0][last];
         fT[1][1] = fT[1][last];
         fUsed = 2;
     }
     fIsCoincident[0] = fIsCoincident[1] = 0x03;
     return true;
 }
 #define LINE_FRACTION 0.1
 // intersect the end of the cubic with the other. Try lines from the end to control and opposite
 // end to determine range of t on opposite cubic.
 bool SkIntersections::cubicExactEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2) {
     int t1Index = start ? 0 : 3;
     double testT = (double) !start;
     bool swap = swapped();
     // quad/quad at this point checks to see if exact matches have already been found
     // cubic/cubic can't reject so easily since cubics can intersect same point more than once
     SkDLine tmpLine;
     tmpLine[0] = tmpLine[1] = cubic2[t1Index];
     tmpLine[1].fX += cubic2[2 - start].fY - cubic2[t1Index].fY;
     tmpLine[1].fY -= cubic2[2 - start].fX - cubic2[t1Index].fX;
     SkIntersections impTs;
     impTs.allowNear(false);
     impTs.intersectRay(cubic1, tmpLine);
     for (int index = 0; index < impTs.used(); ++index) {
         SkDPoint realPt = impTs.pt(index);
         if (!tmpLine[0].approximatelyEqual(realPt)) {
             continue;
         }
         if (swap) {
             insert(testT, impTs[0][index], tmpLine[0]);
         } else {
             insert(impTs[0][index], testT, tmpLine[0]);
         }
         return true;
     }
     return false;
 }
 void SkIntersections::cubicNearEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2,
                          const SkDRect& bounds2) {
     SkDLine line;
     int t1Index = start ? 0 : 3;
     double testT = (double) !start;
    // don't bother if the two cubics are connnected
     static const int kPointsInCubic = 4; // FIXME: move to DCubic, replace '4' with this
     static const int kMaxLineCubicIntersections = 3;
     SkSTArray<(kMaxLineCubicIntersections - 1) * kMaxLineCubicIntersections, double, true> tVals;
     line[0] = cubic1[t1Index];
     // this variant looks for intersections with the end point and lines parallel to other points
     for (int index = 0; index < kPointsInCubic; ++index) {
         if (index == t1Index) {
             continue;
         }
         SkDVector dxy1 = cubic1[index] - line[0];
         dxy1 /= SkDCubic::gPrecisionUnit;
         line[1] = line[0] + dxy1;
         SkDRect lineBounds;
         lineBounds.setBounds(line);
         if (!bounds2.intersects(&lineBounds)) {
             continue;
         }
         SkIntersections local;
         if (!local.intersect(cubic2, line)) {
             continue;
         }
         for (int idx2 = 0; idx2 < local.used(); ++idx2) {
             double foundT = local[0][idx2];
             if (approximately_less_than_zero(foundT)
                     || approximately_greater_than_one(foundT)) {
                 continue;
             }
             if (local.pt(idx2).approximatelyEqual(line[0])) {
                 if (swapped()) {  // FIXME: insert should respect swap
                     insert(foundT, testT, line[0]);
                 } else {
                     insert(testT, foundT, line[0]);
                 }
             } else {
                 tVals.push_back(foundT);
             }
         }
     }
     if (tVals.count() == 0) {
         return;
     }
     SkTQSort<double>(tVals.begin(), tVals.end() - 1);
     double tMin1 = start ? 0 : 1 - LINE_FRACTION;
     double tMax1 = start ? LINE_FRACTION : 1;
     int tIdx = 0;
     do {
         int tLast = tIdx;
         while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) {
             ++tLast;
         }
         double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0);
         double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0);
         int lastUsed = used();
         ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
         if (lastUsed == used()) {
             tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0);
             tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0);
             ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
         }
         tIdx = tLast + 1;
     } while (tIdx < tVals.count());
     return;
 }
 const double CLOSE_ENOUGH = 0.001;
 static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
     if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) {
         return false;
     }
     pt = cubic.ptAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2);
     return true;
 }
 static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
     int last = i.used() - 1;
     if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) {
         return false;
     }
     pt = cubic.ptAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2);
     return true;
 }
 static bool only_end_pts_in_common(const SkDCubic& c1, const SkDCubic& c2) {
 // 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 < 4; ++oddMan) {
         const SkDPoint* endPt[3];
         for (int opp = 1; opp < 4; ++opp) {
             int end = oddMan ^ opp;  // choose a value not equal to oddMan
             endPt[opp - 1] = &c1[end];
         }
         for (int triTest = 0; triTest < 3; ++triTest) {
             double origX = endPt[triTest]->fX;
             double origY = endPt[triTest]->fY;
             int oppTest = triTest + 1;
             if (3 == oppTest) {
                 oppTest = 0;
             }
             double adj = endPt[oppTest]->fX - origX;
             double opp = endPt[oppTest]->fY - origY;
             double sign = (c1[oddMan].fY - origY) * adj - (c1[oddMan].fX - origX) * opp;
             if (approximately_zero(sign)) {
                 goto tryNextHalfPlane;
             }
             for (int n = 0; n < 4; ++n) {
                 double test = (c2[n].fY - origY) * adj - (c2[n].fX - origX) * opp;
                 if (test * sign > 0 && !precisely_zero(test)) {
                     goto tryNextHalfPlane;
                 }
             }
         }
         return true;
 tryNextHalfPlane:
         ;
     }
     return false;
 }
 int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) {
     if (fMax == 0) {
         fMax = 9;
     }
     bool selfIntersect = &c1 == &c2;
     if (selfIntersect) {
         if (c1[0].approximatelyEqual(c1[3])) {
             insert(0, 1, c1[0]);
             return fUsed;
         }
     } else {
         // OPTIMIZATION: set exact end bits here to avoid cubic exact end later
         for (int i1 = 0; i1 < 4; i1 += 3) {
             for (int i2 = 0; i2 < 4; i2 += 3) {
                 if (c1[i1].approximatelyEqual(c2[i2])) {
                     insert(i1 >> 1, i2 >> 1, c1[i1]);
                 }
             }
         }
     }
     SkASSERT(fUsed < 4);
     if (!selfIntersect) {
         if (only_end_pts_in_common(c1, c2)) {
             return fUsed;
         }
         if (only_end_pts_in_common(c2, c1)) {
             return fUsed;
         }
     }
     // quad/quad does linear test here -- cubic does not
     // cubics which are really lines should have been detected in reduce step earlier
     int exactEndBits = 0;
     if (selfIntersect) {
         if (fUsed) {
             return fUsed;
         }
     } else {
         exactEndBits |= cubicExactEnd(c1, false, c2) << 0;
         exactEndBits |= cubicExactEnd(c1, true, c2) << 1;
         swap();
         exactEndBits |= cubicExactEnd(c2, false, c1) << 2;
         exactEndBits |= cubicExactEnd(c2, true, c1) << 3;
         swap();
     }
     if (cubicCheckCoincidence(c1, c2)) {
         SkASSERT(!selfIntersect);
         return fUsed;
     }
     // FIXME: pass in cached bounds from caller
     SkDRect c2Bounds;
     c2Bounds.setBounds(c2);
     if (!(exactEndBits & 4)) {
         cubicNearEnd(c1, false, c2, c2Bounds);
     }
     if (!(exactEndBits & 8)) {
         cubicNearEnd(c1, true, c2, c2Bounds);
     }
     if (!selfIntersect) {
         SkDRect c1Bounds;
         c1Bounds.setBounds(c1);  // OPTIMIZE use setRawBounds ?
         swap();
         if (!(exactEndBits & 1)) {
             cubicNearEnd(c2, false, c1, c1Bounds);
         }
         if (!(exactEndBits & 2)) {
             cubicNearEnd(c2, true, c1, c1Bounds);
         }
         swap();
     }
     if (cubicCheckCoincidence(c1, c2)) {
         SkASSERT(!selfIntersect);
         return fUsed;
     }
     SkIntersections i;
     i.fAllowNear = false;
     i.fMax = 9;
     ::intersect(c1, 0, 1, c2, 0, 1, 1, i);
     int compCount = i.used();
     if (compCount) {
         int exactCount = used();
         if (exactCount == 0) {
             set(i);
         } else {
             // at least one is exact or near, and at least one was computed. Eliminate duplicates
             for (int exIdx = 0; exIdx < exactCount; ++exIdx) {
                 for (int cpIdx = 0; cpIdx < compCount; ) {
                     if (fT[0][0] == i[0][0] && fT[1][0] == i[1][0]) {
                         i.removeOne(cpIdx);
                         --compCount;
                         continue;
                     }
                     double tAvg = (fT[0][exIdx] + i[0][cpIdx]) / 2;
                     SkDPoint pt = c1.ptAtT(tAvg);
                     if (!pt.approximatelyEqual(fPt[exIdx])) {
                         ++cpIdx;
                         continue;
                     }
                     tAvg = (fT[1][exIdx] + i[1][cpIdx]) / 2;
                     pt = c2.ptAtT(tAvg);
                     if (!pt.approximatelyEqual(fPt[exIdx])) {
                         ++cpIdx;
                         continue;
                     }
                     i.removeOne(cpIdx);
                     --compCount;
                 }
             }
             // if mid t evaluates to nearly the same point, skip the t
             for (int cpIdx = 0; cpIdx < compCount - 1; ) {
                 double tAvg = (fT[0][cpIdx] + i[0][cpIdx + 1]) / 2;
                 SkDPoint pt = c1.ptAtT(tAvg);
                 if (!pt.approximatelyEqual(fPt[cpIdx])) {
                     ++cpIdx;
                     continue;
                 }
                 tAvg = (fT[1][cpIdx] + i[1][cpIdx + 1]) / 2;
                 pt = c2.ptAtT(tAvg);
                 if (!pt.approximatelyEqual(fPt[cpIdx])) {
                     ++cpIdx;
                     continue;
                 }
                 i.removeOne(cpIdx);
                 --compCount;
             }
             // in addition to adding below missing function, think about how to say
             append(i);
         }
     }
     // If an end point and a second point very close to the end is returned, the second
     // point may have been detected because the approximate quads
     // intersected at the end and close to it. Verify that the second point is valid.
     if (fUsed <= 1) {
         return fUsed;
     }
     SkDPoint pt[2];
     if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1])
             && pt[0].approximatelyEqual(pt[1])) {
         removeOne(1);
     }
     if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1])
             && pt[0].approximatelyEqual(pt[1])) {
         removeOne(used() - 2);
     }
     // vet the pairs of t values to see if the mid value is also on the curve. If so, mark
     // the span as coincident
     if (fUsed >= 2 && !coincidentUsed()) {
         int last = fUsed - 1;
         int match = 0;
         for (int index = 0; index < last; ++index) {
             double mid1 = (fT[0][index] + fT[0][index + 1]) / 2;
             double mid2 = (fT[1][index] + fT[1][index + 1]) / 2;
             pt[0] = c1.ptAtT(mid1);
             pt[1] = c2.ptAtT(mid2);
             if (pt[0].approximatelyEqual(pt[1])) {
                 match |= 1 << index;
             }
         }
         if (match) {
 #if DEBUG_CONCIDENT
             if (((match + 1) & match) != 0) {
                 SkDebugf("%s coincident hole\n", __FUNCTION__);
             }
 #endif
             // for now, assume that everything from start to finish is coincident
             if (fUsed > 2) {
                   fPt[1] = fPt[last];
                   fT[0][1] = fT[0][last];
                   fT[1][1] = fT[1][last];
                   fIsCoincident[0] = 0x03;
                   fIsCoincident[1] = 0x03;
                   fUsed = 2;
             }
         }
     }
     return fUsed;
 }
 // Up promote the quad to a cubic.
 // OPTIMIZATION If this is a common use case, optimize by duplicating
 // the intersect 3 loop to avoid the promotion  / demotion code
 int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) {
     fMax = 6;
     SkDCubic up = quad.toCubic();
     (void) intersect(cubic, up);
     return used();
 }
 /* http://www.ag.jku.at/compass/compasssample.pdf
 ( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen
 Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth@math.uio.no
 SINTEF Applied Mathematics http://www.sintef.no )
 describes a method to find the self intersection of a cubic by taking the gradient of the implicit
 form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/
 int SkIntersections::intersect(const SkDCubic& c) {
     fMax = 1;
     // check to see if x or y end points are the extrema. Are other quick rejects possible?
     if (c.endsAreExtremaInXOrY()) {
         return false;
     }
     (void) intersect(c, c);
     if (used() > 0) {
         SkASSERT(used() == 1);
         if (fT[0][0] > fT[1][0]) {
             swapPts();
         }
     }
     return used();
 }

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gfx/skia/trunk/src/pathops/SkDCubicIntersection.cpp@b8a032363ba2 (annotated)

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