michael@0: /*
michael@0:  * Copyright 2012 Google Inc.
michael@0:  *
michael@0:  * Use of this source code is governed by a BSD-style license that can be
michael@0:  * found in the LICENSE file.
michael@0:  */
michael@0: 
michael@0: #include "SkIntersections.h"
michael@0: #include "SkPathOpsCubic.h"
michael@0: #include "SkPathOpsLine.h"
michael@0: #include "SkPathOpsPoint.h"
michael@0: #include "SkPathOpsQuad.h"
michael@0: #include "SkPathOpsRect.h"
michael@0: #include "SkReduceOrder.h"
michael@0: #include "SkTSort.h"
michael@0: 
michael@0: #if ONE_OFF_DEBUG
michael@0: static const double tLimits1[2][2] = {{0.3, 0.4}, {0.8, 0.9}};
michael@0: static const double tLimits2[2][2] = {{-0.8, -0.9}, {-0.8, -0.9}};
michael@0: #endif
michael@0: 
michael@0: #define DEBUG_QUAD_PART ONE_OFF_DEBUG && 1
michael@0: #define DEBUG_QUAD_PART_SHOW_SIMPLE DEBUG_QUAD_PART && 0
michael@0: #define SWAP_TOP_DEBUG 0
michael@0: 
michael@0: static const int kCubicToQuadSubdivisionDepth = 8; // slots reserved for cubic to quads subdivision
michael@0: 
michael@0: static int quadPart(const SkDCubic& cubic, double tStart, double tEnd, SkReduceOrder* reducer) {
michael@0:     SkDCubic part = cubic.subDivide(tStart, tEnd);
michael@0:     SkDQuad quad = part.toQuad();
michael@0:     // FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an
michael@0:     // extremely shallow quadratic?
michael@0:     int order = reducer->reduce(quad);
michael@0: #if DEBUG_QUAD_PART
michael@0:     SkDebugf("%s cubic=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
michael@0:             " t=(%1.9g,%1.9g)\n", __FUNCTION__, cubic[0].fX, cubic[0].fY,
michael@0:             cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY,
michael@0:             cubic[3].fX, cubic[3].fY, tStart, tEnd);
michael@0:     SkDebugf("  {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n"
michael@0:              "  {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
michael@0:             part[0].fX, part[0].fY, part[1].fX, part[1].fY, part[2].fX, part[2].fY,
michael@0:             part[3].fX, part[3].fY, quad[0].fX, quad[0].fY,
michael@0:             quad[1].fX, quad[1].fY, quad[2].fX, quad[2].fY);
michael@0: #if DEBUG_QUAD_PART_SHOW_SIMPLE
michael@0:     SkDebugf("%s simple=(%1.9g,%1.9g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY);
michael@0:     if (order > 1) {
michael@0:         SkDebugf(" %1.9g,%1.9g", reducer->fQuad[1].fX, reducer->fQuad[1].fY);
michael@0:     }
michael@0:     if (order > 2) {
michael@0:         SkDebugf(" %1.9g,%1.9g", reducer->fQuad[2].fX, reducer->fQuad[2].fY);
michael@0:     }
michael@0:     SkDebugf(")\n");
michael@0:     SkASSERT(order < 4 && order > 0);
michael@0: #endif
michael@0: #endif
michael@0:     return order;
michael@0: }
michael@0: 
michael@0: static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2,
michael@0:         int order2, SkIntersections& i) {
michael@0:     if (order1 == 3 && order2 == 3) {
michael@0:         i.intersect(simple1, simple2);
michael@0:     } else if (order1 <= 2 && order2 <= 2) {
michael@0:         i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2);
michael@0:     } else if (order1 == 3 && order2 <= 2) {
michael@0:         i.intersect(simple1, (const SkDLine&) simple2);
michael@0:     } else {
michael@0:         SkASSERT(order1 <= 2 && order2 == 3);
michael@0:         i.intersect(simple2, (const SkDLine&) simple1);
michael@0:         i.swapPts();
michael@0:     }
michael@0: }
michael@0: 
michael@0: // this flavor centers potential intersections recursively. In contrast, '2' may inadvertently
michael@0: // chase intersections near quadratic ends, requiring odd hacks to find them.
michael@0: static void intersect(const SkDCubic& cubic1, double t1s, double t1e, const SkDCubic& cubic2,
michael@0:         double t2s, double t2e, double precisionScale, SkIntersections& i) {
michael@0:     i.upDepth();
michael@0:     SkDCubic c1 = cubic1.subDivide(t1s, t1e);
michael@0:     SkDCubic c2 = cubic2.subDivide(t2s, t2e);
michael@0:     SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts1;
michael@0:     // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection)
michael@0:     c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1);
michael@0:     SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts2;
michael@0:     c2.toQuadraticTs(c2.calcPrecision() * precisionScale, &ts2);
michael@0:     double t1Start = t1s;
michael@0:     int ts1Count = ts1.count();
michael@0:     for (int i1 = 0; i1 <= ts1Count; ++i1) {
michael@0:         const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1;
michael@0:         const double t1 = t1s + (t1e - t1s) * tEnd1;
michael@0:         SkReduceOrder s1;
michael@0:         int o1 = quadPart(cubic1, t1Start, t1, &s1);
michael@0:         double t2Start = t2s;
michael@0:         int ts2Count = ts2.count();
michael@0:         for (int i2 = 0; i2 <= ts2Count; ++i2) {
michael@0:             const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1;
michael@0:             const double t2 = t2s + (t2e - t2s) * tEnd2;
michael@0:             if (&cubic1 == &cubic2 && t1Start >= t2Start) {
michael@0:                 t2Start = t2;
michael@0:                 continue;
michael@0:             }
michael@0:             SkReduceOrder s2;
michael@0:             int o2 = quadPart(cubic2, t2Start, t2, &s2);
michael@0:         #if ONE_OFF_DEBUG
michael@0:             char tab[] = "                  ";
michael@0:             if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1
michael@0:                     && tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) {
michael@0:                 SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab,
michael@0:                         __FUNCTION__, t1Start, t1, t2Start, t2);
michael@0:                 SkIntersections xlocals;
michael@0:                 xlocals.allowNear(false);
michael@0:                 intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals);
michael@0:                 SkDebugf(" xlocals.fUsed=%d\n", xlocals.used());
michael@0:             }
michael@0:         #endif
michael@0:             SkIntersections locals;
michael@0:             locals.allowNear(false);
michael@0:             intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals);
michael@0:             int tCount = locals.used();
michael@0:             for (int tIdx = 0; tIdx < tCount; ++tIdx) {
michael@0:                 double to1 = t1Start + (t1 - t1Start) * locals[0][tIdx];
michael@0:                 double to2 = t2Start + (t2 - t2Start) * locals[1][tIdx];
michael@0:     // if the computed t is not sufficiently precise, iterate
michael@0:                 SkDPoint p1 = cubic1.ptAtT(to1);
michael@0:                 SkDPoint p2 = cubic2.ptAtT(to2);
michael@0:                 if (p1.approximatelyEqual(p2)) {
michael@0:     // FIXME: local edge may be coincident -- experiment with not propagating coincidence to caller
michael@0: //                    SkASSERT(!locals.isCoincident(tIdx));
michael@0:                     if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) {
michael@0:                         if (i.swapped()) {  //  FIXME: insert should respect swap
michael@0:                             i.insert(to2, to1, p1);
michael@0:                         } else {
michael@0:                             i.insert(to1, to2, p1);
michael@0:                         }
michael@0:                     }
michael@0:                 } else {
michael@0:                     double offset = precisionScale / 16;  // FIME: const is arbitrary: test, refine
michael@0:                     double c1Bottom = tIdx == 0 ? 0 :
michael@0:                             (t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2;
michael@0:                     double c1Min = SkTMax(c1Bottom, to1 - offset);
michael@0:                     double c1Top = tIdx == tCount - 1 ? 1 :
michael@0:                             (t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2;
michael@0:                     double c1Max = SkTMin(c1Top, to1 + offset);
michael@0:                     double c2Min = SkTMax(0., to2 - offset);
michael@0:                     double c2Max = SkTMin(1., to2 + offset);
michael@0:                 #if ONE_OFF_DEBUG
michael@0:                     SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
michael@0:                             __FUNCTION__,
michael@0:                             c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
michael@0:                          && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
michael@0:                             to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
michael@0:                          && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
michael@0:                             c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
michael@0:                          && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
michael@0:                             to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
michael@0:                          && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
michael@0:                     SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
michael@0:                             " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
michael@0:                             i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1.,
michael@0:                             to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
michael@0:                     SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
michael@0:                             " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
michael@0:                             c1Max, c2Min, c2Max);
michael@0:                 #endif
michael@0:                     intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
michael@0:                 #if ONE_OFF_DEBUG
michael@0:                     SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
michael@0:                             i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
michael@0:                 #endif
michael@0:                     if (tCount > 1) {
michael@0:                         c1Min = SkTMax(0., to1 - offset);
michael@0:                         c1Max = SkTMin(1., to1 + offset);
michael@0:                         double c2Bottom = tIdx == 0 ? to2 :
michael@0:                                 (t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2;
michael@0:                         double c2Top = tIdx == tCount - 1 ? to2 :
michael@0:                                 (t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2;
michael@0:                         if (c2Bottom > c2Top) {
michael@0:                             SkTSwap(c2Bottom, c2Top);
michael@0:                         }
michael@0:                         if (c2Bottom == to2) {
michael@0:                             c2Bottom = 0;
michael@0:                         }
michael@0:                         if (c2Top == to2) {
michael@0:                             c2Top = 1;
michael@0:                         }
michael@0:                         c2Min = SkTMax(c2Bottom, to2 - offset);
michael@0:                         c2Max = SkTMin(c2Top, to2 + offset);
michael@0:                     #if ONE_OFF_DEBUG
michael@0:                         SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
michael@0:                             __FUNCTION__,
michael@0:                             c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
michael@0:                          && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
michael@0:                             to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
michael@0:                          && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
michael@0:                             c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
michael@0:                          && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
michael@0:                             to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
michael@0:                          && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
michael@0:                         SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
michael@0:                                 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
michael@0:                                 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
michael@0:                                 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
michael@0:                         SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
michael@0:                                 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
michael@0:                                 c1Max, c2Min, c2Max);
michael@0:                     #endif
michael@0:                         intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
michael@0:                 #if ONE_OFF_DEBUG
michael@0:                     SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
michael@0:                             i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
michael@0:                 #endif
michael@0:                         c1Min = SkTMax(c1Bottom, to1 - offset);
michael@0:                         c1Max = SkTMin(c1Top, to1 + offset);
michael@0:                     #if ONE_OFF_DEBUG
michael@0:                         SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab,
michael@0:                         __FUNCTION__,
michael@0:                             c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max
michael@0:                          && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max,
michael@0:                             to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset
michael@0:                          && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset,
michael@0:                             c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max
michael@0:                          && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max,
michael@0:                             to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset
michael@0:                          && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset);
michael@0:                         SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g"
michael@0:                                 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n",
michael@0:                                 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top,
michael@0:                                 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset);
michael@0:                         SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g"
michael@0:                                 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min,
michael@0:                                 c1Max, c2Min, c2Max);
michael@0:                     #endif
michael@0:                         intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
michael@0:                 #if ONE_OFF_DEBUG
michael@0:                     SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__,
michael@0:                             i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1);
michael@0:                 #endif
michael@0:                     }
michael@0:           //          intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i);
michael@0:                     // FIXME: if no intersection is found, either quadratics intersected where
michael@0:                     // cubics did not, or the intersection was missed. In the former case, expect
michael@0:                     // the quadratics to be nearly parallel at the point of intersection, and check
michael@0:                     // for that.
michael@0:                 }
michael@0:             }
michael@0:             t2Start = t2;
michael@0:         }
michael@0:         t1Start = t1;
michael@0:     }
michael@0:     i.downDepth();
michael@0: }
michael@0: 
michael@0:     // if two ends intersect, check middle for coincidence
michael@0: bool SkIntersections::cubicCheckCoincidence(const SkDCubic& c1, const SkDCubic& c2) {
michael@0:     if (fUsed < 2) {
michael@0:         return false;
michael@0:     }
michael@0:     int last = fUsed - 1;
michael@0:     double tRange1 = fT[0][last] - fT[0][0];
michael@0:     double tRange2 = fT[1][last] - fT[1][0];
michael@0:     for (int index = 1; index < 5; ++index) {
michael@0:         double testT1 = fT[0][0] + tRange1 * index / 5;
michael@0:         double testT2 = fT[1][0] + tRange2 * index / 5;
michael@0:         SkDPoint testPt1 = c1.ptAtT(testT1);
michael@0:         SkDPoint testPt2 = c2.ptAtT(testT2);
michael@0:         if (!testPt1.approximatelyEqual(testPt2)) {
michael@0:             return false;
michael@0:         }
michael@0:     }
michael@0:     if (fUsed > 2) {
michael@0:         fPt[1] = fPt[last];
michael@0:         fT[0][1] = fT[0][last];
michael@0:         fT[1][1] = fT[1][last];
michael@0:         fUsed = 2;
michael@0:     }
michael@0:     fIsCoincident[0] = fIsCoincident[1] = 0x03;
michael@0:     return true;
michael@0: }
michael@0: 
michael@0: #define LINE_FRACTION 0.1
michael@0: 
michael@0: // intersect the end of the cubic with the other. Try lines from the end to control and opposite
michael@0: // end to determine range of t on opposite cubic.
michael@0: bool SkIntersections::cubicExactEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2) {
michael@0:     int t1Index = start ? 0 : 3;
michael@0:     double testT = (double) !start;
michael@0:     bool swap = swapped();
michael@0:     // quad/quad at this point checks to see if exact matches have already been found
michael@0:     // cubic/cubic can't reject so easily since cubics can intersect same point more than once
michael@0:     SkDLine tmpLine;
michael@0:     tmpLine[0] = tmpLine[1] = cubic2[t1Index];
michael@0:     tmpLine[1].fX += cubic2[2 - start].fY - cubic2[t1Index].fY;
michael@0:     tmpLine[1].fY -= cubic2[2 - start].fX - cubic2[t1Index].fX;
michael@0:     SkIntersections impTs;
michael@0:     impTs.allowNear(false);
michael@0:     impTs.intersectRay(cubic1, tmpLine);
michael@0:     for (int index = 0; index < impTs.used(); ++index) {
michael@0:         SkDPoint realPt = impTs.pt(index);
michael@0:         if (!tmpLine[0].approximatelyEqual(realPt)) {
michael@0:             continue;
michael@0:         }
michael@0:         if (swap) {
michael@0:             insert(testT, impTs[0][index], tmpLine[0]);
michael@0:         } else {
michael@0:             insert(impTs[0][index], testT, tmpLine[0]);
michael@0:         }
michael@0:         return true;
michael@0:     }
michael@0:     return false;
michael@0: }
michael@0: 
michael@0: void SkIntersections::cubicNearEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2,
michael@0:                          const SkDRect& bounds2) {
michael@0:     SkDLine line;
michael@0:     int t1Index = start ? 0 : 3;
michael@0:     double testT = (double) !start;
michael@0:    // don't bother if the two cubics are connnected
michael@0:     static const int kPointsInCubic = 4; // FIXME: move to DCubic, replace '4' with this
michael@0:     static const int kMaxLineCubicIntersections = 3;
michael@0:     SkSTArray<(kMaxLineCubicIntersections - 1) * kMaxLineCubicIntersections, double, true> tVals;
michael@0:     line[0] = cubic1[t1Index];
michael@0:     // this variant looks for intersections with the end point and lines parallel to other points
michael@0:     for (int index = 0; index < kPointsInCubic; ++index) {
michael@0:         if (index == t1Index) {
michael@0:             continue;
michael@0:         }
michael@0:         SkDVector dxy1 = cubic1[index] - line[0];
michael@0:         dxy1 /= SkDCubic::gPrecisionUnit;
michael@0:         line[1] = line[0] + dxy1;
michael@0:         SkDRect lineBounds;
michael@0:         lineBounds.setBounds(line);
michael@0:         if (!bounds2.intersects(&lineBounds)) {
michael@0:             continue;
michael@0:         }
michael@0:         SkIntersections local;
michael@0:         if (!local.intersect(cubic2, line)) {
michael@0:             continue;
michael@0:         }
michael@0:         for (int idx2 = 0; idx2 < local.used(); ++idx2) {
michael@0:             double foundT = local[0][idx2];
michael@0:             if (approximately_less_than_zero(foundT)
michael@0:                     || approximately_greater_than_one(foundT)) {
michael@0:                 continue;
michael@0:             }
michael@0:             if (local.pt(idx2).approximatelyEqual(line[0])) {
michael@0:                 if (swapped()) {  // FIXME: insert should respect swap
michael@0:                     insert(foundT, testT, line[0]);
michael@0:                 } else {
michael@0:                     insert(testT, foundT, line[0]);
michael@0:                 }
michael@0:             } else {
michael@0:                 tVals.push_back(foundT);
michael@0:             }
michael@0:         }
michael@0:     }
michael@0:     if (tVals.count() == 0) {
michael@0:         return;
michael@0:     }
michael@0:     SkTQSort<double>(tVals.begin(), tVals.end() - 1);
michael@0:     double tMin1 = start ? 0 : 1 - LINE_FRACTION;
michael@0:     double tMax1 = start ? LINE_FRACTION : 1;
michael@0:     int tIdx = 0;
michael@0:     do {
michael@0:         int tLast = tIdx;
michael@0:         while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) {
michael@0:             ++tLast;
michael@0:         }
michael@0:         double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0);
michael@0:         double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0);
michael@0:         int lastUsed = used();
michael@0:         ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
michael@0:         if (lastUsed == used()) {
michael@0:             tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0);
michael@0:             tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0);
michael@0:             ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
michael@0:         }
michael@0:         tIdx = tLast + 1;
michael@0:     } while (tIdx < tVals.count());
michael@0:     return;
michael@0: }
michael@0: 
michael@0: const double CLOSE_ENOUGH = 0.001;
michael@0: 
michael@0: static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
michael@0:     if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) {
michael@0:         return false;
michael@0:     }
michael@0:     pt = cubic.ptAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2);
michael@0:     return true;
michael@0: }
michael@0: 
michael@0: static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) {
michael@0:     int last = i.used() - 1;
michael@0:     if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) {
michael@0:         return false;
michael@0:     }
michael@0:     pt = cubic.ptAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2);
michael@0:     return true;
michael@0: }
michael@0: 
michael@0: static bool only_end_pts_in_common(const SkDCubic& c1, const SkDCubic& c2) {
michael@0: // the idea here is to see at minimum do a quick reject by rotating all points
michael@0: // to either side of the line formed by connecting the endpoints
michael@0: // if the opposite curves points are on the line or on the other side, the
michael@0: // curves at most intersect at the endpoints
michael@0:     for (int oddMan = 0; oddMan < 4; ++oddMan) {
michael@0:         const SkDPoint* endPt[3];
michael@0:         for (int opp = 1; opp < 4; ++opp) {
michael@0:             int end = oddMan ^ opp;  // choose a value not equal to oddMan
michael@0:             endPt[opp - 1] = &c1[end];
michael@0:         }
michael@0:         for (int triTest = 0; triTest < 3; ++triTest) {
michael@0:             double origX = endPt[triTest]->fX;
michael@0:             double origY = endPt[triTest]->fY;
michael@0:             int oppTest = triTest + 1;
michael@0:             if (3 == oppTest) {
michael@0:                 oppTest = 0;
michael@0:             }
michael@0:             double adj = endPt[oppTest]->fX - origX;
michael@0:             double opp = endPt[oppTest]->fY - origY;
michael@0:             double sign = (c1[oddMan].fY - origY) * adj - (c1[oddMan].fX - origX) * opp;
michael@0:             if (approximately_zero(sign)) {
michael@0:                 goto tryNextHalfPlane;
michael@0:             }
michael@0:             for (int n = 0; n < 4; ++n) {
michael@0:                 double test = (c2[n].fY - origY) * adj - (c2[n].fX - origX) * opp;
michael@0:                 if (test * sign > 0 && !precisely_zero(test)) {
michael@0:                     goto tryNextHalfPlane;
michael@0:                 }
michael@0:             }
michael@0:         }
michael@0:         return true;
michael@0: tryNextHalfPlane:
michael@0:         ;
michael@0:     }
michael@0:     return false;
michael@0: }
michael@0: 
michael@0: int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) {
michael@0:     if (fMax == 0) {
michael@0:         fMax = 9;
michael@0:     }
michael@0:     bool selfIntersect = &c1 == &c2;
michael@0:     if (selfIntersect) {
michael@0:         if (c1[0].approximatelyEqual(c1[3])) {
michael@0:             insert(0, 1, c1[0]);
michael@0:             return fUsed;
michael@0:         }
michael@0:     } else {
michael@0:         // OPTIMIZATION: set exact end bits here to avoid cubic exact end later
michael@0:         for (int i1 = 0; i1 < 4; i1 += 3) {
michael@0:             for (int i2 = 0; i2 < 4; i2 += 3) {
michael@0:                 if (c1[i1].approximatelyEqual(c2[i2])) {
michael@0:                     insert(i1 >> 1, i2 >> 1, c1[i1]);
michael@0:                 }
michael@0:             }
michael@0:         }
michael@0:     }
michael@0:     SkASSERT(fUsed < 4);
michael@0:     if (!selfIntersect) {
michael@0:         if (only_end_pts_in_common(c1, c2)) {
michael@0:             return fUsed;
michael@0:         }
michael@0:         if (only_end_pts_in_common(c2, c1)) {
michael@0:             return fUsed;
michael@0:         }
michael@0:     }
michael@0:     // quad/quad does linear test here -- cubic does not
michael@0:     // cubics which are really lines should have been detected in reduce step earlier
michael@0:     int exactEndBits = 0;
michael@0:     if (selfIntersect) {
michael@0:         if (fUsed) {
michael@0:             return fUsed;
michael@0:         }
michael@0:     } else {
michael@0:         exactEndBits |= cubicExactEnd(c1, false, c2) << 0;
michael@0:         exactEndBits |= cubicExactEnd(c1, true, c2) << 1;
michael@0:         swap();
michael@0:         exactEndBits |= cubicExactEnd(c2, false, c1) << 2;
michael@0:         exactEndBits |= cubicExactEnd(c2, true, c1) << 3;
michael@0:         swap();
michael@0:     }
michael@0:     if (cubicCheckCoincidence(c1, c2)) {
michael@0:         SkASSERT(!selfIntersect);
michael@0:         return fUsed;
michael@0:     }
michael@0:     // FIXME: pass in cached bounds from caller
michael@0:     SkDRect c2Bounds;
michael@0:     c2Bounds.setBounds(c2);
michael@0:     if (!(exactEndBits & 4)) {
michael@0:         cubicNearEnd(c1, false, c2, c2Bounds);
michael@0:     }
michael@0:     if (!(exactEndBits & 8)) {
michael@0:         cubicNearEnd(c1, true, c2, c2Bounds);
michael@0:     }
michael@0:     if (!selfIntersect) {
michael@0:         SkDRect c1Bounds;
michael@0:         c1Bounds.setBounds(c1);  // OPTIMIZE use setRawBounds ?
michael@0:         swap();
michael@0:         if (!(exactEndBits & 1)) {
michael@0:             cubicNearEnd(c2, false, c1, c1Bounds);
michael@0:         }
michael@0:         if (!(exactEndBits & 2)) {
michael@0:             cubicNearEnd(c2, true, c1, c1Bounds);
michael@0:         }
michael@0:         swap();
michael@0:     }
michael@0:     if (cubicCheckCoincidence(c1, c2)) {
michael@0:         SkASSERT(!selfIntersect);
michael@0:         return fUsed;
michael@0:     }
michael@0:     SkIntersections i;
michael@0:     i.fAllowNear = false;
michael@0:     i.fMax = 9;
michael@0:     ::intersect(c1, 0, 1, c2, 0, 1, 1, i);
michael@0:     int compCount = i.used();
michael@0:     if (compCount) {
michael@0:         int exactCount = used();
michael@0:         if (exactCount == 0) {
michael@0:             set(i);
michael@0:         } else {
michael@0:             // at least one is exact or near, and at least one was computed. Eliminate duplicates
michael@0:             for (int exIdx = 0; exIdx < exactCount; ++exIdx) {
michael@0:                 for (int cpIdx = 0; cpIdx < compCount; ) {
michael@0:                     if (fT[0][0] == i[0][0] && fT[1][0] == i[1][0]) {
michael@0:                         i.removeOne(cpIdx);
michael@0:                         --compCount;
michael@0:                         continue;
michael@0:                     }
michael@0:                     double tAvg = (fT[0][exIdx] + i[0][cpIdx]) / 2;
michael@0:                     SkDPoint pt = c1.ptAtT(tAvg);
michael@0:                     if (!pt.approximatelyEqual(fPt[exIdx])) {
michael@0:                         ++cpIdx;
michael@0:                         continue;
michael@0:                     }
michael@0:                     tAvg = (fT[1][exIdx] + i[1][cpIdx]) / 2;
michael@0:                     pt = c2.ptAtT(tAvg);
michael@0:                     if (!pt.approximatelyEqual(fPt[exIdx])) {
michael@0:                         ++cpIdx;
michael@0:                         continue;
michael@0:                     }
michael@0:                     i.removeOne(cpIdx);
michael@0:                     --compCount;
michael@0:                 }
michael@0:             }
michael@0:             // if mid t evaluates to nearly the same point, skip the t
michael@0:             for (int cpIdx = 0; cpIdx < compCount - 1; ) {
michael@0:                 double tAvg = (fT[0][cpIdx] + i[0][cpIdx + 1]) / 2;
michael@0:                 SkDPoint pt = c1.ptAtT(tAvg);
michael@0:                 if (!pt.approximatelyEqual(fPt[cpIdx])) {
michael@0:                     ++cpIdx;
michael@0:                     continue;
michael@0:                 }
michael@0:                 tAvg = (fT[1][cpIdx] + i[1][cpIdx + 1]) / 2;
michael@0:                 pt = c2.ptAtT(tAvg);
michael@0:                 if (!pt.approximatelyEqual(fPt[cpIdx])) {
michael@0:                     ++cpIdx;
michael@0:                     continue;
michael@0:                 }
michael@0:                 i.removeOne(cpIdx);
michael@0:                 --compCount;
michael@0:             }
michael@0:             // in addition to adding below missing function, think about how to say
michael@0:             append(i);
michael@0:         }
michael@0:     }
michael@0:     // If an end point and a second point very close to the end is returned, the second
michael@0:     // point may have been detected because the approximate quads
michael@0:     // intersected at the end and close to it. Verify that the second point is valid.
michael@0:     if (fUsed <= 1) {
michael@0:         return fUsed;
michael@0:     }
michael@0:     SkDPoint pt[2];
michael@0:     if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1])
michael@0:             && pt[0].approximatelyEqual(pt[1])) {
michael@0:         removeOne(1);
michael@0:     }
michael@0:     if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1])
michael@0:             && pt[0].approximatelyEqual(pt[1])) {
michael@0:         removeOne(used() - 2);
michael@0:     }
michael@0:     // vet the pairs of t values to see if the mid value is also on the curve. If so, mark
michael@0:     // the span as coincident
michael@0:     if (fUsed >= 2 && !coincidentUsed()) {
michael@0:         int last = fUsed - 1;
michael@0:         int match = 0;
michael@0:         for (int index = 0; index < last; ++index) {
michael@0:             double mid1 = (fT[0][index] + fT[0][index + 1]) / 2;
michael@0:             double mid2 = (fT[1][index] + fT[1][index + 1]) / 2;
michael@0:             pt[0] = c1.ptAtT(mid1);
michael@0:             pt[1] = c2.ptAtT(mid2);
michael@0:             if (pt[0].approximatelyEqual(pt[1])) {
michael@0:                 match |= 1 << index;
michael@0:             }
michael@0:         }
michael@0:         if (match) {
michael@0: #if DEBUG_CONCIDENT
michael@0:             if (((match + 1) & match) != 0) {
michael@0:                 SkDebugf("%s coincident hole\n", __FUNCTION__);
michael@0:             }
michael@0: #endif
michael@0:             // for now, assume that everything from start to finish is coincident
michael@0:             if (fUsed > 2) {
michael@0:                   fPt[1] = fPt[last];
michael@0:                   fT[0][1] = fT[0][last];
michael@0:                   fT[1][1] = fT[1][last];
michael@0:                   fIsCoincident[0] = 0x03;
michael@0:                   fIsCoincident[1] = 0x03;
michael@0:                   fUsed = 2;
michael@0:             }
michael@0:         }
michael@0:     }
michael@0:     return fUsed;
michael@0: }
michael@0: 
michael@0: // Up promote the quad to a cubic.
michael@0: // OPTIMIZATION If this is a common use case, optimize by duplicating
michael@0: // the intersect 3 loop to avoid the promotion  / demotion code
michael@0: int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) {
michael@0:     fMax = 6;
michael@0:     SkDCubic up = quad.toCubic();
michael@0:     (void) intersect(cubic, up);
michael@0:     return used();
michael@0: }
michael@0: 
michael@0: /* http://www.ag.jku.at/compass/compasssample.pdf
michael@0: ( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen
michael@0: Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth@math.uio.no
michael@0: SINTEF Applied Mathematics http://www.sintef.no )
michael@0: describes a method to find the self intersection of a cubic by taking the gradient of the implicit
michael@0: form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/
michael@0: 
michael@0: int SkIntersections::intersect(const SkDCubic& c) {
michael@0:     fMax = 1;
michael@0:     // check to see if x or y end points are the extrema. Are other quick rejects possible?
michael@0:     if (c.endsAreExtremaInXOrY()) {
michael@0:         return false;
michael@0:     }
michael@0:     (void) intersect(c, c);
michael@0:     if (used() > 0) {
michael@0:         SkASSERT(used() == 1);
michael@0:         if (fT[0][0] > fT[1][0]) {
michael@0:             swapPts();
michael@0:         }
michael@0:     }
michael@0:     return used();
michael@0: }