| /* | |
| * 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 { | |
| /*for random cubics, 16 below catches 99.997% of the intersections. To test for the remaining 0.003% | |
| look for nearly coincident curves. and check each 1/16th section. | |
| */ | |
| double offset = precisionScale / 16; // FIXME: 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) { | |
| cubicInsert(testT, impTs[0][index], tmpLine[0], cubic2, cubic1); | |
| } else { | |
| cubicInsert(impTs[0][index], testT, tmpLine[0], cubic1, cubic2); | |
| } | |
| return true; | |
| } | |
| return false; | |
| } | |
| void SkIntersections::cubicInsert(double one, double two, const SkDPoint& pt, | |
| const SkDCubic& cubic1, const SkDCubic& cubic2) { | |
| for (int index = 0; index < fUsed; ++index) { | |
| if (fT[0][index] == one) { | |
| double oldTwo = fT[1][index]; | |
| if (oldTwo == two) { | |
| return; | |
| } | |
| SkDPoint mid = cubic2.ptAtT((oldTwo + two) / 2); | |
| if (mid.approximatelyEqual(fPt[index])) { | |
| return; | |
| } | |
| } | |
| if (fT[1][index] == two) { | |
| SkDPoint mid = cubic1.ptAtT((fT[0][index] + two) / 2); | |
| if (mid.approximatelyEqual(fPt[index])) { | |
| return; | |
| } | |
| } | |
| } | |
| insert(one, two, pt); | |
| } | |
| 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(); | |
| if (start ? tMax1 < tMin2 : tMax2 < tMin1) { | |
| ::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); | |
| if (start ? tMax1 < tMin2 : tMax2 < tMin1) { | |
| ::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; | |
| if (adj == 0 && opp == 0) { // if the other point equals the test point, ignore it | |
| continue; | |
| } | |
| 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)) { | |
| if (selfIntersect && fUsed) { | |
| return fUsed; | |
| } | |
| cubicNearEnd(c1, true, c2, c2Bounds); | |
| if (selfIntersect && fUsed && ((approximately_less_than_zero(fT[0][0]) | |
| && approximately_less_than_zero(fT[1][0])) | |
| || (approximately_greater_than_one(fT[0][0]) | |
| && approximately_greater_than_one(fT[1][0])))) { | |
| SkASSERT(fUsed == 1); | |
| fUsed = 0; | |
| return fUsed; | |
| } | |
| } | |
| 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) { | |
| *this = 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; | |
| } | |
| // OPTIMIZATION: could quick reject if neither end point tangent ray intersected the line | |
| // segment formed by the opposite end point to the control point | |
| (void) intersect(c, c); | |
| if (used() > 0) { | |
| if (approximately_equal_double(fT[0][0], fT[1][0])) { | |
| fUsed = 0; | |
| } else { | |
| SkASSERT(used() == 1); | |
| if (fT[0][0] > fT[1][0]) { | |
| swapPts(); | |
| } | |
| } | |
| } | |
| return used(); | |
| } |