| /* |
| * 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(); |
| } |
