| /* |
| * 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 "CubicUtilities.h" |
| #include "CurveIntersection.h" |
| #include "Intersections.h" |
| #include "IntersectionUtilities.h" |
| #include "LineIntersection.h" |
| #include "LineUtilities.h" |
| #include "QuadraticUtilities.h" |
| #include "TSearch.h" |
| |
| #if 0 |
| #undef ONE_OFF_DEBUG |
| #define ONE_OFF_DEBUG 0 |
| #endif |
| |
| #if ONE_OFF_DEBUG |
| static const double tLimits1[2][2] = {{0.36, 0.37}, {0.63, 0.64}}; |
| static const double tLimits2[2][2] = {{-0.865211397, -0.865215212}, {-0.865207696, -0.865208078}}; |
| #endif |
| |
| #define DEBUG_QUAD_PART 0 |
| #define SWAP_TOP_DEBUG 0 |
| |
| static int quadPart(const Cubic& cubic, double tStart, double tEnd, Quadratic& simple) { |
| Cubic part; |
| sub_divide(cubic, tStart, tEnd, part); |
| Quadratic quad; |
| demote_cubic_to_quad(part, quad); |
| // FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an |
| // extremely shallow quadratic? |
| int order = reduceOrder(quad, simple, kReduceOrder_TreatAsFill); |
| #if DEBUG_QUAD_PART |
| SkDebugf("%s cubic=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g) t=(%1.17g,%1.17g)\n", |
| __FUNCTION__, cubic[0].x, cubic[0].y, cubic[1].x, cubic[1].y, cubic[2].x, cubic[2].y, |
| cubic[3].x, cubic[3].y, tStart, tEnd); |
| SkDebugf("%s part=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)" |
| " quad=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)\n", __FUNCTION__, part[0].x, part[0].y, |
| part[1].x, part[1].y, part[2].x, part[2].y, part[3].x, part[3].y, quad[0].x, quad[0].y, |
| quad[1].x, quad[1].y, quad[2].x, quad[2].y); |
| SkDebugf("%s simple=(%1.17g,%1.17g", __FUNCTION__, simple[0].x, simple[0].y); |
| if (order > 1) { |
| SkDebugf(" %1.17g,%1.17g", simple[1].x, simple[1].y); |
| } |
| if (order > 2) { |
| SkDebugf(" %1.17g,%1.17g", simple[2].x, simple[2].y); |
| } |
| SkDebugf(")\n"); |
| SkASSERT(order < 4 && order > 0); |
| #endif |
| return order; |
| } |
| |
| static void intersectWithOrder(const Quadratic& simple1, int order1, const Quadratic& simple2, |
| int order2, Intersections& i) { |
| if (order1 == 3 && order2 == 3) { |
| intersect2(simple1, simple2, i); |
| } else if (order1 <= 2 && order2 <= 2) { |
| intersect((const _Line&) simple1, (const _Line&) simple2, i); |
| } else if (order1 == 3 && order2 <= 2) { |
| intersect(simple1, (const _Line&) simple2, i); |
| } else { |
| SkASSERT(order1 <= 2 && order2 == 3); |
| intersect(simple2, (const _Line&) simple1, i); |
| for (int s = 0; s < i.fUsed; ++s) { |
| SkTSwap(i.fT[0][s], i.fT[1][s]); |
| } |
| } |
| } |
| |
| // this flavor centers potential intersections recursively. In contrast, '2' may inadvertently |
| // chase intersections near quadratic ends, requiring odd hacks to find them. |
| static bool intersect3(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2, |
| double t2s, double t2e, double precisionScale, Intersections& i) { |
| i.upDepth(); |
| bool result = false; |
| Cubic c1, c2; |
| sub_divide(cubic1, t1s, t1e, c1); |
| sub_divide(cubic2, t2s, t2e, c2); |
| SkTDArray<double> ts1; |
| // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection) |
| cubic_to_quadratics(c1, calcPrecision(c1) * precisionScale, ts1); |
| SkTDArray<double> ts2; |
| cubic_to_quadratics(c2, calcPrecision(c2) * 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; |
| Quadratic 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; |
| } |
| Quadratic 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) { |
| Cubic cSub1, cSub2; |
| sub_divide(cubic1, t1Start, t1, cSub1); |
| sub_divide(cubic2, t2Start, t2, cSub2); |
| SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab, __FUNCTION__, |
| t1Start, t1, t2Start, t2); |
| Intersections xlocals; |
| intersectWithOrder(s1, o1, s2, o2, xlocals); |
| SkDebugf(" xlocals.fUsed=%d\n", xlocals.used()); |
| } |
| #endif |
| Intersections locals; |
| intersectWithOrder(s1, o1, s2, o2, locals); |
| double coStart[2] = { -1 }; |
| _Point coPoint; |
| int tCount = locals.used(); |
| for (int tIdx = 0; tIdx < tCount; ++tIdx) { |
| double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx]; |
| double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx]; |
| // if the computed t is not sufficiently precise, iterate |
| _Point p1 = xy_at_t(cubic1, to1); |
| _Point p2 = xy_at_t(cubic2, to2); |
| if (p1.approximatelyEqual(p2)) { |
| if (locals.fIsCoincident[0] & 1 << tIdx) { |
| if (coStart[0] < 0) { |
| coStart[0] = to1; |
| coStart[1] = to2; |
| coPoint = p1; |
| } else { |
| i.insertCoincidentPair(coStart[0], to1, coStart[1], to2, coPoint, p1); |
| coStart[0] = -1; |
| } |
| result = true; |
| } else 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); |
| } |
| result = true; |
| } |
| } else { |
| double offset = precisionScale / 16; // FIME: const is arbitrary -- test & refine |
| #if 1 |
| double c1Bottom = tIdx == 0 ? 0 : |
| (t1Start + (t1 - t1Start) * locals.fT[0][tIdx - 1] + to1) / 2; |
| double c1Min = SkTMax(c1Bottom, to1 - offset); |
| double c1Top = tIdx == tCount - 1 ? 1 : |
| (t1Start + (t1 - t1Start) * locals.fT[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 |
| intersect3(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.fT[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.fT[1][tIdx - 1] + to2) / 2; |
| double c2Top = tIdx == tCount - 1 ? to2 : |
| (t2Start + (t2 - t2Start) * locals.fT[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 |
| intersect3(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.fT[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 |
| intersect3(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.fT[0][i.used() - 1] : -1); |
| #endif |
| } |
| #else |
| double c1Bottom = tIdx == 0 ? 0 : |
| (t1Start + (t1 - t1Start) * locals.fT[0][tIdx - 1] + to1) / 2; |
| double c1Min = SkTMax(c1Bottom, to1 - offset); |
| double c1Top = tIdx == tCount - 1 ? 1 : |
| (t1Start + (t1 - t1Start) * locals.fT[0][tIdx + 1] + to1) / 2; |
| double c1Max = SkTMin(c1Top, to1 + offset); |
| double c2Bottom = tIdx == 0 ? to2 : |
| (t2Start + (t2 - t2Start) * locals.fT[1][tIdx - 1] + to2) / 2; |
| double c2Top = tIdx == tCount - 1 ? to2 : |
| (t2Start + (t2 - t2Start) * locals.fT[1][tIdx + 1] + to2) / 2; |
| if (c2Bottom > c2Top) { |
| SkTSwap(c2Bottom, c2Top); |
| } |
| if (c2Bottom == to2) { |
| c2Bottom = 0; |
| } |
| if (c2Top == to2) { |
| c2Top = 1; |
| } |
| double c2Min = SkTMax(c2Bottom, to2 - offset); |
| double c2Max = SkTMin(c2Top, to2 + offset); |
| #if ONE_OFF_DEBUG |
| SkDebugf("%s contains1=%d/%d contains2=%d/%d\n", __FUNCTION__, |
| c1Min <= 0.210357794 && 0.210357794 <= c1Max |
| && c2Min <= 0.223476406 && 0.223476406 <= c2Max, |
| to1 - offset <= 0.210357794 && 0.210357794 <= to1 + offset |
| && to2 - offset <= 0.223476406 && 0.223476406 <= to2 + offset, |
| c1Min <= 0.211324707 && 0.211324707 <= c1Max |
| && c2Min <= 0.211327209 && 0.211327209 <= c2Max, |
| to1 - offset <= 0.211324707 && 0.211324707 <= to1 + offset |
| && to2 - offset <= 0.211327209 && 0.211327209 <= to2 + offset); |
| SkDebugf("%s 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", |
| __FUNCTION__, c1Bottom, c1Top, c2Bottom, c2Top, |
| to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); |
| SkDebugf("%s to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" |
| " c2Max=%1.9g\n", __FUNCTION__, to1, to2, c1Min, c1Max, c2Min, c2Max); |
| #endif |
| #endif |
| intersect3(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| // TODO: 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. |
| } |
| } |
| SkASSERT(coStart[0] == -1); |
| t2Start = t2; |
| } |
| t1Start = t1; |
| } |
| i.downDepth(); |
| return result; |
| } |
| |
| #if 0 |
| #define LINE_FRACTION (1.0 / gPrecisionUnit) |
| #else |
| #define LINE_FRACTION 0.1 |
| #endif |
| |
| // 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. |
| static bool intersectEnd(const Cubic& cubic1, bool start, const Cubic& cubic2, const _Rect& bounds2, |
| Intersections& i) { |
| // bool selfIntersect = cubic1 == cubic2; |
| _Line line; |
| int t1Index = start ? 0 : 3; |
| line[0] = cubic1[t1Index]; |
| // don't bother if the two cubics are connnected |
| #if 0 |
| if (!selfIntersect && (line[0].approximatelyEqual(cubic2[0]) |
| || line[0].approximatelyEqual(cubic2[3]))) { |
| return false; |
| } |
| #endif |
| bool result = false; |
| SkTDArray<double> tVals; // OPTIMIZE: replace with hard-sized array |
| for (int index = 0; index < 4; ++index) { |
| if (index == t1Index) { |
| continue; |
| } |
| _Vector dxy1 = cubic1[index] - line[0]; |
| dxy1 /= gPrecisionUnit; |
| line[1] = line[0] + dxy1; |
| _Rect lineBounds; |
| lineBounds.setBounds(line); |
| if (!bounds2.intersects(lineBounds)) { |
| continue; |
| } |
| Intersections local; |
| if (!intersect(cubic2, line, local)) { |
| continue; |
| } |
| for (int idx2 = 0; idx2 < local.used(); ++idx2) { |
| double foundT = local.fT[0][idx2]; |
| if (approximately_less_than_zero(foundT) |
| || approximately_greater_than_one(foundT)) { |
| continue; |
| } |
| if (local.fPt[idx2].approximatelyEqual(line[0])) { |
| if (i.swapped()) { // FIXME: insert should respect swap |
| i.insert(foundT, start ? 0 : 1, line[0]); |
| } else { |
| i.insert(start ? 0 : 1, foundT, line[0]); |
| } |
| result = true; |
| } else { |
| *tVals.append() = local.fT[0][idx2]; |
| } |
| } |
| } |
| if (tVals.count() == 0) { |
| return result; |
| } |
| QSort<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 = i.used(); |
| result |= intersect3(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| if (lastUsed == i.used()) { |
| tMin2 = SkTMax(tVals[tIdx] - (1.0 / gPrecisionUnit), 0.0); |
| tMax2 = SkTMin(tVals[tLast] + (1.0 / gPrecisionUnit), 1.0); |
| result |= intersect3(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| } |
| tIdx = tLast + 1; |
| } while (tIdx < tVals.count()); |
| return result; |
| } |
| |
| const double CLOSE_ENOUGH = 0.001; |
| |
| static bool closeStart(const Cubic& cubic, int cubicIndex, Intersections& i, _Point& pt) { |
| if (i.fT[cubicIndex][0] != 0 || i.fT[cubicIndex][1] > CLOSE_ENOUGH) { |
| return false; |
| } |
| pt = xy_at_t(cubic, (i.fT[cubicIndex][0] + i.fT[cubicIndex][1]) / 2); |
| return true; |
| } |
| |
| static bool closeEnd(const Cubic& cubic, int cubicIndex, Intersections& i, _Point& pt) { |
| int last = i.used() - 1; |
| if (i.fT[cubicIndex][last] != 1 || i.fT[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) { |
| return false; |
| } |
| pt = xy_at_t(cubic, (i.fT[cubicIndex][last] + i.fT[cubicIndex][last - 1]) / 2); |
| return true; |
| } |
| |
| bool intersect3(const Cubic& c1, const Cubic& c2, Intersections& i) { |
| bool result = intersect3(c1, 0, 1, c2, 0, 1, 1, i); |
| // FIXME: pass in cached bounds from caller |
| _Rect c1Bounds, c2Bounds; |
| c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ? |
| c2Bounds.setBounds(c2); |
| result |= intersectEnd(c1, false, c2, c2Bounds, i); |
| result |= intersectEnd(c1, true, c2, c2Bounds, i); |
| bool selfIntersect = c1 == c2; |
| if (!selfIntersect) { |
| i.swap(); |
| result |= intersectEnd(c2, false, c1, c1Bounds, i); |
| result |= intersectEnd(c2, true, c1, c1Bounds, i); |
| i.swap(); |
| } |
| // 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 (i.used() <= 1 || i.coincidentUsed()) { |
| return result; |
| } |
| _Point pt[2]; |
| if (closeStart(c1, 0, i, pt[0]) && closeStart(c2, 1, i, pt[1]) |
| && pt[0].approximatelyEqual(pt[1])) { |
| i.removeOne(1); |
| } |
| if (closeEnd(c1, 0, i, pt[0]) && closeEnd(c2, 1, i, pt[1]) |
| && pt[0].approximatelyEqual(pt[1])) { |
| i.removeOne(i.used() - 2); |
| } |
| return result; |
| } |
| |
| // 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 intersect(const Cubic& cubic, const Quadratic& quad, Intersections& i) { |
| Cubic up; |
| toCubic(quad, up); |
| (void) intersect3(cubic, up, i); |
| return i.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 intersect(const Cubic& c, Intersections& i) { |
| // check to see if x or y end points are the extrema. Are other quick rejects possible? |
| if (ends_are_extrema_in_x_or_y(c)) { |
| return false; |
| } |
| (void) intersect3(c, c, i); |
| if (i.used() > 0) { |
| SkASSERT(i.used() == 1); |
| if (i.fT[0][0] > i.fT[1][0]) { |
| SkTSwap(i.fT[0][0], i.fT[1][0]); |
| } |
| } |
| return i.used(); |
| } |
