// 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); SkTDArray<double> ts1; // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection) c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1); SkTDArray<double> 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) { SkDCubic cSub1 = cubic1.subDivide(t1Start, t1); SkDCubic cSub2 = cubic2.subDivide(t2Start, 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; intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals); SkDebugf(" xlocals.fUsed=%d\n", xlocals.used()); } #endif SkIntersections locals; intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals); double coStart[2] = { -1 }; SkDPoint coPoint; 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.xyAtT(to1); SkDPoint p2 = cubic2.xyAtT(to2); if (p1.approximatelyEqual(p2)) { if (locals.isCoincident(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; } } 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); } } } else { double offset = precisionScale / 16; // FIME: const is arbitrary: test, refine #if 1 double c1Bottom = tIdx == 0 ? 0 : (t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2; double c1Min = SkTMax<double>(c1Bottom, to1 - offset); double c1Top = tIdx == tCount - 1 ? 1 : (t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2; double c1Max = SkTMin<double>(c1Top, to1 + offset); double c2Min = SkTMax<double>(0., to2 - offset); double c2Max = SkTMin<double>(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<double>(0., to1 - offset); c1Max = SkTMin<double>(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<double>(c2Bottom, to2 - offset); c2Max = SkTMin<double>(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<double>(c1Bottom, to1 - offset); c1Max = SkTMin<double>(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 } #else double c1Bottom = tIdx == 0 ? 0 : (t1Start + (t1 - t1Start) * locals.fT[0][tIdx - 1] + to1) / 2; double c1Min = SkTMax<double>(c1Bottom, to1 - offset); double c1Top = tIdx == tCount - 1 ? 1 : (t1Start + (t1 - t1Start) * locals.fT[0][tIdx + 1] + to1) / 2; double c1Max = SkTMin<double>(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<double>(c2Bottom, to2 - offset); double c2Max = SkTMin<double>(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 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. } } SkASSERT(coStart[0] == -1); t2Start = t2; } t1Start = t1; } i.downDepth(); }
// 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(); }