/* 令Aij为矩阵的中间元素,按照这个元素将矩阵划为4份,如果num大于Aij,则num可能落在左下、右上、右下三个子矩阵,对它们分别求子问题。 小于时也是类似的讨论。每次都会求三次子问题,每个子问题元素个数是上次的1/4,所以复杂度是f(N)=3f(N/4)+c,其中N=m*n是元素个数,c是大于0的常量, 主方法可求复杂度为O(N^(log4为底3)),计算器大概算了一下log4为底3约等于0.8。所以复杂度为O((m*n)^0.8) */ bool quadPart(int mat[][N] , int key , int l , int u , int r , int d , int &row , int &col) { if(l > r || u > d) return false; if(key < mat[u][l] || key > mat[d][r]) return false; int mid_col = (l+r)>>1; int mid_row = (u+d)>>1; if(mat[mid_row][mid_col] == key) //查找成功 { row = mid_row; col = mid_col; return true; } else if(l == r && u == d) return false; if(mat[mid_row][mid_col] > key) { // 分别在右上角、左上角、左下角中查找 return quadPart(mat , key , mid_col+1 , u , r , mid_row , row , col) || quadPart(mat , key , l , mid_row+1 , mid_col , d , row , col) || quadPart(mat , key , l , u , mid_col , mid_row , row , col) ; } else { // 分别在右上角、左下角、右下角中查找 return quadPart(mat , key , mid_col+1 , u , r , mid_row , row , col) || quadPart(mat , key , l , mid_row+1 , mid_col , d , row , col) || quadPart(mat , key , mid_col+1 , mid_row+1 , r , d , row , col) ; } }
bool quadPart(int mat[][N] , int key , int &row , int &col) { return quadPart(mat , key , 0 , 0 , N-1 , N-1 , row , col); }
// 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; }
// 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(); }