// FIXME: if flat measure is sufficiently large, then probably the quartic solution failed static void relaxed_is_linear(const SkDQuad& q1, const SkDQuad& q2, SkIntersections* i) { double m1 = flat_measure(q1); double m2 = flat_measure(q2); #if DEBUG_FLAT_QUADS double min = SkTMin(m1, m2); if (min > 5) { SkDebugf("%s maybe not flat enough.. %1.9g\n", __FUNCTION__, min); } #endif i->reset(); const SkDQuad& rounder = m2 < m1 ? q1 : q2; const SkDQuad& flatter = m2 < m1 ? q2 : q1; bool subDivide = false; is_linear_inner(flatter, 0, 1, rounder, 0, 1, i, &subDivide); if (subDivide) { SkDQuadPair pair = flatter.chopAt(0.5); SkIntersections firstI, secondI; relaxed_is_linear(pair.first(), rounder, &firstI); for (int index = 0; index < firstI.used(); ++index) { i->insert(firstI[0][index] * 0.5, firstI[1][index], firstI.pt(index)); } relaxed_is_linear(pair.second(), rounder, &secondI); for (int index = 0; index < secondI.used(); ++index) { i->insert(0.5 + secondI[0][index] * 0.5, secondI[1][index], secondI.pt(index)); } } if (m2 < m1) { i->swapPts(); } }
// FIXME: if flat measure is sufficiently large, then probably the quartic solution failed // avoid imprecision incurred with chopAt static void relaxed_is_linear(const SkDQuad* q1, double s1, double e1, const SkDQuad* q2, double s2, double e2, SkIntersections* i) { double m1 = flat_measure(*q1); double m2 = flat_measure(*q2); i->reset(); const SkDQuad* rounder, *flatter; double sf, midf, ef, sr, er; if (m2 < m1) { rounder = q1; sr = s1; er = e1; flatter = q2; sf = s2; midf = (s2 + e2) / 2; ef = e2; } else { rounder = q2; sr = s2; er = e2; flatter = q1; sf = s1; midf = (s1 + e1) / 2; ef = e1; } bool subDivide = false; is_linear_inner(*flatter, sf, ef, *rounder, sr, er, i, &subDivide); if (subDivide) { relaxed_is_linear(flatter, sf, midf, rounder, sr, er, i); relaxed_is_linear(flatter, midf, ef, rounder, sr, er, i); } if (m2 < m1) { i->swapPts(); } }
// FIXME ? should this measure both and then use the quad that is the flattest as the line? static bool is_linear(const SkDQuad& q1, const SkDQuad& q2, SkIntersections* i) { double measure = flat_measure(q1); // OPTIMIZE: (get rid of sqrt) use approximately_zero if (!approximately_zero_sqrt(measure)) { return false; } return is_linear_inner(q1, 0, 1, q2, 0, 1, i, NULL); }
static bool is_linear_inner(const SkDQuad& q1, double t1s, double t1e, const SkDQuad& q2, double t2s, double t2e, SkIntersections* i, bool* subDivide) { SkDQuad hull = q1.subDivide(t1s, t1e); SkDLine line = {{hull[2], hull[0]}}; const SkDLine* testLines[] = { &line, (const SkDLine*) &hull[0], (const SkDLine*) &hull[1] }; const size_t kTestCount = SK_ARRAY_COUNT(testLines); SkSTArray<kTestCount * 2, double, true> tsFound; for (size_t index = 0; index < kTestCount; ++index) { SkIntersections rootTs; rootTs.allowNear(false); int roots = rootTs.intersect(q2, *testLines[index]); for (int idx2 = 0; idx2 < roots; ++idx2) { double t = rootTs[0][idx2]; #ifdef SK_DEBUG SkDPoint qPt = q2.ptAtT(t); SkDPoint lPt = testLines[index]->ptAtT(rootTs[1][idx2]); SkASSERT(qPt.approximatelyEqual(lPt)); #endif if (approximately_negative(t - t2s) || approximately_positive(t - t2e)) { continue; } tsFound.push_back(rootTs[0][idx2]); } } int tCount = tsFound.count(); if (tCount <= 0) { return true; } double tMin, tMax; if (tCount == 1) { tMin = tMax = tsFound[0]; } else { SkASSERT(tCount > 1); SkTQSort<double>(tsFound.begin(), tsFound.end() - 1); tMin = tsFound[0]; tMax = tsFound[tsFound.count() - 1]; } SkDPoint end = q2.ptAtT(t2s); bool startInTriangle = hull.pointInHull(end); if (startInTriangle) { tMin = t2s; } end = q2.ptAtT(t2e); bool endInTriangle = hull.pointInHull(end); if (endInTriangle) { tMax = t2e; } int split = 0; SkDVector dxy1, dxy2; if (tMin != tMax || tCount > 2) { dxy2 = q2.dxdyAtT(tMin); for (int index = 1; index < tCount; ++index) { dxy1 = dxy2; dxy2 = q2.dxdyAtT(tsFound[index]); double dot = dxy1.dot(dxy2); if (dot < 0) { split = index - 1; break; } } } if (split == 0) { // there's one point if (add_intercept(q1, q2, tMin, tMax, i, subDivide)) { return true; } i->swap(); return is_linear_inner(q2, tMin, tMax, q1, t1s, t1e, i, subDivide); } // At this point, we have two ranges of t values -- treat each separately at the split bool result; if (add_intercept(q1, q2, tMin, tsFound[split - 1], i, subDivide)) { result = true; } else { i->swap(); result = is_linear_inner(q2, tMin, tsFound[split - 1], q1, t1s, t1e, i, subDivide); } if (add_intercept(q1, q2, tsFound[split], tMax, i, subDivide)) { result = true; } else { i->swap(); result |= is_linear_inner(q2, tsFound[split], tMax, q1, t1s, t1e, i, subDivide); } return result; }