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Unified Diff: experimental/Intersection/CubicIntersection.cpp

Issue 867213004: remove prototype pathops code (Closed) Base URL: https://skia.googlesource.com/skia.git@master
Patch Set: Created 5 years, 11 months ago
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Index: experimental/Intersection/CubicIntersection.cpp
diff --git a/experimental/Intersection/CubicIntersection.cpp b/experimental/Intersection/CubicIntersection.cpp
deleted file mode 100644
index 175b7b7c460ee0b3d3a30a96b0cfeff6ab53e963..0000000000000000000000000000000000000000
--- a/experimental/Intersection/CubicIntersection.cpp
+++ /dev/null
@@ -1,471 +0,0 @@
-/*
- * 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();
-}
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