remove prototype pathops code

experimental/Intersection/CubicIntersection.cpp

-/*
- * 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();
-}