6d0032a8ec
git-svn-id: http://skia.googlecode.com/svn/trunk@7031 2bbb7eff-a529-9590-31e7-b0007b416f81
404 lines
15 KiB
C++
404 lines
15 KiB
C++
/*
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* Copyright 2012 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "CurveIntersection.h"
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#include "Intersections.h"
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#include "IntersectionUtilities.h"
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#include "LineIntersection.h"
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#include "LineUtilities.h"
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#include "QuadraticLineSegments.h"
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#include "QuadraticUtilities.h"
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#include <algorithm> // for swap
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static const double tClipLimit = 0.8; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf see Multiple intersections
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class QuadraticIntersections {
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public:
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QuadraticIntersections(const Quadratic& q1, const Quadratic& q2, Intersections& i)
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: quad1(q1)
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, quad2(q2)
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, intersections(i)
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, depth(0)
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, splits(0)
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, coinMinT1(-1) {
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}
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bool intersect() {
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double minT1, minT2, maxT1, maxT2;
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if (!bezier_clip(quad2, quad1, minT1, maxT1)) {
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return false;
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}
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if (!bezier_clip(quad1, quad2, minT2, maxT2)) {
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return false;
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}
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quad1Divisions = 1 / subDivisions(quad1);
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quad2Divisions = 1 / subDivisions(quad2);
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int split;
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if (maxT1 - minT1 < maxT2 - minT2) {
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intersections.swap();
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minT2 = 0;
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maxT2 = 1;
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split = maxT1 - minT1 > tClipLimit;
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} else {
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minT1 = 0;
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maxT1 = 1;
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split = (maxT2 - minT2 > tClipLimit) << 1;
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}
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return chop(minT1, maxT1, minT2, maxT2, split);
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}
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protected:
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bool intersect(double minT1, double maxT1, double minT2, double maxT2) {
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bool t1IsLine = maxT1 - minT1 <= quad1Divisions;
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bool t2IsLine = maxT2 - minT2 <= quad2Divisions;
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if (t1IsLine | t2IsLine) {
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return intersectAsLine(minT1, maxT1, minT2, maxT2, t1IsLine, t2IsLine);
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}
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Quadratic smaller, larger;
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// FIXME: carry last subdivide and reduceOrder result with quad
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sub_divide(quad1, minT1, maxT1, intersections.swapped() ? larger : smaller);
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sub_divide(quad2, minT2, maxT2, intersections.swapped() ? smaller : larger);
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double minT, maxT;
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if (!bezier_clip(smaller, larger, minT, maxT)) {
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if (approximately_equal(minT, maxT)) {
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double smallT, largeT;
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_Point q2pt, q1pt;
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if (intersections.swapped()) {
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largeT = interp(minT2, maxT2, minT);
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xy_at_t(quad2, largeT, q2pt.x, q2pt.y);
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xy_at_t(quad1, minT1, q1pt.x, q1pt.y);
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if (AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)) {
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smallT = minT1;
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} else {
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xy_at_t(quad1, maxT1, q1pt.x, q1pt.y); // FIXME: debug code
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assert(AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y));
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smallT = maxT1;
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}
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} else {
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smallT = interp(minT1, maxT1, minT);
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xy_at_t(quad1, smallT, q1pt.x, q1pt.y);
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xy_at_t(quad2, minT2, q2pt.x, q2pt.y);
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if (AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)) {
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largeT = minT2;
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} else {
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xy_at_t(quad2, maxT2, q2pt.x, q2pt.y); // FIXME: debug code
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assert(AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y));
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largeT = maxT2;
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}
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}
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intersections.add(smallT, largeT);
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return true;
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}
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return false;
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}
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int split;
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if (intersections.swapped()) {
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double newMinT1 = interp(minT1, maxT1, minT);
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double newMaxT1 = interp(minT1, maxT1, maxT);
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split = (newMaxT1 - newMinT1 > (maxT1 - minT1) * tClipLimit) << 1;
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#define VERBOSE 0
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#if VERBOSE
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printf("%s d=%d s=%d new1=(%g,%g) old1=(%g,%g) split=%d\n", __FUNCTION__, depth,
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splits, newMinT1, newMaxT1, minT1, maxT1, split);
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#endif
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minT1 = newMinT1;
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maxT1 = newMaxT1;
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} else {
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double newMinT2 = interp(minT2, maxT2, minT);
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double newMaxT2 = interp(minT2, maxT2, maxT);
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split = newMaxT2 - newMinT2 > (maxT2 - minT2) * tClipLimit;
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#if VERBOSE
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printf("%s d=%d s=%d new2=(%g,%g) old2=(%g,%g) split=%d\n", __FUNCTION__, depth,
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splits, newMinT2, newMaxT2, minT2, maxT2, split);
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#endif
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minT2 = newMinT2;
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maxT2 = newMaxT2;
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}
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return chop(minT1, maxT1, minT2, maxT2, split);
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}
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bool intersectAsLine(double minT1, double maxT1, double minT2, double maxT2,
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bool treat1AsLine, bool treat2AsLine)
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{
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_Line line1, line2;
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if (intersections.swapped()) {
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std::swap(treat1AsLine, treat2AsLine);
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std::swap(minT1, minT2);
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std::swap(maxT1, maxT2);
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}
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if (coinMinT1 >= 0) {
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bool earlyExit;
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if ((earlyExit = coinMaxT1 == minT1)) {
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coinMaxT1 = maxT1;
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}
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if (coinMaxT2 == minT2) {
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coinMaxT2 = maxT2;
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return true;
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}
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if (earlyExit) {
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return true;
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}
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coinMinT1 = -1;
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}
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// do line/quadratic or even line/line intersection instead
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if (treat1AsLine) {
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xy_at_t(quad1, minT1, line1[0].x, line1[0].y);
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xy_at_t(quad1, maxT1, line1[1].x, line1[1].y);
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}
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if (treat2AsLine) {
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xy_at_t(quad2, minT2, line2[0].x, line2[0].y);
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xy_at_t(quad2, maxT2, line2[1].x, line2[1].y);
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}
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int pts;
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double smallT1, largeT1, smallT2, largeT2;
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if (treat1AsLine & treat2AsLine) {
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double t1[2], t2[2];
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pts = ::intersect(line1, line2, t1, t2);
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if (pts == 2) {
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smallT1 = interp(minT1, maxT1, t1[0]);
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largeT1 = interp(minT2, maxT2, t2[0]);
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smallT2 = interp(minT1, maxT1, t1[1]);
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largeT2 = interp(minT2, maxT2, t2[1]);
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intersections.addCoincident(smallT1, smallT2, largeT1, largeT2);
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} else {
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smallT1 = interp(minT1, maxT1, t1[0]);
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largeT1 = interp(minT2, maxT2, t2[0]);
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intersections.add(smallT1, largeT1);
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}
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} else {
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Intersections lq;
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pts = ::intersect(treat1AsLine ? quad2 : quad1,
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treat1AsLine ? line1 : line2, lq);
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if (pts == 2) { // if the line and edge are coincident treat differently
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_Point midQuad, midLine;
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double midQuadT = (lq.fT[0][0] + lq.fT[0][1]) / 2;
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xy_at_t(treat1AsLine ? quad2 : quad1, midQuadT, midQuad.x, midQuad.y);
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double lineT = t_at(treat1AsLine ? line1 : line2, midQuad);
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xy_at_t(treat1AsLine ? line1 : line2, lineT, midLine.x, midLine.y);
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if (AlmostEqualUlps(midQuad.x, midLine.x)
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&& AlmostEqualUlps(midQuad.y, midLine.y)) {
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smallT1 = lq.fT[0][0];
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largeT1 = lq.fT[1][0];
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smallT2 = lq.fT[0][1];
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largeT2 = lq.fT[1][1];
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if (treat2AsLine) {
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smallT1 = interp(minT1, maxT1, smallT1);
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smallT2 = interp(minT1, maxT1, smallT2);
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} else {
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largeT1 = interp(minT2, maxT2, largeT1);
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largeT2 = interp(minT2, maxT2, largeT2);
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}
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intersections.addCoincident(smallT1, smallT2, largeT1, largeT2);
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goto setCoinMinMax;
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}
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}
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for (int index = 0; index < pts; ++index) {
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smallT1 = lq.fT[0][index];
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largeT1 = lq.fT[1][index];
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if (treat2AsLine) {
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smallT1 = interp(minT1, maxT1, smallT1);
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} else {
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largeT1 = interp(minT2, maxT2, largeT1);
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}
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intersections.add(smallT1, largeT1);
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}
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}
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if (pts > 0) {
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setCoinMinMax:
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coinMinT1 = minT1;
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coinMaxT1 = maxT1;
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coinMinT2 = minT2;
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coinMaxT2 = maxT2;
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}
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return pts > 0;
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}
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bool chop(double minT1, double maxT1, double minT2, double maxT2, int split) {
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++depth;
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intersections.swap();
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if (split) {
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++splits;
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if (split & 2) {
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double middle1 = (maxT1 + minT1) / 2;
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intersect(minT1, middle1, minT2, maxT2);
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intersect(middle1, maxT1, minT2, maxT2);
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} else {
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double middle2 = (maxT2 + minT2) / 2;
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intersect(minT1, maxT1, minT2, middle2);
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intersect(minT1, maxT1, middle2, maxT2);
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}
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--splits;
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intersections.swap();
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--depth;
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return intersections.intersected();
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}
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bool result = intersect(minT1, maxT1, minT2, maxT2);
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intersections.swap();
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--depth;
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return result;
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}
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private:
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const Quadratic& quad1;
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const Quadratic& quad2;
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Intersections& intersections;
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int depth;
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int splits;
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double quad1Divisions; // line segments to approximate original within error
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double quad2Divisions;
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double coinMinT1; // range of Ts where approximate line intersected curve
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double coinMaxT1;
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double coinMinT2;
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double coinMaxT2;
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};
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#include "LineParameters.h"
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static void hackToFixPartialCoincidence(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
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// look to see if non-coincident data basically has unsortable tangents
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// look to see if a point between non-coincident data is on the curve
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int cIndex;
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for (int uIndex = 0; uIndex < i.fUsed; ) {
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double bestDist1 = 1;
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double bestDist2 = 1;
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int closest1 = -1;
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int closest2 = -1;
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for (cIndex = 0; cIndex < i.fCoincidentUsed; ++cIndex) {
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double dist = fabs(i.fT[0][uIndex] - i.fCoincidentT[0][cIndex]);
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if (bestDist1 > dist) {
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bestDist1 = dist;
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closest1 = cIndex;
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}
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dist = fabs(i.fT[1][uIndex] - i.fCoincidentT[1][cIndex]);
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if (bestDist2 > dist) {
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bestDist2 = dist;
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closest2 = cIndex;
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}
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}
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_Line ends;
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_Point mid;
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double t1 = i.fT[0][uIndex];
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xy_at_t(q1, t1, ends[0].x, ends[0].y);
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xy_at_t(q1, i.fCoincidentT[0][closest1], ends[1].x, ends[1].y);
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double midT = (t1 + i.fCoincidentT[0][closest1]) / 2;
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xy_at_t(q1, midT, mid.x, mid.y);
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LineParameters params;
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params.lineEndPoints(ends);
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double midDist = params.pointDistance(mid);
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// Note that we prefer to always measure t error, which does not scale,
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// instead of point error, which is scale dependent. FIXME
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if (!approximately_zero(midDist)) {
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++uIndex;
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continue;
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}
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double t2 = i.fT[1][uIndex];
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xy_at_t(q2, t2, ends[0].x, ends[0].y);
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xy_at_t(q2, i.fCoincidentT[1][closest2], ends[1].x, ends[1].y);
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midT = (t2 + i.fCoincidentT[1][closest2]) / 2;
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xy_at_t(q2, midT, mid.x, mid.y);
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params.lineEndPoints(ends);
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midDist = params.pointDistance(mid);
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if (!approximately_zero(midDist)) {
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++uIndex;
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continue;
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}
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// if both midpoints are close to the line, lengthen coincident span
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int cEnd = closest1 ^ 1; // assume coincidence always travels in pairs
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if (!between(i.fCoincidentT[0][cEnd], t1, i.fCoincidentT[0][closest1])) {
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i.fCoincidentT[0][closest1] = t1;
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}
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cEnd = closest2 ^ 1;
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if (!between(i.fCoincidentT[0][cEnd], t2, i.fCoincidentT[0][closest2])) {
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i.fCoincidentT[0][closest2] = t2;
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}
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int remaining = --i.fUsed - uIndex;
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if (remaining > 0) {
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memmove(&i.fT[0][uIndex], &i.fT[0][uIndex + 1], sizeof(i.fT[0][0]) * remaining);
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memmove(&i.fT[1][uIndex], &i.fT[1][uIndex + 1], sizeof(i.fT[1][0]) * remaining);
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}
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}
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// if coincident data is subjectively a tiny span, replace it with a single point
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for (cIndex = 0; cIndex < i.fCoincidentUsed; ) {
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double start1 = i.fCoincidentT[0][cIndex];
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double end1 = i.fCoincidentT[0][cIndex + 1];
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_Line ends1;
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xy_at_t(q1, start1, ends1[0].x, ends1[0].y);
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xy_at_t(q1, end1, ends1[1].x, ends1[1].y);
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if (!AlmostEqualUlps(ends1[0].x, ends1[1].x) || AlmostEqualUlps(ends1[0].y, ends1[1].y)) {
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cIndex += 2;
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continue;
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}
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double start2 = i.fCoincidentT[1][cIndex];
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double end2 = i.fCoincidentT[1][cIndex + 1];
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_Line ends2;
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xy_at_t(q2, start2, ends2[0].x, ends2[0].y);
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xy_at_t(q2, end2, ends2[1].x, ends2[1].y);
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// again, approximately should be used with T values, not points FIXME
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if (!AlmostEqualUlps(ends2[0].x, ends2[1].x) || AlmostEqualUlps(ends2[0].y, ends2[1].y)) {
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cIndex += 2;
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continue;
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}
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if (approximately_less_than_zero(start1) || approximately_less_than_zero(end1)) {
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start1 = 0;
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} else if (approximately_greater_than_one(start1) || approximately_greater_than_one(end1)) {
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start1 = 1;
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} else {
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start1 = (start1 + end1) / 2;
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}
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if (approximately_less_than_zero(start2) || approximately_less_than_zero(end2)) {
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start2 = 0;
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} else if (approximately_greater_than_one(start2) || approximately_greater_than_one(end2)) {
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start2 = 1;
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} else {
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start2 = (start2 + end2) / 2;
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}
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i.insert(start1, start2);
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i.fCoincidentUsed -= 2;
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int remaining = i.fCoincidentUsed - cIndex;
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if (remaining > 0) {
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memmove(&i.fCoincidentT[0][cIndex], &i.fCoincidentT[0][cIndex + 2], sizeof(i.fCoincidentT[0][0]) * remaining);
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memmove(&i.fCoincidentT[1][cIndex], &i.fCoincidentT[1][cIndex + 2], sizeof(i.fCoincidentT[1][0]) * remaining);
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}
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}
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}
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bool intersect(const Quadratic& q1, const Quadratic& q2, Intersections& i) {
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if (implicit_matches(q1, q2)) {
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// FIXME: compute T values
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// compute the intersections of the ends to find the coincident span
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bool useVertical = fabs(q1[0].x - q1[2].x) < fabs(q1[0].y - q1[2].y);
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double t;
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if ((t = axialIntersect(q1, q2[0], useVertical)) >= 0) {
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i.addCoincident(t, 0);
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}
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if ((t = axialIntersect(q1, q2[2], useVertical)) >= 0) {
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i.addCoincident(t, 1);
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}
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useVertical = fabs(q2[0].x - q2[2].x) < fabs(q2[0].y - q2[2].y);
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if ((t = axialIntersect(q2, q1[0], useVertical)) >= 0) {
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i.addCoincident(0, t);
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}
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if ((t = axialIntersect(q2, q1[2], useVertical)) >= 0) {
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i.addCoincident(1, t);
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}
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assert(i.fCoincidentUsed <= 2);
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return i.fCoincidentUsed > 0;
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}
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QuadraticIntersections q(q1, q2, i);
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bool result = q.intersect();
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// FIXME: partial coincidence detection is currently poor. For now, try
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// to fix up the data after the fact. In the future, revisit the error
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// term to try to avoid this kind of result in the first place.
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if (i.fUsed && i.fCoincidentUsed) {
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hackToFixPartialCoincidence(q1, q2, i);
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}
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return result;
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}
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