ee235f9062
git-svn-id: http://skia.googlecode.com/svn/trunk@7659 2bbb7eff-a529-9590-31e7-b0007b416f81
659 lines
24 KiB
C++
659 lines
24 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 "CubicUtilities.h"
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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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#define DEBUG_COMPUTE_DELTA 1
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#define COMPUTE_DELTA 0
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#define DEBUG_QUAD_PART 0
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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 CubicIntersections : public Intersections {
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public:
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CubicIntersections(const Cubic& c1, const Cubic& c2, Intersections& i)
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: cubic1(c1)
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, cubic2(c2)
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, intersections(i)
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, depth(0)
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, splits(0) {
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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(cubic2, cubic1, minT1, maxT1)) {
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return false;
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}
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if (!bezier_clip(cubic1, cubic2, minT2, maxT2)) {
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return false;
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}
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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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Cubic smaller, larger;
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// FIXME: carry last subdivide and reduceOrder result with cubic
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sub_divide(cubic1, minT1, maxT1, intersections.swapped() ? larger : smaller);
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sub_divide(cubic2, minT2, maxT2, intersections.swapped() ? smaller : larger);
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Cubic smallResult;
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if (reduceOrder(smaller, smallResult,
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kReduceOrder_NoQuadraticsAllowed) <= 2) {
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Cubic largeResult;
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if (reduceOrder(larger, largeResult,
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kReduceOrder_NoQuadraticsAllowed) <= 2) {
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const _Line& smallLine = (const _Line&) smallResult;
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const _Line& largeLine = (const _Line&) largeResult;
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double smallT[2];
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double largeT[2];
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// FIXME: this doesn't detect or deal with coincident lines
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if (!::intersect(smallLine, largeLine, smallT, largeT)) {
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return false;
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}
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if (intersections.swapped()) {
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smallT[0] = interp(minT2, maxT2, smallT[0]);
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largeT[0] = interp(minT1, maxT1, largeT[0]);
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} else {
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smallT[0] = interp(minT1, maxT1, smallT[0]);
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largeT[0] = interp(minT2, maxT2, largeT[0]);
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}
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intersections.add(smallT[0], largeT[0]);
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return true;
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}
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}
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double minT, maxT;
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if (!bezier_clip(smaller, larger, minT, maxT)) {
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if (minT == maxT) {
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if (intersections.swapped()) {
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minT1 = (minT1 + maxT1) / 2;
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minT2 = interp(minT2, maxT2, minT);
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} else {
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minT1 = interp(minT1, maxT1, minT);
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minT2 = (minT2 + maxT2) / 2;
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}
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intersections.add(minT1, minT2);
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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",
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__FUNCTION__, depth, splits, newMinT1, newMaxT1, minT1, maxT1,
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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",
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__FUNCTION__, depth, splits, newMinT2, newMaxT2, minT2, maxT2,
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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 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 Cubic& cubic1;
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const Cubic& cubic2;
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Intersections& intersections;
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int depth;
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int splits;
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};
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bool intersect(const Cubic& c1, const Cubic& c2, Intersections& i) {
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CubicIntersections c(c1, c2, i);
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return c.intersect();
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}
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#if COMPUTE_DELTA
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static void cubicTangent(const Cubic& cubic, double t, _Line& tangent, _Point& pt, _Point& dxy) {
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xy_at_t(cubic, t, tangent[0].x, tangent[0].y);
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pt = tangent[1] = tangent[0];
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dxdy_at_t(cubic, t, dxy);
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if (dxy.approximatelyZero()) {
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if (approximately_zero(t)) {
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SkASSERT(cubic[0].approximatelyEqual(cubic[1]));
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dxy = cubic[2];
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dxy -= cubic[0];
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} else {
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SkASSERT(approximately_equal(t, 1));
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SkASSERT(cubic[3].approximatelyEqual(cubic[2]));
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dxy = cubic[3];
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dxy -= cubic[1];
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}
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SkASSERT(!dxy.approximatelyZero());
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}
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tangent[0] -= dxy;
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tangent[1] += dxy;
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#if DEBUG_COMPUTE_DELTA
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SkDebugf("%s t=%1.9g tangent=(%1.9g,%1.9g %1.9g,%1.9g)"
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" pt=(%1.9g %1.9g) dxy=(%1.9g %1.9g)\n", __FUNCTION__, t,
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tangent[0].x, tangent[0].y, tangent[1].x, tangent[1].y, pt.x, pt.y,
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dxy.x, dxy.y);
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#endif
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}
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#endif
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#if COMPUTE_DELTA
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static double cubicDelta(const _Point& dxy, _Line& tangent, double scale) {
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double tangentLen = dxy.length();
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tangent[0] -= tangent[1];
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double intersectLen = tangent[0].length();
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double result = intersectLen / tangentLen + scale;
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#if DEBUG_COMPUTE_DELTA
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SkDebugf("%s tangent=(%1.9g,%1.9g %1.9g,%1.9g) intersectLen=%1.9g tangentLen=%1.9g scale=%1.9g"
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" result=%1.9g\n", __FUNCTION__, tangent[0].x, tangent[0].y, tangent[1].x, tangent[1].y,
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intersectLen, tangentLen, scale, result);
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#endif
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return result;
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}
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#endif
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#if COMPUTE_DELTA
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// FIXME: after testing, make this static
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static void computeDelta(const Cubic& c1, double t1, double scale1, const Cubic& c2, double t2,
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double scale2, double& delta1, double& delta2) {
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#if DEBUG_COMPUTE_DELTA
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SkDebugf("%s c1=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) t1=%1.9g scale1=%1.9g"
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" c2=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) t2=%1.9g scale2=%1.9g\n",
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__FUNCTION__,
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c1[0].x, c1[0].y, c1[1].x, c1[1].y, c1[2].x, c1[2].y, c1[3].x, c1[3].y, t1, scale1,
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c2[0].x, c2[0].y, c2[1].x, c2[1].y, c2[2].x, c2[2].y, c2[3].x, c2[3].y, t2, scale2);
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#endif
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_Line tangent1, tangent2, line1, line2;
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_Point dxy1, dxy2;
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cubicTangent(c1, t1, line1, tangent1[0], dxy1);
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cubicTangent(c2, t2, line2, tangent2[0], dxy2);
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double range1[2], range2[2];
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int found = intersect(line1, line2, range1, range2);
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if (found == 0) {
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range1[0] = 0.5;
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} else {
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SkASSERT(found == 1);
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}
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xy_at_t(line1, range1[0], tangent1[1].x, tangent1[1].y);
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#if SK_DEBUG
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if (found == 1) {
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xy_at_t(line2, range2[0], tangent2[1].x, tangent2[1].y);
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SkASSERT(tangent2[1].approximatelyEqual(tangent1[1]));
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}
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#endif
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tangent2[1] = tangent1[1];
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delta1 = cubicDelta(dxy1, tangent1, scale1 / precisionUnit);
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delta2 = cubicDelta(dxy2, tangent2, scale2 / precisionUnit);
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}
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#if SK_DEBUG
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int debugDepth;
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#endif
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#endif
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static int quadPart(const Cubic& cubic, double tStart, double tEnd, Quadratic& simple) {
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Cubic part;
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sub_divide(cubic, tStart, tEnd, part);
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Quadratic quad;
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demote_cubic_to_quad(part, quad);
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// FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an
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// extremely shallow quadratic?
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int order = reduceOrder(quad, simple);
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#if DEBUG_QUAD_PART
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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",
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__FUNCTION__, cubic[0].x, cubic[0].y, cubic[1].x, cubic[1].y, cubic[2].x, cubic[2].y,
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cubic[3].x, cubic[3].y, tStart, tEnd);
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SkDebugf("%s part=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)"
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" quad=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)\n", __FUNCTION__, part[0].x, part[0].y,
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part[1].x, part[1].y, part[2].x, part[2].y, part[3].x, part[3].y, quad[0].x, quad[0].y,
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quad[1].x, quad[1].y, quad[2].x, quad[2].y);
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SkDebugf("%s simple=(%1.17g,%1.17g", __FUNCTION__, simple[0].x, simple[0].y);
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if (order > 1) {
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SkDebugf(" %1.17g,%1.17g", simple[1].x, simple[1].y);
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}
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if (order > 2) {
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SkDebugf(" %1.17g,%1.17g", simple[2].x, simple[2].y);
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}
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SkDebugf(")\n");
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SkASSERT(order < 4 && order > 0);
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#endif
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return order;
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}
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static void intersectWithOrder(const Quadratic& simple1, int order1, const Quadratic& simple2,
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int order2, Intersections& i) {
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if (order1 == 3 && order2 == 3) {
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intersect2(simple1, simple2, i);
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} else if (order1 <= 2 && order2 <= 2) {
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i.fUsed = intersect((const _Line&) simple1, (const _Line&) simple2, i.fT[0], i.fT[1]);
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} else if (order1 == 3 && order2 <= 2) {
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intersect(simple1, (const _Line&) simple2, i);
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} else {
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SkASSERT(order1 <= 2 && order2 == 3);
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intersect(simple2, (const _Line&) simple1, i);
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for (int s = 0; s < i.fUsed; ++s) {
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SkTSwap(i.fT[0][s], i.fT[1][s]);
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}
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}
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}
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static double distanceFromEnd(double t) {
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return t > 0.5 ? 1 - t : t;
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}
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// OPTIMIZATION: this used to try to guess the value for delta, and that may still be worthwhile
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static void bumpForRetry(double t1, double t2, double& s1, double& e1, double& s2, double& e2) {
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double dt1 = distanceFromEnd(t1);
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double dt2 = distanceFromEnd(t2);
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double delta = 1.0 / precisionUnit;
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if (dt1 < dt2) {
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if (t1 == dt1) {
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s1 = SkTMax(s1 - delta, 0.);
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} else {
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e1 = SkTMin(e1 + delta, 1.);
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}
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} else {
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if (t2 == dt2) {
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s2 = SkTMax(s2 - delta, 0.);
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} else {
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e2 = SkTMin(e2 + delta, 1.);
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}
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}
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}
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static bool doIntersect(const Cubic& cubic1, double t1s, double t1m, double t1e,
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const Cubic& cubic2, double t2s, double t2m, double t2e, Intersections& i) {
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bool result = false;
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i.upDepth();
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// divide the quadratics at the new t value and try again
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double p1s = t1s;
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double p1e = t1m;
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for (int p1 = 0; p1 < 2; ++p1) {
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Quadratic s1a;
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int o1a = quadPart(cubic1, p1s, p1e, s1a);
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double p2s = t2s;
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double p2e = t2m;
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for (int p2 = 0; p2 < 2; ++p2) {
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Quadratic s2a;
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int o2a = quadPart(cubic2, p2s, p2e, s2a);
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Intersections locals;
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#if 0 && SK_DEBUG
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if (0.497026154 >= p1s && 0.497026535 <= p1e
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&& 0.710440575 >= p2s && 0.710440956 <= p2e) {
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SkDebugf("t1=(%1.9g,%1.9g) o1=%d t2=(%1.9g,%1.9g) o2=%d\n",
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p1s, p1e, o1a, p2s, p2e, o2a);
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if (o1a == 2) {
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SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
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s1a[0].x, s1a[0].y, s1a[1].x, s1a[1].y);
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} else {
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SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
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s1a[0].x, s1a[0].y, s1a[1].x, s1a[1].y, s1a[2].x, s1a[2].y);
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}
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if (o2a == 2) {
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SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
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s2a[0].x, s2a[0].y, s2a[1].x, s2a[1].y);
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} else {
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SkDebugf("{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
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s2a[0].x, s2a[0].y, s2a[1].x, s2a[1].y, s2a[2].x, s2a[2].y);
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}
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Intersections xlocals;
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intersectWithOrder(s1a, o1a, s2a, o2a, xlocals);
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SkDebugf("xlocals.fUsed=%d\n", xlocals.used());
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}
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#endif
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intersectWithOrder(s1a, o1a, s2a, o2a, locals);
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for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
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double to1 = p1s + (p1e - p1s) * locals.fT[0][tIdx];
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double to2 = p2s + (p2e - p2s) * locals.fT[1][tIdx];
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// if the computed t is not sufficiently precise, iterate
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_Point p1, p2;
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xy_at_t(cubic1, to1, p1.x, p1.y);
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xy_at_t(cubic2, to2, p2.x, p2.y);
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#if 0 && SK_DEBUG
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SkDebugf("to1=%1.9g p1=(%1.9g,%1.9g) to2=%1.9g p2=(%1.9g,%1.9g) d=%1.9g\n",
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to1, p1.x, p1.y, to2, p2.x, p2.y, p1.distance(p2));
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#endif
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if (p1.approximatelyEqual(p2)) {
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i.insert(i.swapped() ? to2 : to1, i.swapped() ? to1 : to2);
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result = true;
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} else {
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result = doIntersect(cubic1, p1s, to1, p1e, cubic2, p2s, to2, p2e, i);
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// if both cubics curve in the same direction, the quadratic intersection
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// may mark a range that does not contain the cubic intersection. If no
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// intersection is found, look again including the t distance of the
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// of the quadratic intersection nearest a quadratic end (which in turn is
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// nearest the actual cubic)
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if (!result) {
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double b1s = p1s;
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double b1e = p1e;
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double b2s = p2s;
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double b2e = p2e;
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bumpForRetry(locals.fT[0][tIdx], locals.fT[1][tIdx], b1s, b1e, b2s, b2e);
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result = doIntersect(cubic1, b1s, to1, b1e, cubic2, b2s, to2, b2e, i);
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}
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}
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}
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p2s = p2e;
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p2e = t2e;
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}
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p1s = p1e;
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p1e = t1e;
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}
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|
i.downDepth();
|
|
return result;
|
|
}
|
|
|
|
// this flavor approximates the cubics with quads to find the intersecting ts
|
|
// OPTIMIZE: if this strategy proves successful, the quad approximations, or the ts used
|
|
// to create the approximations, could be stored in the cubic segment
|
|
// FIXME: this strategy needs to intersect the convex hull on either end with the opposite to
|
|
// account for inset quadratics that cause the endpoint intersection to avoid detection
|
|
// the segments can be very short -- the length of the maximum quadratic error (precision)
|
|
static bool intersect2(const Cubic& cubic1, double t1s, double t1e, const Cubic& cubic2,
|
|
double t2s, double t2e, double precisionScale, Intersections& i) {
|
|
Cubic c1, c2;
|
|
sub_divide(cubic1, t1s, t1e, c1);
|
|
sub_divide(cubic2, t2s, t2e, c2);
|
|
SkTDArray<double> ts1;
|
|
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;
|
|
Quadratic s2;
|
|
int o2 = quadPart(cubic2, t2Start, t2, s2);
|
|
#if 0 && SK_DEBUG
|
|
if (0.497026154 >= t1Start && 0.497026535 <= t1
|
|
&& 0.710440575 + 0.0004 >= t2Start && 0.710440956 <= t2) {
|
|
Cubic cSub1, cSub2;
|
|
sub_divide(cubic1, t1Start, tEnd1, cSub1);
|
|
sub_divide(cubic2, t2Start, tEnd2, cSub2);
|
|
SkDebugf("t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)\n",
|
|
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);
|
|
|
|
for (int tIdx = 0; tIdx < locals.used(); ++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, p2;
|
|
xy_at_t(cubic1, to1, p1.x, p1.y);
|
|
xy_at_t(cubic2, to2, p2.x, p2.y);
|
|
if (p1.approximatelyEqual(p2)) {
|
|
i.insert(i.swapped() ? to2 : to1, i.swapped() ? to1 : to2);
|
|
} else {
|
|
#if COMPUTE_DELTA
|
|
double dt1, dt2;
|
|
computeDelta(cubic1, to1, (t1e - t1s), cubic2, to2, (t2e - t2s), dt1, dt2);
|
|
double scale = precisionScale;
|
|
if (dt1 > 0.125 || dt2 > 0.125) {
|
|
scale /= 2;
|
|
SkDebugf("%s scale=%1.9g\n", __FUNCTION__, scale);
|
|
}
|
|
#if SK_DEBUG
|
|
++debugDepth;
|
|
SkASSERT(debugDepth < 10);
|
|
#endif
|
|
i.swap();
|
|
intersect2(cubic2, SkTMax(to2 - dt2, 0.), SkTMin(to2 + dt2, 1.),
|
|
cubic1, SkTMax(to1 - dt1, 0.), SkTMin(to1 + dt1, 1.), scale, i);
|
|
i.swap();
|
|
#if SK_DEBUG
|
|
--debugDepth;
|
|
#endif
|
|
#else
|
|
#if 0 && SK_DEBUG
|
|
if (0.497026154 >= t1Start && 0.497026535 <= t1
|
|
&& 0.710440575 >= t2Start && 0.710440956 <= t2) {
|
|
SkDebugf("t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)\n",
|
|
t1Start, t1, t2Start, t2);
|
|
}
|
|
#endif
|
|
bool found = doIntersect(cubic1, t1Start, to1, t1, cubic2, t2Start, to2, t2, i);
|
|
if (!found) {
|
|
double b1s = t1Start;
|
|
double b1e = t1;
|
|
double b2s = t2Start;
|
|
double b2e = t2;
|
|
bumpForRetry(locals.fT[0][tIdx], locals.fT[1][tIdx], b1s, b1e, b2s, b2e);
|
|
doIntersect(cubic1, b1s, to1, b1e, cubic2, b2s, to2, b2e, i);
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
if (locals.coincidentUsed()) {
|
|
SkASSERT(locals.coincidentUsed() == 2);
|
|
double coTs[2][2];
|
|
for (int tIdx = 0; tIdx < locals.coincidentUsed(); ++tIdx) {
|
|
coTs[0][tIdx] = t1Start + (t1 - t1Start) * locals.fCoincidentT[0][tIdx];
|
|
coTs[1][tIdx] = t2Start + (t2 - t2Start) * locals.fCoincidentT[1][tIdx];
|
|
}
|
|
i.addCoincident(coTs[0][0], coTs[0][1], coTs[1][0], coTs[1][1]);
|
|
}
|
|
t2Start = t2;
|
|
}
|
|
t1Start = t1;
|
|
}
|
|
return i.intersected();
|
|
}
|
|
|
|
static bool intersectEnd(const Cubic& cubic1, bool start, const Cubic& cubic2, const _Rect& bounds2,
|
|
Intersections& i) {
|
|
_Line line1;
|
|
line1[1] = cubic1[start ? 0 : 3];
|
|
if (line1[1].approximatelyEqual(cubic2[0]) || line1[1].approximatelyEqual(cubic2[3])) {
|
|
return false;
|
|
}
|
|
line1[0] = line1[1];
|
|
_Point dxy1 = line1[0] - cubic1[start ? 1 : 2];
|
|
if (dxy1.approximatelyZero()) {
|
|
dxy1 = line1[0] - cubic1[start ? 2 : 1];
|
|
}
|
|
dxy1 /= precisionUnit;
|
|
line1[1] += dxy1;
|
|
_Rect line1Bounds;
|
|
line1Bounds.setBounds(line1);
|
|
if (!bounds2.intersects(line1Bounds)) {
|
|
return false;
|
|
}
|
|
_Line line2;
|
|
line2[0] = line2[1] = line1[0];
|
|
_Point dxy2 = line2[0] - cubic1[start ? 3 : 0];
|
|
SkASSERT(!dxy2.approximatelyZero());
|
|
dxy2 /= precisionUnit;
|
|
line2[1] += dxy2;
|
|
#if 0 // this is so close to the first bounds test it isn't worth the short circuit test
|
|
_Rect line2Bounds;
|
|
line2Bounds.setBounds(line2);
|
|
if (!bounds2.intersects(line2Bounds)) {
|
|
return false;
|
|
}
|
|
#endif
|
|
Intersections local1;
|
|
if (!intersect(cubic2, line1, local1)) {
|
|
return false;
|
|
}
|
|
Intersections local2;
|
|
if (!intersect(cubic2, line2, local2)) {
|
|
return false;
|
|
}
|
|
double tMin, tMax;
|
|
tMin = tMax = local1.fT[0][0];
|
|
for (int index = 1; index < local1.fUsed; ++index) {
|
|
tMin = SkTMin(tMin, local1.fT[0][index]);
|
|
tMax = SkTMax(tMax, local1.fT[0][index]);
|
|
}
|
|
for (int index = 1; index < local2.fUsed; ++index) {
|
|
tMin = SkTMin(tMin, local2.fT[0][index]);
|
|
tMax = SkTMax(tMax, local2.fT[0][index]);
|
|
}
|
|
#if SK_DEBUG && COMPUTE_DELTA
|
|
debugDepth = 0;
|
|
#endif
|
|
return intersect2(cubic1, start ? 0 : 1, start ? 1.0 / precisionUnit : 1 - 1.0 / precisionUnit,
|
|
cubic2, tMin, tMax, 1, i);
|
|
}
|
|
|
|
// FIXME: add intersection of convex hull on cubics' ends with the opposite cubic. The hull line
|
|
// segments can be constructed to be only as long as the calculated precision suggests. If the hull
|
|
// line segments intersect the cubic, then use the intersections to construct a subdivision for
|
|
// quadratic curve fitting.
|
|
bool intersect2(const Cubic& c1, const Cubic& c2, Intersections& i) {
|
|
#if SK_DEBUG && COMPUTE_DELTA
|
|
debugDepth = 0;
|
|
#endif
|
|
bool result = intersect2(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);
|
|
i.swap();
|
|
result |= intersectEnd(c2, false, c1, c1Bounds, i);
|
|
result |= intersectEnd(c2, true, c1, c1Bounds, i);
|
|
i.swap();
|
|
return result;
|
|
}
|
|
|
|
int intersect(const Cubic& cubic, const Quadratic& quad, Intersections& i) {
|
|
SkTDArray<double> ts;
|
|
double precision = calcPrecision(cubic);
|
|
cubic_to_quadratics(cubic, precision, ts);
|
|
double tStart = 0;
|
|
Cubic part;
|
|
int tsCount = ts.count();
|
|
for (int idx = 0; idx <= tsCount; ++idx) {
|
|
double t = idx < tsCount ? ts[idx] : 1;
|
|
Quadratic q1;
|
|
sub_divide(cubic, tStart, t, part);
|
|
demote_cubic_to_quad(part, q1);
|
|
Intersections locals;
|
|
intersect2(q1, quad, locals);
|
|
for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
|
|
double globalT = tStart + (t - tStart) * locals.fT[0][tIdx];
|
|
i.insertOne(globalT, 0);
|
|
globalT = locals.fT[1][tIdx];
|
|
i.insertOne(globalT, 1);
|
|
}
|
|
tStart = t;
|
|
}
|
|
return i.used();
|
|
}
|
|
|
|
bool intersect(const Cubic& cubic, Intersections& i) {
|
|
SkTDArray<double> ts;
|
|
double precision = calcPrecision(cubic);
|
|
cubic_to_quadratics(cubic, precision, ts);
|
|
int tsCount = ts.count();
|
|
if (tsCount == 1) {
|
|
return false;
|
|
}
|
|
double t1Start = 0;
|
|
Cubic part;
|
|
for (int idx = 0; idx < tsCount; ++idx) {
|
|
double t1 = ts[idx];
|
|
Quadratic q1;
|
|
sub_divide(cubic, t1Start, t1, part);
|
|
demote_cubic_to_quad(part, q1);
|
|
double t2Start = t1;
|
|
for (int i2 = idx + 1; i2 <= tsCount; ++i2) {
|
|
const double t2 = i2 < tsCount ? ts[i2] : 1;
|
|
Quadratic q2;
|
|
sub_divide(cubic, t2Start, t2, part);
|
|
demote_cubic_to_quad(part, q2);
|
|
Intersections locals;
|
|
intersect2(q1, q2, locals);
|
|
for (int tIdx = 0; tIdx < locals.used(); ++tIdx) {
|
|
// discard intersections at cusp? (maximum curvature)
|
|
double t1sect = locals.fT[0][tIdx];
|
|
double t2sect = locals.fT[1][tIdx];
|
|
if (idx + 1 == i2 && t1sect == 1 && t2sect == 0) {
|
|
continue;
|
|
}
|
|
double to1 = t1Start + (t1 - t1Start) * t1sect;
|
|
double to2 = t2Start + (t2 - t2Start) * t2sect;
|
|
i.insert(to1, to2);
|
|
}
|
|
t2Start = t2;
|
|
}
|
|
t1Start = t1;
|
|
}
|
|
return i.intersected();
|
|
}
|