| /* |
| * 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 "CurveIntersection.h" |
| #include "Intersections.h" |
| #include "IntersectionUtilities.h" |
| #include "LineIntersection.h" |
| |
| static const double tClipLimit = 0.8; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf see Multiple intersections |
| |
| class CubicIntersections : public Intersections { |
| public: |
| |
| CubicIntersections(const Cubic& c1, const Cubic& c2, Intersections& i) |
| : cubic1(c1) |
| , cubic2(c2) |
| , intersections(i) |
| , depth(0) |
| , splits(0) { |
| } |
| |
| bool intersect() { |
| double minT1, minT2, maxT1, maxT2; |
| if (!bezier_clip(cubic2, cubic1, minT1, maxT1)) { |
| return false; |
| } |
| if (!bezier_clip(cubic1, cubic2, minT2, maxT2)) { |
| return false; |
| } |
| int split; |
| if (maxT1 - minT1 < maxT2 - minT2) { |
| intersections.swap(); |
| minT2 = 0; |
| maxT2 = 1; |
| split = maxT1 - minT1 > tClipLimit; |
| } else { |
| minT1 = 0; |
| maxT1 = 1; |
| split = (maxT2 - minT2 > tClipLimit) << 1; |
| } |
| return chop(minT1, maxT1, minT2, maxT2, split); |
| } |
| |
| protected: |
| |
| bool intersect(double minT1, double maxT1, double minT2, double maxT2) { |
| Cubic smaller, larger; |
| // FIXME: carry last subdivide and reduceOrder result with cubic |
| sub_divide(cubic1, minT1, maxT1, intersections.swapped() ? larger : smaller); |
| sub_divide(cubic2, minT2, maxT2, intersections.swapped() ? smaller : larger); |
| Cubic smallResult; |
| if (reduceOrder(smaller, smallResult, |
| kReduceOrder_NoQuadraticsAllowed) <= 2) { |
| Cubic largeResult; |
| if (reduceOrder(larger, largeResult, |
| kReduceOrder_NoQuadraticsAllowed) <= 2) { |
| const _Line& smallLine = (const _Line&) smallResult; |
| const _Line& largeLine = (const _Line&) largeResult; |
| double smallT[2]; |
| double largeT[2]; |
| // FIXME: this doesn't detect or deal with coincident lines |
| if (!::intersect(smallLine, largeLine, smallT, largeT)) { |
| return false; |
| } |
| if (intersections.swapped()) { |
| smallT[0] = interp(minT2, maxT2, smallT[0]); |
| largeT[0] = interp(minT1, maxT1, largeT[0]); |
| } else { |
| smallT[0] = interp(minT1, maxT1, smallT[0]); |
| largeT[0] = interp(minT2, maxT2, largeT[0]); |
| } |
| intersections.add(smallT[0], largeT[0]); |
| return true; |
| } |
| } |
| double minT, maxT; |
| if (!bezier_clip(smaller, larger, minT, maxT)) { |
| if (minT == maxT) { |
| if (intersections.swapped()) { |
| minT1 = (minT1 + maxT1) / 2; |
| minT2 = interp(minT2, maxT2, minT); |
| } else { |
| minT1 = interp(minT1, maxT1, minT); |
| minT2 = (minT2 + maxT2) / 2; |
| } |
| intersections.add(minT1, minT2); |
| return true; |
| } |
| return false; |
| } |
| |
| int split; |
| if (intersections.swapped()) { |
| double newMinT1 = interp(minT1, maxT1, minT); |
| double newMaxT1 = interp(minT1, maxT1, maxT); |
| split = (newMaxT1 - newMinT1 > (maxT1 - minT1) * tClipLimit) << 1; |
| #define VERBOSE 0 |
| #if VERBOSE |
| printf("%s d=%d s=%d new1=(%g,%g) old1=(%g,%g) split=%d\n", |
| __FUNCTION__, depth, splits, newMinT1, newMaxT1, minT1, maxT1, |
| split); |
| #endif |
| minT1 = newMinT1; |
| maxT1 = newMaxT1; |
| } else { |
| double newMinT2 = interp(minT2, maxT2, minT); |
| double newMaxT2 = interp(minT2, maxT2, maxT); |
| split = newMaxT2 - newMinT2 > (maxT2 - minT2) * tClipLimit; |
| #if VERBOSE |
| printf("%s d=%d s=%d new2=(%g,%g) old2=(%g,%g) split=%d\n", |
| __FUNCTION__, depth, splits, newMinT2, newMaxT2, minT2, maxT2, |
| split); |
| #endif |
| minT2 = newMinT2; |
| maxT2 = newMaxT2; |
| } |
| return chop(minT1, maxT1, minT2, maxT2, split); |
| } |
| |
| bool chop(double minT1, double maxT1, double minT2, double maxT2, int split) { |
| ++depth; |
| intersections.swap(); |
| if (split) { |
| ++splits; |
| if (split & 2) { |
| double middle1 = (maxT1 + minT1) / 2; |
| intersect(minT1, middle1, minT2, maxT2); |
| intersect(middle1, maxT1, minT2, maxT2); |
| } else { |
| double middle2 = (maxT2 + minT2) / 2; |
| intersect(minT1, maxT1, minT2, middle2); |
| intersect(minT1, maxT1, middle2, maxT2); |
| } |
| --splits; |
| intersections.swap(); |
| --depth; |
| return intersections.intersected(); |
| } |
| bool result = intersect(minT1, maxT1, minT2, maxT2); |
| intersections.swap(); |
| --depth; |
| return result; |
| } |
| |
| private: |
| |
| const Cubic& cubic1; |
| const Cubic& cubic2; |
| Intersections& intersections; |
| int depth; |
| int splits; |
| }; |
| |
| bool intersect(const Cubic& c1, const Cubic& c2, Intersections& i) { |
| CubicIntersections c(c1, c2, i); |
| return c.intersect(); |
| } |
| |
| #include "CubicUtilities.h" |
| |
| // 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 add short line segments on either end, or similarly extend the |
| // initial and final quadratics |
| bool intersect2(const Cubic& c1, const Cubic& c2, Intersections& i) { |
| SkTDArray<double> ts1; |
| double precision1 = calcPrecision(c1); |
| cubic_to_quadratics(c1, precision1, ts1); |
| SkTDArray<double> ts2; |
| double precision2 = calcPrecision(c2); |
| cubic_to_quadratics(c2, precision2, ts2); |
| double t1Start = 0; |
| int ts1Count = ts1.count(); |
| for (int i1 = 0; i1 <= ts1Count; ++i1) { |
| const double t1 = i1 < ts1Count ? ts1[i1] : 1; |
| Cubic part1; |
| sub_divide(c1, t1Start, t1, part1); |
| Quadratic q1; |
| demote_cubic_to_quad(part1, q1); |
| // start here; |
| // should reduceOrder be looser in this use case if quartic is going to blow up on an |
| // extremely shallow quadratic? |
| // maybe quadratics to lines need the same sort of recursive solution that I hope to find |
| // for cubics to quadratics ... |
| Quadratic s1; |
| int o1 = reduceOrder(q1, s1); |
| double t2Start = 0; |
| int ts2Count = ts2.count(); |
| for (int i2 = 0; i2 <= ts2Count; ++i2) { |
| const double t2 = i2 < ts2Count ? ts2[i2] : 1; |
| Cubic part2; |
| sub_divide(c2, t2Start, t2, part2); |
| Quadratic q2; |
| demote_cubic_to_quad(part2, q2); |
| Quadratic s2; |
| double o2 = reduceOrder(q2, s2); |
| Intersections locals; |
| if (o1 == 3 && o2 == 3) { |
| intersect2(q1, q2, locals); |
| } else if (o1 <= 2 && o2 <= 2) { |
| i.fUsed = intersect((const _Line&) s1, (const _Line&) s2, i.fT[0], i.fT[1]); |
| } else if (o1 == 3 && o2 <= 2) { |
| intersect(q1, (const _Line&) s2, i); |
| } else { |
| SkASSERT(o1 <= 2 && o2 == 3); |
| intersect(q2, (const _Line&) s1, i); |
| for (int s = 0; s < i.fUsed; ++s) { |
| SkTSwap(i.fT[0][s], i.fT[1][s]); |
| } |
| } |
| 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]; |
| i.insert(to1, to2); |
| } |
| t2Start = t2; |
| } |
| t1Start = t1; |
| } |
| return i.intersected(); |
| } |
| |
| 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(); |
| } |