| /* |
| * 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" |
| #include "LineUtilities.h" |
| #include "QuadraticLineSegments.h" |
| #include "QuadraticUtilities.h" |
| #include <algorithm> // for swap |
| |
| static const double tClipLimit = 0.8; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf see Multiple intersections |
| |
| class QuadraticIntersections { |
| public: |
| |
| QuadraticIntersections(const Quadratic& q1, const Quadratic& q2, Intersections& i) |
| : quad1(q1) |
| , quad2(q2) |
| , intersections(i) |
| , depth(0) |
| , splits(0) |
| , coinMinT1(-1) { |
| } |
| |
| bool intersect() { |
| double minT1, minT2, maxT1, maxT2; |
| if (!bezier_clip(quad2, quad1, minT1, maxT1)) { |
| return false; |
| } |
| if (!bezier_clip(quad1, quad2, minT2, maxT2)) { |
| return false; |
| } |
| quad1Divisions = 1 / subDivisions(quad1); |
| quad2Divisions = 1 / subDivisions(quad2); |
| 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) { |
| bool t1IsLine = maxT1 - minT1 <= quad1Divisions; |
| bool t2IsLine = maxT2 - minT2 <= quad2Divisions; |
| if (t1IsLine | t2IsLine) { |
| return intersectAsLine(minT1, maxT1, minT2, maxT2, t1IsLine, t2IsLine); |
| } |
| Quadratic smaller, larger; |
| // FIXME: carry last subdivide and reduceOrder result with quad |
| sub_divide(quad1, minT1, maxT1, intersections.swapped() ? larger : smaller); |
| sub_divide(quad2, minT2, maxT2, intersections.swapped() ? smaller : larger); |
| double minT, maxT; |
| if (!bezier_clip(smaller, larger, minT, maxT)) { |
| if (approximately_equal(minT, maxT)) { |
| double smallT, largeT; |
| _Point q2pt, q1pt; |
| if (intersections.swapped()) { |
| largeT = interp(minT2, maxT2, minT); |
| xy_at_t(quad2, largeT, q2pt.x, q2pt.y); |
| xy_at_t(quad1, minT1, q1pt.x, q1pt.y); |
| if (AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)) { |
| smallT = minT1; |
| } else { |
| xy_at_t(quad1, maxT1, q1pt.x, q1pt.y); // FIXME: debug code |
| SkASSERT(AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)); |
| smallT = maxT1; |
| } |
| } else { |
| smallT = interp(minT1, maxT1, minT); |
| xy_at_t(quad1, smallT, q1pt.x, q1pt.y); |
| xy_at_t(quad2, minT2, q2pt.x, q2pt.y); |
| if (AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)) { |
| largeT = minT2; |
| } else { |
| xy_at_t(quad2, maxT2, q2pt.x, q2pt.y); // FIXME: debug code |
| SkASSERT(AlmostEqualUlps(q2pt.x, q1pt.x) && AlmostEqualUlps(q2pt.y, q1pt.y)); |
| largeT = maxT2; |
| } |
| } |
| intersections.add(smallT, largeT); |
| 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 intersectAsLine(double minT1, double maxT1, double minT2, double maxT2, |
| bool treat1AsLine, bool treat2AsLine) |
| { |
| _Line line1, line2; |
| if (intersections.swapped()) { |
| SkTSwap(treat1AsLine, treat2AsLine); |
| SkTSwap(minT1, minT2); |
| SkTSwap(maxT1, maxT2); |
| } |
| if (coinMinT1 >= 0) { |
| bool earlyExit; |
| if ((earlyExit = coinMaxT1 == minT1)) { |
| coinMaxT1 = maxT1; |
| } |
| if (coinMaxT2 == minT2) { |
| coinMaxT2 = maxT2; |
| return true; |
| } |
| if (earlyExit) { |
| return true; |
| } |
| coinMinT1 = -1; |
| } |
| // do line/quadratic or even line/line intersection instead |
| if (treat1AsLine) { |
| xy_at_t(quad1, minT1, line1[0].x, line1[0].y); |
| xy_at_t(quad1, maxT1, line1[1].x, line1[1].y); |
| } |
| if (treat2AsLine) { |
| xy_at_t(quad2, minT2, line2[0].x, line2[0].y); |
| xy_at_t(quad2, maxT2, line2[1].x, line2[1].y); |
| } |
| int pts; |
| double smallT1, largeT1, smallT2, largeT2; |
| if (treat1AsLine & treat2AsLine) { |
| double t1[2], t2[2]; |
| pts = ::intersect(line1, line2, t1, t2); |
| if (pts == 2) { |
| smallT1 = interp(minT1, maxT1, t1[0]); |
| largeT1 = interp(minT2, maxT2, t2[0]); |
| smallT2 = interp(minT1, maxT1, t1[1]); |
| largeT2 = interp(minT2, maxT2, t2[1]); |
| intersections.addCoincident(smallT1, smallT2, largeT1, largeT2); |
| } else { |
| smallT1 = interp(minT1, maxT1, t1[0]); |
| largeT1 = interp(minT2, maxT2, t2[0]); |
| intersections.add(smallT1, largeT1); |
| } |
| } else { |
| Intersections lq; |
| pts = ::intersect(treat1AsLine ? quad2 : quad1, |
| treat1AsLine ? line1 : line2, lq); |
| if (pts == 2) { // if the line and edge are coincident treat differently |
| _Point midQuad, midLine; |
| double midQuadT = (lq.fT[0][0] + lq.fT[0][1]) / 2; |
| xy_at_t(treat1AsLine ? quad2 : quad1, midQuadT, midQuad.x, midQuad.y); |
| double lineT = t_at(treat1AsLine ? line1 : line2, midQuad); |
| xy_at_t(treat1AsLine ? line1 : line2, lineT, midLine.x, midLine.y); |
| if (AlmostEqualUlps(midQuad.x, midLine.x) |
| && AlmostEqualUlps(midQuad.y, midLine.y)) { |
| smallT1 = lq.fT[0][0]; |
| largeT1 = lq.fT[1][0]; |
| smallT2 = lq.fT[0][1]; |
| largeT2 = lq.fT[1][1]; |
| if (treat2AsLine) { |
| smallT1 = interp(minT1, maxT1, smallT1); |
| smallT2 = interp(minT1, maxT1, smallT2); |
| } else { |
| largeT1 = interp(minT2, maxT2, largeT1); |
| largeT2 = interp(minT2, maxT2, largeT2); |
| } |
| intersections.addCoincident(smallT1, smallT2, largeT1, largeT2); |
| goto setCoinMinMax; |
| } |
| } |
| for (int index = 0; index < pts; ++index) { |
| smallT1 = lq.fT[0][index]; |
| largeT1 = lq.fT[1][index]; |
| if (treat2AsLine) { |
| smallT1 = interp(minT1, maxT1, smallT1); |
| } else { |
| largeT1 = interp(minT2, maxT2, largeT1); |
| } |
| intersections.add(smallT1, largeT1); |
| } |
| } |
| if (pts > 0) { |
| setCoinMinMax: |
| coinMinT1 = minT1; |
| coinMaxT1 = maxT1; |
| coinMinT2 = minT2; |
| coinMaxT2 = maxT2; |
| } |
| return pts > 0; |
| } |
| |
| 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 Quadratic& quad1; |
| const Quadratic& quad2; |
| Intersections& intersections; |
| int depth; |
| int splits; |
| double quad1Divisions; // line segments to approximate original within error |
| double quad2Divisions; |
| double coinMinT1; // range of Ts where approximate line intersected curve |
| double coinMaxT1; |
| double coinMinT2; |
| double coinMaxT2; |
| }; |
| |
| #include "LineParameters.h" |
| |
| static void hackToFixPartialCoincidence(const Quadratic& q1, const Quadratic& q2, Intersections& i) { |
| // look to see if non-coincident data basically has unsortable tangents |
| |
| // look to see if a point between non-coincident data is on the curve |
| int cIndex; |
| for (int uIndex = 0; uIndex < i.fUsed; ) { |
| double bestDist1 = 1; |
| double bestDist2 = 1; |
| int closest1 = -1; |
| int closest2 = -1; |
| for (cIndex = 0; cIndex < i.fCoincidentUsed; ++cIndex) { |
| double dist = fabs(i.fT[0][uIndex] - i.fCoincidentT[0][cIndex]); |
| if (bestDist1 > dist) { |
| bestDist1 = dist; |
| closest1 = cIndex; |
| } |
| dist = fabs(i.fT[1][uIndex] - i.fCoincidentT[1][cIndex]); |
| if (bestDist2 > dist) { |
| bestDist2 = dist; |
| closest2 = cIndex; |
| } |
| } |
| _Line ends; |
| _Point mid; |
| double t1 = i.fT[0][uIndex]; |
| xy_at_t(q1, t1, ends[0].x, ends[0].y); |
| xy_at_t(q1, i.fCoincidentT[0][closest1], ends[1].x, ends[1].y); |
| double midT = (t1 + i.fCoincidentT[0][closest1]) / 2; |
| xy_at_t(q1, midT, mid.x, mid.y); |
| LineParameters params; |
| params.lineEndPoints(ends); |
| double midDist = params.pointDistance(mid); |
| // Note that we prefer to always measure t error, which does not scale, |
| // instead of point error, which is scale dependent. FIXME |
| if (!approximately_zero(midDist)) { |
| ++uIndex; |
| continue; |
| } |
| double t2 = i.fT[1][uIndex]; |
| xy_at_t(q2, t2, ends[0].x, ends[0].y); |
| xy_at_t(q2, i.fCoincidentT[1][closest2], ends[1].x, ends[1].y); |
| midT = (t2 + i.fCoincidentT[1][closest2]) / 2; |
| xy_at_t(q2, midT, mid.x, mid.y); |
| params.lineEndPoints(ends); |
| midDist = params.pointDistance(mid); |
| if (!approximately_zero(midDist)) { |
| ++uIndex; |
| continue; |
| } |
| // if both midpoints are close to the line, lengthen coincident span |
| int cEnd = closest1 ^ 1; // assume coincidence always travels in pairs |
| if (!between(i.fCoincidentT[0][cEnd], t1, i.fCoincidentT[0][closest1])) { |
| i.fCoincidentT[0][closest1] = t1; |
| } |
| cEnd = closest2 ^ 1; |
| if (!between(i.fCoincidentT[0][cEnd], t2, i.fCoincidentT[0][closest2])) { |
| i.fCoincidentT[0][closest2] = t2; |
| } |
| int remaining = --i.fUsed - uIndex; |
| if (remaining > 0) { |
| memmove(&i.fT[0][uIndex], &i.fT[0][uIndex + 1], sizeof(i.fT[0][0]) * remaining); |
| memmove(&i.fT[1][uIndex], &i.fT[1][uIndex + 1], sizeof(i.fT[1][0]) * remaining); |
| } |
| } |
| // if coincident data is subjectively a tiny span, replace it with a single point |
| for (cIndex = 0; cIndex < i.fCoincidentUsed; ) { |
| double start1 = i.fCoincidentT[0][cIndex]; |
| double end1 = i.fCoincidentT[0][cIndex + 1]; |
| _Line ends1; |
| xy_at_t(q1, start1, ends1[0].x, ends1[0].y); |
| xy_at_t(q1, end1, ends1[1].x, ends1[1].y); |
| if (!AlmostEqualUlps(ends1[0].x, ends1[1].x) || AlmostEqualUlps(ends1[0].y, ends1[1].y)) { |
| cIndex += 2; |
| continue; |
| } |
| double start2 = i.fCoincidentT[1][cIndex]; |
| double end2 = i.fCoincidentT[1][cIndex + 1]; |
| _Line ends2; |
| xy_at_t(q2, start2, ends2[0].x, ends2[0].y); |
| xy_at_t(q2, end2, ends2[1].x, ends2[1].y); |
| // again, approximately should be used with T values, not points FIXME |
| if (!AlmostEqualUlps(ends2[0].x, ends2[1].x) || AlmostEqualUlps(ends2[0].y, ends2[1].y)) { |
| cIndex += 2; |
| continue; |
| } |
| if (approximately_less_than_zero(start1) || approximately_less_than_zero(end1)) { |
| start1 = 0; |
| } else if (approximately_greater_than_one(start1) || approximately_greater_than_one(end1)) { |
| start1 = 1; |
| } else { |
| start1 = (start1 + end1) / 2; |
| } |
| if (approximately_less_than_zero(start2) || approximately_less_than_zero(end2)) { |
| start2 = 0; |
| } else if (approximately_greater_than_one(start2) || approximately_greater_than_one(end2)) { |
| start2 = 1; |
| } else { |
| start2 = (start2 + end2) / 2; |
| } |
| i.insert(start1, start2); |
| i.fCoincidentUsed -= 2; |
| int remaining = i.fCoincidentUsed - cIndex; |
| if (remaining > 0) { |
| memmove(&i.fCoincidentT[0][cIndex], &i.fCoincidentT[0][cIndex + 2], sizeof(i.fCoincidentT[0][0]) * remaining); |
| memmove(&i.fCoincidentT[1][cIndex], &i.fCoincidentT[1][cIndex + 2], sizeof(i.fCoincidentT[1][0]) * remaining); |
| } |
| } |
| } |
| |
| bool intersect(const Quadratic& q1, const Quadratic& q2, Intersections& i) { |
| if (implicit_matches(q1, q2)) { |
| // FIXME: compute T values |
| // compute the intersections of the ends to find the coincident span |
| bool useVertical = fabs(q1[0].x - q1[2].x) < fabs(q1[0].y - q1[2].y); |
| double t; |
| if ((t = axialIntersect(q1, q2[0], useVertical)) >= 0) { |
| i.addCoincident(t, 0); |
| } |
| if ((t = axialIntersect(q1, q2[2], useVertical)) >= 0) { |
| i.addCoincident(t, 1); |
| } |
| useVertical = fabs(q2[0].x - q2[2].x) < fabs(q2[0].y - q2[2].y); |
| if ((t = axialIntersect(q2, q1[0], useVertical)) >= 0) { |
| i.addCoincident(0, t); |
| } |
| if ((t = axialIntersect(q2, q1[2], useVertical)) >= 0) { |
| i.addCoincident(1, t); |
| } |
| SkASSERT(i.fCoincidentUsed <= 2); |
| return i.fCoincidentUsed > 0; |
| } |
| QuadraticIntersections q(q1, q2, i); |
| bool result = q.intersect(); |
| // FIXME: partial coincidence detection is currently poor. For now, try |
| // to fix up the data after the fact. In the future, revisit the error |
| // term to try to avoid this kind of result in the first place. |
| if (i.fUsed && i.fCoincidentUsed) { |
| hackToFixPartialCoincidence(q1, q2, i); |
| } |
| return result; |
| } |
