caryclark@google.com | 9e49fb6 | 2012-08-27 14:11:33 +0000 | [diff] [blame] | 1 | /* |
| 2 | * Copyright 2012 Google Inc. |
| 3 | * |
| 4 | * Use of this source code is governed by a BSD-style license that can be |
| 5 | * found in the LICENSE file. |
| 6 | */ |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 7 | #include "CurveIntersection.h" |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 8 | #include "Intersections.h" |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 9 | #include "IntersectionUtilities.h" |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 10 | #include "LineIntersection.h" |
| 11 | |
caryclark@google.com | 0d3d09e | 2012-12-10 14:50:04 +0000 | [diff] [blame] | 12 | static const double tClipLimit = 0.8; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf see Multiple intersections |
| 13 | |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 14 | class CubicIntersections : public Intersections { |
| 15 | public: |
| 16 | |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 17 | CubicIntersections(const Cubic& c1, const Cubic& c2, Intersections& i) |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 18 | : cubic1(c1) |
| 19 | , cubic2(c2) |
| 20 | , intersections(i) |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 21 | , depth(0) |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 22 | , splits(0) { |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 23 | } |
| 24 | |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 25 | bool intersect() { |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 26 | double minT1, minT2, maxT1, maxT2; |
| 27 | if (!bezier_clip(cubic2, cubic1, minT1, maxT1)) { |
| 28 | return false; |
| 29 | } |
| 30 | if (!bezier_clip(cubic1, cubic2, minT2, maxT2)) { |
| 31 | return false; |
| 32 | } |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 33 | int split; |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 34 | if (maxT1 - minT1 < maxT2 - minT2) { |
| 35 | intersections.swap(); |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 36 | minT2 = 0; |
| 37 | maxT2 = 1; |
| 38 | split = maxT1 - minT1 > tClipLimit; |
| 39 | } else { |
| 40 | minT1 = 0; |
| 41 | maxT1 = 1; |
| 42 | split = (maxT2 - minT2 > tClipLimit) << 1; |
| 43 | } |
| 44 | return chop(minT1, maxT1, minT2, maxT2, split); |
caryclark@google.com | 639df89 | 2012-01-10 21:46:10 +0000 | [diff] [blame] | 45 | } |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 46 | |
| 47 | protected: |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 48 | |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 49 | bool intersect(double minT1, double maxT1, double minT2, double maxT2) { |
| 50 | Cubic smaller, larger; |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 51 | // FIXME: carry last subdivide and reduceOrder result with cubic |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 52 | sub_divide(cubic1, minT1, maxT1, intersections.swapped() ? larger : smaller); |
| 53 | sub_divide(cubic2, minT2, maxT2, intersections.swapped() ? smaller : larger); |
| 54 | Cubic smallResult; |
| 55 | if (reduceOrder(smaller, smallResult, |
| 56 | kReduceOrder_NoQuadraticsAllowed) <= 2) { |
| 57 | Cubic largeResult; |
| 58 | if (reduceOrder(larger, largeResult, |
| 59 | kReduceOrder_NoQuadraticsAllowed) <= 2) { |
| 60 | const _Line& smallLine = (const _Line&) smallResult; |
| 61 | const _Line& largeLine = (const _Line&) largeResult; |
| 62 | double smallT[2]; |
| 63 | double largeT[2]; |
| 64 | // FIXME: this doesn't detect or deal with coincident lines |
| 65 | if (!::intersect(smallLine, largeLine, smallT, largeT)) { |
| 66 | return false; |
| 67 | } |
| 68 | if (intersections.swapped()) { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 69 | smallT[0] = interp(minT2, maxT2, smallT[0]); |
| 70 | largeT[0] = interp(minT1, maxT1, largeT[0]); |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 71 | } else { |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 72 | smallT[0] = interp(minT1, maxT1, smallT[0]); |
| 73 | largeT[0] = interp(minT2, maxT2, largeT[0]); |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 74 | } |
| 75 | intersections.add(smallT[0], largeT[0]); |
| 76 | return true; |
| 77 | } |
| 78 | } |
| 79 | double minT, maxT; |
| 80 | if (!bezier_clip(smaller, larger, minT, maxT)) { |
| 81 | if (minT == maxT) { |
| 82 | if (intersections.swapped()) { |
| 83 | minT1 = (minT1 + maxT1) / 2; |
| 84 | minT2 = interp(minT2, maxT2, minT); |
| 85 | } else { |
| 86 | minT1 = interp(minT1, maxT1, minT); |
| 87 | minT2 = (minT2 + maxT2) / 2; |
| 88 | } |
| 89 | intersections.add(minT1, minT2); |
| 90 | return true; |
| 91 | } |
| 92 | return false; |
| 93 | } |
rmistry@google.com | d6176b0 | 2012-08-23 18:14:13 +0000 | [diff] [blame] | 94 | |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 95 | int split; |
| 96 | if (intersections.swapped()) { |
| 97 | double newMinT1 = interp(minT1, maxT1, minT); |
| 98 | double newMaxT1 = interp(minT1, maxT1, maxT); |
| 99 | split = (newMaxT1 - newMinT1 > (maxT1 - minT1) * tClipLimit) << 1; |
| 100 | #define VERBOSE 0 |
| 101 | #if VERBOSE |
| 102 | printf("%s d=%d s=%d new1=(%g,%g) old1=(%g,%g) split=%d\n", |
| 103 | __FUNCTION__, depth, splits, newMinT1, newMaxT1, minT1, maxT1, |
| 104 | split); |
| 105 | #endif |
| 106 | minT1 = newMinT1; |
| 107 | maxT1 = newMaxT1; |
| 108 | } else { |
| 109 | double newMinT2 = interp(minT2, maxT2, minT); |
| 110 | double newMaxT2 = interp(minT2, maxT2, maxT); |
| 111 | split = newMaxT2 - newMinT2 > (maxT2 - minT2) * tClipLimit; |
| 112 | #if VERBOSE |
| 113 | printf("%s d=%d s=%d new2=(%g,%g) old2=(%g,%g) split=%d\n", |
| 114 | __FUNCTION__, depth, splits, newMinT2, newMaxT2, minT2, maxT2, |
| 115 | split); |
| 116 | #endif |
| 117 | minT2 = newMinT2; |
| 118 | maxT2 = newMaxT2; |
| 119 | } |
| 120 | return chop(minT1, maxT1, minT2, maxT2, split); |
| 121 | } |
| 122 | |
| 123 | bool chop(double minT1, double maxT1, double minT2, double maxT2, int split) { |
| 124 | ++depth; |
| 125 | intersections.swap(); |
| 126 | if (split) { |
| 127 | ++splits; |
| 128 | if (split & 2) { |
| 129 | double middle1 = (maxT1 + minT1) / 2; |
| 130 | intersect(minT1, middle1, minT2, maxT2); |
| 131 | intersect(middle1, maxT1, minT2, maxT2); |
| 132 | } else { |
| 133 | double middle2 = (maxT2 + minT2) / 2; |
| 134 | intersect(minT1, maxT1, minT2, middle2); |
| 135 | intersect(minT1, maxT1, middle2, maxT2); |
| 136 | } |
| 137 | --splits; |
| 138 | intersections.swap(); |
| 139 | --depth; |
| 140 | return intersections.intersected(); |
| 141 | } |
| 142 | bool result = intersect(minT1, maxT1, minT2, maxT2); |
| 143 | intersections.swap(); |
| 144 | --depth; |
| 145 | return result; |
| 146 | } |
| 147 | |
| 148 | private: |
| 149 | |
caryclark@google.com | c682590 | 2012-02-03 22:07:47 +0000 | [diff] [blame] | 150 | const Cubic& cubic1; |
| 151 | const Cubic& cubic2; |
| 152 | Intersections& intersections; |
| 153 | int depth; |
| 154 | int splits; |
| 155 | }; |
| 156 | |
| 157 | bool intersect(const Cubic& c1, const Cubic& c2, Intersections& i) { |
| 158 | CubicIntersections c(c1, c2, i); |
| 159 | return c.intersect(); |
| 160 | } |
| 161 | |
caryclark@google.com | 73ca624 | 2013-01-17 21:02:47 +0000 | [diff] [blame^] | 162 | #include "CubicUtilities.h" |
| 163 | |
| 164 | // this flavor approximates the cubics with quads to find the intersecting ts |
| 165 | // OPTIMIZE: if this strategy proves successful, the quad approximations, or the ts used |
| 166 | // to create the approximations, could be stored in the cubic segment |
| 167 | // fixme: this strategy needs to add short line segments on either end, or similarly extend the |
| 168 | // initial and final quadratics |
| 169 | bool intersect2(const Cubic& c1, const Cubic& c2, Intersections& i) { |
| 170 | SkTDArray<double> ts1; |
| 171 | double precision1 = calcPrecision(c1); |
| 172 | cubic_to_quadratics(c1, precision1, ts1); |
| 173 | SkTDArray<double> ts2; |
| 174 | double precision2 = calcPrecision(c2); |
| 175 | cubic_to_quadratics(c2, precision2, ts2); |
| 176 | double t1Start = 0; |
| 177 | int ts1Count = ts1.count(); |
| 178 | for (int i1 = 0; i1 <= ts1Count; ++i1) { |
| 179 | const double t1 = i1 < ts1Count ? ts1[i1] : 1; |
| 180 | Cubic part1; |
| 181 | sub_divide(c1, t1Start, t1, part1); |
| 182 | Quadratic q1; |
| 183 | demote_cubic_to_quad(part1, q1); |
| 184 | // start here; |
| 185 | // should reduceOrder be looser in this use case if quartic is going to blow up on an |
| 186 | // extremely shallow quadratic? |
| 187 | // maybe quadratics to lines need the same sort of recursive solution that I hope to find |
| 188 | // for cubics to quadratics ... |
| 189 | Quadratic s1; |
| 190 | int o1 = reduceOrder(q1, s1); |
| 191 | double t2Start = 0; |
| 192 | int ts2Count = ts2.count(); |
| 193 | for (int i2 = 0; i2 <= ts2Count; ++i2) { |
| 194 | const double t2 = i2 < ts2Count ? ts2[i2] : 1; |
| 195 | Cubic part2; |
| 196 | sub_divide(c2, t2Start, t2, part2); |
| 197 | Quadratic q2; |
| 198 | demote_cubic_to_quad(part2, q2); |
| 199 | Quadratic s2; |
| 200 | double o2 = reduceOrder(q2, s2); |
| 201 | Intersections locals; |
| 202 | if (o1 == 3 && o2 == 3) { |
| 203 | intersect2(q1, q2, locals); |
| 204 | } else if (o1 <= 2 && o2 <= 2) { |
| 205 | i.fUsed = intersect((const _Line&) s1, (const _Line&) s2, i.fT[0], i.fT[1]); |
| 206 | } else if (o1 == 3 && o2 <= 2) { |
| 207 | intersect(q1, (const _Line&) s2, i); |
| 208 | } else { |
| 209 | SkASSERT(o1 <= 2 && o2 == 3); |
| 210 | intersect(q2, (const _Line&) s1, i); |
| 211 | for (int s = 0; s < i.fUsed; ++s) { |
| 212 | SkTSwap(i.fT[0][s], i.fT[1][s]); |
| 213 | } |
| 214 | } |
| 215 | for (int tIdx = 0; tIdx < locals.used(); ++tIdx) { |
| 216 | double to1 = t1Start + (t1 - t1Start) * locals.fT[0][tIdx]; |
| 217 | double to2 = t2Start + (t2 - t2Start) * locals.fT[1][tIdx]; |
| 218 | i.insert(to1, to2); |
| 219 | } |
| 220 | t2Start = t2; |
| 221 | } |
| 222 | t1Start = t1; |
| 223 | } |
| 224 | return i.intersected(); |
| 225 | } |
| 226 | |
| 227 | int intersect(const Cubic& cubic, const Quadratic& quad, Intersections& i) { |
| 228 | SkTDArray<double> ts; |
| 229 | double precision = calcPrecision(cubic); |
| 230 | cubic_to_quadratics(cubic, precision, ts); |
| 231 | double tStart = 0; |
| 232 | Cubic part; |
| 233 | int tsCount = ts.count(); |
| 234 | for (int idx = 0; idx <= tsCount; ++idx) { |
| 235 | double t = idx < tsCount ? ts[idx] : 1; |
| 236 | Quadratic q1; |
| 237 | sub_divide(cubic, tStart, t, part); |
| 238 | demote_cubic_to_quad(part, q1); |
| 239 | Intersections locals; |
| 240 | intersect2(q1, quad, locals); |
| 241 | for (int tIdx = 0; tIdx < locals.used(); ++tIdx) { |
| 242 | double globalT = tStart + (t - tStart) * locals.fT[0][tIdx]; |
| 243 | i.insertOne(globalT, 0); |
| 244 | globalT = locals.fT[1][tIdx]; |
| 245 | i.insertOne(globalT, 1); |
| 246 | } |
| 247 | tStart = t; |
| 248 | } |
| 249 | return i.used(); |
| 250 | } |
| 251 | |
| 252 | bool intersect(const Cubic& cubic, Intersections& i) { |
| 253 | SkTDArray<double> ts; |
| 254 | double precision = calcPrecision(cubic); |
| 255 | cubic_to_quadratics(cubic, precision, ts); |
| 256 | int tsCount = ts.count(); |
| 257 | if (tsCount == 1) { |
| 258 | return false; |
| 259 | } |
| 260 | double t1Start = 0; |
| 261 | Cubic part; |
| 262 | for (int idx = 0; idx < tsCount; ++idx) { |
| 263 | double t1 = ts[idx]; |
| 264 | Quadratic q1; |
| 265 | sub_divide(cubic, t1Start, t1, part); |
| 266 | demote_cubic_to_quad(part, q1); |
| 267 | double t2Start = t1; |
| 268 | for (int i2 = idx + 1; i2 <= tsCount; ++i2) { |
| 269 | const double t2 = i2 < tsCount ? ts[i2] : 1; |
| 270 | Quadratic q2; |
| 271 | sub_divide(cubic, t2Start, t2, part); |
| 272 | demote_cubic_to_quad(part, q2); |
| 273 | Intersections locals; |
| 274 | intersect2(q1, q2, locals); |
| 275 | for (int tIdx = 0; tIdx < locals.used(); ++tIdx) { |
| 276 | // discard intersections at cusp? (maximum curvature) |
| 277 | double t1sect = locals.fT[0][tIdx]; |
| 278 | double t2sect = locals.fT[1][tIdx]; |
| 279 | if (idx + 1 == i2 && t1sect == 1 && t2sect == 0) { |
| 280 | continue; |
| 281 | } |
| 282 | double to1 = t1Start + (t1 - t1Start) * t1sect; |
| 283 | double to2 = t2Start + (t2 - t2Start) * t2sect; |
| 284 | i.insert(to1, to2); |
| 285 | } |
| 286 | t2Start = t2; |
| 287 | } |
| 288 | t1Start = t1; |
| 289 | } |
| 290 | return i.intersected(); |
| 291 | } |