caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +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 | */ |
| 7 | |
| 8 | #include "SkIntersections.h" |
| 9 | #include "SkPathOpsCubic.h" |
| 10 | #include "SkPathOpsLine.h" |
| 11 | #include "SkPathOpsPoint.h" |
| 12 | #include "SkPathOpsQuad.h" |
| 13 | #include "SkPathOpsRect.h" |
| 14 | #include "SkReduceOrder.h" |
| 15 | #include "SkTDArray.h" |
commit-bot@chromium.org | b76d3b6 | 2013-04-22 19:55:19 +0000 | [diff] [blame] | 16 | #include "SkTSort.h" |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 17 | |
| 18 | #if ONE_OFF_DEBUG |
| 19 | static const double tLimits1[2][2] = {{0.36, 0.37}, {0.63, 0.64}}; |
| 20 | static const double tLimits2[2][2] = {{-0.865211397, -0.865215212}, {-0.865207696, -0.865208078}}; |
| 21 | #endif |
| 22 | |
| 23 | #define DEBUG_QUAD_PART 0 |
| 24 | #define SWAP_TOP_DEBUG 0 |
| 25 | |
| 26 | static int quadPart(const SkDCubic& cubic, double tStart, double tEnd, SkReduceOrder* reducer) { |
| 27 | SkDCubic part = cubic.subDivide(tStart, tEnd); |
| 28 | SkDQuad quad = part.toQuad(); |
| 29 | // FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an |
| 30 | // extremely shallow quadratic? |
| 31 | int order = reducer->reduce(quad, SkReduceOrder::kFill_Style); |
| 32 | #if DEBUG_QUAD_PART |
| 33 | SkDebugf("%s cubic=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)" |
| 34 | " t=(%1.17g,%1.17g)\n", __FUNCTION__, cubic[0].fX, cubic[0].fY, |
| 35 | cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY, |
| 36 | cubic[3].fX, cubic[3].fY, tStart, tEnd); |
| 37 | SkDebugf("%s part=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)" |
| 38 | " quad=(%1.17g,%1.17g %1.17g,%1.17g %1.17g,%1.17g)\n", __FUNCTION__, |
| 39 | part[0].fX, part[0].fY, part[1].fX, part[1].fY, part[2].fX, part[2].fY, |
| 40 | part[3].fX, part[3].fY, quad[0].fX, quad[0].fY, |
| 41 | quad[1].fX, quad[1].fY, quad[2].fX, quad[2].fY); |
| 42 | SkDebugf("%s simple=(%1.17g,%1.17g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY); |
| 43 | if (order > 1) { |
| 44 | SkDebugf(" %1.17g,%1.17g", reducer->fQuad[1].fX, reducer->fQuad[1].fY); |
| 45 | } |
| 46 | if (order > 2) { |
| 47 | SkDebugf(" %1.17g,%1.17g", reducer->fQuad[2].fX, reducer->fQuad[2].fY); |
| 48 | } |
| 49 | SkDebugf(")\n"); |
| 50 | SkASSERT(order < 4 && order > 0); |
| 51 | #endif |
| 52 | return order; |
| 53 | } |
| 54 | |
| 55 | static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2, |
| 56 | int order2, SkIntersections& i) { |
| 57 | if (order1 == 3 && order2 == 3) { |
| 58 | i.intersect(simple1, simple2); |
| 59 | } else if (order1 <= 2 && order2 <= 2) { |
| 60 | i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2); |
| 61 | } else if (order1 == 3 && order2 <= 2) { |
| 62 | i.intersect(simple1, (const SkDLine&) simple2); |
| 63 | } else { |
| 64 | SkASSERT(order1 <= 2 && order2 == 3); |
| 65 | i.intersect(simple2, (const SkDLine&) simple1); |
| 66 | i.swapPts(); |
| 67 | } |
| 68 | } |
| 69 | |
| 70 | // this flavor centers potential intersections recursively. In contrast, '2' may inadvertently |
| 71 | // chase intersections near quadratic ends, requiring odd hacks to find them. |
| 72 | static void intersect(const SkDCubic& cubic1, double t1s, double t1e, const SkDCubic& cubic2, |
| 73 | double t2s, double t2e, double precisionScale, SkIntersections& i) { |
| 74 | i.upDepth(); |
| 75 | SkDCubic c1 = cubic1.subDivide(t1s, t1e); |
| 76 | SkDCubic c2 = cubic2.subDivide(t2s, t2e); |
| 77 | SkTDArray<double> ts1; |
| 78 | // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection) |
| 79 | c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1); |
| 80 | SkTDArray<double> ts2; |
| 81 | c2.toQuadraticTs(c2.calcPrecision() * precisionScale, &ts2); |
| 82 | double t1Start = t1s; |
| 83 | int ts1Count = ts1.count(); |
| 84 | for (int i1 = 0; i1 <= ts1Count; ++i1) { |
| 85 | const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1; |
| 86 | const double t1 = t1s + (t1e - t1s) * tEnd1; |
| 87 | SkReduceOrder s1; |
| 88 | int o1 = quadPart(cubic1, t1Start, t1, &s1); |
| 89 | double t2Start = t2s; |
| 90 | int ts2Count = ts2.count(); |
| 91 | for (int i2 = 0; i2 <= ts2Count; ++i2) { |
| 92 | const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1; |
| 93 | const double t2 = t2s + (t2e - t2s) * tEnd2; |
| 94 | if (&cubic1 == &cubic2 && t1Start >= t2Start) { |
| 95 | t2Start = t2; |
| 96 | continue; |
| 97 | } |
| 98 | SkReduceOrder s2; |
| 99 | int o2 = quadPart(cubic2, t2Start, t2, &s2); |
| 100 | #if ONE_OFF_DEBUG |
| 101 | char tab[] = " "; |
| 102 | if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1 |
| 103 | && tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 104 | SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab, |
| 105 | __FUNCTION__, t1Start, t1, t2Start, t2); |
| 106 | SkIntersections xlocals; |
| 107 | intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals); |
| 108 | SkDebugf(" xlocals.fUsed=%d\n", xlocals.used()); |
| 109 | } |
| 110 | #endif |
| 111 | SkIntersections locals; |
| 112 | intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals); |
| 113 | double coStart[2] = { -1 }; |
| 114 | SkDPoint coPoint; |
| 115 | int tCount = locals.used(); |
| 116 | for (int tIdx = 0; tIdx < tCount; ++tIdx) { |
| 117 | double to1 = t1Start + (t1 - t1Start) * locals[0][tIdx]; |
| 118 | double to2 = t2Start + (t2 - t2Start) * locals[1][tIdx]; |
| 119 | // if the computed t is not sufficiently precise, iterate |
| 120 | SkDPoint p1 = cubic1.xyAtT(to1); |
| 121 | SkDPoint p2 = cubic2.xyAtT(to2); |
| 122 | if (p1.approximatelyEqual(p2)) { |
| 123 | if (locals.isCoincident(tIdx)) { |
| 124 | if (coStart[0] < 0) { |
| 125 | coStart[0] = to1; |
| 126 | coStart[1] = to2; |
| 127 | coPoint = p1; |
| 128 | } else { |
| 129 | i.insertCoincidentPair(coStart[0], to1, coStart[1], to2, coPoint, p1); |
| 130 | coStart[0] = -1; |
| 131 | } |
| 132 | } else if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) { |
| 133 | if (i.swapped()) { // FIXME: insert should respect swap |
| 134 | i.insert(to2, to1, p1); |
| 135 | } else { |
| 136 | i.insert(to1, to2, p1); |
| 137 | } |
| 138 | } |
| 139 | } else { |
| 140 | double offset = precisionScale / 16; // FIME: const is arbitrary: test, refine |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 141 | double c1Bottom = tIdx == 0 ? 0 : |
| 142 | (t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2; |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 143 | double c1Min = SkTMax(c1Bottom, to1 - offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 144 | double c1Top = tIdx == tCount - 1 ? 1 : |
| 145 | (t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2; |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 146 | double c1Max = SkTMin(c1Top, to1 + offset); |
| 147 | double c2Min = SkTMax(0., to2 - offset); |
| 148 | double c2Max = SkTMin(1., to2 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 149 | #if ONE_OFF_DEBUG |
| 150 | SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, |
| 151 | __FUNCTION__, |
| 152 | c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max |
| 153 | && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, |
| 154 | to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset |
| 155 | && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, |
| 156 | c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max |
| 157 | && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, |
| 158 | to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset |
| 159 | && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); |
| 160 | SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" |
| 161 | " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", |
| 162 | i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1., |
| 163 | to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); |
| 164 | SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" |
| 165 | " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, |
| 166 | c1Max, c2Min, c2Max); |
| 167 | #endif |
| 168 | intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| 169 | #if ONE_OFF_DEBUG |
| 170 | SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, |
| 171 | i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); |
| 172 | #endif |
| 173 | if (tCount > 1) { |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 174 | c1Min = SkTMax(0., to1 - offset); |
| 175 | c1Max = SkTMin(1., to1 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 176 | double c2Bottom = tIdx == 0 ? to2 : |
| 177 | (t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2; |
| 178 | double c2Top = tIdx == tCount - 1 ? to2 : |
| 179 | (t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2; |
| 180 | if (c2Bottom > c2Top) { |
| 181 | SkTSwap(c2Bottom, c2Top); |
| 182 | } |
| 183 | if (c2Bottom == to2) { |
| 184 | c2Bottom = 0; |
| 185 | } |
| 186 | if (c2Top == to2) { |
| 187 | c2Top = 1; |
| 188 | } |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 189 | c2Min = SkTMax(c2Bottom, to2 - offset); |
| 190 | c2Max = SkTMin(c2Top, to2 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 191 | #if ONE_OFF_DEBUG |
| 192 | SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, |
| 193 | __FUNCTION__, |
| 194 | c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max |
| 195 | && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, |
| 196 | to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset |
| 197 | && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, |
| 198 | c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max |
| 199 | && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, |
| 200 | to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset |
| 201 | && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); |
| 202 | SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" |
| 203 | " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", |
| 204 | i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, |
| 205 | to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); |
| 206 | SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" |
| 207 | " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, |
| 208 | c1Max, c2Min, c2Max); |
| 209 | #endif |
| 210 | intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| 211 | #if ONE_OFF_DEBUG |
| 212 | SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, |
| 213 | i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); |
| 214 | #endif |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 215 | c1Min = SkTMax(c1Bottom, to1 - offset); |
| 216 | c1Max = SkTMin(c1Top, to1 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 217 | #if ONE_OFF_DEBUG |
| 218 | SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, |
| 219 | __FUNCTION__, |
| 220 | c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max |
| 221 | && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, |
| 222 | to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset |
| 223 | && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, |
| 224 | c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max |
| 225 | && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, |
| 226 | to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset |
| 227 | && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); |
| 228 | SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" |
| 229 | " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", |
| 230 | i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, |
| 231 | to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); |
| 232 | SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" |
| 233 | " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, |
| 234 | c1Max, c2Min, c2Max); |
| 235 | #endif |
| 236 | intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| 237 | #if ONE_OFF_DEBUG |
| 238 | SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, |
| 239 | i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); |
| 240 | #endif |
| 241 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 242 | intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| 243 | // FIXME: if no intersection is found, either quadratics intersected where |
| 244 | // cubics did not, or the intersection was missed. In the former case, expect |
| 245 | // the quadratics to be nearly parallel at the point of intersection, and check |
| 246 | // for that. |
| 247 | } |
| 248 | } |
| 249 | SkASSERT(coStart[0] == -1); |
| 250 | t2Start = t2; |
| 251 | } |
| 252 | t1Start = t1; |
| 253 | } |
| 254 | i.downDepth(); |
| 255 | } |
| 256 | |
| 257 | #define LINE_FRACTION 0.1 |
| 258 | |
| 259 | // intersect the end of the cubic with the other. Try lines from the end to control and opposite |
| 260 | // end to determine range of t on opposite cubic. |
| 261 | static void intersectEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2, |
| 262 | const SkDRect& bounds2, SkIntersections& i) { |
| 263 | SkDLine line; |
| 264 | int t1Index = start ? 0 : 3; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 265 | // don't bother if the two cubics are connnected |
caryclark@google.com | a5e5592 | 2013-05-07 18:51:31 +0000 | [diff] [blame^] | 266 | #if 1 |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 267 | SkTDArray<double> tVals; // OPTIMIZE: replace with hard-sized array |
caryclark@google.com | a5e5592 | 2013-05-07 18:51:31 +0000 | [diff] [blame^] | 268 | line[0] = cubic1[t1Index]; |
| 269 | // this variant looks for intersections with the end point and lines parallel to other points |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 270 | for (int index = 0; index < 4; ++index) { |
| 271 | if (index == t1Index) { |
| 272 | continue; |
| 273 | } |
| 274 | SkDVector dxy1 = cubic1[index] - line[0]; |
| 275 | dxy1 /= SkDCubic::gPrecisionUnit; |
| 276 | line[1] = line[0] + dxy1; |
| 277 | SkDRect lineBounds; |
| 278 | lineBounds.setBounds(line); |
| 279 | if (!bounds2.intersects(&lineBounds)) { |
| 280 | continue; |
| 281 | } |
| 282 | SkIntersections local; |
| 283 | if (!local.intersect(cubic2, line)) { |
| 284 | continue; |
| 285 | } |
| 286 | for (int idx2 = 0; idx2 < local.used(); ++idx2) { |
| 287 | double foundT = local[0][idx2]; |
| 288 | if (approximately_less_than_zero(foundT) |
| 289 | || approximately_greater_than_one(foundT)) { |
| 290 | continue; |
| 291 | } |
| 292 | if (local.pt(idx2).approximatelyEqual(line[0])) { |
| 293 | if (i.swapped()) { // FIXME: insert should respect swap |
| 294 | i.insert(foundT, start ? 0 : 1, line[0]); |
| 295 | } else { |
| 296 | i.insert(start ? 0 : 1, foundT, line[0]); |
| 297 | } |
| 298 | } else { |
caryclark@google.com | a5e5592 | 2013-05-07 18:51:31 +0000 | [diff] [blame^] | 299 | *tVals.append() = foundT; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 300 | } |
| 301 | } |
| 302 | } |
| 303 | if (tVals.count() == 0) { |
| 304 | return; |
| 305 | } |
commit-bot@chromium.org | b76d3b6 | 2013-04-22 19:55:19 +0000 | [diff] [blame] | 306 | SkTQSort<double>(tVals.begin(), tVals.end() - 1); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 307 | double tMin1 = start ? 0 : 1 - LINE_FRACTION; |
| 308 | double tMax1 = start ? LINE_FRACTION : 1; |
| 309 | int tIdx = 0; |
| 310 | do { |
| 311 | int tLast = tIdx; |
| 312 | while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) { |
| 313 | ++tLast; |
| 314 | } |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 315 | double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0); |
| 316 | double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 317 | int lastUsed = i.used(); |
| 318 | intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| 319 | if (lastUsed == i.used()) { |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 320 | tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0); |
| 321 | tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 322 | intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| 323 | } |
| 324 | tIdx = tLast + 1; |
| 325 | } while (tIdx < tVals.count()); |
caryclark@google.com | a5e5592 | 2013-05-07 18:51:31 +0000 | [diff] [blame^] | 326 | #else |
| 327 | const SkDPoint& endPt = cubic1[t1Index]; |
| 328 | if (!bounds2.contains(endPt)) { |
| 329 | return; |
| 330 | } |
| 331 | // this variant looks for intersections within an 'x' of the endpoint |
| 332 | double delta = SkTMax(bounds2.width(), bounds2.height()); |
| 333 | for (int index = 0; index < 2; ++index) { |
| 334 | if (index == 0) { |
| 335 | line[0].fY = line[1].fY = endPt.fY; |
| 336 | line[0].fX = endPt.fX - delta; |
| 337 | line[1].fX = endPt.fX + delta; |
| 338 | } else { |
| 339 | line[0].fX = line[1].fX = cubic1[t1Index].fX; |
| 340 | line[0].fY = endPt.fY - delta; |
| 341 | line[1].fY = endPt.fY + delta; |
| 342 | } |
| 343 | SkIntersections local; |
| 344 | local.intersectRay(cubic2, line); // OPTIMIZE: special for horizontal/vertical lines |
| 345 | int used = local.used(); |
| 346 | for (int index = 0; index < used; ++index) { |
| 347 | double foundT = local[0][index]; |
| 348 | if (approximately_less_than_zero(foundT) || approximately_greater_than_one(foundT)) { |
| 349 | continue; |
| 350 | } |
| 351 | if (!local.pt(index).approximatelyEqual(endPt)) { |
| 352 | continue; |
| 353 | } |
| 354 | if (i.swapped()) { // FIXME: insert should respect swap |
| 355 | i.insert(foundT, start ? 0 : 1, endPt); |
| 356 | } else { |
| 357 | i.insert(start ? 0 : 1, foundT, endPt); |
| 358 | } |
| 359 | return; |
| 360 | } |
| 361 | } |
| 362 | // the above doesn't catch when the end of the cubic missed the other cubic because the quad |
| 363 | // approximation moved too far away, so something like the below is still needed. The enabled |
| 364 | // code above tries to avoid this heavy lifting unless the convex hull intersected the cubic. |
| 365 | double tMin1 = start ? 0 : 1 - LINE_FRACTION; |
| 366 | double tMax1 = start ? LINE_FRACTION : 1; |
| 367 | double tMin2 = SkTMax(foundT - LINE_FRACTION, 0.0); |
| 368 | double tMax2 = SkTMin(foundT + LINE_FRACTION, 1.0); |
| 369 | int lastUsed = i.used(); |
| 370 | intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| 371 | if (lastUsed == i.used()) { |
| 372 | tMin2 = SkTMax(foundT - (1.0 / SkDCubic::gPrecisionUnit), 0.0); |
| 373 | tMax2 = SkTMin(foundT + (1.0 / SkDCubic::gPrecisionUnit), 1.0); |
| 374 | intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| 375 | } |
| 376 | #endif |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 377 | return; |
| 378 | } |
| 379 | |
| 380 | const double CLOSE_ENOUGH = 0.001; |
| 381 | |
| 382 | static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { |
| 383 | if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) { |
| 384 | return false; |
| 385 | } |
| 386 | pt = cubic.xyAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2); |
| 387 | return true; |
| 388 | } |
| 389 | |
| 390 | static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { |
| 391 | int last = i.used() - 1; |
| 392 | if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) { |
| 393 | return false; |
| 394 | } |
| 395 | pt = cubic.xyAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2); |
| 396 | return true; |
| 397 | } |
| 398 | |
| 399 | int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) { |
| 400 | ::intersect(c1, 0, 1, c2, 0, 1, 1, *this); |
| 401 | // FIXME: pass in cached bounds from caller |
| 402 | SkDRect c1Bounds, c2Bounds; |
| 403 | c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ? |
| 404 | c2Bounds.setBounds(c2); |
| 405 | intersectEnd(c1, false, c2, c2Bounds, *this); |
| 406 | intersectEnd(c1, true, c2, c2Bounds, *this); |
| 407 | bool selfIntersect = &c1 == &c2; |
| 408 | if (!selfIntersect) { |
| 409 | swap(); |
| 410 | intersectEnd(c2, false, c1, c1Bounds, *this); |
| 411 | intersectEnd(c2, true, c1, c1Bounds, *this); |
| 412 | swap(); |
| 413 | } |
| 414 | // If an end point and a second point very close to the end is returned, the second |
| 415 | // point may have been detected because the approximate quads |
| 416 | // intersected at the end and close to it. Verify that the second point is valid. |
| 417 | if (fUsed <= 1 || coincidentUsed()) { |
| 418 | return fUsed; |
| 419 | } |
| 420 | SkDPoint pt[2]; |
| 421 | if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1]) |
| 422 | && pt[0].approximatelyEqual(pt[1])) { |
| 423 | removeOne(1); |
| 424 | } |
| 425 | if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1]) |
| 426 | && pt[0].approximatelyEqual(pt[1])) { |
| 427 | removeOne(used() - 2); |
| 428 | } |
| 429 | return fUsed; |
| 430 | } |
| 431 | |
| 432 | // Up promote the quad to a cubic. |
| 433 | // OPTIMIZATION If this is a common use case, optimize by duplicating |
| 434 | // the intersect 3 loop to avoid the promotion / demotion code |
| 435 | int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) { |
| 436 | SkDCubic up = quad.toCubic(); |
| 437 | (void) intersect(cubic, up); |
| 438 | return used(); |
| 439 | } |
| 440 | |
| 441 | /* http://www.ag.jku.at/compass/compasssample.pdf |
| 442 | ( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen |
| 443 | Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth@math.uio.no |
| 444 | SINTEF Applied Mathematics http://www.sintef.no ) |
| 445 | describes a method to find the self intersection of a cubic by taking the gradient of the implicit |
| 446 | form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/ |
| 447 | |
| 448 | int SkIntersections::intersect(const SkDCubic& c) { |
| 449 | // check to see if x or y end points are the extrema. Are other quick rejects possible? |
| 450 | if (c.endsAreExtremaInXOrY()) { |
| 451 | return false; |
| 452 | } |
| 453 | (void) intersect(c, c); |
| 454 | if (used() > 0) { |
| 455 | SkASSERT(used() == 1); |
| 456 | if (fT[0][0] > fT[1][0]) { |
| 457 | swapPts(); |
| 458 | } |
| 459 | } |
| 460 | return used(); |
| 461 | } |