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comparison: gfx/skia/trunk/src/pathops/SkDCubicIntersection.cpp
gfx/skia/trunk/src/pathops/SkDCubicIntersection.cpp
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| -1:000000000000 | 0:8cbc52d83624 |
|---|---|
| 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 "SkTSort.h" | |
| 16 | |
| 17 #if ONE_OFF_DEBUG | |
| 18 static const double tLimits1[2][2] = {{0.3, 0.4}, {0.8, 0.9}}; | |
| 19 static const double tLimits2[2][2] = {{-0.8, -0.9}, {-0.8, -0.9}}; | |
| 20 #endif | |
| 21 | |
| 22 #define DEBUG_QUAD_PART ONE_OFF_DEBUG && 1 | |
| 23 #define DEBUG_QUAD_PART_SHOW_SIMPLE DEBUG_QUAD_PART && 0 | |
| 24 #define SWAP_TOP_DEBUG 0 | |
| 25 | |
| 26 static const int kCubicToQuadSubdivisionDepth = 8; // slots reserved for cubic to quads subdivision | |
| 27 | |
| 28 static int quadPart(const SkDCubic& cubic, double tStart, double tEnd, SkReduceOrder* reducer) { | |
| 29 SkDCubic part = cubic.subDivide(tStart, tEnd); | |
| 30 SkDQuad quad = part.toQuad(); | |
| 31 // FIXME: should reduceOrder be looser in this use case if quartic is going to blow up on an | |
| 32 // extremely shallow quadratic? | |
| 33 int order = reducer->reduce(quad); | |
| 34 #if DEBUG_QUAD_PART | |
| 35 SkDebugf("%s cubic=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)" | |
| 36 " t=(%1.9g,%1.9g)\n", __FUNCTION__, cubic[0].fX, cubic[0].fY, | |
| 37 cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY, | |
| 38 cubic[3].fX, cubic[3].fY, tStart, tEnd); | |
| 39 SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n" | |
| 40 " {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", | |
| 41 part[0].fX, part[0].fY, part[1].fX, part[1].fY, part[2].fX, part[2].fY, | |
| 42 part[3].fX, part[3].fY, quad[0].fX, quad[0].fY, | |
| 43 quad[1].fX, quad[1].fY, quad[2].fX, quad[2].fY); | |
| 44 #if DEBUG_QUAD_PART_SHOW_SIMPLE | |
| 45 SkDebugf("%s simple=(%1.9g,%1.9g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY); | |
| 46 if (order > 1) { | |
| 47 SkDebugf(" %1.9g,%1.9g", reducer->fQuad[1].fX, reducer->fQuad[1].fY); | |
| 48 } | |
| 49 if (order > 2) { | |
| 50 SkDebugf(" %1.9g,%1.9g", reducer->fQuad[2].fX, reducer->fQuad[2].fY); | |
| 51 } | |
| 52 SkDebugf(")\n"); | |
| 53 SkASSERT(order < 4 && order > 0); | |
| 54 #endif | |
| 55 #endif | |
| 56 return order; | |
| 57 } | |
| 58 | |
| 59 static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2, | |
| 60 int order2, SkIntersections& i) { | |
| 61 if (order1 == 3 && order2 == 3) { | |
| 62 i.intersect(simple1, simple2); | |
| 63 } else if (order1 <= 2 && order2 <= 2) { | |
| 64 i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2); | |
| 65 } else if (order1 == 3 && order2 <= 2) { | |
| 66 i.intersect(simple1, (const SkDLine&) simple2); | |
| 67 } else { | |
| 68 SkASSERT(order1 <= 2 && order2 == 3); | |
| 69 i.intersect(simple2, (const SkDLine&) simple1); | |
| 70 i.swapPts(); | |
| 71 } | |
| 72 } | |
| 73 | |
| 74 // this flavor centers potential intersections recursively. In contrast, '2' may inadvertently | |
| 75 // chase intersections near quadratic ends, requiring odd hacks to find them. | |
| 76 static void intersect(const SkDCubic& cubic1, double t1s, double t1e, const SkDCubic& cubic2, | |
| 77 double t2s, double t2e, double precisionScale, SkIntersections& i) { | |
| 78 i.upDepth(); | |
| 79 SkDCubic c1 = cubic1.subDivide(t1s, t1e); | |
| 80 SkDCubic c2 = cubic2.subDivide(t2s, t2e); | |
| 81 SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts1; | |
| 82 // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection) | |
| 83 c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1); | |
| 84 SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts2; | |
| 85 c2.toQuadraticTs(c2.calcPrecision() * precisionScale, &ts2); | |
| 86 double t1Start = t1s; | |
| 87 int ts1Count = ts1.count(); | |
| 88 for (int i1 = 0; i1 <= ts1Count; ++i1) { | |
| 89 const double tEnd1 = i1 < ts1Count ? ts1[i1] : 1; | |
| 90 const double t1 = t1s + (t1e - t1s) * tEnd1; | |
| 91 SkReduceOrder s1; | |
| 92 int o1 = quadPart(cubic1, t1Start, t1, &s1); | |
| 93 double t2Start = t2s; | |
| 94 int ts2Count = ts2.count(); | |
| 95 for (int i2 = 0; i2 <= ts2Count; ++i2) { | |
| 96 const double tEnd2 = i2 < ts2Count ? ts2[i2] : 1; | |
| 97 const double t2 = t2s + (t2e - t2s) * tEnd2; | |
| 98 if (&cubic1 == &cubic2 && t1Start >= t2Start) { | |
| 99 t2Start = t2; | |
| 100 continue; | |
| 101 } | |
| 102 SkReduceOrder s2; | |
| 103 int o2 = quadPart(cubic2, t2Start, t2, &s2); | |
| 104 #if ONE_OFF_DEBUG | |
| 105 char tab[] = " "; | |
| 106 if (tLimits1[0][0] >= t1Start && tLimits1[0][1] <= t1 | |
| 107 && tLimits1[1][0] >= t2Start && tLimits1[1][1] <= t2) { | |
| 108 SkDebugf("%.*s %s t1=(%1.9g,%1.9g) t2=(%1.9g,%1.9g)", i.depth()*2, tab, | |
| 109 __FUNCTION__, t1Start, t1, t2Start, t2); | |
| 110 SkIntersections xlocals; | |
| 111 xlocals.allowNear(false); | |
| 112 intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals); | |
| 113 SkDebugf(" xlocals.fUsed=%d\n", xlocals.used()); | |
| 114 } | |
| 115 #endif | |
| 116 SkIntersections locals; | |
| 117 locals.allowNear(false); | |
| 118 intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals); | |
| 119 int tCount = locals.used(); | |
| 120 for (int tIdx = 0; tIdx < tCount; ++tIdx) { | |
| 121 double to1 = t1Start + (t1 - t1Start) * locals[0][tIdx]; | |
| 122 double to2 = t2Start + (t2 - t2Start) * locals[1][tIdx]; | |
| 123 // if the computed t is not sufficiently precise, iterate | |
| 124 SkDPoint p1 = cubic1.ptAtT(to1); | |
| 125 SkDPoint p2 = cubic2.ptAtT(to2); | |
| 126 if (p1.approximatelyEqual(p2)) { | |
| 127 // FIXME: local edge may be coincident -- experiment with not propagating coincidence to caller | |
| 128 // SkASSERT(!locals.isCoincident(tIdx)); | |
| 129 if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) { | |
| 130 if (i.swapped()) { // FIXME: insert should respect swap | |
| 131 i.insert(to2, to1, p1); | |
| 132 } else { | |
| 133 i.insert(to1, to2, p1); | |
| 134 } | |
| 135 } | |
| 136 } else { | |
| 137 double offset = precisionScale / 16; // FIME: const is arbitrary: test, refine | |
| 138 double c1Bottom = tIdx == 0 ? 0 : | |
| 139 (t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2; | |
| 140 double c1Min = SkTMax(c1Bottom, to1 - offset); | |
| 141 double c1Top = tIdx == tCount - 1 ? 1 : | |
| 142 (t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2; | |
| 143 double c1Max = SkTMin(c1Top, to1 + offset); | |
| 144 double c2Min = SkTMax(0., to2 - offset); | |
| 145 double c2Max = SkTMin(1., to2 + offset); | |
| 146 #if ONE_OFF_DEBUG | |
| 147 SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, | |
| 148 __FUNCTION__, | |
| 149 c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max | |
| 150 && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, | |
| 151 to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset | |
| 152 && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, | |
| 153 c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max | |
| 154 && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, | |
| 155 to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset | |
| 156 && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); | |
| 157 SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" | |
| 158 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", | |
| 159 i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1., | |
| 160 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); | |
| 161 SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" | |
| 162 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, | |
| 163 c1Max, c2Min, c2Max); | |
| 164 #endif | |
| 165 intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); | |
| 166 #if ONE_OFF_DEBUG | |
| 167 SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, | |
| 168 i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); | |
| 169 #endif | |
| 170 if (tCount > 1) { | |
| 171 c1Min = SkTMax(0., to1 - offset); | |
| 172 c1Max = SkTMin(1., to1 + offset); | |
| 173 double c2Bottom = tIdx == 0 ? to2 : | |
| 174 (t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2; | |
| 175 double c2Top = tIdx == tCount - 1 ? to2 : | |
| 176 (t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2; | |
| 177 if (c2Bottom > c2Top) { | |
| 178 SkTSwap(c2Bottom, c2Top); | |
| 179 } | |
| 180 if (c2Bottom == to2) { | |
| 181 c2Bottom = 0; | |
| 182 } | |
| 183 if (c2Top == to2) { | |
| 184 c2Top = 1; | |
| 185 } | |
| 186 c2Min = SkTMax(c2Bottom, to2 - offset); | |
| 187 c2Max = SkTMin(c2Top, to2 + offset); | |
| 188 #if ONE_OFF_DEBUG | |
| 189 SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, | |
| 190 __FUNCTION__, | |
| 191 c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max | |
| 192 && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, | |
| 193 to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset | |
| 194 && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, | |
| 195 c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max | |
| 196 && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, | |
| 197 to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset | |
| 198 && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); | |
| 199 SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" | |
| 200 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", | |
| 201 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, | |
| 202 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); | |
| 203 SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" | |
| 204 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, | |
| 205 c1Max, c2Min, c2Max); | |
| 206 #endif | |
| 207 intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); | |
| 208 #if ONE_OFF_DEBUG | |
| 209 SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, | |
| 210 i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); | |
| 211 #endif | |
| 212 c1Min = SkTMax(c1Bottom, to1 - offset); | |
| 213 c1Max = SkTMin(c1Top, to1 + offset); | |
| 214 #if ONE_OFF_DEBUG | |
| 215 SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, | |
| 216 __FUNCTION__, | |
| 217 c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max | |
| 218 && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, | |
| 219 to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset | |
| 220 && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, | |
| 221 c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max | |
| 222 && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, | |
| 223 to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset | |
| 224 && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); | |
| 225 SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" | |
| 226 " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", | |
| 227 i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, | |
| 228 to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); | |
| 229 SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" | |
| 230 " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, | |
| 231 c1Max, c2Min, c2Max); | |
| 232 #endif | |
| 233 intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); | |
| 234 #if ONE_OFF_DEBUG | |
| 235 SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, | |
| 236 i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); | |
| 237 #endif | |
| 238 } | |
| 239 // intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); | |
| 240 // FIXME: if no intersection is found, either quadratics intersected where | |
| 241 // cubics did not, or the intersection was missed. In the former case, expect | |
| 242 // the quadratics to be nearly parallel at the point of intersection, and check | |
| 243 // for that. | |
| 244 } | |
| 245 } | |
| 246 t2Start = t2; | |
| 247 } | |
| 248 t1Start = t1; | |
| 249 } | |
| 250 i.downDepth(); | |
| 251 } | |
| 252 | |
| 253 // if two ends intersect, check middle for coincidence | |
| 254 bool SkIntersections::cubicCheckCoincidence(const SkDCubic& c1, const SkDCubic& c2) { | |
| 255 if (fUsed < 2) { | |
| 256 return false; | |
| 257 } | |
| 258 int last = fUsed - 1; | |
| 259 double tRange1 = fT[0][last] - fT[0][0]; | |
| 260 double tRange2 = fT[1][last] - fT[1][0]; | |
| 261 for (int index = 1; index < 5; ++index) { | |
| 262 double testT1 = fT[0][0] + tRange1 * index / 5; | |
| 263 double testT2 = fT[1][0] + tRange2 * index / 5; | |
| 264 SkDPoint testPt1 = c1.ptAtT(testT1); | |
| 265 SkDPoint testPt2 = c2.ptAtT(testT2); | |
| 266 if (!testPt1.approximatelyEqual(testPt2)) { | |
| 267 return false; | |
| 268 } | |
| 269 } | |
| 270 if (fUsed > 2) { | |
| 271 fPt[1] = fPt[last]; | |
| 272 fT[0][1] = fT[0][last]; | |
| 273 fT[1][1] = fT[1][last]; | |
| 274 fUsed = 2; | |
| 275 } | |
| 276 fIsCoincident[0] = fIsCoincident[1] = 0x03; | |
| 277 return true; | |
| 278 } | |
| 279 | |
| 280 #define LINE_FRACTION 0.1 | |
| 281 | |
| 282 // intersect the end of the cubic with the other. Try lines from the end to control and opposite | |
| 283 // end to determine range of t on opposite cubic. | |
| 284 bool SkIntersections::cubicExactEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2) { | |
| 285 int t1Index = start ? 0 : 3; | |
| 286 double testT = (double) !start; | |
| 287 bool swap = swapped(); | |
| 288 // quad/quad at this point checks to see if exact matches have already been found | |
| 289 // cubic/cubic can't reject so easily since cubics can intersect same point more than once | |
| 290 SkDLine tmpLine; | |
| 291 tmpLine[0] = tmpLine[1] = cubic2[t1Index]; | |
| 292 tmpLine[1].fX += cubic2[2 - start].fY - cubic2[t1Index].fY; | |
| 293 tmpLine[1].fY -= cubic2[2 - start].fX - cubic2[t1Index].fX; | |
| 294 SkIntersections impTs; | |
| 295 impTs.allowNear(false); | |
| 296 impTs.intersectRay(cubic1, tmpLine); | |
| 297 for (int index = 0; index < impTs.used(); ++index) { | |
| 298 SkDPoint realPt = impTs.pt(index); | |
| 299 if (!tmpLine[0].approximatelyEqual(realPt)) { | |
| 300 continue; | |
| 301 } | |
| 302 if (swap) { | |
| 303 insert(testT, impTs[0][index], tmpLine[0]); | |
| 304 } else { | |
| 305 insert(impTs[0][index], testT, tmpLine[0]); | |
| 306 } | |
| 307 return true; | |
| 308 } | |
| 309 return false; | |
| 310 } | |
| 311 | |
| 312 void SkIntersections::cubicNearEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2, | |
| 313 const SkDRect& bounds2) { | |
| 314 SkDLine line; | |
| 315 int t1Index = start ? 0 : 3; | |
| 316 double testT = (double) !start; | |
| 317 // don't bother if the two cubics are connnected | |
| 318 static const int kPointsInCubic = 4; // FIXME: move to DCubic, replace '4' with this | |
| 319 static const int kMaxLineCubicIntersections = 3; | |
| 320 SkSTArray<(kMaxLineCubicIntersections - 1) * kMaxLineCubicIntersections, double, true> tVals; | |
| 321 line[0] = cubic1[t1Index]; | |
| 322 // this variant looks for intersections with the end point and lines parallel to other points | |
| 323 for (int index = 0; index < kPointsInCubic; ++index) { | |
| 324 if (index == t1Index) { | |
| 325 continue; | |
| 326 } | |
| 327 SkDVector dxy1 = cubic1[index] - line[0]; | |
| 328 dxy1 /= SkDCubic::gPrecisionUnit; | |
| 329 line[1] = line[0] + dxy1; | |
| 330 SkDRect lineBounds; | |
| 331 lineBounds.setBounds(line); | |
| 332 if (!bounds2.intersects(&lineBounds)) { | |
| 333 continue; | |
| 334 } | |
| 335 SkIntersections local; | |
| 336 if (!local.intersect(cubic2, line)) { | |
| 337 continue; | |
| 338 } | |
| 339 for (int idx2 = 0; idx2 < local.used(); ++idx2) { | |
| 340 double foundT = local[0][idx2]; | |
| 341 if (approximately_less_than_zero(foundT) | |
| 342 || approximately_greater_than_one(foundT)) { | |
| 343 continue; | |
| 344 } | |
| 345 if (local.pt(idx2).approximatelyEqual(line[0])) { | |
| 346 if (swapped()) { // FIXME: insert should respect swap | |
| 347 insert(foundT, testT, line[0]); | |
| 348 } else { | |
| 349 insert(testT, foundT, line[0]); | |
| 350 } | |
| 351 } else { | |
| 352 tVals.push_back(foundT); | |
| 353 } | |
| 354 } | |
| 355 } | |
| 356 if (tVals.count() == 0) { | |
| 357 return; | |
| 358 } | |
| 359 SkTQSort<double>(tVals.begin(), tVals.end() - 1); | |
| 360 double tMin1 = start ? 0 : 1 - LINE_FRACTION; | |
| 361 double tMax1 = start ? LINE_FRACTION : 1; | |
| 362 int tIdx = 0; | |
| 363 do { | |
| 364 int tLast = tIdx; | |
| 365 while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) { | |
| 366 ++tLast; | |
| 367 } | |
| 368 double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0); | |
| 369 double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0); | |
| 370 int lastUsed = used(); | |
| 371 ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this); | |
| 372 if (lastUsed == used()) { | |
| 373 tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0); | |
| 374 tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0); | |
| 375 ::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this); | |
| 376 } | |
| 377 tIdx = tLast + 1; | |
| 378 } while (tIdx < tVals.count()); | |
| 379 return; | |
| 380 } | |
| 381 | |
| 382 const double CLOSE_ENOUGH = 0.001; | |
| 383 | |
| 384 static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { | |
| 385 if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) { | |
| 386 return false; | |
| 387 } | |
| 388 pt = cubic.ptAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2); | |
| 389 return true; | |
| 390 } | |
| 391 | |
| 392 static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { | |
| 393 int last = i.used() - 1; | |
| 394 if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) { | |
| 395 return false; | |
| 396 } | |
| 397 pt = cubic.ptAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2); | |
| 398 return true; | |
| 399 } | |
| 400 | |
| 401 static bool only_end_pts_in_common(const SkDCubic& c1, const SkDCubic& c2) { | |
| 402 // the idea here is to see at minimum do a quick reject by rotating all points | |
| 403 // to either side of the line formed by connecting the endpoints | |
| 404 // if the opposite curves points are on the line or on the other side, the | |
| 405 // curves at most intersect at the endpoints | |
| 406 for (int oddMan = 0; oddMan < 4; ++oddMan) { | |
| 407 const SkDPoint* endPt[3]; | |
| 408 for (int opp = 1; opp < 4; ++opp) { | |
| 409 int end = oddMan ^ opp; // choose a value not equal to oddMan | |
| 410 endPt[opp - 1] = &c1[end]; | |
| 411 } | |
| 412 for (int triTest = 0; triTest < 3; ++triTest) { | |
| 413 double origX = endPt[triTest]->fX; | |
| 414 double origY = endPt[triTest]->fY; | |
| 415 int oppTest = triTest + 1; | |
| 416 if (3 == oppTest) { | |
| 417 oppTest = 0; | |
| 418 } | |
| 419 double adj = endPt[oppTest]->fX - origX; | |
| 420 double opp = endPt[oppTest]->fY - origY; | |
| 421 double sign = (c1[oddMan].fY - origY) * adj - (c1[oddMan].fX - origX) * opp; | |
| 422 if (approximately_zero(sign)) { | |
| 423 goto tryNextHalfPlane; | |
| 424 } | |
| 425 for (int n = 0; n < 4; ++n) { | |
| 426 double test = (c2[n].fY - origY) * adj - (c2[n].fX - origX) * opp; | |
| 427 if (test * sign > 0 && !precisely_zero(test)) { | |
| 428 goto tryNextHalfPlane; | |
| 429 } | |
| 430 } | |
| 431 } | |
| 432 return true; | |
| 433 tryNextHalfPlane: | |
| 434 ; | |
| 435 } | |
| 436 return false; | |
| 437 } | |
| 438 | |
| 439 int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) { | |
| 440 if (fMax == 0) { | |
| 441 fMax = 9; | |
| 442 } | |
| 443 bool selfIntersect = &c1 == &c2; | |
| 444 if (selfIntersect) { | |
| 445 if (c1[0].approximatelyEqual(c1[3])) { | |
| 446 insert(0, 1, c1[0]); | |
| 447 return fUsed; | |
| 448 } | |
| 449 } else { | |
| 450 // OPTIMIZATION: set exact end bits here to avoid cubic exact end later | |
| 451 for (int i1 = 0; i1 < 4; i1 += 3) { | |
| 452 for (int i2 = 0; i2 < 4; i2 += 3) { | |
| 453 if (c1[i1].approximatelyEqual(c2[i2])) { | |
| 454 insert(i1 >> 1, i2 >> 1, c1[i1]); | |
| 455 } | |
| 456 } | |
| 457 } | |
| 458 } | |
| 459 SkASSERT(fUsed < 4); | |
| 460 if (!selfIntersect) { | |
| 461 if (only_end_pts_in_common(c1, c2)) { | |
| 462 return fUsed; | |
| 463 } | |
| 464 if (only_end_pts_in_common(c2, c1)) { | |
| 465 return fUsed; | |
| 466 } | |
| 467 } | |
| 468 // quad/quad does linear test here -- cubic does not | |
| 469 // cubics which are really lines should have been detected in reduce step earlier | |
| 470 int exactEndBits = 0; | |
| 471 if (selfIntersect) { | |
| 472 if (fUsed) { | |
| 473 return fUsed; | |
| 474 } | |
| 475 } else { | |
| 476 exactEndBits |= cubicExactEnd(c1, false, c2) << 0; | |
| 477 exactEndBits |= cubicExactEnd(c1, true, c2) << 1; | |
| 478 swap(); | |
| 479 exactEndBits |= cubicExactEnd(c2, false, c1) << 2; | |
| 480 exactEndBits |= cubicExactEnd(c2, true, c1) << 3; | |
| 481 swap(); | |
| 482 } | |
| 483 if (cubicCheckCoincidence(c1, c2)) { | |
| 484 SkASSERT(!selfIntersect); | |
| 485 return fUsed; | |
| 486 } | |
| 487 // FIXME: pass in cached bounds from caller | |
| 488 SkDRect c2Bounds; | |
| 489 c2Bounds.setBounds(c2); | |
| 490 if (!(exactEndBits & 4)) { | |
| 491 cubicNearEnd(c1, false, c2, c2Bounds); | |
| 492 } | |
| 493 if (!(exactEndBits & 8)) { | |
| 494 cubicNearEnd(c1, true, c2, c2Bounds); | |
| 495 } | |
| 496 if (!selfIntersect) { | |
| 497 SkDRect c1Bounds; | |
| 498 c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ? | |
| 499 swap(); | |
| 500 if (!(exactEndBits & 1)) { | |
| 501 cubicNearEnd(c2, false, c1, c1Bounds); | |
| 502 } | |
| 503 if (!(exactEndBits & 2)) { | |
| 504 cubicNearEnd(c2, true, c1, c1Bounds); | |
| 505 } | |
| 506 swap(); | |
| 507 } | |
| 508 if (cubicCheckCoincidence(c1, c2)) { | |
| 509 SkASSERT(!selfIntersect); | |
| 510 return fUsed; | |
| 511 } | |
| 512 SkIntersections i; | |
| 513 i.fAllowNear = false; | |
| 514 i.fMax = 9; | |
| 515 ::intersect(c1, 0, 1, c2, 0, 1, 1, i); | |
| 516 int compCount = i.used(); | |
| 517 if (compCount) { | |
| 518 int exactCount = used(); | |
| 519 if (exactCount == 0) { | |
| 520 set(i); | |
| 521 } else { | |
| 522 // at least one is exact or near, and at least one was computed. Eliminate duplicates | |
| 523 for (int exIdx = 0; exIdx < exactCount; ++exIdx) { | |
| 524 for (int cpIdx = 0; cpIdx < compCount; ) { | |
| 525 if (fT[0][0] == i[0][0] && fT[1][0] == i[1][0]) { | |
| 526 i.removeOne(cpIdx); | |
| 527 --compCount; | |
| 528 continue; | |
| 529 } | |
| 530 double tAvg = (fT[0][exIdx] + i[0][cpIdx]) / 2; | |
| 531 SkDPoint pt = c1.ptAtT(tAvg); | |
| 532 if (!pt.approximatelyEqual(fPt[exIdx])) { | |
| 533 ++cpIdx; | |
| 534 continue; | |
| 535 } | |
| 536 tAvg = (fT[1][exIdx] + i[1][cpIdx]) / 2; | |
| 537 pt = c2.ptAtT(tAvg); | |
| 538 if (!pt.approximatelyEqual(fPt[exIdx])) { | |
| 539 ++cpIdx; | |
| 540 continue; | |
| 541 } | |
| 542 i.removeOne(cpIdx); | |
| 543 --compCount; | |
| 544 } | |
| 545 } | |
| 546 // if mid t evaluates to nearly the same point, skip the t | |
| 547 for (int cpIdx = 0; cpIdx < compCount - 1; ) { | |
| 548 double tAvg = (fT[0][cpIdx] + i[0][cpIdx + 1]) / 2; | |
| 549 SkDPoint pt = c1.ptAtT(tAvg); | |
| 550 if (!pt.approximatelyEqual(fPt[cpIdx])) { | |
| 551 ++cpIdx; | |
| 552 continue; | |
| 553 } | |
| 554 tAvg = (fT[1][cpIdx] + i[1][cpIdx + 1]) / 2; | |
| 555 pt = c2.ptAtT(tAvg); | |
| 556 if (!pt.approximatelyEqual(fPt[cpIdx])) { | |
| 557 ++cpIdx; | |
| 558 continue; | |
| 559 } | |
| 560 i.removeOne(cpIdx); | |
| 561 --compCount; | |
| 562 } | |
| 563 // in addition to adding below missing function, think about how to say | |
| 564 append(i); | |
| 565 } | |
| 566 } | |
| 567 // If an end point and a second point very close to the end is returned, the second | |
| 568 // point may have been detected because the approximate quads | |
| 569 // intersected at the end and close to it. Verify that the second point is valid. | |
| 570 if (fUsed <= 1) { | |
| 571 return fUsed; | |
| 572 } | |
| 573 SkDPoint pt[2]; | |
| 574 if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1]) | |
| 575 && pt[0].approximatelyEqual(pt[1])) { | |
| 576 removeOne(1); | |
| 577 } | |
| 578 if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1]) | |
| 579 && pt[0].approximatelyEqual(pt[1])) { | |
| 580 removeOne(used() - 2); | |
| 581 } | |
| 582 // vet the pairs of t values to see if the mid value is also on the curve. If so, mark | |
| 583 // the span as coincident | |
| 584 if (fUsed >= 2 && !coincidentUsed()) { | |
| 585 int last = fUsed - 1; | |
| 586 int match = 0; | |
| 587 for (int index = 0; index < last; ++index) { | |
| 588 double mid1 = (fT[0][index] + fT[0][index + 1]) / 2; | |
| 589 double mid2 = (fT[1][index] + fT[1][index + 1]) / 2; | |
| 590 pt[0] = c1.ptAtT(mid1); | |
| 591 pt[1] = c2.ptAtT(mid2); | |
| 592 if (pt[0].approximatelyEqual(pt[1])) { | |
| 593 match |= 1 << index; | |
| 594 } | |
| 595 } | |
| 596 if (match) { | |
| 597 #if DEBUG_CONCIDENT | |
| 598 if (((match + 1) & match) != 0) { | |
| 599 SkDebugf("%s coincident hole\n", __FUNCTION__); | |
| 600 } | |
| 601 #endif | |
| 602 // for now, assume that everything from start to finish is coincident | |
| 603 if (fUsed > 2) { | |
| 604 fPt[1] = fPt[last]; | |
| 605 fT[0][1] = fT[0][last]; | |
| 606 fT[1][1] = fT[1][last]; | |
| 607 fIsCoincident[0] = 0x03; | |
| 608 fIsCoincident[1] = 0x03; | |
| 609 fUsed = 2; | |
| 610 } | |
| 611 } | |
| 612 } | |
| 613 return fUsed; | |
| 614 } | |
| 615 | |
| 616 // Up promote the quad to a cubic. | |
| 617 // OPTIMIZATION If this is a common use case, optimize by duplicating | |
| 618 // the intersect 3 loop to avoid the promotion / demotion code | |
| 619 int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) { | |
| 620 fMax = 6; | |
| 621 SkDCubic up = quad.toCubic(); | |
| 622 (void) intersect(cubic, up); | |
| 623 return used(); | |
| 624 } | |
| 625 | |
| 626 /* http://www.ag.jku.at/compass/compasssample.pdf | |
| 627 ( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen | |
| 628 Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth@math.uio.no | |
| 629 SINTEF Applied Mathematics http://www.sintef.no ) | |
| 630 describes a method to find the self intersection of a cubic by taking the gradient of the implicit | |
| 631 form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/ | |
| 632 | |
| 633 int SkIntersections::intersect(const SkDCubic& c) { | |
| 634 fMax = 1; | |
| 635 // check to see if x or y end points are the extrema. Are other quick rejects possible? | |
| 636 if (c.endsAreExtremaInXOrY()) { | |
| 637 return false; | |
| 638 } | |
| 639 (void) intersect(c, c); | |
| 640 if (used() > 0) { | |
| 641 SkASSERT(used() == 1); | |
| 642 if (fT[0][0] > fT[1][0]) { | |
| 643 swapPts(); | |
| 644 } | |
| 645 } | |
| 646 return used(); | |
| 647 } |
