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" |
commit-bot@chromium.org | b76d3b6 | 2013-04-22 19:55:19 +0000 | [diff] [blame] | 15 | #include "SkTSort.h" |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 16 | |
| 17 | #if ONE_OFF_DEBUG |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 18 | static const double tLimits1[2][2] = {{0.388600450, 0.388600452}, {0.245852802, 0.245852804}}; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 19 | static const double tLimits2[2][2] = {{-0.865211397, -0.865215212}, {-0.865207696, -0.865208078}}; |
| 20 | #endif |
| 21 | |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 22 | #define DEBUG_QUAD_PART ONE_OFF_DEBUG && 1 |
| 23 | #define DEBUG_QUAD_PART_SHOW_SIMPLE DEBUG_QUAD_PART && 0 |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 24 | #define SWAP_TOP_DEBUG 0 |
| 25 | |
caryclark@google.com | d892bd8 | 2013-06-17 14:10:36 +0000 | [diff] [blame] | 26 | static const int kCubicToQuadSubdivisionDepth = 8; // slots reserved for cubic to quads subdivision |
| 27 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 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, SkReduceOrder::kFill_Style); |
| 34 | #if DEBUG_QUAD_PART |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 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, |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 37 | cubic[1].fX, cubic[1].fY, cubic[2].fX, cubic[2].fY, |
| 38 | cubic[3].fX, cubic[3].fY, tStart, tEnd); |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 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", |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 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); |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 44 | #if DEBUG_QUAD_PART_SHOW_SIMPLE |
| 45 | SkDebugf("%s simple=(%1.9g,%1.9g", __FUNCTION__, reducer->fQuad[0].fX, reducer->fQuad[0].fY); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 46 | if (order > 1) { |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 47 | SkDebugf(" %1.9g,%1.9g", reducer->fQuad[1].fX, reducer->fQuad[1].fY); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 48 | } |
| 49 | if (order > 2) { |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 50 | SkDebugf(" %1.9g,%1.9g", reducer->fQuad[2].fX, reducer->fQuad[2].fY); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 51 | } |
| 52 | SkDebugf(")\n"); |
| 53 | SkASSERT(order < 4 && order > 0); |
| 54 | #endif |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 55 | #endif |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 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); |
caryclark@google.com | d892bd8 | 2013-06-17 14:10:36 +0000 | [diff] [blame] | 81 | SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts1; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 82 | // OPTIMIZE: if c1 == c2, call once (happens when detecting self-intersection) |
| 83 | c1.toQuadraticTs(c1.calcPrecision() * precisionScale, &ts1); |
caryclark@google.com | d892bd8 | 2013-06-17 14:10:36 +0000 | [diff] [blame] | 84 | SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts2; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 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) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 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; |
caryclark@google.com | 570863f | 2013-09-16 15:55:01 +0000 | [diff] [blame^] | 111 | xlocals.allowNear(false); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 112 | intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, xlocals); |
| 113 | SkDebugf(" xlocals.fUsed=%d\n", xlocals.used()); |
| 114 | } |
| 115 | #endif |
| 116 | SkIntersections locals; |
caryclark@google.com | 570863f | 2013-09-16 15:55:01 +0000 | [diff] [blame^] | 117 | locals.allowNear(false); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 118 | intersectWithOrder(s1.fQuad, o1, s2.fQuad, o2, locals); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 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 |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 124 | SkDPoint p1 = cubic1.ptAtT(to1); |
| 125 | SkDPoint p2 = cubic2.ptAtT(to2); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 126 | if (p1.approximatelyEqual(p2)) { |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 127 | SkASSERT(!locals.isCoincident(tIdx)); |
| 128 | if (&cubic1 != &cubic2 || !approximately_equal(to1, to2)) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 129 | if (i.swapped()) { // FIXME: insert should respect swap |
| 130 | i.insert(to2, to1, p1); |
| 131 | } else { |
| 132 | i.insert(to1, to2, p1); |
| 133 | } |
| 134 | } |
| 135 | } else { |
| 136 | double offset = precisionScale / 16; // FIME: const is arbitrary: test, refine |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 137 | double c1Bottom = tIdx == 0 ? 0 : |
| 138 | (t1Start + (t1 - t1Start) * locals[0][tIdx - 1] + to1) / 2; |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 139 | double c1Min = SkTMax(c1Bottom, to1 - offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 140 | double c1Top = tIdx == tCount - 1 ? 1 : |
| 141 | (t1Start + (t1 - t1Start) * locals[0][tIdx + 1] + to1) / 2; |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 142 | double c1Max = SkTMin(c1Top, to1 + offset); |
| 143 | double c2Min = SkTMax(0., to2 - offset); |
| 144 | double c2Max = SkTMin(1., to2 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 145 | #if ONE_OFF_DEBUG |
| 146 | SkDebugf("%.*s %s 1 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, |
| 147 | __FUNCTION__, |
| 148 | c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max |
| 149 | && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, |
| 150 | to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset |
| 151 | && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, |
| 152 | c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max |
| 153 | && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, |
| 154 | to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset |
| 155 | && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); |
| 156 | SkDebugf("%.*s %s 1 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" |
| 157 | " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", |
| 158 | i.depth()*2, tab, __FUNCTION__, c1Bottom, c1Top, 0., 1., |
| 159 | to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); |
| 160 | SkDebugf("%.*s %s 1 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" |
| 161 | " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, |
| 162 | c1Max, c2Min, c2Max); |
| 163 | #endif |
| 164 | intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| 165 | #if ONE_OFF_DEBUG |
| 166 | SkDebugf("%.*s %s 1 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, |
| 167 | i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); |
| 168 | #endif |
| 169 | if (tCount > 1) { |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 170 | c1Min = SkTMax(0., to1 - offset); |
| 171 | c1Max = SkTMin(1., to1 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 172 | double c2Bottom = tIdx == 0 ? to2 : |
| 173 | (t2Start + (t2 - t2Start) * locals[1][tIdx - 1] + to2) / 2; |
| 174 | double c2Top = tIdx == tCount - 1 ? to2 : |
| 175 | (t2Start + (t2 - t2Start) * locals[1][tIdx + 1] + to2) / 2; |
| 176 | if (c2Bottom > c2Top) { |
| 177 | SkTSwap(c2Bottom, c2Top); |
| 178 | } |
| 179 | if (c2Bottom == to2) { |
| 180 | c2Bottom = 0; |
| 181 | } |
| 182 | if (c2Top == to2) { |
| 183 | c2Top = 1; |
| 184 | } |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 185 | c2Min = SkTMax(c2Bottom, to2 - offset); |
| 186 | c2Max = SkTMin(c2Top, to2 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 187 | #if ONE_OFF_DEBUG |
| 188 | SkDebugf("%.*s %s 2 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, |
| 189 | __FUNCTION__, |
| 190 | c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max |
| 191 | && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, |
| 192 | to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset |
| 193 | && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, |
| 194 | c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max |
| 195 | && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, |
| 196 | to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset |
| 197 | && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); |
| 198 | SkDebugf("%.*s %s 2 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" |
| 199 | " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", |
| 200 | i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, |
| 201 | to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); |
| 202 | SkDebugf("%.*s %s 2 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" |
| 203 | " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, |
| 204 | c1Max, c2Min, c2Max); |
| 205 | #endif |
| 206 | intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| 207 | #if ONE_OFF_DEBUG |
| 208 | SkDebugf("%.*s %s 2 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, |
| 209 | i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); |
| 210 | #endif |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 211 | c1Min = SkTMax(c1Bottom, to1 - offset); |
| 212 | c1Max = SkTMin(c1Top, to1 + offset); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 213 | #if ONE_OFF_DEBUG |
| 214 | SkDebugf("%.*s %s 3 contains1=%d/%d contains2=%d/%d\n", i.depth()*2, tab, |
| 215 | __FUNCTION__, |
| 216 | c1Min <= tLimits1[0][1] && tLimits1[0][0] <= c1Max |
| 217 | && c2Min <= tLimits1[1][1] && tLimits1[1][0] <= c2Max, |
| 218 | to1 - offset <= tLimits1[0][1] && tLimits1[0][0] <= to1 + offset |
| 219 | && to2 - offset <= tLimits1[1][1] && tLimits1[1][0] <= to2 + offset, |
| 220 | c1Min <= tLimits2[0][1] && tLimits2[0][0] <= c1Max |
| 221 | && c2Min <= tLimits2[1][1] && tLimits2[1][0] <= c2Max, |
| 222 | to1 - offset <= tLimits2[0][1] && tLimits2[0][0] <= to1 + offset |
| 223 | && to2 - offset <= tLimits2[1][1] && tLimits2[1][0] <= to2 + offset); |
| 224 | SkDebugf("%.*s %s 3 c1Bottom=%1.9g c1Top=%1.9g c2Bottom=%1.9g c2Top=%1.9g" |
| 225 | " 1-o=%1.9g 1+o=%1.9g 2-o=%1.9g 2+o=%1.9g offset=%1.9g\n", |
| 226 | i.depth()*2, tab, __FUNCTION__, 0., 1., c2Bottom, c2Top, |
| 227 | to1 - offset, to1 + offset, to2 - offset, to2 + offset, offset); |
| 228 | SkDebugf("%.*s %s 3 to1=%1.9g to2=%1.9g c1Min=%1.9g c1Max=%1.9g c2Min=%1.9g" |
| 229 | " c2Max=%1.9g\n", i.depth()*2, tab, __FUNCTION__, to1, to2, c1Min, |
| 230 | c1Max, c2Min, c2Max); |
| 231 | #endif |
| 232 | intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
| 233 | #if ONE_OFF_DEBUG |
| 234 | SkDebugf("%.*s %s 3 i.used=%d t=%1.9g\n", i.depth()*2, tab, __FUNCTION__, |
| 235 | i.used(), i.used() > 0 ? i[0][i.used() - 1] : -1); |
| 236 | #endif |
| 237 | } |
caryclark@google.com | fa2aeee | 2013-07-15 13:29:13 +0000 | [diff] [blame] | 238 | // intersect(cubic1, c1Min, c1Max, cubic2, c2Min, c2Max, offset, i); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 239 | // FIXME: if no intersection is found, either quadratics intersected where |
| 240 | // cubics did not, or the intersection was missed. In the former case, expect |
| 241 | // the quadratics to be nearly parallel at the point of intersection, and check |
| 242 | // for that. |
| 243 | } |
| 244 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 245 | t2Start = t2; |
| 246 | } |
| 247 | t1Start = t1; |
| 248 | } |
| 249 | i.downDepth(); |
| 250 | } |
| 251 | |
| 252 | #define LINE_FRACTION 0.1 |
| 253 | |
| 254 | // intersect the end of the cubic with the other. Try lines from the end to control and opposite |
| 255 | // end to determine range of t on opposite cubic. |
| 256 | static void intersectEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2, |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 257 | const SkDRect& bounds2, bool selfIntersect, SkIntersections& i) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 258 | SkDLine line; |
| 259 | int t1Index = start ? 0 : 3; |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 260 | bool swap = i.swapped(); |
| 261 | double testT = (double) !start; |
| 262 | // quad/quad at this point checks to see if exact matches have already been found |
| 263 | // cubic/cubic can't reject so easily since cubics can intersect same point more than once |
| 264 | if (!selfIntersect) { |
| 265 | SkDLine tmpLine; |
| 266 | tmpLine[0] = tmpLine[1] = cubic2[t1Index]; |
| 267 | tmpLine[1].fX += cubic2[2 - start].fY - cubic2[t1Index].fY; |
| 268 | tmpLine[1].fY -= cubic2[2 - start].fX - cubic2[t1Index].fX; |
| 269 | SkIntersections impTs; |
| 270 | impTs.intersectRay(cubic1, tmpLine); |
| 271 | for (int index = 0; index < impTs.used(); ++index) { |
| 272 | SkDPoint realPt = impTs.pt(index); |
| 273 | if (!tmpLine[0].approximatelyEqualHalf(realPt)) { |
| 274 | continue; |
| 275 | } |
| 276 | if (swap) { |
| 277 | i.insert(testT, impTs[0][index], tmpLine[0]); |
| 278 | } else { |
| 279 | i.insert(impTs[0][index], testT, tmpLine[0]); |
| 280 | } |
| 281 | return; |
| 282 | } |
| 283 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 284 | // don't bother if the two cubics are connnected |
caryclark@google.com | d892bd8 | 2013-06-17 14:10:36 +0000 | [diff] [blame] | 285 | static const int kPointsInCubic = 4; // FIXME: move to DCubic, replace '4' with this |
| 286 | static const int kMaxLineCubicIntersections = 3; |
| 287 | SkSTArray<(kMaxLineCubicIntersections - 1) * kMaxLineCubicIntersections, double, true> tVals; |
caryclark@google.com | a5e5592 | 2013-05-07 18:51:31 +0000 | [diff] [blame] | 288 | line[0] = cubic1[t1Index]; |
| 289 | // this variant looks for intersections with the end point and lines parallel to other points |
caryclark@google.com | d892bd8 | 2013-06-17 14:10:36 +0000 | [diff] [blame] | 290 | for (int index = 0; index < kPointsInCubic; ++index) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 291 | if (index == t1Index) { |
| 292 | continue; |
| 293 | } |
| 294 | SkDVector dxy1 = cubic1[index] - line[0]; |
| 295 | dxy1 /= SkDCubic::gPrecisionUnit; |
| 296 | line[1] = line[0] + dxy1; |
| 297 | SkDRect lineBounds; |
| 298 | lineBounds.setBounds(line); |
| 299 | if (!bounds2.intersects(&lineBounds)) { |
| 300 | continue; |
| 301 | } |
| 302 | SkIntersections local; |
| 303 | if (!local.intersect(cubic2, line)) { |
| 304 | continue; |
| 305 | } |
| 306 | for (int idx2 = 0; idx2 < local.used(); ++idx2) { |
| 307 | double foundT = local[0][idx2]; |
| 308 | if (approximately_less_than_zero(foundT) |
| 309 | || approximately_greater_than_one(foundT)) { |
| 310 | continue; |
| 311 | } |
| 312 | if (local.pt(idx2).approximatelyEqual(line[0])) { |
| 313 | if (i.swapped()) { // FIXME: insert should respect swap |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 314 | i.insert(foundT, testT, line[0]); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 315 | } else { |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 316 | i.insert(testT, foundT, line[0]); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 317 | } |
| 318 | } else { |
caryclark@google.com | d892bd8 | 2013-06-17 14:10:36 +0000 | [diff] [blame] | 319 | tVals.push_back(foundT); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 320 | } |
| 321 | } |
| 322 | } |
| 323 | if (tVals.count() == 0) { |
| 324 | return; |
| 325 | } |
commit-bot@chromium.org | b76d3b6 | 2013-04-22 19:55:19 +0000 | [diff] [blame] | 326 | SkTQSort<double>(tVals.begin(), tVals.end() - 1); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 327 | double tMin1 = start ? 0 : 1 - LINE_FRACTION; |
| 328 | double tMax1 = start ? LINE_FRACTION : 1; |
| 329 | int tIdx = 0; |
| 330 | do { |
| 331 | int tLast = tIdx; |
| 332 | while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) { |
| 333 | ++tLast; |
| 334 | } |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 335 | double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0); |
| 336 | double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 337 | int lastUsed = i.used(); |
| 338 | intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| 339 | if (lastUsed == i.used()) { |
caryclark@google.com | 3b97af5 | 2013-04-23 11:56:44 +0000 | [diff] [blame] | 340 | tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0); |
| 341 | tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 342 | intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i); |
| 343 | } |
| 344 | tIdx = tLast + 1; |
| 345 | } while (tIdx < tVals.count()); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 346 | return; |
| 347 | } |
| 348 | |
| 349 | const double CLOSE_ENOUGH = 0.001; |
| 350 | |
| 351 | static bool closeStart(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { |
| 352 | if (i[cubicIndex][0] != 0 || i[cubicIndex][1] > CLOSE_ENOUGH) { |
| 353 | return false; |
| 354 | } |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 355 | pt = cubic.ptAtT((i[cubicIndex][0] + i[cubicIndex][1]) / 2); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 356 | return true; |
| 357 | } |
| 358 | |
| 359 | static bool closeEnd(const SkDCubic& cubic, int cubicIndex, SkIntersections& i, SkDPoint& pt) { |
| 360 | int last = i.used() - 1; |
| 361 | if (i[cubicIndex][last] != 1 || i[cubicIndex][last - 1] < 1 - CLOSE_ENOUGH) { |
| 362 | return false; |
| 363 | } |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 364 | pt = cubic.ptAtT((i[cubicIndex][last] + i[cubicIndex][last - 1]) / 2); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 365 | return true; |
| 366 | } |
| 367 | |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 368 | static bool only_end_pts_in_common(const SkDCubic& c1, const SkDCubic& c2) { |
| 369 | // the idea here is to see at minimum do a quick reject by rotating all points |
| 370 | // to either side of the line formed by connecting the endpoints |
| 371 | // if the opposite curves points are on the line or on the other side, the |
| 372 | // curves at most intersect at the endpoints |
| 373 | for (int oddMan = 0; oddMan < 4; ++oddMan) { |
| 374 | const SkDPoint* endPt[3]; |
| 375 | for (int opp = 1; opp < 4; ++opp) { |
| 376 | int end = oddMan ^ opp; // choose a value not equal to oddMan |
| 377 | endPt[opp - 1] = &c1[end]; |
| 378 | } |
| 379 | for (int triTest = 0; triTest < 3; ++triTest) { |
| 380 | double origX = endPt[triTest]->fX; |
| 381 | double origY = endPt[triTest]->fY; |
| 382 | int oppTest = triTest + 1; |
| 383 | if (3 == oppTest) { |
| 384 | oppTest = 0; |
| 385 | } |
| 386 | double adj = endPt[oppTest]->fX - origX; |
| 387 | double opp = endPt[oppTest]->fY - origY; |
| 388 | double sign = (c1[oddMan].fY - origY) * adj - (c1[oddMan].fX - origX) * opp; |
| 389 | if (approximately_zero(sign)) { |
| 390 | goto tryNextHalfPlane; |
| 391 | } |
| 392 | for (int n = 0; n < 4; ++n) { |
| 393 | double test = (c2[n].fY - origY) * adj - (c2[n].fX - origX) * opp; |
| 394 | if (test * sign > 0 && !precisely_zero(test)) { |
| 395 | goto tryNextHalfPlane; |
| 396 | } |
| 397 | } |
| 398 | } |
| 399 | return true; |
| 400 | tryNextHalfPlane: |
| 401 | ; |
| 402 | } |
| 403 | return false; |
| 404 | } |
| 405 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 406 | int SkIntersections::intersect(const SkDCubic& c1, const SkDCubic& c2) { |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 407 | bool selfIntersect = &c1 == &c2; |
| 408 | if (selfIntersect) { |
| 409 | if (c1[0].approximatelyEqualHalf(c1[3])) { |
| 410 | insert(0, 1, c1[0]); |
| 411 | } |
| 412 | } else { |
| 413 | for (int i1 = 0; i1 < 4; i1 += 3) { |
| 414 | for (int i2 = 0; i2 < 4; i2 += 3) { |
| 415 | if (c1[i1].approximatelyEqualHalf(c2[i2])) { |
| 416 | insert(i1 >> 1, i2 >> 1, c1[i1]); |
| 417 | } |
| 418 | } |
| 419 | } |
| 420 | } |
| 421 | SkASSERT(fUsed < 4); |
| 422 | if (!selfIntersect) { |
| 423 | if (only_end_pts_in_common(c1, c2)) { |
| 424 | return fUsed; |
| 425 | } |
| 426 | if (only_end_pts_in_common(c2, c1)) { |
| 427 | return fUsed; |
| 428 | } |
| 429 | } |
| 430 | // quad/quad does linear test here -- cubic does not |
| 431 | // cubics which are really lines should have been detected in reduce step earlier |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 432 | SkDRect c1Bounds, c2Bounds; |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 433 | // FIXME: pass in cached bounds from caller |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 434 | c1Bounds.setBounds(c1); // OPTIMIZE use setRawBounds ? |
| 435 | c2Bounds.setBounds(c2); |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 436 | intersectEnd(c1, false, c2, c2Bounds, selfIntersect, *this); |
| 437 | intersectEnd(c1, true, c2, c2Bounds, selfIntersect, *this); |
| 438 | if (selfIntersect) { |
| 439 | if (fUsed) { |
| 440 | return fUsed; |
| 441 | } |
| 442 | } else { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 443 | swap(); |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 444 | intersectEnd(c2, false, c1, c1Bounds, false, *this); |
| 445 | intersectEnd(c2, true, c1, c1Bounds, false, *this); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 446 | swap(); |
| 447 | } |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 448 | // if two ends intersect, check middle for coincidence |
| 449 | if (fUsed >= 2) { |
| 450 | SkASSERT(!selfIntersect); |
| 451 | int last = fUsed - 1; |
| 452 | double tRange1 = fT[0][last] - fT[0][0]; |
| 453 | double tRange2 = fT[1][last] - fT[1][0]; |
| 454 | for (int index = 1; index < 5; ++index) { |
| 455 | double testT1 = fT[0][0] + tRange1 * index / 5; |
| 456 | double testT2 = fT[1][0] + tRange2 * index / 5; |
| 457 | SkDPoint testPt1 = c1.ptAtT(testT1); |
| 458 | SkDPoint testPt2 = c2.ptAtT(testT2); |
| 459 | if (!testPt1.approximatelyEqual(testPt2)) { |
| 460 | goto skipCoincidence; |
| 461 | } |
| 462 | } |
| 463 | if (fUsed > 2) { |
| 464 | fPt[1] = fPt[last]; |
| 465 | fT[0][1] = fT[0][last]; |
| 466 | fT[1][1] = fT[1][last]; |
| 467 | fUsed = 2; |
| 468 | } |
| 469 | fIsCoincident[0] = fIsCoincident[1] = 0x03; |
| 470 | return fUsed; |
| 471 | } |
| 472 | skipCoincidence: |
| 473 | ::intersect(c1, 0, 1, c2, 0, 1, 1, *this); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 474 | // If an end point and a second point very close to the end is returned, the second |
| 475 | // point may have been detected because the approximate quads |
| 476 | // intersected at the end and close to it. Verify that the second point is valid. |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 477 | if (fUsed <= 1) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 478 | return fUsed; |
| 479 | } |
| 480 | SkDPoint pt[2]; |
| 481 | if (closeStart(c1, 0, *this, pt[0]) && closeStart(c2, 1, *this, pt[1]) |
| 482 | && pt[0].approximatelyEqual(pt[1])) { |
| 483 | removeOne(1); |
| 484 | } |
| 485 | if (closeEnd(c1, 0, *this, pt[0]) && closeEnd(c2, 1, *this, pt[1]) |
| 486 | && pt[0].approximatelyEqual(pt[1])) { |
| 487 | removeOne(used() - 2); |
| 488 | } |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 489 | // vet the pairs of t values to see if the mid value is also on the curve. If so, mark |
| 490 | // the span as coincident |
| 491 | if (fUsed >= 2 && !coincidentUsed()) { |
| 492 | int last = fUsed - 1; |
| 493 | int match = 0; |
| 494 | for (int index = 0; index < last; ++index) { |
| 495 | double mid1 = (fT[0][index] + fT[0][index + 1]) / 2; |
| 496 | double mid2 = (fT[1][index] + fT[1][index + 1]) / 2; |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 497 | pt[0] = c1.ptAtT(mid1); |
| 498 | pt[1] = c2.ptAtT(mid2); |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 499 | if (pt[0].approximatelyEqual(pt[1])) { |
| 500 | match |= 1 << index; |
| 501 | } |
| 502 | } |
| 503 | if (match) { |
| 504 | if (((match + 1) & match) != 0) { |
| 505 | SkDebugf("%s coincident hole\n", __FUNCTION__); |
| 506 | } |
| 507 | // for now, assume that everything from start to finish is coincident |
| 508 | if (fUsed > 2) { |
| 509 | fPt[1] = fPt[last]; |
| 510 | fT[0][1] = fT[0][last]; |
| 511 | fT[1][1] = fT[1][last]; |
| 512 | fIsCoincident[0] = 0x03; |
| 513 | fIsCoincident[1] = 0x03; |
| 514 | fUsed = 2; |
| 515 | } |
| 516 | } |
| 517 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 518 | return fUsed; |
| 519 | } |
| 520 | |
| 521 | // Up promote the quad to a cubic. |
| 522 | // OPTIMIZATION If this is a common use case, optimize by duplicating |
| 523 | // the intersect 3 loop to avoid the promotion / demotion code |
| 524 | int SkIntersections::intersect(const SkDCubic& cubic, const SkDQuad& quad) { |
| 525 | SkDCubic up = quad.toCubic(); |
| 526 | (void) intersect(cubic, up); |
| 527 | return used(); |
| 528 | } |
| 529 | |
| 530 | /* http://www.ag.jku.at/compass/compasssample.pdf |
| 531 | ( Self-Intersection Problems and Approximate Implicitization by Jan B. Thomassen |
| 532 | Centre of Mathematics for Applications, University of Oslo http://www.cma.uio.no janbth@math.uio.no |
| 533 | SINTEF Applied Mathematics http://www.sintef.no ) |
| 534 | describes a method to find the self intersection of a cubic by taking the gradient of the implicit |
| 535 | form dotted with the normal, and solving for the roots. My math foo is too poor to implement this.*/ |
| 536 | |
| 537 | int SkIntersections::intersect(const SkDCubic& c) { |
| 538 | // check to see if x or y end points are the extrema. Are other quick rejects possible? |
| 539 | if (c.endsAreExtremaInXOrY()) { |
| 540 | return false; |
| 541 | } |
| 542 | (void) intersect(c, c); |
| 543 | if (used() > 0) { |
| 544 | SkASSERT(used() == 1); |
| 545 | if (fT[0][0] > fT[1][0]) { |
| 546 | swapPts(); |
| 547 | } |
| 548 | } |
| 549 | return used(); |
| 550 | } |