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 | */ |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 7 | #include "SkGeometry.h" |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 8 | #include "SkLineParameters.h" |
caryclark | 1049f12 | 2015-04-20 08:31:59 -0700 | [diff] [blame] | 9 | #include "SkPathOpsConic.h" |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 10 | #include "SkPathOpsCubic.h" |
caryclark | 03b03ca | 2015-04-23 09:13:37 -0700 | [diff] [blame] | 11 | #include "SkPathOpsCurve.h" |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 12 | #include "SkPathOpsLine.h" |
| 13 | #include "SkPathOpsQuad.h" |
| 14 | #include "SkPathOpsRect.h" |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 15 | #include "SkTSort.h" |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 16 | |
| 17 | const int SkDCubic::gPrecisionUnit = 256; // FIXME: test different values in test framework |
| 18 | |
caryclark | 624637c | 2015-05-11 07:21:27 -0700 | [diff] [blame] | 19 | void SkDCubic::align(int endIndex, int ctrlIndex, SkDPoint* dstPt) const { |
| 20 | if (fPts[endIndex].fX == fPts[ctrlIndex].fX) { |
| 21 | dstPt->fX = fPts[endIndex].fX; |
| 22 | } |
| 23 | if (fPts[endIndex].fY == fPts[ctrlIndex].fY) { |
| 24 | dstPt->fY = fPts[endIndex].fY; |
| 25 | } |
| 26 | } |
| 27 | |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 28 | // give up when changing t no longer moves point |
| 29 | // also, copy point rather than recompute it when it does change |
| 30 | double SkDCubic::binarySearch(double min, double max, double axisIntercept, |
| 31 | SearchAxis xAxis) const { |
| 32 | double t = (min + max) / 2; |
| 33 | double step = (t - min) / 2; |
| 34 | SkDPoint cubicAtT = ptAtT(t); |
| 35 | double calcPos = (&cubicAtT.fX)[xAxis]; |
| 36 | double calcDist = calcPos - axisIntercept; |
| 37 | do { |
Cary Clark | 74b4290 | 2018-03-09 07:38:47 -0500 | [diff] [blame] | 38 | double priorT = std::max(min, t - step); |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 39 | SkDPoint lessPt = ptAtT(priorT); |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 40 | if (approximately_equal_half(lessPt.fX, cubicAtT.fX) |
| 41 | && approximately_equal_half(lessPt.fY, cubicAtT.fY)) { |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 42 | return -1; // binary search found no point at this axis intercept |
| 43 | } |
| 44 | double lessDist = (&lessPt.fX)[xAxis] - axisIntercept; |
| 45 | #if DEBUG_CUBIC_BINARY_SEARCH |
| 46 | SkDebugf("t=%1.9g calc=%1.9g dist=%1.9g step=%1.9g less=%1.9g\n", t, calcPos, calcDist, |
| 47 | step, lessDist); |
| 48 | #endif |
| 49 | double lastStep = step; |
| 50 | step /= 2; |
| 51 | if (calcDist > 0 ? calcDist > lessDist : calcDist < lessDist) { |
| 52 | t = priorT; |
| 53 | } else { |
| 54 | double nextT = t + lastStep; |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 55 | if (nextT > max) { |
| 56 | return -1; |
| 57 | } |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 58 | SkDPoint morePt = ptAtT(nextT); |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 59 | if (approximately_equal_half(morePt.fX, cubicAtT.fX) |
| 60 | && approximately_equal_half(morePt.fY, cubicAtT.fY)) { |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 61 | return -1; // binary search found no point at this axis intercept |
| 62 | } |
| 63 | double moreDist = (&morePt.fX)[xAxis] - axisIntercept; |
| 64 | if (calcDist > 0 ? calcDist <= moreDist : calcDist >= moreDist) { |
| 65 | continue; |
| 66 | } |
| 67 | t = nextT; |
| 68 | } |
| 69 | SkDPoint testAtT = ptAtT(t); |
| 70 | cubicAtT = testAtT; |
| 71 | calcPos = (&cubicAtT.fX)[xAxis]; |
| 72 | calcDist = calcPos - axisIntercept; |
| 73 | } while (!approximately_equal(calcPos, axisIntercept)); |
| 74 | return t; |
| 75 | } |
| 76 | |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 77 | // get the rough scale of the cubic; used to determine if curvature is extreme |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 78 | double SkDCubic::calcPrecision() const { |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 79 | return ((fPts[1] - fPts[0]).length() |
| 80 | + (fPts[2] - fPts[1]).length() |
| 81 | + (fPts[3] - fPts[2]).length()) / gPrecisionUnit; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 82 | } |
| 83 | |
caryclark | 624637c | 2015-05-11 07:21:27 -0700 | [diff] [blame] | 84 | /* classic one t subdivision */ |
| 85 | static void interp_cubic_coords(const double* src, double* dst, double t) { |
| 86 | double ab = SkDInterp(src[0], src[2], t); |
| 87 | double bc = SkDInterp(src[2], src[4], t); |
| 88 | double cd = SkDInterp(src[4], src[6], t); |
| 89 | double abc = SkDInterp(ab, bc, t); |
| 90 | double bcd = SkDInterp(bc, cd, t); |
| 91 | double abcd = SkDInterp(abc, bcd, t); |
| 92 | |
| 93 | dst[0] = src[0]; |
| 94 | dst[2] = ab; |
| 95 | dst[4] = abc; |
| 96 | dst[6] = abcd; |
| 97 | dst[8] = bcd; |
| 98 | dst[10] = cd; |
| 99 | dst[12] = src[6]; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 100 | } |
| 101 | |
caryclark | 624637c | 2015-05-11 07:21:27 -0700 | [diff] [blame] | 102 | SkDCubicPair SkDCubic::chopAt(double t) const { |
| 103 | SkDCubicPair dst; |
| 104 | if (t == 0.5) { |
| 105 | dst.pts[0] = fPts[0]; |
| 106 | dst.pts[1].fX = (fPts[0].fX + fPts[1].fX) / 2; |
| 107 | dst.pts[1].fY = (fPts[0].fY + fPts[1].fY) / 2; |
| 108 | dst.pts[2].fX = (fPts[0].fX + 2 * fPts[1].fX + fPts[2].fX) / 4; |
| 109 | dst.pts[2].fY = (fPts[0].fY + 2 * fPts[1].fY + fPts[2].fY) / 4; |
| 110 | dst.pts[3].fX = (fPts[0].fX + 3 * (fPts[1].fX + fPts[2].fX) + fPts[3].fX) / 8; |
| 111 | dst.pts[3].fY = (fPts[0].fY + 3 * (fPts[1].fY + fPts[2].fY) + fPts[3].fY) / 8; |
| 112 | dst.pts[4].fX = (fPts[1].fX + 2 * fPts[2].fX + fPts[3].fX) / 4; |
| 113 | dst.pts[4].fY = (fPts[1].fY + 2 * fPts[2].fY + fPts[3].fY) / 4; |
| 114 | dst.pts[5].fX = (fPts[2].fX + fPts[3].fX) / 2; |
| 115 | dst.pts[5].fY = (fPts[2].fY + fPts[3].fY) / 2; |
| 116 | dst.pts[6] = fPts[3]; |
| 117 | return dst; |
| 118 | } |
| 119 | interp_cubic_coords(&fPts[0].fX, &dst.pts[0].fX, t); |
| 120 | interp_cubic_coords(&fPts[0].fY, &dst.pts[0].fY, t); |
| 121 | return dst; |
caryclark | 03b03ca | 2015-04-23 09:13:37 -0700 | [diff] [blame] | 122 | } |
| 123 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 124 | void SkDCubic::Coefficients(const double* src, double* A, double* B, double* C, double* D) { |
| 125 | *A = src[6]; // d |
| 126 | *B = src[4] * 3; // 3*c |
| 127 | *C = src[2] * 3; // 3*b |
| 128 | *D = src[0]; // a |
| 129 | *A -= *D - *C + *B; // A = -a + 3*b - 3*c + d |
| 130 | *B += 3 * *D - 2 * *C; // B = 3*a - 6*b + 3*c |
| 131 | *C -= 3 * *D; // C = -3*a + 3*b |
| 132 | } |
| 133 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 134 | bool SkDCubic::endsAreExtremaInXOrY() const { |
| 135 | return (between(fPts[0].fX, fPts[1].fX, fPts[3].fX) |
| 136 | && between(fPts[0].fX, fPts[2].fX, fPts[3].fX)) |
| 137 | || (between(fPts[0].fY, fPts[1].fY, fPts[3].fY) |
| 138 | && between(fPts[0].fY, fPts[2].fY, fPts[3].fY)); |
| 139 | } |
| 140 | |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 141 | // Do a quick reject by rotating all points relative to a line formed by |
| 142 | // a pair of one cubic's points. If the 2nd cubic's points |
| 143 | // are on the line or on the opposite side from the 1st cubic's 'odd man', the |
| 144 | // curves at most intersect at the endpoints. |
| 145 | /* if returning true, check contains true if cubic's hull collapsed, making the cubic linear |
| 146 | if returning false, check contains true if the the cubic pair have only the end point in common |
| 147 | */ |
caryclark | 1049f12 | 2015-04-20 08:31:59 -0700 | [diff] [blame] | 148 | bool SkDCubic::hullIntersects(const SkDPoint* pts, int ptCount, bool* isLinear) const { |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 149 | bool linear = true; |
| 150 | char hullOrder[4]; |
| 151 | int hullCount = convexHull(hullOrder); |
| 152 | int end1 = hullOrder[0]; |
| 153 | int hullIndex = 0; |
| 154 | const SkDPoint* endPt[2]; |
| 155 | endPt[0] = &fPts[end1]; |
| 156 | do { |
| 157 | hullIndex = (hullIndex + 1) % hullCount; |
| 158 | int end2 = hullOrder[hullIndex]; |
| 159 | endPt[1] = &fPts[end2]; |
| 160 | double origX = endPt[0]->fX; |
| 161 | double origY = endPt[0]->fY; |
| 162 | double adj = endPt[1]->fX - origX; |
| 163 | double opp = endPt[1]->fY - origY; |
| 164 | int oddManMask = other_two(end1, end2); |
| 165 | int oddMan = end1 ^ oddManMask; |
| 166 | double sign = (fPts[oddMan].fY - origY) * adj - (fPts[oddMan].fX - origX) * opp; |
| 167 | int oddMan2 = end2 ^ oddManMask; |
| 168 | double sign2 = (fPts[oddMan2].fY - origY) * adj - (fPts[oddMan2].fX - origX) * opp; |
| 169 | if (sign * sign2 < 0) { |
| 170 | continue; |
| 171 | } |
| 172 | if (approximately_zero(sign)) { |
| 173 | sign = sign2; |
| 174 | if (approximately_zero(sign)) { |
| 175 | continue; |
| 176 | } |
| 177 | } |
| 178 | linear = false; |
| 179 | bool foundOutlier = false; |
caryclark | 1049f12 | 2015-04-20 08:31:59 -0700 | [diff] [blame] | 180 | for (int n = 0; n < ptCount; ++n) { |
| 181 | double test = (pts[n].fY - origY) * adj - (pts[n].fX - origX) * opp; |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 182 | if (test * sign > 0 && !precisely_zero(test)) { |
| 183 | foundOutlier = true; |
| 184 | break; |
| 185 | } |
| 186 | } |
| 187 | if (!foundOutlier) { |
| 188 | return false; |
| 189 | } |
| 190 | endPt[0] = endPt[1]; |
| 191 | end1 = end2; |
| 192 | } while (hullIndex); |
| 193 | *isLinear = linear; |
| 194 | return true; |
| 195 | } |
| 196 | |
caryclark | 1049f12 | 2015-04-20 08:31:59 -0700 | [diff] [blame] | 197 | bool SkDCubic::hullIntersects(const SkDCubic& c2, bool* isLinear) const { |
| 198 | return hullIntersects(c2.fPts, c2.kPointCount, isLinear); |
| 199 | } |
| 200 | |
| 201 | bool SkDCubic::hullIntersects(const SkDQuad& quad, bool* isLinear) const { |
| 202 | return hullIntersects(quad.fPts, quad.kPointCount, isLinear); |
| 203 | } |
| 204 | |
| 205 | bool SkDCubic::hullIntersects(const SkDConic& conic, bool* isLinear) const { |
| 206 | |
| 207 | return hullIntersects(conic.fPts, isLinear); |
| 208 | } |
| 209 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 210 | bool SkDCubic::isLinear(int startIndex, int endIndex) const { |
caryclark | e3a4e99 | 2016-09-28 09:22:17 -0700 | [diff] [blame] | 211 | if (fPts[0].approximatelyDEqual(fPts[3])) { |
| 212 | return ((const SkDQuad *) this)->isLinear(0, 2); |
| 213 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 214 | SkLineParameters lineParameters; |
| 215 | lineParameters.cubicEndPoints(*this, startIndex, endIndex); |
| 216 | // FIXME: maybe it's possible to avoid this and compare non-normalized |
| 217 | lineParameters.normalize(); |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 218 | double tiniest = SkTMin(SkTMin(SkTMin(SkTMin(SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), |
| 219 | fPts[1].fX), fPts[1].fY), fPts[2].fX), fPts[2].fY), fPts[3].fX), fPts[3].fY); |
| 220 | double largest = SkTMax(SkTMax(SkTMax(SkTMax(SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), |
| 221 | fPts[1].fX), fPts[1].fY), fPts[2].fX), fPts[2].fY), fPts[3].fX), fPts[3].fY); |
| 222 | largest = SkTMax(largest, -tiniest); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 223 | double distance = lineParameters.controlPtDistance(*this, 1); |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 224 | if (!approximately_zero_when_compared_to(distance, largest)) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 225 | return false; |
| 226 | } |
| 227 | distance = lineParameters.controlPtDistance(*this, 2); |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 228 | return approximately_zero_when_compared_to(distance, largest); |
| 229 | } |
| 230 | |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 231 | // from http://www.cs.sunysb.edu/~qin/courses/geometry/4.pdf |
| 232 | // c(t) = a(1-t)^3 + 3bt(1-t)^2 + 3c(1-t)t^2 + dt^3 |
| 233 | // c'(t) = -3a(1-t)^2 + 3b((1-t)^2 - 2t(1-t)) + 3c(2t(1-t) - t^2) + 3dt^2 |
| 234 | // = 3(b-a)(1-t)^2 + 6(c-b)t(1-t) + 3(d-c)t^2 |
| 235 | static double derivative_at_t(const double* src, double t) { |
| 236 | double one_t = 1 - t; |
| 237 | double a = src[0]; |
| 238 | double b = src[2]; |
| 239 | double c = src[4]; |
| 240 | double d = src[6]; |
| 241 | return 3 * ((b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t); |
| 242 | } |
| 243 | |
| 244 | int SkDCubic::ComplexBreak(const SkPoint pointsPtr[4], SkScalar* t) { |
| 245 | SkDCubic cubic; |
| 246 | cubic.set(pointsPtr); |
| 247 | if (cubic.monotonicInX() && cubic.monotonicInY()) { |
| 248 | return 0; |
| 249 | } |
Chris Dalton | 390f6cd | 2017-06-12 11:22:54 -0600 | [diff] [blame] | 250 | double tt[2], ss[2]; |
Chris Dalton | febbffa | 2017-06-08 13:12:02 -0600 | [diff] [blame] | 251 | SkCubicType cubicType = SkClassifyCubic(pointsPtr, tt, ss); |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 252 | switch (cubicType) { |
Chris Dalton | 4343654 | 2017-04-13 14:26:00 -0600 | [diff] [blame] | 253 | case SkCubicType::kLoop: { |
Chris Dalton | 390f6cd | 2017-06-12 11:22:54 -0600 | [diff] [blame] | 254 | const double &td = tt[0], &te = tt[1], &sd = ss[0], &se = ss[1]; |
Christopher Dalton | 7f5af0c | 2017-06-06 14:26:27 -0600 | [diff] [blame] | 255 | if (roughly_between(0, td, sd) && roughly_between(0, te, se)) { |
Chris Dalton | 390f6cd | 2017-06-12 11:22:54 -0600 | [diff] [blame] | 256 | t[0] = static_cast<SkScalar>((td * se + te * sd) / (2 * sd * se)); |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 257 | return (int) (t[0] > 0 && t[0] < 1); |
| 258 | } |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 259 | } |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 260 | // fall through if no t value found |
Chris Dalton | 4343654 | 2017-04-13 14:26:00 -0600 | [diff] [blame] | 261 | case SkCubicType::kSerpentine: |
| 262 | case SkCubicType::kLocalCusp: |
Chris Dalton | febbffa | 2017-06-08 13:12:02 -0600 | [diff] [blame] | 263 | case SkCubicType::kCuspAtInfinity: { |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 264 | double inflectionTs[2]; |
| 265 | int infTCount = cubic.findInflections(inflectionTs); |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 266 | double maxCurvature[3]; |
| 267 | int roots = cubic.findMaxCurvature(maxCurvature); |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 268 | #if DEBUG_CUBIC_SPLIT |
caryclark | 03b03ca | 2015-04-23 09:13:37 -0700 | [diff] [blame] | 269 | SkDebugf("%s\n", __FUNCTION__); |
| 270 | cubic.dump(); |
| 271 | for (int index = 0; index < infTCount; ++index) { |
| 272 | SkDebugf("inflectionsTs[%d]=%1.9g ", index, inflectionTs[index]); |
| 273 | SkDPoint pt = cubic.ptAtT(inflectionTs[index]); |
| 274 | SkDVector dPt = cubic.dxdyAtT(inflectionTs[index]); |
| 275 | SkDLine perp = {{pt - dPt, pt + dPt}}; |
| 276 | perp.dump(); |
| 277 | } |
| 278 | for (int index = 0; index < roots; ++index) { |
| 279 | SkDebugf("maxCurvature[%d]=%1.9g ", index, maxCurvature[index]); |
| 280 | SkDPoint pt = cubic.ptAtT(maxCurvature[index]); |
| 281 | SkDVector dPt = cubic.dxdyAtT(maxCurvature[index]); |
| 282 | SkDLine perp = {{pt - dPt, pt + dPt}}; |
| 283 | perp.dump(); |
| 284 | } |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 285 | #endif |
| 286 | if (infTCount == 2) { |
| 287 | for (int index = 0; index < roots; ++index) { |
| 288 | if (between(inflectionTs[0], maxCurvature[index], inflectionTs[1])) { |
| 289 | t[0] = maxCurvature[index]; |
| 290 | return (int) (t[0] > 0 && t[0] < 1); |
| 291 | } |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 292 | } |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 293 | } else { |
| 294 | int resultCount = 0; |
| 295 | // FIXME: constant found through experimentation -- maybe there's a better way.... |
| 296 | double precision = cubic.calcPrecision() * 2; |
| 297 | for (int index = 0; index < roots; ++index) { |
| 298 | double testT = maxCurvature[index]; |
| 299 | if (0 >= testT || testT >= 1) { |
| 300 | continue; |
| 301 | } |
| 302 | // don't call dxdyAtT since we want (0,0) results |
| 303 | SkDVector dPt = { derivative_at_t(&cubic.fPts[0].fX, testT), |
| 304 | derivative_at_t(&cubic.fPts[0].fY, testT) }; |
| 305 | double dPtLen = dPt.length(); |
| 306 | if (dPtLen < precision) { |
| 307 | t[resultCount++] = testT; |
| 308 | } |
| 309 | } |
| 310 | if (!resultCount && infTCount == 1) { |
| 311 | t[0] = inflectionTs[0]; |
| 312 | resultCount = (int) (t[0] > 0 && t[0] < 1); |
| 313 | } |
| 314 | return resultCount; |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 315 | } |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 316 | } |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 317 | default: |
| 318 | ; |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 319 | } |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 320 | return 0; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 321 | } |
| 322 | |
caryclark | aec2510 | 2015-04-29 08:28:30 -0700 | [diff] [blame] | 323 | bool SkDCubic::monotonicInX() const { |
| 324 | return precisely_between(fPts[0].fX, fPts[1].fX, fPts[3].fX) |
| 325 | && precisely_between(fPts[0].fX, fPts[2].fX, fPts[3].fX); |
| 326 | } |
| 327 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 328 | bool SkDCubic::monotonicInY() const { |
caryclark | aec2510 | 2015-04-29 08:28:30 -0700 | [diff] [blame] | 329 | return precisely_between(fPts[0].fY, fPts[1].fY, fPts[3].fY) |
| 330 | && precisely_between(fPts[0].fY, fPts[2].fY, fPts[3].fY); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 331 | } |
| 332 | |
caryclark | 5435929 | 2015-03-26 07:52:43 -0700 | [diff] [blame] | 333 | void SkDCubic::otherPts(int index, const SkDPoint* o1Pts[kPointCount - 1]) const { |
| 334 | int offset = (int) !SkToBool(index); |
| 335 | o1Pts[0] = &fPts[offset]; |
| 336 | o1Pts[1] = &fPts[++offset]; |
| 337 | o1Pts[2] = &fPts[++offset]; |
| 338 | } |
| 339 | |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 340 | int SkDCubic::searchRoots(double extremeTs[6], int extrema, double axisIntercept, |
| 341 | SearchAxis xAxis, double* validRoots) const { |
| 342 | extrema += findInflections(&extremeTs[extrema]); |
| 343 | extremeTs[extrema++] = 0; |
| 344 | extremeTs[extrema] = 1; |
caryclark | 8a8accb | 2016-07-22 10:56:26 -0700 | [diff] [blame] | 345 | SkASSERT(extrema < 6); |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 346 | SkTQSort(extremeTs, extremeTs + extrema); |
| 347 | int validCount = 0; |
| 348 | for (int index = 0; index < extrema; ) { |
| 349 | double min = extremeTs[index]; |
| 350 | double max = extremeTs[++index]; |
| 351 | if (min == max) { |
| 352 | continue; |
| 353 | } |
| 354 | double newT = binarySearch(min, max, axisIntercept, xAxis); |
| 355 | if (newT >= 0) { |
caryclark | 8a8accb | 2016-07-22 10:56:26 -0700 | [diff] [blame] | 356 | if (validCount >= 3) { |
| 357 | return 0; |
| 358 | } |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 359 | validRoots[validCount++] = newT; |
| 360 | } |
| 361 | } |
| 362 | return validCount; |
| 363 | } |
| 364 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 365 | // cubic roots |
| 366 | |
| 367 | static const double PI = 3.141592653589793; |
| 368 | |
| 369 | // from SkGeometry.cpp (and Numeric Solutions, 5.6) |
| 370 | int SkDCubic::RootsValidT(double A, double B, double C, double D, double t[3]) { |
| 371 | double s[3]; |
| 372 | int realRoots = RootsReal(A, B, C, D, s); |
| 373 | int foundRoots = SkDQuad::AddValidTs(s, realRoots, t); |
caryclark | aec2510 | 2015-04-29 08:28:30 -0700 | [diff] [blame] | 374 | for (int index = 0; index < realRoots; ++index) { |
| 375 | double tValue = s[index]; |
| 376 | if (!approximately_one_or_less(tValue) && between(1, tValue, 1.00005)) { |
| 377 | for (int idx2 = 0; idx2 < foundRoots; ++idx2) { |
| 378 | if (approximately_equal(t[idx2], 1)) { |
| 379 | goto nextRoot; |
| 380 | } |
| 381 | } |
| 382 | SkASSERT(foundRoots < 3); |
| 383 | t[foundRoots++] = 1; |
| 384 | } else if (!approximately_zero_or_more(tValue) && between(-0.00005, tValue, 0)) { |
| 385 | for (int idx2 = 0; idx2 < foundRoots; ++idx2) { |
| 386 | if (approximately_equal(t[idx2], 0)) { |
| 387 | goto nextRoot; |
| 388 | } |
| 389 | } |
| 390 | SkASSERT(foundRoots < 3); |
| 391 | t[foundRoots++] = 0; |
| 392 | } |
| 393 | nextRoot: |
| 394 | ; |
| 395 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 396 | return foundRoots; |
| 397 | } |
| 398 | |
| 399 | int SkDCubic::RootsReal(double A, double B, double C, double D, double s[3]) { |
| 400 | #ifdef SK_DEBUG |
| 401 | // create a string mathematica understands |
| 402 | // GDB set print repe 15 # if repeated digits is a bother |
| 403 | // set print elements 400 # if line doesn't fit |
| 404 | char str[1024]; |
| 405 | sk_bzero(str, sizeof(str)); |
| 406 | SK_SNPRINTF(str, sizeof(str), "Solve[%1.19g x^3 + %1.19g x^2 + %1.19g x + %1.19g == 0, x]", |
| 407 | A, B, C, D); |
caryclark@google.com | 570863f | 2013-09-16 15:55:01 +0000 | [diff] [blame] | 408 | SkPathOpsDebug::MathematicaIze(str, sizeof(str)); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 409 | #if ONE_OFF_DEBUG && ONE_OFF_DEBUG_MATHEMATICA |
| 410 | SkDebugf("%s\n", str); |
| 411 | #endif |
| 412 | #endif |
| 413 | if (approximately_zero(A) |
| 414 | && approximately_zero_when_compared_to(A, B) |
| 415 | && approximately_zero_when_compared_to(A, C) |
| 416 | && approximately_zero_when_compared_to(A, D)) { // we're just a quadratic |
| 417 | return SkDQuad::RootsReal(B, C, D, s); |
| 418 | } |
| 419 | if (approximately_zero_when_compared_to(D, A) |
| 420 | && approximately_zero_when_compared_to(D, B) |
| 421 | && approximately_zero_when_compared_to(D, C)) { // 0 is one root |
| 422 | int num = SkDQuad::RootsReal(A, B, C, s); |
| 423 | for (int i = 0; i < num; ++i) { |
| 424 | if (approximately_zero(s[i])) { |
| 425 | return num; |
| 426 | } |
| 427 | } |
| 428 | s[num++] = 0; |
| 429 | return num; |
| 430 | } |
| 431 | if (approximately_zero(A + B + C + D)) { // 1 is one root |
| 432 | int num = SkDQuad::RootsReal(A, A + B, -D, s); |
| 433 | for (int i = 0; i < num; ++i) { |
caryclark@google.com | 7eaa53d | 2013-10-02 14:49:34 +0000 | [diff] [blame] | 434 | if (AlmostDequalUlps(s[i], 1)) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 435 | return num; |
| 436 | } |
| 437 | } |
| 438 | s[num++] = 1; |
| 439 | return num; |
| 440 | } |
| 441 | double a, b, c; |
| 442 | { |
| 443 | double invA = 1 / A; |
| 444 | a = B * invA; |
| 445 | b = C * invA; |
| 446 | c = D * invA; |
| 447 | } |
| 448 | double a2 = a * a; |
| 449 | double Q = (a2 - b * 3) / 9; |
| 450 | double R = (2 * a2 * a - 9 * a * b + 27 * c) / 54; |
| 451 | double R2 = R * R; |
| 452 | double Q3 = Q * Q * Q; |
| 453 | double R2MinusQ3 = R2 - Q3; |
| 454 | double adiv3 = a / 3; |
| 455 | double r; |
| 456 | double* roots = s; |
| 457 | if (R2MinusQ3 < 0) { // we have 3 real roots |
caryclark | 93ca884 | 2016-05-27 05:24:37 -0700 | [diff] [blame] | 458 | // the divide/root can, due to finite precisions, be slightly outside of -1...1 |
| 459 | double theta = acos(SkTPin(R / sqrt(Q3), -1., 1.)); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 460 | double neg2RootQ = -2 * sqrt(Q); |
| 461 | |
| 462 | r = neg2RootQ * cos(theta / 3) - adiv3; |
| 463 | *roots++ = r; |
| 464 | |
| 465 | r = neg2RootQ * cos((theta + 2 * PI) / 3) - adiv3; |
caryclark@google.com | 7eaa53d | 2013-10-02 14:49:34 +0000 | [diff] [blame] | 466 | if (!AlmostDequalUlps(s[0], r)) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 467 | *roots++ = r; |
| 468 | } |
| 469 | r = neg2RootQ * cos((theta - 2 * PI) / 3) - adiv3; |
caryclark@google.com | 7eaa53d | 2013-10-02 14:49:34 +0000 | [diff] [blame] | 470 | if (!AlmostDequalUlps(s[0], r) && (roots - s == 1 || !AlmostDequalUlps(s[1], r))) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 471 | *roots++ = r; |
| 472 | } |
| 473 | } else { // we have 1 real root |
| 474 | double sqrtR2MinusQ3 = sqrt(R2MinusQ3); |
| 475 | double A = fabs(R) + sqrtR2MinusQ3; |
| 476 | A = SkDCubeRoot(A); |
| 477 | if (R > 0) { |
| 478 | A = -A; |
| 479 | } |
| 480 | if (A != 0) { |
| 481 | A += Q / A; |
| 482 | } |
| 483 | r = A - adiv3; |
| 484 | *roots++ = r; |
commit-bot@chromium.org | 2db7fe7 | 2014-05-07 15:31:40 +0000 | [diff] [blame] | 485 | if (AlmostDequalUlps((double) R2, (double) Q3)) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 486 | r = -A / 2 - adiv3; |
caryclark@google.com | 7eaa53d | 2013-10-02 14:49:34 +0000 | [diff] [blame] | 487 | if (!AlmostDequalUlps(s[0], r)) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 488 | *roots++ = r; |
| 489 | } |
| 490 | } |
| 491 | } |
| 492 | return static_cast<int>(roots - s); |
| 493 | } |
| 494 | |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 495 | // OPTIMIZE? compute t^2, t(1-t), and (1-t)^2 and pass them to another version of derivative at t? |
| 496 | SkDVector SkDCubic::dxdyAtT(double t) const { |
| 497 | SkDVector result = { derivative_at_t(&fPts[0].fX, t), derivative_at_t(&fPts[0].fY, t) }; |
caryclark | 94c902e | 2015-08-18 07:12:43 -0700 | [diff] [blame] | 498 | if (result.fX == 0 && result.fY == 0) { |
| 499 | if (t == 0) { |
| 500 | result = fPts[2] - fPts[0]; |
| 501 | } else if (t == 1) { |
| 502 | result = fPts[3] - fPts[1]; |
| 503 | } else { |
| 504 | // incomplete |
| 505 | SkDebugf("!c"); |
| 506 | } |
| 507 | if (result.fX == 0 && result.fY == 0 && zero_or_one(t)) { |
| 508 | result = fPts[3] - fPts[0]; |
| 509 | } |
| 510 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 511 | return result; |
| 512 | } |
| 513 | |
| 514 | // OPTIMIZE? share code with formulate_F1DotF2 |
| 515 | int SkDCubic::findInflections(double tValues[]) const { |
| 516 | double Ax = fPts[1].fX - fPts[0].fX; |
| 517 | double Ay = fPts[1].fY - fPts[0].fY; |
| 518 | double Bx = fPts[2].fX - 2 * fPts[1].fX + fPts[0].fX; |
| 519 | double By = fPts[2].fY - 2 * fPts[1].fY + fPts[0].fY; |
| 520 | double Cx = fPts[3].fX + 3 * (fPts[1].fX - fPts[2].fX) - fPts[0].fX; |
| 521 | double Cy = fPts[3].fY + 3 * (fPts[1].fY - fPts[2].fY) - fPts[0].fY; |
| 522 | return SkDQuad::RootsValidT(Bx * Cy - By * Cx, Ax * Cy - Ay * Cx, Ax * By - Ay * Bx, tValues); |
| 523 | } |
| 524 | |
| 525 | static void formulate_F1DotF2(const double src[], double coeff[4]) { |
| 526 | double a = src[2] - src[0]; |
| 527 | double b = src[4] - 2 * src[2] + src[0]; |
| 528 | double c = src[6] + 3 * (src[2] - src[4]) - src[0]; |
| 529 | coeff[0] = c * c; |
| 530 | coeff[1] = 3 * b * c; |
| 531 | coeff[2] = 2 * b * b + c * a; |
| 532 | coeff[3] = a * b; |
| 533 | } |
| 534 | |
| 535 | /** SkDCubic'(t) = At^2 + Bt + C, where |
| 536 | A = 3(-a + 3(b - c) + d) |
| 537 | B = 6(a - 2b + c) |
| 538 | C = 3(b - a) |
| 539 | Solve for t, keeping only those that fit between 0 < t < 1 |
| 540 | */ |
caryclark | aec2510 | 2015-04-29 08:28:30 -0700 | [diff] [blame] | 541 | int SkDCubic::FindExtrema(const double src[], double tValues[2]) { |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 542 | // we divide A,B,C by 3 to simplify |
caryclark | aec2510 | 2015-04-29 08:28:30 -0700 | [diff] [blame] | 543 | double a = src[0]; |
| 544 | double b = src[2]; |
| 545 | double c = src[4]; |
| 546 | double d = src[6]; |
| 547 | double A = d - a + 3 * (b - c); |
| 548 | double B = 2 * (a - b - b + c); |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 549 | double C = b - a; |
| 550 | |
| 551 | return SkDQuad::RootsValidT(A, B, C, tValues); |
| 552 | } |
| 553 | |
| 554 | /* from SkGeometry.cpp |
| 555 | Looking for F' dot F'' == 0 |
| 556 | |
| 557 | A = b - a |
| 558 | B = c - 2b + a |
| 559 | C = d - 3c + 3b - a |
| 560 | |
| 561 | F' = 3Ct^2 + 6Bt + 3A |
| 562 | F'' = 6Ct + 6B |
| 563 | |
| 564 | F' dot F'' -> CCt^3 + 3BCt^2 + (2BB + CA)t + AB |
| 565 | */ |
| 566 | int SkDCubic::findMaxCurvature(double tValues[]) const { |
| 567 | double coeffX[4], coeffY[4]; |
| 568 | int i; |
| 569 | formulate_F1DotF2(&fPts[0].fX, coeffX); |
| 570 | formulate_F1DotF2(&fPts[0].fY, coeffY); |
| 571 | for (i = 0; i < 4; i++) { |
| 572 | coeffX[i] = coeffX[i] + coeffY[i]; |
| 573 | } |
| 574 | return RootsValidT(coeffX[0], coeffX[1], coeffX[2], coeffX[3], tValues); |
| 575 | } |
| 576 | |
caryclark@google.com | 4fdbb22 | 2013-07-23 15:27:41 +0000 | [diff] [blame] | 577 | SkDPoint SkDCubic::ptAtT(double t) const { |
| 578 | if (0 == t) { |
| 579 | return fPts[0]; |
| 580 | } |
| 581 | if (1 == t) { |
| 582 | return fPts[3]; |
| 583 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 584 | double one_t = 1 - t; |
| 585 | double one_t2 = one_t * one_t; |
| 586 | double a = one_t2 * one_t; |
| 587 | double b = 3 * one_t2 * t; |
| 588 | double t2 = t * t; |
| 589 | double c = 3 * one_t * t2; |
| 590 | double d = t2 * t; |
| 591 | SkDPoint result = {a * fPts[0].fX + b * fPts[1].fX + c * fPts[2].fX + d * fPts[3].fX, |
| 592 | a * fPts[0].fY + b * fPts[1].fY + c * fPts[2].fY + d * fPts[3].fY}; |
| 593 | return result; |
| 594 | } |
| 595 | |
| 596 | /* |
| 597 | Given a cubic c, t1, and t2, find a small cubic segment. |
| 598 | |
| 599 | The new cubic is defined as points A, B, C, and D, where |
| 600 | s1 = 1 - t1 |
| 601 | s2 = 1 - t2 |
| 602 | A = c[0]*s1*s1*s1 + 3*c[1]*s1*s1*t1 + 3*c[2]*s1*t1*t1 + c[3]*t1*t1*t1 |
| 603 | D = c[0]*s2*s2*s2 + 3*c[1]*s2*s2*t2 + 3*c[2]*s2*t2*t2 + c[3]*t2*t2*t2 |
| 604 | |
| 605 | We don't have B or C. So We define two equations to isolate them. |
| 606 | First, compute two reference T values 1/3 and 2/3 from t1 to t2: |
| 607 | |
| 608 | c(at (2*t1 + t2)/3) == E |
| 609 | c(at (t1 + 2*t2)/3) == F |
| 610 | |
| 611 | Next, compute where those values must be if we know the values of B and C: |
| 612 | |
| 613 | _12 = A*2/3 + B*1/3 |
| 614 | 12_ = A*1/3 + B*2/3 |
| 615 | _23 = B*2/3 + C*1/3 |
| 616 | 23_ = B*1/3 + C*2/3 |
| 617 | _34 = C*2/3 + D*1/3 |
| 618 | 34_ = C*1/3 + D*2/3 |
| 619 | _123 = (A*2/3 + B*1/3)*2/3 + (B*2/3 + C*1/3)*1/3 = A*4/9 + B*4/9 + C*1/9 |
| 620 | 123_ = (A*1/3 + B*2/3)*1/3 + (B*1/3 + C*2/3)*2/3 = A*1/9 + B*4/9 + C*4/9 |
| 621 | _234 = (B*2/3 + C*1/3)*2/3 + (C*2/3 + D*1/3)*1/3 = B*4/9 + C*4/9 + D*1/9 |
| 622 | 234_ = (B*1/3 + C*2/3)*1/3 + (C*1/3 + D*2/3)*2/3 = B*1/9 + C*4/9 + D*4/9 |
| 623 | _1234 = (A*4/9 + B*4/9 + C*1/9)*2/3 + (B*4/9 + C*4/9 + D*1/9)*1/3 |
| 624 | = A*8/27 + B*12/27 + C*6/27 + D*1/27 |
| 625 | = E |
| 626 | 1234_ = (A*1/9 + B*4/9 + C*4/9)*1/3 + (B*1/9 + C*4/9 + D*4/9)*2/3 |
| 627 | = A*1/27 + B*6/27 + C*12/27 + D*8/27 |
| 628 | = F |
| 629 | E*27 = A*8 + B*12 + C*6 + D |
| 630 | F*27 = A + B*6 + C*12 + D*8 |
| 631 | |
| 632 | Group the known values on one side: |
| 633 | |
| 634 | M = E*27 - A*8 - D = B*12 + C* 6 |
| 635 | N = F*27 - A - D*8 = B* 6 + C*12 |
| 636 | M*2 - N = B*18 |
| 637 | N*2 - M = C*18 |
| 638 | B = (M*2 - N)/18 |
| 639 | C = (N*2 - M)/18 |
| 640 | */ |
| 641 | |
| 642 | static double interp_cubic_coords(const double* src, double t) { |
| 643 | double ab = SkDInterp(src[0], src[2], t); |
| 644 | double bc = SkDInterp(src[2], src[4], t); |
| 645 | double cd = SkDInterp(src[4], src[6], t); |
| 646 | double abc = SkDInterp(ab, bc, t); |
| 647 | double bcd = SkDInterp(bc, cd, t); |
| 648 | double abcd = SkDInterp(abc, bcd, t); |
| 649 | return abcd; |
| 650 | } |
| 651 | |
| 652 | SkDCubic SkDCubic::subDivide(double t1, double t2) const { |
caryclark@google.com | d892bd8 | 2013-06-17 14:10:36 +0000 | [diff] [blame] | 653 | if (t1 == 0 || t2 == 1) { |
| 654 | if (t1 == 0 && t2 == 1) { |
| 655 | return *this; |
| 656 | } |
| 657 | SkDCubicPair pair = chopAt(t1 == 0 ? t2 : t1); |
| 658 | SkDCubic dst = t1 == 0 ? pair.first() : pair.second(); |
| 659 | return dst; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 660 | } |
| 661 | SkDCubic dst; |
| 662 | double ax = dst[0].fX = interp_cubic_coords(&fPts[0].fX, t1); |
| 663 | double ay = dst[0].fY = interp_cubic_coords(&fPts[0].fY, t1); |
| 664 | double ex = interp_cubic_coords(&fPts[0].fX, (t1*2+t2)/3); |
| 665 | double ey = interp_cubic_coords(&fPts[0].fY, (t1*2+t2)/3); |
| 666 | double fx = interp_cubic_coords(&fPts[0].fX, (t1+t2*2)/3); |
| 667 | double fy = interp_cubic_coords(&fPts[0].fY, (t1+t2*2)/3); |
| 668 | double dx = dst[3].fX = interp_cubic_coords(&fPts[0].fX, t2); |
| 669 | double dy = dst[3].fY = interp_cubic_coords(&fPts[0].fY, t2); |
| 670 | double mx = ex * 27 - ax * 8 - dx; |
| 671 | double my = ey * 27 - ay * 8 - dy; |
| 672 | double nx = fx * 27 - ax - dx * 8; |
| 673 | double ny = fy * 27 - ay - dy * 8; |
| 674 | /* bx = */ dst[1].fX = (mx * 2 - nx) / 18; |
| 675 | /* by = */ dst[1].fY = (my * 2 - ny) / 18; |
| 676 | /* cx = */ dst[2].fX = (nx * 2 - mx) / 18; |
| 677 | /* cy = */ dst[2].fY = (ny * 2 - my) / 18; |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 678 | // FIXME: call align() ? |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 679 | return dst; |
| 680 | } |
| 681 | |
| 682 | void SkDCubic::subDivide(const SkDPoint& a, const SkDPoint& d, |
| 683 | double t1, double t2, SkDPoint dst[2]) const { |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 684 | SkASSERT(t1 != t2); |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 685 | // this approach assumes that the control points computed directly are accurate enough |
| 686 | SkDCubic sub = subDivide(t1, t2); |
| 687 | dst[0] = sub[1] + (a - sub[0]); |
| 688 | dst[1] = sub[2] + (d - sub[3]); |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 689 | if (t1 == 0 || t2 == 0) { |
| 690 | align(0, 1, t1 == 0 ? &dst[0] : &dst[1]); |
| 691 | } |
| 692 | if (t1 == 1 || t2 == 1) { |
| 693 | align(3, 2, t1 == 1 ? &dst[0] : &dst[1]); |
| 694 | } |
commit-bot@chromium.org | 4431e77 | 2014-04-14 17:08:59 +0000 | [diff] [blame] | 695 | if (AlmostBequalUlps(dst[0].fX, a.fX)) { |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 696 | dst[0].fX = a.fX; |
| 697 | } |
commit-bot@chromium.org | 4431e77 | 2014-04-14 17:08:59 +0000 | [diff] [blame] | 698 | if (AlmostBequalUlps(dst[0].fY, a.fY)) { |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 699 | dst[0].fY = a.fY; |
| 700 | } |
commit-bot@chromium.org | 4431e77 | 2014-04-14 17:08:59 +0000 | [diff] [blame] | 701 | if (AlmostBequalUlps(dst[1].fX, d.fX)) { |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 702 | dst[1].fX = d.fX; |
| 703 | } |
commit-bot@chromium.org | 4431e77 | 2014-04-14 17:08:59 +0000 | [diff] [blame] | 704 | if (AlmostBequalUlps(dst[1].fY, d.fY)) { |
caryclark@google.com | cffbcc3 | 2013-06-04 17:59:42 +0000 | [diff] [blame] | 705 | dst[1].fY = d.fY; |
| 706 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 707 | } |
| 708 | |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 709 | bool SkDCubic::toFloatPoints(SkPoint* pts) const { |
| 710 | const double* dCubic = &fPts[0].fX; |
| 711 | SkScalar* cubic = &pts[0].fX; |
| 712 | for (int index = 0; index < kPointCount * 2; ++index) { |
Cary Clark | afca4d6 | 2017-12-01 15:23:00 -0500 | [diff] [blame] | 713 | cubic[index] = SkDoubleToScalar(dCubic[index]); |
| 714 | if (SkScalarAbs(cubic[index]) < FLT_EPSILON_ORDERABLE_ERR) { |
| 715 | cubic[index] = 0; |
| 716 | } |
Cary Clark | 7eb01e0 | 2016-12-08 14:36:32 -0500 | [diff] [blame] | 717 | } |
| 718 | return SkScalarsAreFinite(&pts->fX, kPointCount * 2); |
| 719 | } |
| 720 | |
caryclark | 624637c | 2015-05-11 07:21:27 -0700 | [diff] [blame] | 721 | double SkDCubic::top(const SkDCubic& dCurve, double startT, double endT, SkDPoint*topPt) const { |
| 722 | double extremeTs[2]; |
| 723 | double topT = -1; |
| 724 | int roots = SkDCubic::FindExtrema(&fPts[0].fY, extremeTs); |
| 725 | for (int index = 0; index < roots; ++index) { |
| 726 | double t = startT + (endT - startT) * extremeTs[index]; |
| 727 | SkDPoint mid = dCurve.ptAtT(t); |
| 728 | if (topPt->fY > mid.fY || (topPt->fY == mid.fY && topPt->fX > mid.fX)) { |
| 729 | topT = t; |
| 730 | *topPt = mid; |
| 731 | } |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 732 | } |
caryclark | 624637c | 2015-05-11 07:21:27 -0700 | [diff] [blame] | 733 | return topT; |
caryclark@google.com | 07393ca | 2013-04-08 11:47:37 +0000 | [diff] [blame] | 734 | } |
Cary Clark | 0a67198 | 2018-10-11 12:16:49 -0400 | [diff] [blame^] | 735 | |
| 736 | #if PATH_OP_COMPILE_FOR_SIZE |
| 737 | |
| 738 | int SkTCubic::intersectRay(SkIntersections* i, const SkDLine& line) const { |
| 739 | return i->intersectRay(fCubic, line); |
| 740 | } |
| 741 | |
| 742 | bool SkTCubic::hullIntersects(const SkDQuad& quad, bool* isLinear) const { |
| 743 | return quad.hullIntersects(fCubic, isLinear); |
| 744 | } |
| 745 | |
| 746 | bool SkTCubic::hullIntersects(const SkDConic& conic, bool* isLinear) const { |
| 747 | return conic.hullIntersects(fCubic, isLinear); |
| 748 | } |
| 749 | |
| 750 | void SkTCubic::setBounds(SkDRect* rect) const { |
| 751 | rect->setBounds(fCubic); |
| 752 | } |
| 753 | |
| 754 | #endif |