1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/gfx/skia/trunk/src/pathops/SkOpAngle.cpp Wed Dec 31 06:09:35 2014 +0100
1.3 @@ -0,0 +1,435 @@
1.4 +/*
1.5 + * Copyright 2012 Google Inc.
1.6 + *
1.7 + * Use of this source code is governed by a BSD-style license that can be
1.8 + * found in the LICENSE file.
1.9 + */
1.10 +#include "SkIntersections.h"
1.11 +#include "SkOpAngle.h"
1.12 +#include "SkOpSegment.h"
1.13 +#include "SkPathOpsCurve.h"
1.14 +#include "SkTSort.h"
1.15 +
1.16 +#if DEBUG_ANGLE
1.17 +#include "SkString.h"
1.18 +
1.19 +static const char funcName[] = "SkOpSegment::operator<";
1.20 +static const int bugChar = strlen(funcName) + 1;
1.21 +#endif
1.22 +
1.23 +/* Angles are sorted counterclockwise. The smallest angle has a positive x and the smallest
1.24 + positive y. The largest angle has a positive x and a zero y. */
1.25 +
1.26 +#if DEBUG_ANGLE
1.27 + static bool CompareResult(SkString* bugOut, const char* append, bool compare) {
1.28 + bugOut->appendf("%s", append);
1.29 + bugOut->writable_str()[bugChar] = "><"[compare];
1.30 + SkDebugf("%s\n", bugOut->c_str());
1.31 + return compare;
1.32 + }
1.33 +
1.34 + #define COMPARE_RESULT(append, compare) CompareResult(&bugOut, append, compare)
1.35 +#else
1.36 + #define COMPARE_RESULT(append, compare) compare
1.37 +#endif
1.38 +
1.39 +bool SkOpAngle::calcSlop(double x, double y, double rx, double ry, bool* result) const{
1.40 + double absX = fabs(x);
1.41 + double absY = fabs(y);
1.42 + double length = absX < absY ? absX / 2 + absY : absX + absY / 2;
1.43 + int exponent;
1.44 + (void) frexp(length, &exponent);
1.45 + double epsilon = ldexp(FLT_EPSILON, exponent);
1.46 + SkPath::Verb verb = fSegment->verb();
1.47 + SkASSERT(verb == SkPath::kQuad_Verb || verb == SkPath::kCubic_Verb);
1.48 + // FIXME: the quad and cubic factors are made up ; determine actual values
1.49 + double slop = verb == SkPath::kQuad_Verb ? 4 * epsilon : 512 * epsilon;
1.50 + double xSlop = slop;
1.51 + double ySlop = x * y < 0 ? -xSlop : xSlop; // OPTIMIZATION: use copysign / _copysign ?
1.52 + double x1 = x - xSlop;
1.53 + double y1 = y + ySlop;
1.54 + double x_ry1 = x1 * ry;
1.55 + double rx_y1 = rx * y1;
1.56 + *result = x_ry1 < rx_y1;
1.57 + double x2 = x + xSlop;
1.58 + double y2 = y - ySlop;
1.59 + double x_ry2 = x2 * ry;
1.60 + double rx_y2 = rx * y2;
1.61 + bool less2 = x_ry2 < rx_y2;
1.62 + return *result == less2;
1.63 +}
1.64 +
1.65 +/*
1.66 +for quads and cubics, set up a parameterized line (e.g. LineParameters )
1.67 +for points [0] to [1]. See if point [2] is on that line, or on one side
1.68 +or the other. If it both quads' end points are on the same side, choose
1.69 +the shorter tangent. If the tangents are equal, choose the better second
1.70 +tangent angle
1.71 +
1.72 +FIXME: maybe I could set up LineParameters lazily
1.73 +*/
1.74 +bool SkOpAngle::operator<(const SkOpAngle& rh) const { // this/lh: left-hand; rh: right-hand
1.75 + double y = dy();
1.76 + double ry = rh.dy();
1.77 +#if DEBUG_ANGLE
1.78 + SkString bugOut;
1.79 + bugOut.printf("%s _ id=%d segId=%d tStart=%1.9g tEnd=%1.9g"
1.80 + " | id=%d segId=%d tStart=%1.9g tEnd=%1.9g ", funcName,
1.81 + fID, fSegment->debugID(), fSegment->t(fStart), fSegment->t(fEnd),
1.82 + rh.fID, rh.fSegment->debugID(), rh.fSegment->t(rh.fStart), rh.fSegment->t(rh.fEnd));
1.83 +#endif
1.84 + double y_ry = y * ry;
1.85 + if (y_ry < 0) { // if y's are opposite signs, we can do a quick return
1.86 + return COMPARE_RESULT("1 y * ry < 0", y < 0);
1.87 + }
1.88 + // at this point, both y's must be the same sign, or one (or both) is zero
1.89 + double x = dx();
1.90 + double rx = rh.dx();
1.91 + if (x * rx < 0) { // if x's are opposite signs, use y to determine first or second half
1.92 + if (y < 0 && ry < 0) { // if y's are negative, lh x is smaller if positive
1.93 + return COMPARE_RESULT("2 x_rx < 0 && y < 0 ...", x > 0);
1.94 + }
1.95 + if (y >= 0 && ry >= 0) { // if y's are zero or positive, lh x is smaller if negative
1.96 + return COMPARE_RESULT("3 x_rx < 0 && y >= 0 ...", x < 0);
1.97 + }
1.98 + SkASSERT((y == 0) ^ (ry == 0)); // if one y is zero and one is negative, neg y is smaller
1.99 + return COMPARE_RESULT("4 x_rx < 0 && y == 0 ...", y < 0);
1.100 + }
1.101 + // at this point, both x's must be the same sign, or one (or both) is zero
1.102 + if (y_ry == 0) { // if either y is zero
1.103 + if (y + ry < 0) { // if the other y is less than zero, it must be smaller
1.104 + return COMPARE_RESULT("5 y_ry == 0 && y + ry < 0", y < 0);
1.105 + }
1.106 + if (y + ry > 0) { // if a y is greater than zero and an x is positive, non zero is smaller
1.107 + return COMPARE_RESULT("6 y_ry == 0 && y + ry > 0", (x + rx > 0) ^ (y == 0));
1.108 + }
1.109 + // at this point, both y's are zero, so lines are coincident or one is degenerate
1.110 + SkASSERT(x * rx != 0); // and a degenerate line should haven't gotten this far
1.111 + }
1.112 + // see if either curve can be lengthened before trying the tangent
1.113 + if (fSegment->other(fEnd) != rh.fSegment // tangents not absolutely identical
1.114 + && rh.fSegment->other(rh.fEnd) != fSegment
1.115 + && y != -DBL_EPSILON
1.116 + && ry != -DBL_EPSILON) { // and not intersecting
1.117 + SkOpAngle longer = *this;
1.118 + SkOpAngle rhLonger = rh;
1.119 + if ((longer.lengthen(rh) | rhLonger.lengthen(*this)) // lengthen both
1.120 + && (fUnorderable || !longer.fUnorderable)
1.121 + && (rh.fUnorderable || !rhLonger.fUnorderable)) {
1.122 +#if DEBUG_ANGLE
1.123 + bugOut.prepend(" ");
1.124 +#endif
1.125 + return COMPARE_RESULT("10 longer.lengthen(rh) ...", longer < rhLonger);
1.126 + }
1.127 + }
1.128 + SkPath::Verb verb = fSegment->verb();
1.129 + SkPath::Verb rVerb = rh.fSegment->verb();
1.130 + if (y_ry != 0) { // if they aren't coincident, look for a stable cross product
1.131 + // at this point, y's are the same sign, neither is zero
1.132 + // and x's are the same sign, or one (or both) is zero
1.133 + double x_ry = x * ry;
1.134 + double rx_y = rx * y;
1.135 + if (!fComputed && !rh.fComputed) {
1.136 + if (!SkDLine::NearRay(x, y, rx, ry) && x_ry != rx_y) {
1.137 + return COMPARE_RESULT("7 !fComputed && !rh.fComputed", x_ry < rx_y);
1.138 + }
1.139 + if (fSide2 == 0 && rh.fSide2 == 0) {
1.140 + return COMPARE_RESULT("7a !fComputed && !rh.fComputed", x_ry < rx_y);
1.141 + }
1.142 + } else {
1.143 + // if the vector was a result of subdividing a curve, see if it is stable
1.144 + bool sloppy1 = x_ry < rx_y;
1.145 + bool sloppy2 = !sloppy1;
1.146 + if ((!fComputed || calcSlop(x, y, rx, ry, &sloppy1))
1.147 + && (!rh.fComputed || rh.calcSlop(rx, ry, x, y, &sloppy2))
1.148 + && sloppy1 != sloppy2) {
1.149 + return COMPARE_RESULT("8 CalcSlop(x, y ...", sloppy1);
1.150 + }
1.151 + }
1.152 + }
1.153 + if (fSide2 * rh.fSide2 == 0) { // one is zero
1.154 +#if DEBUG_ANGLE
1.155 + if (fSide2 == rh.fSide2 && y_ry) { // both is zero; coincidence was undetected
1.156 + SkDebugf("%s coincidence!\n", __FUNCTION__);
1.157 + }
1.158 +#endif
1.159 + return COMPARE_RESULT("9a fSide2 * rh.fSide2 == 0 ...", fSide2 < rh.fSide2);
1.160 + }
1.161 + // at this point, the initial tangent line is nearly coincident
1.162 + // see if edges curl away from each other
1.163 + if (fSide * rh.fSide < 0 && (!approximately_zero(fSide) || !approximately_zero(rh.fSide))) {
1.164 + return COMPARE_RESULT("9b fSide * rh.fSide < 0 ...", fSide < rh.fSide);
1.165 + }
1.166 + if (fUnsortable || rh.fUnsortable) {
1.167 + // even with no solution, return a stable sort
1.168 + return COMPARE_RESULT("11 fUnsortable || rh.fUnsortable", this < &rh);
1.169 + }
1.170 + if ((verb == SkPath::kLine_Verb && approximately_zero(y) && approximately_zero(x))
1.171 + || (rVerb == SkPath::kLine_Verb
1.172 + && approximately_zero(ry) && approximately_zero(rx))) {
1.173 + // See general unsortable comment below. This case can happen when
1.174 + // one line has a non-zero change in t but no change in x and y.
1.175 + fUnsortable = true;
1.176 + return COMPARE_RESULT("12 verb == SkPath::kLine_Verb ...", this < &rh);
1.177 + }
1.178 + if (fSegment->isTiny(this) || rh.fSegment->isTiny(&rh)) {
1.179 + fUnsortable = true;
1.180 + return COMPARE_RESULT("13 verb == fSegment->isTiny(this) ...", this < &rh);
1.181 + }
1.182 + SkASSERT(verb >= SkPath::kQuad_Verb);
1.183 + SkASSERT(rVerb >= SkPath::kQuad_Verb);
1.184 + // FIXME: until I can think of something better, project a ray from the
1.185 + // end of the shorter tangent to midway between the end points
1.186 + // through both curves and use the resulting angle to sort
1.187 + // FIXME: some of this setup can be moved to set() if it works, or cached if it's expensive
1.188 + double len = fTangentPart.normalSquared();
1.189 + double rlen = rh.fTangentPart.normalSquared();
1.190 + SkDLine ray;
1.191 + SkIntersections i, ri;
1.192 + int roots, rroots;
1.193 + bool flip = false;
1.194 + bool useThis;
1.195 + bool leftLessThanRight = fSide > 0;
1.196 + do {
1.197 + useThis = (len < rlen) ^ flip;
1.198 + const SkDCubic& part = useThis ? fCurvePart : rh.fCurvePart;
1.199 + SkPath::Verb partVerb = useThis ? verb : rVerb;
1.200 + ray[0] = partVerb == SkPath::kCubic_Verb && part[0].approximatelyEqual(part[1]) ?
1.201 + part[2] : part[1];
1.202 + ray[1] = SkDPoint::Mid(part[0], part[SkPathOpsVerbToPoints(partVerb)]);
1.203 + SkASSERT(ray[0] != ray[1]);
1.204 + roots = (i.*CurveRay[SkPathOpsVerbToPoints(verb)])(fSegment->pts(), ray);
1.205 + rroots = (ri.*CurveRay[SkPathOpsVerbToPoints(rVerb)])(rh.fSegment->pts(), ray);
1.206 + } while ((roots == 0 || rroots == 0) && (flip ^= true));
1.207 + if (roots == 0 || rroots == 0) {
1.208 + // FIXME: we don't have a solution in this case. The interim solution
1.209 + // is to mark the edges as unsortable, exclude them from this and
1.210 + // future computations, and allow the returned path to be fragmented
1.211 + fUnsortable = true;
1.212 + return COMPARE_RESULT("roots == 0 || rroots == 0", this < &rh);
1.213 + }
1.214 + SkASSERT(fSide != 0 && rh.fSide != 0);
1.215 + if (fSide * rh.fSide < 0) {
1.216 + fUnsortable = true;
1.217 + return COMPARE_RESULT("14 fSide * rh.fSide < 0", this < &rh);
1.218 + }
1.219 + SkDPoint lLoc;
1.220 + double best = SK_ScalarInfinity;
1.221 +#if DEBUG_SORT
1.222 + SkDebugf("lh=%d rh=%d use-lh=%d ray={{%1.9g,%1.9g}, {%1.9g,%1.9g}} %c\n",
1.223 + fSegment->debugID(), rh.fSegment->debugID(), useThis, ray[0].fX, ray[0].fY,
1.224 + ray[1].fX, ray[1].fY, "-+"[fSide > 0]);
1.225 +#endif
1.226 + for (int index = 0; index < roots; ++index) {
1.227 + SkDPoint loc = i.pt(index);
1.228 + SkDVector dxy = loc - ray[0];
1.229 + double dist = dxy.lengthSquared();
1.230 +#if DEBUG_SORT
1.231 + SkDebugf("best=%1.9g dist=%1.9g loc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n",
1.232 + best, dist, loc.fX, loc.fY, dxy.fX, dxy.fY);
1.233 +#endif
1.234 + if (best > dist) {
1.235 + lLoc = loc;
1.236 + best = dist;
1.237 + }
1.238 + }
1.239 + flip = false;
1.240 + SkDPoint rLoc;
1.241 + for (int index = 0; index < rroots; ++index) {
1.242 + rLoc = ri.pt(index);
1.243 + SkDVector dxy = rLoc - ray[0];
1.244 + double dist = dxy.lengthSquared();
1.245 +#if DEBUG_SORT
1.246 + SkDebugf("best=%1.9g dist=%1.9g %c=(fSide < 0) rLoc={%1.9g,%1.9g} dxy={%1.9g,%1.9g}\n",
1.247 + best, dist, "><"[fSide < 0], rLoc.fX, rLoc.fY, dxy.fX, dxy.fY);
1.248 +#endif
1.249 + if (best > dist) {
1.250 + flip = true;
1.251 + break;
1.252 + }
1.253 + }
1.254 + if (flip) {
1.255 + leftLessThanRight = !leftLessThanRight;
1.256 + }
1.257 + return COMPARE_RESULT("15 leftLessThanRight", leftLessThanRight);
1.258 +}
1.259 +
1.260 +bool SkOpAngle::isHorizontal() const {
1.261 + return dy() == 0 && fSegment->verb() == SkPath::kLine_Verb;
1.262 +}
1.263 +
1.264 +// lengthen cannot cross opposite angle
1.265 +bool SkOpAngle::lengthen(const SkOpAngle& opp) {
1.266 + if (fSegment->other(fEnd) == opp.fSegment) {
1.267 + return false;
1.268 + }
1.269 + // FIXME: make this a while loop instead and make it as large as possible?
1.270 + int newEnd = fEnd;
1.271 + if (fStart < fEnd ? ++newEnd < fSegment->count() : --newEnd >= 0) {
1.272 + fEnd = newEnd;
1.273 + setSpans();
1.274 + return true;
1.275 + }
1.276 + return false;
1.277 +}
1.278 +
1.279 +void SkOpAngle::set(const SkOpSegment* segment, int start, int end) {
1.280 + fSegment = segment;
1.281 + fStart = start;
1.282 + fEnd = end;
1.283 + setSpans();
1.284 +}
1.285 +
1.286 +void SkOpAngle::setSpans() {
1.287 + fUnorderable = fSegment->isTiny(this);
1.288 + fLastMarked = NULL;
1.289 + fUnsortable = false;
1.290 + const SkPoint* pts = fSegment->pts();
1.291 + if (fSegment->verb() != SkPath::kLine_Verb) {
1.292 + fComputed = fSegment->subDivide(fStart, fEnd, &fCurvePart);
1.293 + fSegment->subDivide(fStart, fStart < fEnd ? fSegment->count() - 1 : 0, &fCurveHalf);
1.294 + }
1.295 + // FIXME: slight errors in subdivision cause sort trouble later on. As an experiment, try
1.296 + // rounding the curve part to float precision here
1.297 + // fCurvePart.round(fSegment->verb());
1.298 + switch (fSegment->verb()) {
1.299 + case SkPath::kLine_Verb: {
1.300 + SkASSERT(fStart != fEnd);
1.301 + fCurvePart[0].set(pts[fStart > fEnd]);
1.302 + fCurvePart[1].set(pts[fStart < fEnd]);
1.303 + fComputed = false;
1.304 + // OPTIMIZATION: for pure line compares, we never need fTangentPart.c
1.305 + fTangentPart.lineEndPoints(*SkTCast<SkDLine*>(&fCurvePart));
1.306 + fSide = 0;
1.307 + fSide2 = 0;
1.308 + } break;
1.309 + case SkPath::kQuad_Verb: {
1.310 + fSide2 = -fTangentHalf.quadPart(*SkTCast<SkDQuad*>(&fCurveHalf));
1.311 + SkDQuad& quad = *SkTCast<SkDQuad*>(&fCurvePart);
1.312 + fTangentPart.quadEndPoints(quad);
1.313 + fSide = -fTangentPart.pointDistance(fCurvePart[2]); // not normalized -- compare sign only
1.314 + if (fComputed && dx() > 0 && approximately_zero(dy())) {
1.315 + SkDCubic origCurve; // can't use segment's curve in place since it may be flipped
1.316 + int last = fSegment->count() - 1;
1.317 + fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve);
1.318 + SkLineParameters origTan;
1.319 + origTan.quadEndPoints(*SkTCast<SkDQuad*>(&origCurve));
1.320 + if (origTan.dx() <= 0
1.321 + || (dy() != origTan.dy() && dy() * origTan.dy() <= 0)) { // signs match?
1.322 + fUnorderable = true;
1.323 + return;
1.324 + }
1.325 + }
1.326 + } break;
1.327 + case SkPath::kCubic_Verb: {
1.328 + double startT = fSegment->t(fStart);
1.329 + fSide2 = -fTangentHalf.cubicPart(fCurveHalf);
1.330 + fTangentPart.cubicEndPoints(fCurvePart);
1.331 + double testTs[4];
1.332 + // OPTIMIZATION: keep inflections precomputed with cubic segment?
1.333 + int testCount = SkDCubic::FindInflections(pts, testTs);
1.334 + double endT = fSegment->t(fEnd);
1.335 + double limitT = endT;
1.336 + int index;
1.337 + for (index = 0; index < testCount; ++index) {
1.338 + if (!between(startT, testTs[index], limitT)) {
1.339 + testTs[index] = -1;
1.340 + }
1.341 + }
1.342 + testTs[testCount++] = startT;
1.343 + testTs[testCount++] = endT;
1.344 + SkTQSort<double>(testTs, &testTs[testCount - 1]);
1.345 + double bestSide = 0;
1.346 + int testCases = (testCount << 1) - 1;
1.347 + index = 0;
1.348 + while (testTs[index] < 0) {
1.349 + ++index;
1.350 + }
1.351 + index <<= 1;
1.352 + for (; index < testCases; ++index) {
1.353 + int testIndex = index >> 1;
1.354 + double testT = testTs[testIndex];
1.355 + if (index & 1) {
1.356 + testT = (testT + testTs[testIndex + 1]) / 2;
1.357 + }
1.358 + // OPTIMIZE: could avoid call for t == startT, endT
1.359 + SkDPoint pt = dcubic_xy_at_t(pts, testT);
1.360 + double testSide = fTangentPart.pointDistance(pt);
1.361 + if (fabs(bestSide) < fabs(testSide)) {
1.362 + bestSide = testSide;
1.363 + }
1.364 + }
1.365 + fSide = -bestSide; // compare sign only
1.366 + SkASSERT(fSide == 0 || fSide2 != 0);
1.367 + if (fComputed && dx() > 0 && approximately_zero(dy())) {
1.368 + SkDCubic origCurve; // can't use segment's curve in place since it may be flipped
1.369 + int last = fSegment->count() - 1;
1.370 + fSegment->subDivide(fStart < fEnd ? 0 : last, fStart < fEnd ? last : 0, &origCurve);
1.371 + SkDCubicPair split = origCurve.chopAt(startT);
1.372 + SkLineParameters splitTan;
1.373 + splitTan.cubicEndPoints(fStart < fEnd ? split.second() : split.first());
1.374 + if (splitTan.dx() <= 0) {
1.375 + fUnorderable = true;
1.376 + fUnsortable = fSegment->isTiny(this);
1.377 + return;
1.378 + }
1.379 + // if one is < 0 and the other is >= 0
1.380 + if (dy() * splitTan.dy() < 0) {
1.381 + fUnorderable = true;
1.382 + fUnsortable = fSegment->isTiny(this);
1.383 + return;
1.384 + }
1.385 + }
1.386 + } break;
1.387 + default:
1.388 + SkASSERT(0);
1.389 + }
1.390 + if ((fUnsortable = approximately_zero(dx()) && approximately_zero(dy()))) {
1.391 + return;
1.392 + }
1.393 + if (fSegment->verb() == SkPath::kLine_Verb) {
1.394 + return;
1.395 + }
1.396 + SkASSERT(fStart != fEnd);
1.397 + int smaller = SkMin32(fStart, fEnd);
1.398 + int larger = SkMax32(fStart, fEnd);
1.399 + while (smaller < larger && fSegment->span(smaller).fTiny) {
1.400 + ++smaller;
1.401 + }
1.402 + if (precisely_equal(fSegment->span(smaller).fT, fSegment->span(larger).fT)) {
1.403 + #if DEBUG_UNSORTABLE
1.404 + SkPoint iPt = fSegment->xyAtT(fStart);
1.405 + SkPoint ePt = fSegment->xyAtT(fEnd);
1.406 + SkDebugf("%s all tiny unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__,
1.407 + fStart, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY);
1.408 + #endif
1.409 + fUnsortable = true;
1.410 + return;
1.411 + }
1.412 + fUnsortable = fStart < fEnd ? fSegment->span(smaller).fUnsortableStart
1.413 + : fSegment->span(larger).fUnsortableEnd;
1.414 +#if DEBUG_UNSORTABLE
1.415 + if (fUnsortable) {
1.416 + SkPoint iPt = fSegment->xyAtT(smaller);
1.417 + SkPoint ePt = fSegment->xyAtT(larger);
1.418 + SkDebugf("%s unsortable [%d] (%1.9g,%1.9g) [%d] (%1.9g,%1.9g)\n", __FUNCTION__,
1.419 + smaller, iPt.fX, iPt.fY, fEnd, ePt.fX, ePt.fY);
1.420 + }
1.421 +#endif
1.422 + return;
1.423 +}
1.424 +
1.425 +#ifdef SK_DEBUG
1.426 +void SkOpAngle::dump() const {
1.427 + const SkOpSpan& spanStart = fSegment->span(fStart);
1.428 + const SkOpSpan& spanEnd = fSegment->span(fEnd);
1.429 + const SkOpSpan& spanMin = fStart < fEnd ? spanStart : spanEnd;
1.430 + SkDebugf("id=%d (%1.9g,%1.9g) start=%d (%1.9g) end=%d (%1.9g) sumWind=",
1.431 + fSegment->debugID(), fSegment->xAtT(fStart), fSegment->yAtT(fStart),
1.432 + fStart, spanStart.fT, fEnd, spanEnd.fT);
1.433 + SkPathOpsDebug::WindingPrintf(spanMin.fWindSum);
1.434 + SkDebugf(" oppWind=");
1.435 + SkPathOpsDebug::WindingPrintf(spanMin.fOppSum),
1.436 + SkDebugf(" done=%d\n", spanMin.fDone);
1.437 +}
1.438 +#endif
