static double testArc(skiatest::Reporter* reporter, const SkDQuad& quad, const SkDQuad& arcRef,
int octant) {
SkDQuad arc = arcRef;
SkDVector offset = {quad[0].fX, quad[0].fY};
arc[0] += offset;
arc[1] += offset;
arc[2] += offset;
SkIntersections i;
i.intersect(arc, quad);
if (i.used() == 0) {
return -1;
}
int smallest = -1;
double t = 2;
for (int idx = 0; idx < i.used(); ++idx) {
if (i[0][idx] > 1 || i[0][idx] < 0) {
i.reset();
i.intersect(arc, quad);
}
if (i[1][idx] > 1 || i[1][idx] < 0) {
i.reset();
i.intersect(arc, quad);
}
if (t > i[1][idx]) {
smallest = idx;
t = i[1][idx];
}
}
REPORTER_ASSERT(reporter, smallest >= 0);
REPORTER_ASSERT(reporter, t >= 0 && t <= 1);
return i[1][smallest];
}
static void TestLineIntersection(skiatest::Reporter* reporter) {
size_t index;
for (index = 0; index < tests_count; ++index) {
const SkDLine& line1 = tests[index][0];
const SkDLine& line2 = tests[index][1];
SkIntersections ts;
int pts = ts.intersect(line1, line2);
REPORTER_ASSERT(reporter, pts);
for (int i = 0; i < pts; ++i) {
SkDPoint result1 = line1.xyAtT(ts[0][i]);
SkDPoint result2 = line2.xyAtT(ts[1][i]);
if (!result1.approximatelyEqual(result2)) {
REPORTER_ASSERT(reporter, pts != 1);
result2 = line2.xyAtT(ts[1][i ^ 1]);
REPORTER_ASSERT(reporter, result1.approximatelyEqual(result2));
}
}
}
for (index = 0; index < noIntersect_count; ++index) {
const SkDLine& line1 = noIntersect[index][0];
const SkDLine& line2 = noIntersect[index][1];
SkIntersections ts;
int pts = ts.intersect(line1, line2);
REPORTER_ASSERT(reporter, !pts);
}
}
static void intersectWithOrder(const SkDQuad& simple1, int order1, const SkDQuad& simple2,
int order2, SkIntersections& i) {
if (order1 == 3 && order2 == 3) {
i.intersect(simple1, simple2);
} else if (order1 <= 2 && order2 <= 2) {
i.intersect((const SkDLine&) simple1, (const SkDLine&) simple2);
} else if (order1 == 3 && order2 <= 2) {
i.intersect(simple1, (const SkDLine&) simple2);
} else {
SkASSERT(order1 <= 2 && order2 == 3);
i.intersect(simple2, (const SkDLine&) simple1);
i.swapPts();
}
}
static void cubicQuadIntersection(skiatest::Reporter* reporter, int index) {
int iIndex = static_cast<int>(index);
const SkDCubic& cubic = quadCubicTests[index].cubic;
SkASSERT(ValidCubic(cubic));
const SkDQuad& quad = quadCubicTests[index].quad;
SkASSERT(ValidQuad(quad));
SkReduceOrder reduce1;
SkReduceOrder reduce2;
int order1 = reduce1.reduce(cubic, SkReduceOrder::kNo_Quadratics);
int order2 = reduce2.reduce(quad);
if (order1 != 4) {
SkDebugf("[%d] cubic order=%d\n", iIndex, order1);
REPORTER_ASSERT(reporter, 0);
}
if (order2 != 3) {
SkDebugf("[%d] quad order=%d\n", iIndex, order2);
REPORTER_ASSERT(reporter, 0);
}
SkIntersections i;
int roots = i.intersect(cubic, quad);
for (int pt = 0; pt < roots; ++pt) {
double tt1 = i[0][pt];
SkDPoint xy1 = cubic.ptAtT(tt1);
double tt2 = i[1][pt];
SkDPoint xy2 = quad.ptAtT(tt2);
if (!xy1.approximatelyEqual(xy2)) {
SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, iIndex, pt, tt1, xy1.fX, xy1.fY, tt2, xy2.fX, xy2.fY);
}
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
}
reporter->bumpTestCount();
}
static void oneOff(skiatest::Reporter* reporter, const SkDConic& c1, const SkDConic& c2,
bool coin) {
#if DEBUG_VISUALIZE_CONICS
writeFrames();
#endif
chopBothWays(c1, 0.5, "c1");
chopBothWays(c2, 0.5, "c2");
#if DEBUG_VISUALIZE_CONICS
writeDPng(c1, "d1");
writeDPng(c2, "d2");
#endif
SkASSERT(ValidConic(c1));
SkASSERT(ValidConic(c2));
SkIntersections intersections;
intersections.intersect(c1, c2);
if (coin && intersections.used() != 2) {
SkDebugf("");
}
REPORTER_ASSERT(reporter, !coin || intersections.used() == 2);
double tt1, tt2;
SkDPoint xy1, xy2;
for (int pt3 = 0; pt3 < intersections.used(); ++pt3) {
tt1 = intersections[0][pt3];
xy1 = c1.ptAtT(tt1);
tt2 = intersections[1][pt3];
xy2 = c2.ptAtT(tt2);
const SkDPoint& iPt = intersections.pt(pt3);
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(iPt));
REPORTER_ASSERT(reporter, xy2.approximatelyEqual(iPt));
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
}
reporter->bumpTestCount();
}
static int doIntersect(SkIntersections& intersections, const SkDConic& conic, const SkDLine& line,
bool& flipped) {
int result;
flipped = false;
if (line[0].fX == line[1].fX) {
double top = line[0].fY;
double bottom = line[1].fY;
flipped = top > bottom;
if (flipped) {
SkTSwap<double>(top, bottom);
}
result = intersections.vertical(conic, top, bottom, line[0].fX, flipped);
} else if (line[0].fY == line[1].fY) {
double left = line[0].fX;
double right = line[1].fX;
flipped = left > right;
if (flipped) {
SkTSwap<double>(left, right);
}
result = intersections.horizontal(conic, left, right, line[0].fY, flipped);
} else {
intersections.intersect(conic, line);
result = intersections.used();
}
return result;
}
DEF_TEST(PathOpsAngleFindQuadEpsilon, reporter) {
if (gDisableAngleTests) {
return;
}
SkRandom ran;
int maxEpsilon = 0;
double maxAngle = 0;
for (int index = 0; index < 100000; ++index) {
SkDLine line = {{{0, 0}, {ran.nextRangeF(0.0001f, 1000), ran.nextRangeF(0.0001f, 1000)}}};
float t = ran.nextRangeF(0.0001f, 1);
SkDPoint dPt = line.ptAtT(t);
float t2 = ran.nextRangeF(0.0001f, 1);
SkDPoint qPt = line.ptAtT(t2);
float t3 = ran.nextRangeF(0.0001f, 1);
SkDPoint qPt2 = line.ptAtT(t3);
qPt.fX += qPt2.fY;
qPt.fY -= qPt2.fX;
QuadPts q = {{line[0], dPt, qPt}};
SkDQuad quad;
quad.debugSet(q.fPts);
// binary search for maximum movement of quad[1] towards test that still has 1 intersection
double moveT = 0.5f;
double deltaT = moveT / 2;
SkDPoint last;
do {
last = quad[1];
quad[1].fX = dPt.fX - line[1].fY * moveT;
quad[1].fY = dPt.fY + line[1].fX * moveT;
SkIntersections i;
i.intersect(quad, line);
REPORTER_ASSERT(reporter, i.used() > 0);
if (i.used() == 1) {
moveT += deltaT;
} else {
moveT -= deltaT;
}
deltaT /= 2;
} while (last.asSkPoint() != quad[1].asSkPoint());
float p1 = SkDoubleToScalar(line[1].fX * last.fY);
float p2 = SkDoubleToScalar(line[1].fY * last.fX);
int p1Bits = SkFloatAs2sCompliment(p1);
int p2Bits = SkFloatAs2sCompliment(p2);
int epsilon = SkTAbs(p1Bits - p2Bits);
if (maxEpsilon < epsilon) {
SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g/%1.7g/%1.7g moveT=%1.7g"
" pt={%1.7g, %1.7g} epsilon=%d\n",
line[1].fX, line[1].fY, t, t2, t3, moveT, last.fX, last.fY, epsilon);
maxEpsilon = epsilon;
}
double a1 = atan2(line[1].fY, line[1].fX);
double a2 = atan2(last.fY, last.fX);
double angle = fabs(a1 - a2);
if (maxAngle < angle) {
SkDebugf("line={{0, 0}, {%1.7g, %1.7g}} t=%1.7g/%1.7g/%1.7g moveT=%1.7g"
" pt={%1.7g, %1.7g} angle=%1.7g\n",
line[1].fX, line[1].fY, t, t2, t3, moveT, last.fX, last.fY, angle);
maxAngle = angle;
}
}
}
// returns false if there's more than one intercept or the intercept doesn't match the point
// returns true if the intercept was successfully added or if the
// original quads need to be subdivided
static bool add_intercept(const SkDQuad& q1, const SkDQuad& q2, double tMin, double tMax,
SkIntersections* i, bool* subDivide) {
double tMid = (tMin + tMax) / 2;
SkDPoint mid = q2.ptAtT(tMid);
SkDLine line;
line[0] = line[1] = mid;
SkDVector dxdy = q2.dxdyAtT(tMid);
line[0] -= dxdy;
line[1] += dxdy;
SkIntersections rootTs;
rootTs.allowNear(false);
int roots = rootTs.intersect(q1, line);
if (roots == 0) {
if (subDivide) {
*subDivide = true;
}
return true;
}
if (roots == 2) {
return false;
}
SkDPoint pt2 = q1.ptAtT(rootTs[0][0]);
if (!pt2.approximatelyEqualHalf(mid)) {
return false;
}
i->insertSwap(rootTs[0][0], tMid, pt2);
return true;
}
static void selfOneOff(skiatest::Reporter* reporter, int index) {
const SkDCubic& cubic = selfSet[index];
#if ONE_OFF_DEBUG
int idx2;
double max[3];
int ts = cubic.findMaxCurvature(max);
for (idx2 = 0; idx2 < ts; ++idx2) {
SkDebugf("%s max[%d]=%1.9g (%1.9g, %1.9g)\n", __FUNCTION__, idx2,
max[idx2], cubic.ptAtT(max[idx2]).fX, cubic.ptAtT(max[idx2]).fY);
}
SkTArray<double, true> ts1;
SkTArray<SkDQuad, true> quads1;
cubic.toQuadraticTs(cubic.calcPrecision(), &ts1);
for (idx2 = 0; idx2 < ts1.count(); ++idx2) {
SkDebugf("%s t[%d]=%1.9g\n", __FUNCTION__, idx2, ts1[idx2]);
}
CubicToQuads(cubic, cubic.calcPrecision(), quads1);
for (idx2 = 0; idx2 < quads1.count(); ++idx2) {
const SkDQuad& q = quads1[idx2];
SkDebugf(" {{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}},\n",
q[0].fX, q[0].fY, q[1].fX, q[1].fY, q[2].fX, q[2].fY);
}
SkDebugf("\n");
#endif
SkIntersections i;
int result = i.intersect(cubic);
REPORTER_ASSERT(reporter, result == 1);
REPORTER_ASSERT(reporter, i.used() == 1);
REPORTER_ASSERT(reporter, !approximately_equal(i[0][0], i[1][0]));
SkDPoint pt1 = cubic.ptAtT(i[0][0]);
SkDPoint pt2 = cubic.ptAtT(i[1][0]);
REPORTER_ASSERT(reporter, pt1.approximatelyEqual(pt2));
reporter->bumpTestCount();
}
static int doIntersect(SkIntersections& intersections, const SkDQuad& quad, const SkDLine& line,
bool& flipped) {
int result;
flipped = false;
if (line[0].fX == line[1].fX) {
double top = line[0].fY;
double bottom = line[1].fY;
flipped = top > bottom;
if (flipped) {
using std::swap;
swap(top, bottom);
}
result = intersections.vertical(quad, top, bottom, line[0].fX, flipped);
} else if (line[0].fY == line[1].fY) {
double left = line[0].fX;
double right = line[1].fX;
flipped = left > right;
if (flipped) {
using std::swap;
swap(left, right);
}
result = intersections.horizontal(quad, left, right, line[0].fY, flipped);
} else {
intersections.intersect(quad, line);
result = intersections.used();
}
return result;
}
static void PathOpsCubicLineIntersectionTest(skiatest::Reporter* reporter) {
for (size_t index = 0; index < lineCubicTests_count; ++index) {
int iIndex = static_cast<int>(index);
const SkDCubic& cubic = lineCubicTests[index].cubic;
const SkDLine& line = lineCubicTests[index].line;
SkReduceOrder reduce1;
SkReduceOrder reduce2;
int order1 = reduce1.reduce(cubic, SkReduceOrder::kNo_Quadratics,
SkReduceOrder::kFill_Style);
int order2 = reduce2.reduce(line);
if (order1 < 4) {
SkDebugf("[%d] cubic order=%d\n", iIndex, order1);
REPORTER_ASSERT(reporter, 0);
}
if (order2 < 2) {
SkDebugf("[%d] line order=%d\n", iIndex, order2);
REPORTER_ASSERT(reporter, 0);
}
if (order1 == 4 && order2 == 2) {
SkIntersections i;
int roots = i.intersect(cubic, line);
for (int pt = 0; pt < roots; ++pt) {
double tt1 = i[0][pt];
SkDPoint xy1 = cubic.xyAtT(tt1);
double tt2 = i[1][pt];
SkDPoint xy2 = line.xyAtT(tt2);
if (!xy1.approximatelyEqual(xy2)) {
SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, iIndex, pt, tt1, xy1.fX, xy1.fY, tt2, xy2.fX, xy2.fY);
}
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
}
}
}
}
static void selfOneOff(skiatest::Reporter* reporter, int index) {
const CubicPts& cubic = selfSet[index];
SkPoint c[4];
for (int i = 0; i < 4; ++i) {
c[i] = cubic.fPts[i].asSkPoint();
}
SkScalar loopT;
SkScalar d[3];
SkCubicType cubicType = SkClassifyCubic(c, d);
if (SkDCubic::ComplexBreak(c, &loopT) && cubicType == SkCubicType::kLoop_SkCubicType) {
SkIntersections i;
SkPoint twoCubics[7];
SkChopCubicAt(c, twoCubics, loopT);
SkDCubic chopped[2];
chopped[0].set(&twoCubics[0]);
chopped[1].set(&twoCubics[3]);
int result = i.intersect(chopped[0], chopped[1]);
REPORTER_ASSERT(reporter, result == 2);
REPORTER_ASSERT(reporter, i.used() == 2);
for (int index = 0; index < result; ++index) {
SkDPoint pt1 = chopped[0].ptAtT(i[0][index]);
SkDPoint pt2 = chopped[1].ptAtT(i[1][index]);
REPORTER_ASSERT(reporter, pt1.approximatelyEqual(pt2));
reporter->bumpTestCount();
}
}
}
static void oneOff(skiatest::Reporter* reporter, const SkDCubic& cubic1, const SkDCubic& cubic2,
bool coin) {
SkASSERT(ValidCubic(cubic1));
SkASSERT(ValidCubic(cubic2));
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics given\n");
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
cubic1[0].fX, cubic1[0].fY, cubic1[1].fX, cubic1[1].fY,
cubic1[2].fX, cubic1[2].fY, cubic1[3].fX, cubic1[3].fY);
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
cubic2[0].fX, cubic2[0].fY, cubic2[1].fX, cubic2[1].fY,
cubic2[2].fX, cubic2[2].fY, cubic2[3].fX, cubic2[3].fY);
#endif
SkTArray<SkDQuad, true> quads1;
CubicToQuads(cubic1, cubic1.calcPrecision(), quads1);
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics set 1\n");
for (int index = 0; index < quads1.count(); ++index) {
const SkDQuad& q = quads1[index];
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].fX, q[0].fY,
q[1].fX, q[1].fY, q[2].fX, q[2].fY);
}
#endif
SkTArray<SkDQuad, true> quads2;
CubicToQuads(cubic2, cubic2.calcPrecision(), quads2);
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics set 2\n");
for (int index = 0; index < quads2.count(); ++index) {
const SkDQuad& q = quads2[index];
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n", q[0].fX, q[0].fY,
q[1].fX, q[1].fY, q[2].fX, q[2].fY);
}
#endif
SkIntersections intersections;
intersections.intersect(cubic1, cubic2);
REPORTER_ASSERT(reporter, !coin || intersections.used() == 2);
double tt1, tt2;
SkDPoint xy1, xy2;
for (int pt3 = 0; pt3 < intersections.used(); ++pt3) {
tt1 = intersections[0][pt3];
xy1 = cubic1.ptAtT(tt1);
tt2 = intersections[1][pt3];
xy2 = cubic2.ptAtT(tt2);
const SkDPoint& iPt = intersections.pt(pt3);
#if ONE_OFF_DEBUG
SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
__FUNCTION__, tt1, xy1.fX, xy1.fY, iPt.fX,
iPt.fY, xy2.fX, xy2.fY, tt2);
#endif
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(iPt));
REPORTER_ASSERT(reporter, xy2.approximatelyEqual(iPt));
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
}
reporter->bumpTestCount();
}
static void standardTestCases(skiatest::Reporter* reporter) {
for (size_t index = firstCubicIntersectionTest; index < tests_count; ++index) {
int iIndex = static_cast<int>(index);
const CubicPts& cubic1 = tests[index][0];
const CubicPts& cubic2 = tests[index][1];
SkDCubic c1, c2;
c1.debugSet(cubic1.fPts);
c2.debugSet(cubic2.fPts);
SkReduceOrder reduce1, reduce2;
int order1 = reduce1.reduce(c1, SkReduceOrder::kNo_Quadratics);
int order2 = reduce2.reduce(c2, SkReduceOrder::kNo_Quadratics);
const bool showSkipped = false;
if (order1 < 4) {
if (showSkipped) {
SkDebugf("%s [%d] cubic1 order=%d\n", __FUNCTION__, iIndex, order1);
}
continue;
}
if (order2 < 4) {
if (showSkipped) {
SkDebugf("%s [%d] cubic2 order=%d\n", __FUNCTION__, iIndex, order2);
}
continue;
}
SkIntersections tIntersections;
tIntersections.intersect(c1, c2);
if (!tIntersections.used()) {
if (showSkipped) {
SkDebugf("%s [%d] no intersection\n", __FUNCTION__, iIndex);
}
continue;
}
if (tIntersections.isCoincident(0)) {
if (showSkipped) {
SkDebugf("%s [%d] coincident\n", __FUNCTION__, iIndex);
}
continue;
}
for (int pt = 0; pt < tIntersections.used(); ++pt) {
double tt1 = tIntersections[0][pt];
SkDPoint xy1 = c1.ptAtT(tt1);
double tt2 = tIntersections[1][pt];
SkDPoint xy2 = c2.ptAtT(tt2);
if (!xy1.approximatelyEqual(xy2)) {
SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, (int)index, pt, tt1, xy1.fX, xy1.fY, tt2, xy2.fX, xy2.fY);
}
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
}
reporter->bumpTestCount();
}
}
static void hullIntersect(const SkDQuad& q1, const SkDQuad& q2) {
SkDebugf("%s", __FUNCTION__);
SkIntersections ts;
for (int i1 = 0; i1 < 3; ++i1) {
SkDLine l1 = {{q1[i1], q1[(i1 + 1) % 3]}};
for (int i2 = 0; i2 < 3; ++i2) {
SkDLine l2 = {{q2[i2], q2[(i2 + 1) % 3]}};
if (ts.intersect(l1, l2)) {
SkDebugf(" [%d,%d]", i1, i2);
}
}
}
SkDebugf("\n");
}
static void oneOff(skiatest::Reporter* reporter, const CubicPts& cubic1, const CubicPts& cubic2,
bool coin) {
SkDCubic c1, c2;
c1.debugSet(cubic1.fPts);
c2.debugSet(cubic2.fPts);
SkASSERT(ValidCubic(c1));
SkASSERT(ValidCubic(c2));
#if ONE_OFF_DEBUG
SkDebugf("computed quadratics given\n");
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
cubic1[0].fX, cubic1[0].fY, cubic1[1].fX, cubic1[1].fY,
cubic1[2].fX, cubic1[2].fY, cubic1[3].fX, cubic1[3].fY);
SkDebugf(" {{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}},\n",
cubic2[0].fX, cubic2[0].fY, cubic2[1].fX, cubic2[1].fY,
cubic2[2].fX, cubic2[2].fY, cubic2[3].fX, cubic2[3].fY);
#endif
SkIntersections intersections;
intersections.intersect(c1, c2);
#if DEBUG_T_SECT_DUMP == 3
SkDebugf("</div>\n\n");
SkDebugf("<script type=\"text/javascript\">\n\n");
SkDebugf("var testDivs = [\n");
for (int index = 1; index <= gDumpTSectNum; ++index) {
SkDebugf("sect%d,\n", index);
}
#endif
if (coin && intersections.used() < 2) {
SkDebugf("");
}
REPORTER_ASSERT(reporter, !coin || intersections.used() >= 2);
double tt1, tt2;
SkDPoint xy1, xy2;
for (int pt3 = 0; pt3 < intersections.used(); ++pt3) {
tt1 = intersections[0][pt3];
xy1 = c1.ptAtT(tt1);
tt2 = intersections[1][pt3];
xy2 = c2.ptAtT(tt2);
const SkDPoint& iPt = intersections.pt(pt3);
#if ONE_OFF_DEBUG
SkDebugf("%s t1=%1.9g (%1.9g, %1.9g) (%1.9g, %1.9g) (%1.9g, %1.9g) t2=%1.9g\n",
__FUNCTION__, tt1, xy1.fX, xy1.fY, iPt.fX,
iPt.fY, xy2.fX, xy2.fY, tt2);
#endif
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(iPt));
REPORTER_ASSERT(reporter, xy2.approximatelyEqual(iPt));
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
}
reporter->bumpTestCount();
}
static void testOneCoincident(skiatest::Reporter* reporter, const SkDLine& line1,
const SkDLine& line2) {
SkASSERT(ValidLine(line1));
SkASSERT(ValidLine(line2));
SkIntersections ts2;
int pts2 = ts2.intersect(line1, line2);
REPORTER_ASSERT(reporter, pts2 == 2);
REPORTER_ASSERT(reporter, pts2 == ts2.used());
check_results(reporter, line1, line2, ts2);
#if 0
SkIntersections ts;
int pts = ts.intersect(line1, line2);
REPORTER_ASSERT(reporter, pts == pts2);
REPORTER_ASSERT(reporter, pts == 2);
REPORTER_ASSERT(reporter, pts == ts.used());
check_results(reporter, line1, line2, ts);
#endif
}
static void PathOpsCubicQuadIntersectionTest(skiatest::Reporter* reporter) {
for (size_t index = 0; index < quadCubicTests_count; ++index) {
int iIndex = static_cast<int>(index);
const SkDCubic& cubic = quadCubicTests[index].cubic;
const SkDQuad& quad = quadCubicTests[index].quad;
SkReduceOrder reduce1;
SkReduceOrder reduce2;
int order1 = reduce1.reduce(cubic, SkReduceOrder::kNo_Quadratics,
SkReduceOrder::kFill_Style);
int order2 = reduce2.reduce(quad, SkReduceOrder::kFill_Style);
if (order1 != 4) {
SkDebugf("[%d] cubic order=%d\n", iIndex, order1);
REPORTER_ASSERT(reporter, 0);
}
if (order2 != 3) {
SkDebugf("[%d] quad order=%d\n", iIndex, order2);
REPORTER_ASSERT(reporter, 0);
}
SkIntersections i;
int roots = i.intersect(cubic, quad);
SkASSERT(roots == quadCubicTests[index].answerCount);
for (int pt = 0; pt < roots; ++pt) {
double tt1 = i[0][pt];
SkDPoint xy1 = cubic.xyAtT(tt1);
double tt2 = i[1][pt];
SkDPoint xy2 = quad.xyAtT(tt2);
if (!xy1.approximatelyEqual(xy2)) {
SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, iIndex, pt, tt1, xy1.fX, xy1.fY, tt2, xy2.fX, xy2.fY);
}
REPORTER_ASSERT(reporter, xy1.approximatelyEqual(xy2));
bool found = false;
for (int idx2 = 0; idx2 < quadCubicTests[index].answerCount; ++idx2) {
found |= quadCubicTests[index].answers[idx2].approximatelyEqual(xy1);
}
REPORTER_ASSERT(reporter, found);
}
reporter->bumpTestCount();
}
}
static void standardTestCases(skiatest::Reporter* reporter) {
bool showSkipped = false;
for (size_t index = 0; index < quadraticTests_count; ++index) {
const SkDQuad& quad1 = quadraticTests[index][0];
SkASSERT(ValidQuad(quad1));
const SkDQuad& quad2 = quadraticTests[index][1];
SkASSERT(ValidQuad(quad2));
SkReduceOrder reduce1, reduce2;
int order1 = reduce1.reduce(quad1);
int order2 = reduce2.reduce(quad2);
if (order1 < 3) {
if (showSkipped) {
SkDebugf("[%d] quad1 order=%d\n", static_cast<int>(index), order1);
}
}
if (order2 < 3) {
if (showSkipped) {
SkDebugf("[%d] quad2 order=%d\n", static_cast<int>(index), order2);
}
}
if (order1 == 3 && order2 == 3) {
SkIntersections intersections;
intersections.intersect(quad1, quad2);
if (intersections.used() > 0) {
for (int pt = 0; pt < intersections.used(); ++pt) {
double tt1 = intersections[0][pt];
SkDPoint xy1 = quad1.ptAtT(tt1);
double tt2 = intersections[1][pt];
SkDPoint xy2 = quad2.ptAtT(tt2);
if (!xy1.approximatelyEqual(xy2)) {
SkDebugf("%s [%d,%d] x!= t1=%g (%g,%g) t2=%g (%g,%g)\n",
__FUNCTION__, static_cast<int>(index), pt, tt1, xy1.fX, xy1.fY,
tt2, xy2.fX, xy2.fY);
REPORTER_ASSERT(reporter, 0);
}
}
}
}
}
}
static void testOne(skiatest::Reporter* reporter, const SkDLine& line1, const SkDLine& line2) {
SkASSERT(ValidLine(line1));
SkASSERT(ValidLine(line2));
SkIntersections i;
int pts = i.intersect(line1, line2);
REPORTER_ASSERT(reporter, pts);
REPORTER_ASSERT(reporter, pts == i.used());
check_results(reporter, line1, line2, i);
if (line1[0] == line1[1] || line2[0] == line2[1]) {
return;
}
if (line1[0].fY == line1[1].fY) {
double left = SkTMin(line1[0].fX, line1[1].fX);
double right = SkTMax(line1[0].fX, line1[1].fX);
SkIntersections ts;
ts.horizontal(line2, left, right, line1[0].fY, line1[0].fX != left);
check_results(reporter, line2, line1, ts);
}
if (line2[0].fY == line2[1].fY) {
double left = SkTMin(line2[0].fX, line2[1].fX);
double right = SkTMax(line2[0].fX, line2[1].fX);
SkIntersections ts;
ts.horizontal(line1, left, right, line2[0].fY, line2[0].fX != left);
check_results(reporter, line1, line2, ts);
}
if (line1[0].fX == line1[1].fX) {
double top = SkTMin(line1[0].fY, line1[1].fY);
double bottom = SkTMax(line1[0].fY, line1[1].fY);
SkIntersections ts;
ts.vertical(line2, top, bottom, line1[0].fX, line1[0].fY != top);
check_results(reporter, line2, line1, ts);
}
if (line2[0].fX == line2[1].fX) {
double top = SkTMin(line2[0].fY, line2[1].fY);
double bottom = SkTMax(line2[0].fY, line2[1].fY);
SkIntersections ts;
ts.vertical(line1, top, bottom, line2[0].fX, line2[0].fY != top);
check_results(reporter, line1, line2, ts);
}
}
static void PathOpsLineIntersectionTest(skiatest::Reporter* reporter) {
size_t index;
for (index = 0; index < coincidentTests_count; ++index) {
const SkDLine& line1 = coincidentTests[index][0];
const SkDLine& line2 = coincidentTests[index][1];
testOneCoincident(reporter, line1, line2);
reporter->bumpTestCount();
}
for (index = 0; index < tests_count; ++index) {
const SkDLine& line1 = tests[index][0];
const SkDLine& line2 = tests[index][1];
testOne(reporter, line1, line2);
reporter->bumpTestCount();
}
for (index = 0; index < noIntersect_count; ++index) {
const SkDLine& line1 = noIntersect[index][0];
const SkDLine& line2 = noIntersect[index][1];
SkIntersections ts;
int pts = ts.intersect(line1, line2);
REPORTER_ASSERT(reporter, !pts);
REPORTER_ASSERT(reporter, pts == ts.used());
reporter->bumpTestCount();
}
}
// intersect the end of the cubic with the other. Try lines from the end to control and opposite
// end to determine range of t on opposite cubic.
static void intersectEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2,
const SkDRect& bounds2, SkIntersections& i) {
SkDLine line;
int t1Index = start ? 0 : 3;
line[0] = cubic1[t1Index];
// don't bother if the two cubics are connnected
SkTDArray<double> tVals; // OPTIMIZE: replace with hard-sized array
for (int index = 0; index < 4; ++index) {
if (index == t1Index) {
continue;
}
SkDVector dxy1 = cubic1[index] - line[0];
dxy1 /= SkDCubic::gPrecisionUnit;
line[1] = line[0] + dxy1;
SkDRect lineBounds;
lineBounds.setBounds(line);
if (!bounds2.intersects(&lineBounds)) {
continue;
}
SkIntersections local;
if (!local.intersect(cubic2, line)) {
continue;
}
for (int idx2 = 0; idx2 < local.used(); ++idx2) {
double foundT = local[0][idx2];
if (approximately_less_than_zero(foundT)
|| approximately_greater_than_one(foundT)) {
continue;
}
if (local.pt(idx2).approximatelyEqual(line[0])) {
if (i.swapped()) { // FIXME: insert should respect swap
i.insert(foundT, start ? 0 : 1, line[0]);
} else {
i.insert(start ? 0 : 1, foundT, line[0]);
}
} else {
*tVals.append() = local[0][idx2];
}
}
}
if (tVals.count() == 0) {
return;
}
QSort<double>(tVals.begin(), tVals.end() - 1);
double tMin1 = start ? 0 : 1 - LINE_FRACTION;
double tMax1 = start ? LINE_FRACTION : 1;
int tIdx = 0;
do {
int tLast = tIdx;
while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) {
++tLast;
}
double tMin2 = SkTMax<double>(tVals[tIdx] - LINE_FRACTION, 0.0);
double tMax2 = SkTMin<double>(tVals[tLast] + LINE_FRACTION, 1.0);
int lastUsed = i.used();
intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
if (lastUsed == i.used()) {
tMin2 = SkTMax<double>(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0);
tMax2 = SkTMin<double>(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0);
intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, i);
}
tIdx = tLast + 1;
} while (tIdx < tVals.count());
return;
}
// determine that slop required after quad/quad finds a candidate intersection
// use the cross of the tangents plus the distance from 1 or 0 as knobs
DEF_TEST(PathOpsCubicQuadSlop, reporter) {
// create a random non-selfintersecting cubic
// break it into quadratics
// offset the quadratic, measuring the slop required to find the intersection
if (!gPathOpCubicQuadSlopVerbose) { // takes a while to run -- so exclude it by default
return;
}
int results[101];
sk_bzero(results, sizeof(results));
double minCross[101];
sk_bzero(minCross, sizeof(minCross));
double maxCross[101];
sk_bzero(maxCross, sizeof(maxCross));
double sumCross[101];
sk_bzero(sumCross, sizeof(sumCross));
int foundOne = 0;
int slopCount = 1;
SkRandom ran;
for (int index = 0; index < 10000000; ++index) {
if (index % 1000 == 999) SkDebugf(".");
SkDCubic cubic = {{
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)},
{ran.nextRangeF(-1000, 1000), ran.nextRangeF(-1000, 1000)}
}};
SkIntersections i;
if (i.intersect(cubic)) {
continue;
}
SkSTArray<kCubicToQuadSubdivisionDepth, double, true> ts;
cubic.toQuadraticTs(cubic.calcPrecision(), &ts);
double tStart = 0;
int tsCount = ts.count();
for (int i1 = 0; i1 <= tsCount; ++i1) {
const double tEnd = i1 < tsCount ? ts[i1] : 1;
SkDCubic part = cubic.subDivide(tStart, tEnd);
SkDQuad quad = part.toQuad();
SkReduceOrder reducer;
int order = reducer.reduce(quad);
if (order != 3) {
continue;
}
for (int i2 = 0; i2 < 100; ++i2) {
SkDPoint endDisplacement = {ran.nextRangeF(-100, 100), ran.nextRangeF(-100, 100)};
SkDQuad nearby = {{
{quad[0].fX + endDisplacement.fX, quad[0].fY + endDisplacement.fY},
{quad[1].fX + ran.nextRangeF(-100, 100), quad[1].fY + ran.nextRangeF(-100, 100)},
{quad[2].fX - endDisplacement.fX, quad[2].fY - endDisplacement.fY}
}};
order = reducer.reduce(nearby);
if (order != 3) {
continue;
}
SkIntersections locals;
locals.allowNear(false);
locals.intersect(quad, nearby);
if (locals.used() != 1) {
continue;
}
// brute force find actual intersection
SkDLine cubicLine = {{ {0, 0}, {cubic[0].fX, cubic[0].fY } }};
SkIntersections liner;
int i3;
int found = -1;
int foundErr = true;
for (i3 = 1; i3 <= 1000; ++i3) {
cubicLine[0] = cubicLine[1];
cubicLine[1] = cubic.ptAtT(i3 / 1000.);
liner.reset();
liner.allowNear(false);
liner.intersect(nearby, cubicLine);
if (liner.used() == 0) {
continue;
}
if (liner.used() > 1) {
foundErr = true;
break;
}
if (found > 0) {
foundErr = true;
break;
}
foundErr = false;
found = i3;
}
if (foundErr) {
continue;
}
SkDVector dist = liner.pt(0) - locals.pt(0);
SkDVector qV = nearby.dxdyAtT(locals[0][0]);
double cubicT = (found - 1 + liner[1][0]) / 1000.;
SkDVector cV = cubic.dxdyAtT(cubicT);
double qxc = qV.crossCheck(cV);
double qvLen = qV.length();
double cvLen = cV.length();
double maxLen = SkTMax(qvLen, cvLen);
qxc /= maxLen;
double quadT = tStart + (tEnd - tStart) * locals[0][0];
double diffT = fabs(cubicT - quadT);
int diffIdx = (int) (diffT * 100);
results[diffIdx]++;
double absQxc = fabs(qxc);
if (sumCross[diffIdx] == 0) {
minCross[diffIdx] = maxCross[diffIdx] = sumCross[diffIdx] = absQxc;
} else {
minCross[diffIdx] = SkTMin(minCross[diffIdx], absQxc);
maxCross[diffIdx] = SkTMax(maxCross[diffIdx], absQxc);
sumCross[diffIdx] += absQxc;
}
if (diffIdx >= 20) {
#if 01
SkDebugf("cubic={{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
" quad={{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
" {{{%1.9g,%1.9g}, {%1.9g,%1.9g}}}"
" qT=%1.9g cT=%1.9g dist=%1.9g cross=%1.9g\n",
cubic[0].fX, cubic[0].fY, cubic[1].fX, cubic[1].fY,
cubic[2].fX, cubic[2].fY, cubic[3].fX, cubic[3].fY,
nearby[0].fX, nearby[0].fY, nearby[1].fX, nearby[1].fY,
nearby[2].fX, nearby[2].fY,
liner.pt(0).fX, liner.pt(0).fY,
locals.pt(0).fX, locals.pt(0).fY, quadT, cubicT, dist.length(), qxc);
#else
SkDebugf("qT=%1.9g cT=%1.9g dist=%1.9g cross=%1.9g\n",
quadT, cubicT, dist.length(), qxc);
SkDebugf("<div id=\"slop%d\">\n", ++slopCount);
SkDebugf("{{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n"
"{{{%1.9g,%1.9g}, {%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n"
"{{{%1.9g,%1.9g}, {%1.9g,%1.9g}}}\n",
cubic[0].fX, cubic[0].fY, cubic[1].fX, cubic[1].fY,
cubic[2].fX, cubic[2].fY, cubic[3].fX, cubic[3].fY,
nearby[0].fX, nearby[0].fY, nearby[1].fX, nearby[1].fY,
nearby[2].fX, nearby[2].fY,
liner.pt(0).fX, liner.pt(0).fY,
locals.pt(0).fX, locals.pt(0).fY);
SkDebugf("</div>\n\n");
#endif
}
++foundOne;
}
tStart = tEnd;
}
if (++foundOne >= 100000) {
break;
}
}
#if 01
SkDebugf("slopCount=%d\n", slopCount);
int max = 100;
while (results[max] == 0) {
--max;
}
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%d ", results[i]);
}
SkDebugf("min\n");
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%1.9g ", minCross[i]);
}
SkDebugf("max\n");
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%1.9g ", maxCross[i]);
}
SkDebugf("avg\n");
for (int i = 0; i <= max; ++i) {
if (i > 0 && i % 10 == 0) {
SkDebugf("\n");
}
SkDebugf("%1.9g ", sumCross[i] / results[i]);
}
#else
for (int i = 1; i < slopCount; ++i) {
SkDebugf(" slop%d,\n", i);
}
#endif
SkDebugf("\n");
}
void SkIntersections::cubicNearEnd(const SkDCubic& cubic1, bool start, const SkDCubic& cubic2,
const SkDRect& bounds2) {
SkDLine line;
int t1Index = start ? 0 : 3;
double testT = (double) !start;
// don't bother if the two cubics are connnected
static const int kPointsInCubic = 4; // FIXME: move to DCubic, replace '4' with this
static const int kMaxLineCubicIntersections = 3;
SkSTArray<(kMaxLineCubicIntersections - 1) * kMaxLineCubicIntersections, double, true> tVals;
line[0] = cubic1[t1Index];
// this variant looks for intersections with the end point and lines parallel to other points
for (int index = 0; index < kPointsInCubic; ++index) {
if (index == t1Index) {
continue;
}
SkDVector dxy1 = cubic1[index] - line[0];
dxy1 /= SkDCubic::gPrecisionUnit;
line[1] = line[0] + dxy1;
SkDRect lineBounds;
lineBounds.setBounds(line);
if (!bounds2.intersects(&lineBounds)) {
continue;
}
SkIntersections local;
if (!local.intersect(cubic2, line)) {
continue;
}
for (int idx2 = 0; idx2 < local.used(); ++idx2) {
double foundT = local[0][idx2];
if (approximately_less_than_zero(foundT)
|| approximately_greater_than_one(foundT)) {
continue;
}
if (local.pt(idx2).approximatelyEqual(line[0])) {
if (swapped()) { // FIXME: insert should respect swap
insert(foundT, testT, line[0]);
} else {
insert(testT, foundT, line[0]);
}
} else {
tVals.push_back(foundT);
}
}
}
if (tVals.count() == 0) {
return;
}
SkTQSort<double>(tVals.begin(), tVals.end() - 1);
double tMin1 = start ? 0 : 1 - LINE_FRACTION;
double tMax1 = start ? LINE_FRACTION : 1;
int tIdx = 0;
do {
int tLast = tIdx;
while (tLast + 1 < tVals.count() && roughly_equal(tVals[tLast + 1], tVals[tIdx])) {
++tLast;
}
double tMin2 = SkTMax(tVals[tIdx] - LINE_FRACTION, 0.0);
double tMax2 = SkTMin(tVals[tLast] + LINE_FRACTION, 1.0);
int lastUsed = used();
if (start ? tMax1 < tMin2 : tMax2 < tMin1) {
::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
}
if (lastUsed == used()) {
tMin2 = SkTMax(tVals[tIdx] - (1.0 / SkDCubic::gPrecisionUnit), 0.0);
tMax2 = SkTMin(tVals[tLast] + (1.0 / SkDCubic::gPrecisionUnit), 1.0);
if (start ? tMax1 < tMin2 : tMax2 < tMin1) {
::intersect(cubic1, tMin1, tMax1, cubic2, tMin2, tMax2, 1, *this);
}
}
tIdx = tLast + 1;
} while (tIdx < tVals.count());
return;
}
static bool is_linear_inner(const SkDQuad& q1, double t1s, double t1e, const SkDQuad& q2,
double t2s, double t2e, SkIntersections* i, bool* subDivide) {
SkDQuad hull = q1.subDivide(t1s, t1e);
SkDLine line = {{hull[2], hull[0]}};
const SkDLine* testLines[] = { &line, (const SkDLine*) &hull[0], (const SkDLine*) &hull[1] };
const size_t kTestCount = SK_ARRAY_COUNT(testLines);
SkSTArray<kTestCount * 2, double, true> tsFound;
for (size_t index = 0; index < kTestCount; ++index) {
SkIntersections rootTs;
rootTs.allowNear(false);
int roots = rootTs.intersect(q2, *testLines[index]);
for (int idx2 = 0; idx2 < roots; ++idx2) {
double t = rootTs[0][idx2];
#ifdef SK_DEBUG
SkDPoint qPt = q2.ptAtT(t);
SkDPoint lPt = testLines[index]->ptAtT(rootTs[1][idx2]);
SkASSERT(qPt.approximatelyEqual(lPt));
#endif
if (approximately_negative(t - t2s) || approximately_positive(t - t2e)) {
continue;
}
tsFound.push_back(rootTs[0][idx2]);
}
}
int tCount = tsFound.count();
if (tCount <= 0) {
return true;
}
double tMin, tMax;
if (tCount == 1) {
tMin = tMax = tsFound[0];
} else {
SkASSERT(tCount > 1);
SkTQSort<double>(tsFound.begin(), tsFound.end() - 1);
tMin = tsFound[0];
tMax = tsFound[tsFound.count() - 1];
}
SkDPoint end = q2.ptAtT(t2s);
bool startInTriangle = hull.pointInHull(end);
if (startInTriangle) {
tMin = t2s;
}
end = q2.ptAtT(t2e);
bool endInTriangle = hull.pointInHull(end);
if (endInTriangle) {
tMax = t2e;
}
int split = 0;
SkDVector dxy1, dxy2;
if (tMin != tMax || tCount > 2) {
dxy2 = q2.dxdyAtT(tMin);
for (int index = 1; index < tCount; ++index) {
dxy1 = dxy2;
dxy2 = q2.dxdyAtT(tsFound[index]);
double dot = dxy1.dot(dxy2);
if (dot < 0) {
split = index - 1;
break;
}
}
}
if (split == 0) { // there's one point
if (add_intercept(q1, q2, tMin, tMax, i, subDivide)) {
return true;
}
i->swap();
return is_linear_inner(q2, tMin, tMax, q1, t1s, t1e, i, subDivide);
}
// At this point, we have two ranges of t values -- treat each separately at the split
bool result;
if (add_intercept(q1, q2, tMin, tsFound[split - 1], i, subDivide)) {
result = true;
} else {
i->swap();
result = is_linear_inner(q2, tMin, tsFound[split - 1], q1, t1s, t1e, i, subDivide);
}
if (add_intercept(q1, q2, tsFound[split], tMax, i, subDivide)) {
result = true;
} else {
i->swap();
result |= is_linear_inner(q2, tsFound[split], tMax, q1, t1s, t1e, i, subDivide);
}
return result;
}
