static void standardTestCases(skiatest::Reporter* reporter) {
size_t index;
SkReduceOrder reducer;
int order;
enum {
RunAll,
RunQuadraticLines,
RunQuadraticModLines,
RunNone
} run = RunAll;
int firstTestIndex = 0;
#if 0
run = RunQuadraticLines;
firstTestIndex = 1;
#endif
int firstQuadraticLineTest = run == RunAll ? 0 : run == RunQuadraticLines ? firstTestIndex
: SK_MaxS32;
int firstQuadraticModLineTest = run == RunAll ? 0 : run == RunQuadraticModLines ? firstTestIndex
: SK_MaxS32;
for (index = firstQuadraticLineTest; index < quadraticLines_count; ++index) {
const SkDQuad& quad = quadraticLines[index];
order = reducer.reduce(quad);
if (order != 2) {
SkDebugf("[%d] line quad order=%d\n", (int) index, order);
}
}
for (index = firstQuadraticModLineTest; index < quadraticModEpsilonLines_count; ++index) {
const SkDQuad& quad = quadraticModEpsilonLines[index];
order = reducer.reduce(quad);
if (order != 2 && order != 3) { // FIXME: data probably is not good
SkDebugf("[%d] line mod quad order=%d\n", (int) index, order);
}
}
}
static void oneOffTest(skiatest::Reporter* reporter) {
for (size_t index = 0; index < testSetCount; ++index) {
const SkDQuad& quad = testSet[index];
SkReduceOrder reducer;
SkDEBUGCODE(int result = ) reducer.reduce(quad);
SkASSERT(result == 3);
}
}
SkPath::Verb SkReduceOrder::Cubic(const SkPoint a[4], SkPoint* reducePts) {
SkDCubic cubic;
cubic.set(a);
SkReduceOrder reducer;
int order = reducer.reduce(cubic, kAllow_Quadratics);
if (order == 2 || order == 3) { // cubic became line or quad
for (int index = 0; index < order; ++index) {
*reducePts++ = reducer.fQuad[index].asSkPoint();
}
}
return SkPathOpsPointsToVerb(order - 1);
}
SkPath::Verb SkReduceOrder::Quad(const SkPoint a[3], SkPoint* reducePts) {
SkDQuad quad;
quad.set(a);
SkReduceOrder reducer;
int order = reducer.reduce(quad);
if (order == 2) { // quad became line
for (int index = 0; index < order; ++index) {
*reducePts++ = reducer.fLine[index].asSkPoint();
}
}
return SkPathOpsPointsToVerb(order - 1);
}
DEF_TEST(PathOpsConicLineIntersection, reporter) {
for (size_t index = 0; index < lineConicTests_count; ++index) {
int iIndex = static_cast<int>(index);
const SkDConic& conic = lineConicTests[index].conic;
SkASSERT(ValidConic(conic));
const SkDLine& line = lineConicTests[index].line;
SkASSERT(ValidLine(line));
SkReduceOrder reducer;
SkPoint pts[3] = { conic.fPts.fPts[0].asSkPoint(), conic.fPts.fPts[1].asSkPoint(),
conic.fPts.fPts[2].asSkPoint() };
SkPoint reduced[3];
SkPath::Verb order1 = SkReduceOrder::Conic(pts, conic.fWeight, reduced);
if (order1 != SkPath::kConic_Verb) {
SkDebugf("%s [%d] conic verb=%d\n", __FUNCTION__, iIndex, order1);
REPORTER_ASSERT(reporter, 0);
}
int order2 = reducer.reduce(line);
if (order2 < 2) {
SkDebugf("%s [%d] line order=%d\n", __FUNCTION__, iIndex, order2);
REPORTER_ASSERT(reporter, 0);
}
SkIntersections intersections;
bool flipped = false;
int result = doIntersect(intersections, conic, line, flipped);
REPORTER_ASSERT(reporter, result == lineConicTests[index].result);
if (intersections.used() <= 0) {
continue;
}
for (int pt = 0; pt < result; ++pt) {
double tt1 = intersections[0][pt];
REPORTER_ASSERT(reporter, tt1 >= 0 && tt1 <= 1);
SkDPoint t1 = conic.ptAtT(tt1);
double tt2 = intersections[1][pt];
REPORTER_ASSERT(reporter, tt2 >= 0 && tt2 <= 1);
SkDPoint t2 = line.ptAtT(tt2);
if (!t1.approximatelyEqual(t2)) {
SkDebugf("%s [%d,%d] x!= t1=%1.9g (%1.9g,%1.9g) t2=%1.9g (%1.9g,%1.9g)\n",
__FUNCTION__, iIndex, pt, tt1, t1.fX, t1.fY, tt2, t2.fX, t2.fY);
REPORTER_ASSERT(reporter, 0);
}
if (!t1.approximatelyEqual(lineConicTests[index].expected[0])
&& (lineConicTests[index].result == 1
|| !t1.approximatelyEqual(lineConicTests[index].expected[1]))) {
SkDebugf("%s t1=(%1.9g,%1.9g)\n", __FUNCTION__, t1.fX, t1.fY);
REPORTER_ASSERT(reporter, 0);
}
}
}
}
SkPath::Verb SkReduceOrder::Cubic(const SkPoint a[4], SkPoint* reducePts) {
if (SkDPoint::ApproximatelyEqual(a[0], a[1]) && SkDPoint::ApproximatelyEqual(a[0], a[2])
&& SkDPoint::ApproximatelyEqual(a[0], a[3])) {
reducePts[0] = a[0];
return SkPath::kMove_Verb;
}
SkDCubic cubic;
cubic.set(a);
SkReduceOrder reducer;
int order = reducer.reduce(cubic, kAllow_Quadratics);
if (order == 2 || order == 3) { // cubic became line or quad
for (int index = 0; index < order; ++index) {
*reducePts++ = reducer.fQuad[index].asSkPoint();
}
}
return SkPathOpsPointsToVerb(order - 1);
}
// find a point on a quad by choosing a t from 0 to 1
// create a vertical span above and below the point
// verify that intersecting the vertical span and the quad returns t
// verify that a vertical span starting at quad[0] intersects at t=0
// verify that a vertical span starting at quad[2] intersects at t=1
static void testQuadLineIntersectMain(PathOpsThreadState* data)
{
PathOpsThreadState& state = *data;
REPORTER_ASSERT(state.fReporter, data);
int ax = state.fA & 0x03;
int ay = state.fA >> 2;
int bx = state.fB & 0x03;
int by = state.fB >> 2;
int cx = state.fC & 0x03;
int cy = state.fC >> 2;
SkDQuad quad = {{{(double) ax, (double) ay}, {(double) bx, (double) by},
{(double) cx, (double) cy}
}
};
SkReduceOrder reducer;
int order = reducer.reduce(quad);
if (order < 3) {
return;
}
for (int tIndex = 0; tIndex <= 4; ++tIndex) {
SkDPoint xy = quad.ptAtT(tIndex / 4.0);
for (int h = -2; h <= 2; ++h) {
for (int v = -2; v <= 2; ++v) {
if (h == v && abs(h) != 1) {
continue;
}
double x = xy.fX;
double y = xy.fY;
SkDLine line = {{{x - h, y - v}, {x, y}}};
testLineIntersect(state.fReporter, quad, line, x, y);
state.fReporter->bumpTestCount();
SkDLine line2 = {{{x, y}, {x + h, y + v}}};
testLineIntersect(state.fReporter, quad, line2, x, y);
state.fReporter->bumpTestCount();
SkDLine line3 = {{{x - h, y - v}, {x + h, y + v}}};
testLineIntersect(state.fReporter, quad, line3, x, y);
state.fReporter->bumpTestCount();
}
}
}
}
// 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");
}
// flavor that returns T values only, deferring computing the quads until they are needed
// FIXME: when called from recursive intersect 2, this could take the original cubic
// and do a more precise job when calling chop at and sub divide by computing the fractional ts.
// it would still take the prechopped cubic for reduce order and find cubic inflections
void SkDCubic::toQuadraticTs(double precision, SkTDArray<double>* ts) const {
SkReduceOrder reducer;
int order = reducer.reduce(*this, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
if (order < 3) {
return;
}
double inflectT[5];
int inflections = findInflections(inflectT);
SkASSERT(inflections <= 2);
if (!endsAreExtremaInXOrY()) {
inflections += findMaxCurvature(&inflectT[inflections]);
SkASSERT(inflections <= 5);
}
QSort<double>(inflectT, &inflectT[inflections - 1]);
// OPTIMIZATION: is this filtering common enough that it needs to be pulled out into its
// own subroutine?
while (inflections && approximately_less_than_zero(inflectT[0])) {
memmove(inflectT, &inflectT[1], sizeof(inflectT[0]) * --inflections);
}
int start = 0;
do {
int next = start + 1;
if (next >= inflections) {
break;
}
if (!approximately_equal(inflectT[start], inflectT[next])) {
++start;
continue;
}
memmove(&inflectT[start], &inflectT[next], sizeof(inflectT[0]) * (--inflections - start));
} while (true);
while (inflections && approximately_greater_than_one(inflectT[inflections - 1])) {
--inflections;
}
SkDCubicPair pair;
if (inflections == 1) {
pair = chopAt(inflectT[0]);
int orderP1 = reducer.reduce(pair.first(), SkReduceOrder::kNo_Quadratics,
SkReduceOrder::kFill_Style);
if (orderP1 < 2) {
--inflections;
} else {
int orderP2 = reducer.reduce(pair.second(), SkReduceOrder::kNo_Quadratics,
SkReduceOrder::kFill_Style);
if (orderP2 < 2) {
--inflections;
}
}
}
if (inflections == 0 && add_simple_ts(*this, precision, ts)) {
return;
}
if (inflections == 1) {
pair = chopAt(inflectT[0]);
addTs(pair.first(), precision, 0, inflectT[0], ts);
addTs(pair.second(), precision, inflectT[0], 1, ts);
return;
}
if (inflections > 1) {
SkDCubic part = subDivide(0, inflectT[0]);
addTs(part, precision, 0, inflectT[0], ts);
int last = inflections - 1;
for (int idx = 0; idx < last; ++idx) {
part = subDivide(inflectT[idx], inflectT[idx + 1]);
addTs(part, precision, inflectT[idx], inflectT[idx + 1], ts);
}
part = subDivide(inflectT[last], 1);
addTs(part, precision, inflectT[last], 1, ts);
return;
}
addTs(*this, precision, 0, 1, ts);
}
