static void TestGeometry(skiatest::Reporter* reporter) {
SkPoint pts[3], dst[5];
pts[0].set(0, 0);
pts[1].set(100, 50);
pts[2].set(0, 100);
int count = SkChopQuadAtMaxCurvature(pts, dst);
REPORTER_ASSERT(reporter, count == 1 || count == 2);
pts[0].set(0, 0);
pts[1].set(SkIntToScalar(3), 0);
pts[2].set(SkIntToScalar(3), SkIntToScalar(3));
SkConvertQuadToCubic(pts, dst);
const SkPoint cubic[] = {
{ 0, 0, },
{ SkIntToScalar(2), 0, },
{ SkIntToScalar(3), SkIntToScalar(1), },
{ SkIntToScalar(3), SkIntToScalar(3) },
};
for (int i = 0; i < 4; ++i) {
REPORTER_ASSERT(reporter, nearly_equal(cubic[i], dst[i]));
}
testChopCubic(reporter);
}
DEF_TEST(Geometry, reporter) {
SkPoint pts[3], dst[5];
pts[0].set(0, 0);
pts[1].set(100, 50);
pts[2].set(0, 100);
int count = SkChopQuadAtMaxCurvature(pts, dst);
REPORTER_ASSERT(reporter, count == 1 || count == 2);
pts[0].set(0, 0);
pts[1].set(3, 0);
pts[2].set(3, 3);
SkConvertQuadToCubic(pts, dst);
const SkPoint cubic[] = {
{ 0, 0, }, { 2, 0, }, { 3, 1, }, { 3, 3 },
};
for (int i = 0; i < 4; ++i) {
REPORTER_ASSERT(reporter, nearly_equal(cubic[i], dst[i]));
}
testChopCubic(reporter);
test_evalquadat(reporter);
test_conic(reporter);
test_cubic_tangents(reporter);
test_quad_tangents(reporter);
test_conic_tangents(reporter);
}
void SkPathStroker::quadTo(const SkPoint& pt1, const SkPoint& pt2) {
bool degenerateAB = SkPath::IsLineDegenerate(fPrevPt, pt1);
bool degenerateBC = SkPath::IsLineDegenerate(pt1, pt2);
if (degenerateAB | degenerateBC) {
if (degenerateAB ^ degenerateBC) {
this->lineTo(pt2);
}
return;
}
SkVector normalAB, unitAB, normalBC, unitBC;
this->preJoinTo(pt1, &normalAB, &unitAB, false);
{
SkPoint pts[3], tmp[5];
pts[0] = fPrevPt;
pts[1] = pt1;
pts[2] = pt2;
if (SkChopQuadAtMaxCurvature(pts, tmp) == 2) {
unitBC.setNormalize(pts[2].fX - pts[1].fX, pts[2].fY - pts[1].fY);
unitBC.rotateCCW();
if (normals_too_pinchy(unitAB, unitBC)) {
normalBC = unitBC;
normalBC.scale(fRadius);
fOuter.lineTo(tmp[2].fX + normalAB.fX, tmp[2].fY + normalAB.fY);
fOuter.lineTo(tmp[2].fX + normalBC.fX, tmp[2].fY + normalBC.fY);
fOuter.lineTo(tmp[4].fX + normalBC.fX, tmp[4].fY + normalBC.fY);
fInner.lineTo(tmp[2].fX - normalAB.fX, tmp[2].fY - normalAB.fY);
fInner.lineTo(tmp[2].fX - normalBC.fX, tmp[2].fY - normalBC.fY);
fInner.lineTo(tmp[4].fX - normalBC.fX, tmp[4].fY - normalBC.fY);
fExtra.addCircle(tmp[2].fX, tmp[2].fY, fRadius,
SkPath::kCW_Direction);
} else {
this->quad_to(&tmp[0], normalAB, unitAB, &normalBC, &unitBC,
kMaxQuadSubdivide);
SkVector n = normalBC;
SkVector u = unitBC;
this->quad_to(&tmp[2], n, u, &normalBC, &unitBC,
kMaxQuadSubdivide);
}
} else {
this->quad_to(pts, normalAB, unitAB, &normalBC, &unitBC,
kMaxQuadSubdivide);
}
}
this->postJoinTo(pt2, normalBC, unitBC);
}
/**
* Generates the lines and quads to be rendered. Lines are always recorded in
* device space. We will do a device space bloat to account for the 1pixel
* thickness.
* Quads are recorded in device space unless m contains
* perspective, then in they are in src space. We do this because we will
* subdivide large quads to reduce over-fill. This subdivision has to be
* performed before applying the perspective matrix.
*/
static int gather_lines_and_quads(const SkPath& path,
const SkMatrix& m,
const SkIRect& devClipBounds,
GrAAHairLinePathRenderer::PtArray* lines,
GrAAHairLinePathRenderer::PtArray* quads,
GrAAHairLinePathRenderer::PtArray* conics,
GrAAHairLinePathRenderer::IntArray* quadSubdivCnts,
GrAAHairLinePathRenderer::FloatArray* conicWeights) {
SkPath::Iter iter(path, false);
int totalQuadCount = 0;
SkRect bounds;
SkIRect ibounds;
bool persp = m.hasPerspective();
for (;;) {
SkPoint pathPts[4];
SkPoint devPts[4];
SkPath::Verb verb = iter.next(pathPts);
switch (verb) {
case SkPath::kConic_Verb: {
SkConic dst[4];
// We chop the conics to create tighter clipping to hide error
// that appears near max curvature of very thin conics. Thin
// hyperbolas with high weight still show error.
int conicCnt = chop_conic(pathPts, dst, iter.conicWeight());
for (int i = 0; i < conicCnt; ++i) {
SkPoint* chopPnts = dst[i].fPts;
m.mapPoints(devPts, chopPnts, 3);
bounds.setBounds(devPts, 3);
bounds.outset(SK_Scalar1, SK_Scalar1);
bounds.roundOut(&ibounds);
if (SkIRect::Intersects(devClipBounds, ibounds)) {
if (is_degen_quad_or_conic(devPts)) {
SkPoint* pts = lines->push_back_n(4);
pts[0] = devPts[0];
pts[1] = devPts[1];
pts[2] = devPts[1];
pts[3] = devPts[2];
} else {
// when in perspective keep conics in src space
SkPoint* cPts = persp ? chopPnts : devPts;
SkPoint* pts = conics->push_back_n(3);
pts[0] = cPts[0];
pts[1] = cPts[1];
pts[2] = cPts[2];
conicWeights->push_back() = dst[i].fW;
}
}
}
break;
}
case SkPath::kMove_Verb:
break;
case SkPath::kLine_Verb:
m.mapPoints(devPts, pathPts, 2);
bounds.setBounds(devPts, 2);
bounds.outset(SK_Scalar1, SK_Scalar1);
bounds.roundOut(&ibounds);
if (SkIRect::Intersects(devClipBounds, ibounds)) {
SkPoint* pts = lines->push_back_n(2);
pts[0] = devPts[0];
pts[1] = devPts[1];
}
break;
case SkPath::kQuad_Verb: {
SkPoint choppedPts[5];
// Chopping the quad helps when the quad is either degenerate or nearly degenerate.
// When it is degenerate it allows the approximation with lines to work since the
// chop point (if there is one) will be at the parabola's vertex. In the nearly
// degenerate the QuadUVMatrix computed for the points is almost singular which
// can cause rendering artifacts.
int n = SkChopQuadAtMaxCurvature(pathPts, choppedPts);
for (int i = 0; i < n; ++i) {
SkPoint* quadPts = choppedPts + i * 2;
m.mapPoints(devPts, quadPts, 3);
bounds.setBounds(devPts, 3);
bounds.outset(SK_Scalar1, SK_Scalar1);
bounds.roundOut(&ibounds);
if (SkIRect::Intersects(devClipBounds, ibounds)) {
int subdiv = num_quad_subdivs(devPts);
SkASSERT(subdiv >= -1);
if (-1 == subdiv) {
SkPoint* pts = lines->push_back_n(4);
pts[0] = devPts[0];
pts[1] = devPts[1];
pts[2] = devPts[1];
pts[3] = devPts[2];
} else {
// when in perspective keep quads in src space
SkPoint* qPts = persp ? quadPts : devPts;
SkPoint* pts = quads->push_back_n(3);
pts[0] = qPts[0];
pts[1] = qPts[1];
pts[2] = qPts[2];
quadSubdivCnts->push_back() = subdiv;
totalQuadCount += 1 << subdiv;
}
}
}
break;
}
case SkPath::kCubic_Verb:
m.mapPoints(devPts, pathPts, 4);
bounds.setBounds(devPts, 4);
bounds.outset(SK_Scalar1, SK_Scalar1);
bounds.roundOut(&ibounds);
if (SkIRect::Intersects(devClipBounds, ibounds)) {
PREALLOC_PTARRAY(32) q;
// we don't need a direction if we aren't constraining the subdivision
const SkPathPriv::FirstDirection kDummyDir = SkPathPriv::kCCW_FirstDirection;
// We convert cubics to quadratics (for now).
// In perspective have to do conversion in src space.
if (persp) {
SkScalar tolScale =
GrPathUtils::scaleToleranceToSrc(SK_Scalar1, m,
path.getBounds());
GrPathUtils::convertCubicToQuads(pathPts, tolScale, false, kDummyDir, &q);
} else {
GrPathUtils::convertCubicToQuads(devPts, SK_Scalar1, false, kDummyDir, &q);
}
for (int i = 0; i < q.count(); i += 3) {
SkPoint* qInDevSpace;
// bounds has to be calculated in device space, but q is
// in src space when there is perspective.
if (persp) {
m.mapPoints(devPts, &q[i], 3);
bounds.setBounds(devPts, 3);
qInDevSpace = devPts;
} else {
bounds.setBounds(&q[i], 3);
qInDevSpace = &q[i];
}
bounds.outset(SK_Scalar1, SK_Scalar1);
bounds.roundOut(&ibounds);
if (SkIRect::Intersects(devClipBounds, ibounds)) {
int subdiv = num_quad_subdivs(qInDevSpace);
SkASSERT(subdiv >= -1);
if (-1 == subdiv) {
SkPoint* pts = lines->push_back_n(4);
// lines should always be in device coords
pts[0] = qInDevSpace[0];
pts[1] = qInDevSpace[1];
pts[2] = qInDevSpace[1];
pts[3] = qInDevSpace[2];
} else {
SkPoint* pts = quads->push_back_n(3);
// q is already in src space when there is no
// perspective and dev coords otherwise.
pts[0] = q[0 + i];
pts[1] = q[1 + i];
pts[2] = q[2 + i];
quadSubdivCnts->push_back() = subdiv;
totalQuadCount += 1 << subdiv;
}
}
}
}
break;
case SkPath::kClose_Verb:
break;
case SkPath::kDone_Verb:
return totalQuadCount;
}
}
}
bool SkOpEdgeBuilder::walk() {
uint8_t* verbPtr = fPathVerbs.begin();
uint8_t* endOfFirstHalf = &verbPtr[fSecondHalf];
SkPoint* pointsPtr = fPathPts.begin() - 1;
SkScalar* weightPtr = fWeights.begin();
SkPath::Verb verb;
while ((verb = (SkPath::Verb) *verbPtr) != SkPath::kDone_Verb) {
if (verbPtr == endOfFirstHalf) {
fOperand = true;
}
verbPtr++;
switch (verb) {
case SkPath::kMove_Verb:
if (fCurrentContour && fCurrentContour->count()) {
if (fAllowOpenContours) {
complete();
} else if (!close()) {
return false;
}
}
if (!fCurrentContour) {
fCurrentContour = fContoursHead->appendContour();
}
fCurrentContour->init(fGlobalState, fOperand,
fXorMask[fOperand] == kEvenOdd_PathOpsMask);
pointsPtr += 1;
continue;
case SkPath::kLine_Verb:
fCurrentContour->addLine(pointsPtr);
break;
case SkPath::kQuad_Verb:
{
SkVector v1 = pointsPtr[1] - pointsPtr[0];
SkVector v2 = pointsPtr[2] - pointsPtr[1];
if (v1.dot(v2) < 0) {
SkPoint pair[5];
if (SkChopQuadAtMaxCurvature(pointsPtr, pair) == 1) {
goto addOneQuad;
}
if (!SkScalarsAreFinite(&pair[0].fX, SK_ARRAY_COUNT(pair) * 2)) {
return false;
}
SkPoint cStorage[2][2];
SkPath::Verb v1 = SkReduceOrder::Quad(&pair[0], cStorage[0]);
SkPath::Verb v2 = SkReduceOrder::Quad(&pair[2], cStorage[1]);
SkPoint* curve1 = v1 != SkPath::kLine_Verb ? &pair[0] : cStorage[0];
SkPoint* curve2 = v2 != SkPath::kLine_Verb ? &pair[2] : cStorage[1];
if (can_add_curve(v1, curve1) && can_add_curve(v2, curve2)) {
fCurrentContour->addCurve(v1, curve1);
fCurrentContour->addCurve(v2, curve2);
break;
}
}
}
addOneQuad:
fCurrentContour->addQuad(pointsPtr);
break;
case SkPath::kConic_Verb: {
SkVector v1 = pointsPtr[1] - pointsPtr[0];
SkVector v2 = pointsPtr[2] - pointsPtr[1];
SkScalar weight = *weightPtr++;
if (v1.dot(v2) < 0) {
// FIXME: max curvature for conics hasn't been implemented; use placeholder
SkScalar maxCurvature = SkFindQuadMaxCurvature(pointsPtr);
if (maxCurvature > 0) {
SkConic conic(pointsPtr, weight);
SkConic pair[2];
if (!conic.chopAt(maxCurvature, pair)) {
// if result can't be computed, use original
fCurrentContour->addConic(pointsPtr, weight);
break;
}
SkPoint cStorage[2][3];
SkPath::Verb v1 = SkReduceOrder::Conic(pair[0], cStorage[0]);
SkPath::Verb v2 = SkReduceOrder::Conic(pair[1], cStorage[1]);
SkPoint* curve1 = v1 != SkPath::kLine_Verb ? pair[0].fPts : cStorage[0];
SkPoint* curve2 = v2 != SkPath::kLine_Verb ? pair[1].fPts : cStorage[1];
if (can_add_curve(v1, curve1) && can_add_curve(v2, curve2)) {
fCurrentContour->addCurve(v1, curve1, pair[0].fW);
fCurrentContour->addCurve(v2, curve2, pair[1].fW);
break;
}
}
}
fCurrentContour->addConic(pointsPtr, weight);
} break;
case SkPath::kCubic_Verb:
{
// Split complex cubics (such as self-intersecting curves or
// ones with difficult curvature) in two before proceeding.
// This can be required for intersection to succeed.
SkScalar splitT;
if (SkDCubic::ComplexBreak(pointsPtr, &splitT)) {
SkPoint pair[7];
SkChopCubicAt(pointsPtr, pair, splitT);
if (!SkScalarsAreFinite(&pair[0].fX, SK_ARRAY_COUNT(pair) * 2)) {
return false;
}
SkPoint cStorage[2][4];
SkPath::Verb v1 = SkReduceOrder::Cubic(&pair[0], cStorage[0]);
SkPath::Verb v2 = SkReduceOrder::Cubic(&pair[3], cStorage[1]);
SkPoint* curve1 = v1 == SkPath::kCubic_Verb ? &pair[0] : cStorage[0];
SkPoint* curve2 = v2 == SkPath::kCubic_Verb ? &pair[3] : cStorage[1];
if (can_add_curve(v1, curve1) && can_add_curve(v2, curve2)) {
fCurrentContour->addCurve(v1, curve1);
fCurrentContour->addCurve(v2, curve2);
break;
}
}
}
fCurrentContour->addCubic(pointsPtr);
break;
case SkPath::kClose_Verb:
SkASSERT(fCurrentContour);
if (!close()) {
return false;
}
continue;
default:
SkDEBUGFAIL("bad verb");
return false;
}
SkASSERT(fCurrentContour);
fCurrentContour->debugValidate();
pointsPtr += SkPathOpsVerbToPoints(verb);
}
if (fCurrentContour && fCurrentContour->count() &&!fAllowOpenContours && !close()) {
return false;
}
return true;
}
bool SkOpEdgeBuilder::walk() {
uint8_t* verbPtr = fPathVerbs.begin();
uint8_t* endOfFirstHalf = &verbPtr[fSecondHalf];
SkPoint* pointsPtr = fPathPts.begin() - 1;
SkScalar* weightPtr = fWeights.begin();
SkPath::Verb verb;
SkOpContour* contour = fContourBuilder.contour();
while ((verb = (SkPath::Verb) *verbPtr) != SkPath::kDone_Verb) {
if (verbPtr == endOfFirstHalf) {
fOperand = true;
}
verbPtr++;
switch (verb) {
case SkPath::kMove_Verb:
if (contour && contour->count()) {
if (fAllowOpenContours) {
complete();
} else if (!close()) {
return false;
}
}
if (!contour) {
fContourBuilder.setContour(contour = fContoursHead->appendContour());
}
contour->init(fGlobalState, fOperand,
fXorMask[fOperand] == kEvenOdd_PathOpsMask);
pointsPtr += 1;
continue;
case SkPath::kLine_Verb:
fContourBuilder.addLine(pointsPtr);
break;
case SkPath::kQuad_Verb:
{
SkVector v1 = pointsPtr[1] - pointsPtr[0];
SkVector v2 = pointsPtr[2] - pointsPtr[1];
if (v1.dot(v2) < 0) {
SkPoint pair[5];
if (SkChopQuadAtMaxCurvature(pointsPtr, pair) == 1) {
goto addOneQuad;
}
if (!SkScalarsAreFinite(&pair[0].fX, SK_ARRAY_COUNT(pair) * 2)) {
return false;
}
for (unsigned index = 0; index < SK_ARRAY_COUNT(pair); ++index) {
force_small_to_zero(&pair[index]);
}
SkPoint cStorage[2][2];
SkPath::Verb v1 = SkReduceOrder::Quad(&pair[0], cStorage[0]);
SkPath::Verb v2 = SkReduceOrder::Quad(&pair[2], cStorage[1]);
SkPoint* curve1 = v1 != SkPath::kLine_Verb ? &pair[0] : cStorage[0];
SkPoint* curve2 = v2 != SkPath::kLine_Verb ? &pair[2] : cStorage[1];
if (can_add_curve(v1, curve1) && can_add_curve(v2, curve2)) {
fContourBuilder.addCurve(v1, curve1);
fContourBuilder.addCurve(v2, curve2);
break;
}
}
}
addOneQuad:
fContourBuilder.addQuad(pointsPtr);
break;
case SkPath::kConic_Verb: {
SkVector v1 = pointsPtr[1] - pointsPtr[0];
SkVector v2 = pointsPtr[2] - pointsPtr[1];
SkScalar weight = *weightPtr++;
if (v1.dot(v2) < 0) {
// FIXME: max curvature for conics hasn't been implemented; use placeholder
SkScalar maxCurvature = SkFindQuadMaxCurvature(pointsPtr);
if (maxCurvature > 0) {
SkConic conic(pointsPtr, weight);
SkConic pair[2];
if (!conic.chopAt(maxCurvature, pair)) {
// if result can't be computed, use original
fContourBuilder.addConic(pointsPtr, weight);
break;
}
SkPoint cStorage[2][3];
SkPath::Verb v1 = SkReduceOrder::Conic(pair[0], cStorage[0]);
SkPath::Verb v2 = SkReduceOrder::Conic(pair[1], cStorage[1]);
SkPoint* curve1 = v1 != SkPath::kLine_Verb ? pair[0].fPts : cStorage[0];
SkPoint* curve2 = v2 != SkPath::kLine_Verb ? pair[1].fPts : cStorage[1];
if (can_add_curve(v1, curve1) && can_add_curve(v2, curve2)) {
fContourBuilder.addCurve(v1, curve1, pair[0].fW);
fContourBuilder.addCurve(v2, curve2, pair[1].fW);
break;
}
}
}
fContourBuilder.addConic(pointsPtr, weight);
} break;
case SkPath::kCubic_Verb:
{
// Split complex cubics (such as self-intersecting curves or
// ones with difficult curvature) in two before proceeding.
// This can be required for intersection to succeed.
SkScalar splitT[3];
int breaks = SkDCubic::ComplexBreak(pointsPtr, splitT);
if (!breaks) {
fContourBuilder.addCubic(pointsPtr);
break;
}
SkASSERT(breaks <= (int) SK_ARRAY_COUNT(splitT));
struct Splitsville {
double fT[2];
SkPoint fPts[4];
SkPoint fReduced[4];
SkPath::Verb fVerb;
bool fCanAdd;
} splits[4];
SkASSERT(SK_ARRAY_COUNT(splits) == SK_ARRAY_COUNT(splitT) + 1);
SkTQSort(splitT, &splitT[breaks - 1]);
for (int index = 0; index <= breaks; ++index) {
Splitsville* split = &splits[index];
split->fT[0] = index ? splitT[index - 1] : 0;
split->fT[1] = index < breaks ? splitT[index] : 1;
SkDCubic part = SkDCubic::SubDivide(pointsPtr, split->fT[0], split->fT[1]);
if (!part.toFloatPoints(split->fPts)) {
return false;
}
split->fVerb = SkReduceOrder::Cubic(split->fPts, split->fReduced);
SkPoint* curve = SkPath::kCubic_Verb == verb
? split->fPts : split->fReduced;
split->fCanAdd = can_add_curve(split->fVerb, curve);
}
for (int index = 0; index <= breaks; ++index) {
Splitsville* split = &splits[index];
if (!split->fCanAdd) {
continue;
}
int prior = index;
while (prior > 0 && !splits[prior - 1].fCanAdd) {
--prior;
}
if (prior < index) {
split->fT[0] = splits[prior].fT[0];
split->fPts[0] = splits[prior].fPts[0];
}
int next = index;
int breakLimit = SkTMin(breaks, (int) SK_ARRAY_COUNT(splits) - 1);
while (next < breakLimit && !splits[next + 1].fCanAdd) {
++next;
}
if (next > index) {
split->fT[1] = splits[next].fT[1];
split->fPts[3] = splits[next].fPts[3];
}
if (prior < index || next > index) {
split->fVerb = SkReduceOrder::Cubic(split->fPts, split->fReduced);
}
SkPoint* curve = SkPath::kCubic_Verb == split->fVerb
? split->fPts : split->fReduced;
if (!can_add_curve(split->fVerb, curve)) {
return false;
}
fContourBuilder.addCurve(split->fVerb, curve);
}
}
break;
case SkPath::kClose_Verb:
SkASSERT(contour);
if (!close()) {
return false;
}
contour = nullptr;
continue;
default:
SkDEBUGFAIL("bad verb");
return false;
}
SkASSERT(contour);
if (contour->count()) {
contour->debugValidate();
}
pointsPtr += SkPathOpsVerbToPoints(verb);
}
fContourBuilder.flush();
if (contour && contour->count() &&!fAllowOpenContours && !close()) {
return false;
}
return true;
}
