static void tesselate(const SkPath& src, SkPath* dst) {
SkPath::Iter iter(src, true);
SkPoint pts[4];
SkPath::Verb verb;
while ((verb = iter.next(pts)) != SkPath::kDone_Verb) {
switch (verb) {
case SkPath::kMove_Verb:
dst->moveTo(pts[0]);
break;
case SkPath::kLine_Verb:
dst->lineTo(pts[1]);
break;
case SkPath::kQuad_Verb: {
SkPoint p;
for (int i = 1; i <= 8; ++i) {
SkEvalQuadAt(pts, i / 8.0f, &p, NULL);
dst->lineTo(p);
}
} break;
case SkPath::kCubic_Verb: {
SkPoint p;
for (int i = 1; i <= 8; ++i) {
SkEvalCubicAt(pts, i / 8.0f, &p, NULL, NULL);
dst->lineTo(p);
}
} break;
}
}
}
/// Used inside SkCurveMeasure::getTime's Newton's iteration
static inline SkPoint evaluate(const SkPoint pts[4], SkSegType segType,
SkScalar t) {
SkPoint pos;
switch (segType) {
case kQuad_SegType:
pos = SkEvalQuadAt(pts, t);
break;
case kLine_SegType:
pos = SkPoint::Make(SkScalarInterp(pts[0].x(), pts[1].x(), t),
SkScalarInterp(pts[0].y(), pts[1].y(), t));
break;
case kCubic_SegType:
SkEvalCubicAt(pts, t, &pos, nullptr, nullptr);
break;
case kConic_SegType: {
SkConic conic(pts, pts[3].x());
conic.evalAt(t, &pos);
}
break;
default:
UNIMPLEMENTED;
}
return pos;
}
SkPoint SkCubicBoundary::eval(Edge e, SkScalar t) {
SkASSERT((unsigned)e < 4);
// ensure our 4th cubic wraps to the start of the first
fPts[12] = fPts[0];
SkPoint loc;
SkEvalCubicAt(&fPts[e * 3], t, &loc, NULL, NULL);
return loc;
}
static void eval_patch_edge(const SkPoint cubic[], SkPoint samples[], int segs) {
SkScalar t = 0;
SkScalar dt = SK_Scalar1 / segs;
samples[0] = cubic[0];
for (int i = 1; i < segs; i++) {
t += dt;
SkEvalCubicAt(cubic, t, &samples[i], nullptr, nullptr);
}
}
static void test_cubic_tangents(skiatest::Reporter* reporter) {
SkPoint pts[] = {
{ 10, 20}, {10, 20}, {20, 30}, {30, 40},
{ 10, 20}, {15, 25}, {20, 30}, {30, 40},
{ 10, 20}, {20, 30}, {30, 40}, {30, 40},
};
int count = (int) SK_ARRAY_COUNT(pts) / 4;
for (int index = 0; index < count; ++index) {
SkConic conic(&pts[index * 3], 0.707f);
SkVector start, mid, end;
SkEvalCubicAt(&pts[index * 4], 0, nullptr, &start, nullptr);
SkEvalCubicAt(&pts[index * 4], .5f, nullptr, &mid, nullptr);
SkEvalCubicAt(&pts[index * 4], 1, nullptr, &end, nullptr);
REPORTER_ASSERT(reporter, start.fX && start.fY);
REPORTER_ASSERT(reporter, mid.fX && mid.fY);
REPORTER_ASSERT(reporter, end.fX && end.fY);
REPORTER_ASSERT(reporter, SkScalarNearlyZero(start.cross(mid)));
REPORTER_ASSERT(reporter, SkScalarNearlyZero(mid.cross(end)));
}
}
/// Used inside SkCurveMeasure::getTime's Newton's iteration
static inline SkVector evaluateDerivative(const SkPoint pts[4],
SkSegType segType, SkScalar t) {
SkVector tan;
switch (segType) {
case kQuad_SegType:
tan = SkEvalQuadTangentAt(pts, t);
break;
case kLine_SegType:
tan = pts[1] - pts[0];
break;
case kCubic_SegType:
SkEvalCubicAt(pts, t, nullptr, &tan, nullptr);
break;
case kConic_SegType: {
SkConic conic(pts, pts[3].x());
conic.evalAt(t, nullptr, &tan);
}
break;
default:
UNIMPLEMENTED;
}
return tan;
}
void SkPathStroker::cubicTo(const SkPoint& pt1, const SkPoint& pt2,
const SkPoint& pt3) {
bool degenerateAB = SkPath::IsLineDegenerate(fPrevPt, pt1);
bool degenerateBC = SkPath::IsLineDegenerate(pt1, pt2);
bool degenerateCD = SkPath::IsLineDegenerate(pt2, pt3);
if (degenerateAB + degenerateBC + degenerateCD >= 2) {
this->lineTo(pt3);
return;
}
SkVector normalAB, unitAB, normalCD, unitCD;
// find the first tangent (which might be pt1 or pt2
{
const SkPoint* nextPt = &pt1;
if (degenerateAB)
nextPt = &pt2;
this->preJoinTo(*nextPt, &normalAB, &unitAB, false);
}
{
SkPoint pts[4], tmp[13];
int i, count;
SkVector n, u;
SkScalar tValues[3];
pts[0] = fPrevPt;
pts[1] = pt1;
pts[2] = pt2;
pts[3] = pt3;
#if 1
count = SkChopCubicAtMaxCurvature(pts, tmp, tValues);
#else
count = 1;
memcpy(tmp, pts, 4 * sizeof(SkPoint));
#endif
n = normalAB;
u = unitAB;
for (i = 0; i < count; i++) {
this->cubic_to(&tmp[i * 3], n, u, &normalCD, &unitCD,
kMaxCubicSubdivide);
if (i == count - 1) {
break;
}
n = normalCD;
u = unitCD;
}
// check for too pinchy
for (i = 1; i < count; i++) {
SkPoint p;
SkVector v, c;
SkEvalCubicAt(pts, tValues[i - 1], &p, &v, &c);
SkScalar dot = SkPoint::DotProduct(c, c);
v.scale(SkScalarInvert(dot));
if (SkScalarNearlyZero(v.fX) && SkScalarNearlyZero(v.fY)) {
fExtra.addCircle(p.fX, p.fY, fRadius, SkPath::kCW_Direction);
}
}
}
this->postJoinTo(pt3, normalCD, unitCD);
}
bool SkXRayCrossesMonotonicCubic(const SkXRay& pt, const SkPoint cubic[4]) {
// Find the minimum and maximum y of the extrema, which are the
// first and last points since this cubic is monotonic
SkScalar min_y = SkMinScalar(cubic[0].fY, cubic[3].fY);
SkScalar max_y = SkMaxScalar(cubic[0].fY, cubic[3].fY);
if (pt.fY == cubic[0].fY
|| pt.fY < min_y
|| pt.fY > max_y) {
// The query line definitely does not cross the curve
return false;
}
SkScalar min_x =
SkMinScalar(
SkMinScalar(
SkMinScalar(cubic[0].fX, cubic[1].fX),
cubic[2].fX),
cubic[3].fX);
if (pt.fX < min_x) {
// The query line definitely crosses the curve
return true;
}
SkScalar max_x =
SkMaxScalar(
SkMaxScalar(
SkMaxScalar(cubic[0].fX, cubic[1].fX),
cubic[2].fX),
cubic[3].fX);
if (pt.fX > max_x) {
// The query line definitely does not cross the curve
return false;
}
// Do a binary search to find the parameter value which makes y as
// close as possible to the query point. See whether the query
// line's origin is to the left of the associated x coordinate.
// kMaxIter is chosen as the number of mantissa bits for a float,
// since there's no way we are going to get more precision by
// iterating more times than that.
const int kMaxIter = 23;
SkPoint eval;
int iter = 0;
SkScalar upper_t;
SkScalar lower_t;
// Need to invert direction of t parameter if cubic goes up
// instead of down
if (cubic[3].fY > cubic[0].fY) {
upper_t = SK_Scalar1;
lower_t = SkFloatToScalar(0);
} else {
upper_t = SkFloatToScalar(0);
lower_t = SK_Scalar1;
}
do {
SkScalar t = SkScalarAve(upper_t, lower_t);
SkEvalCubicAt(cubic, t, &eval, NULL, NULL);
if (pt.fY > eval.fY) {
lower_t = t;
} else {
upper_t = t;
}
} while (++iter < kMaxIter
&& !SkScalarNearlyZero(eval.fY - pt.fY));
if (pt.fX <= eval.fX) {
return true;
}
return false;
}
