/*
* Copyright 2011 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "GrPathUtils.h"
#include "GrPoint.h"
#include "SkGeometry.h"
SkScalar GrPathUtils::scaleToleranceToSrc(SkScalar devTol,
const SkMatrix& viewM,
const GrRect& pathBounds) {
// In order to tesselate the path we get a bound on how much the matrix can
// stretch when mapping to screen coordinates.
SkScalar stretch = viewM.getMaxStretch();
SkScalar srcTol = devTol;
if (stretch < 0) {
// take worst case mapRadius amoung four corners.
// (less than perfect)
for (int i = 0; i < 4; ++i) {
SkMatrix mat;
mat.setTranslate((i % 2) ? pathBounds.fLeft : pathBounds.fRight,
(i < 2) ? pathBounds.fTop : pathBounds.fBottom);
mat.postConcat(viewM);
stretch = SkMaxScalar(stretch, mat.mapRadius(SK_Scalar1));
}
}
srcTol = SkScalarDiv(srcTol, stretch);
return srcTol;
}
static const int MAX_POINTS_PER_CURVE = 1 << 10;
static const SkScalar gMinCurveTol = SkFloatToScalar(0.0001f);
uint32_t GrPathUtils::quadraticPointCount(const GrPoint points[],
SkScalar tol) {
if (tol < gMinCurveTol) {
tol = gMinCurveTol;
}
GrAssert(tol > 0);
SkScalar d = points[1].distanceToLineSegmentBetween(points[0], points[2]);
if (d <= tol) {
return 1;
} else {
// Each time we subdivide, d should be cut in 4. So we need to
// subdivide x = log4(d/tol) times. x subdivisions creates 2^(x)
// points.
// 2^(log4(x)) = sqrt(x);
int temp = SkScalarCeil(SkScalarSqrt(SkScalarDiv(d, tol)));
int pow2 = GrNextPow2(temp);
// Because of NaNs & INFs we can wind up with a degenerate temp
// such that pow2 comes out negative. Also, our point generator
// will always output at least one pt.
if (pow2 < 1) {
pow2 = 1;
}
return GrMin(pow2, MAX_POINTS_PER_CURVE);
}
}
uint32_t GrPathUtils::generateQuadraticPoints(const GrPoint& p0,
const GrPoint& p1,
const GrPoint& p2,
SkScalar tolSqd,
GrPoint** points,
uint32_t pointsLeft) {
if (pointsLeft < 2 ||
(p1.distanceToLineSegmentBetweenSqd(p0, p2)) < tolSqd) {
(*points)[0] = p2;
*points += 1;
return 1;
}
GrPoint q[] = {
{ SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
{ SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
};
GrPoint r = { SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) };
pointsLeft >>= 1;
uint32_t a = generateQuadraticPoints(p0, q[0], r, tolSqd, points, pointsLeft);
uint32_t b = generateQuadraticPoints(r, q[1], p2, tolSqd, points, pointsLeft);
return a + b;
}
uint32_t GrPathUtils::cubicPointCount(const GrPoint points[],
SkScalar tol) {
if (tol < gMinCurveTol) {
tol = gMinCurveTol;
}
GrAssert(tol > 0);
SkScalar d = GrMax(
points[1].distanceToLineSegmentBetweenSqd(points[0], points[3]),
points[2].distanceToLineSegmentBetweenSqd(points[0], points[3]));
d = SkScalarSqrt(d);
if (d <= tol) {
return 1;
} else {
int temp = SkScalarCeil(SkScalarSqrt(SkScalarDiv(d, tol)));
int pow2 = GrNextPow2(temp);
// Because of NaNs & INFs we can wind up with a degenerate temp
// such that pow2 comes out negative. Also, our point generator
// will always output at least one pt.
if (pow2 < 1) {
pow2 = 1;
}
return GrMin(pow2, MAX_POINTS_PER_CURVE);
}
}
uint32_t GrPathUtils::generateCubicPoints(const GrPoint& p0,
const GrPoint& p1,
const GrPoint& p2,
const GrPoint& p3,
SkScalar tolSqd,
GrPoint** points,
uint32_t pointsLeft) {
if (pointsLeft < 2 ||
(p1.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd &&
p2.distanceToLineSegmentBetweenSqd(p0, p3) < tolSqd)) {
(*points)[0] = p3;
*points += 1;
return 1;
}
GrPoint q[] = {
{ SkScalarAve(p0.fX, p1.fX), SkScalarAve(p0.fY, p1.fY) },
{ SkScalarAve(p1.fX, p2.fX), SkScalarAve(p1.fY, p2.fY) },
{ SkScalarAve(p2.fX, p3.fX), SkScalarAve(p2.fY, p3.fY) }
};
GrPoint r[] = {
{ SkScalarAve(q[0].fX, q[1].fX), SkScalarAve(q[0].fY, q[1].fY) },
{ SkScalarAve(q[1].fX, q[2].fX), SkScalarAve(q[1].fY, q[2].fY) }
};
GrPoint s = { SkScalarAve(r[0].fX, r[1].fX), SkScalarAve(r[0].fY, r[1].fY) };
pointsLeft >>= 1;
uint32_t a = generateCubicPoints(p0, q[0], r[0], s, tolSqd, points, pointsLeft);
uint32_t b = generateCubicPoints(s, r[1], q[2], p3, tolSqd, points, pointsLeft);
return a + b;
}
int GrPathUtils::worstCasePointCount(const SkPath& path, int* subpaths,
SkScalar tol) {
if (tol < gMinCurveTol) {
tol = gMinCurveTol;
}
GrAssert(tol > 0);
int pointCount = 0;
*subpaths = 1;
bool first = true;
SkPath::Iter iter(path, false);
GrPathCmd cmd;
GrPoint pts[4];
while ((cmd = (GrPathCmd)iter.next(pts)) != kEnd_PathCmd) {
switch (cmd) {
case kLine_PathCmd:
pointCount += 1;
break;
case kQuadratic_PathCmd:
pointCount += quadraticPointCount(pts, tol);
break;
case kCubic_PathCmd:
pointCount += cubicPointCount(pts, tol);
break;
case kMove_PathCmd:
pointCount += 1;
if (!first) {
++(*subpaths);
}
break;
default:
break;
}
first = false;
}
return pointCount;
}
void GrPathUtils::QuadUVMatrix::set(const GrPoint qPts[3]) {
// can't make this static, no cons :(
SkMatrix UVpts;
#ifndef SK_SCALAR_IS_FLOAT
GrCrash("Expected scalar is float.");
#endif
SkMatrix m;
// We want M such that M * xy_pt = uv_pt
// We know M * control_pts = [0 1/2 1]
// [0 0 1]
// [1 1 1]
// We invert the control pt matrix and post concat to both sides to get M.
UVpts.setAll(0, SK_ScalarHalf, SK_Scalar1,
0, 0, SK_Scalar1,
SkScalarToPersp(SK_Scalar1),
SkScalarToPersp(SK_Scalar1),
SkScalarToPersp(SK_Scalar1));
m.setAll(qPts[0].fX, qPts[1].fX, qPts[2].fX,
qPts[0].fY, qPts[1].fY, qPts[2].fY,
SkScalarToPersp(SK_Scalar1),
SkScalarToPersp(SK_Scalar1),
SkScalarToPersp(SK_Scalar1));
if (!m.invert(&m)) {
// The quad is degenerate. Hopefully this is rare. Find the pts that are
// farthest apart to compute a line (unless it is really a pt).
SkScalar maxD = qPts[0].distanceToSqd(qPts[1]);
int maxEdge = 0;
SkScalar d = qPts[1].distanceToSqd(qPts[2]);
if (d > maxD) {
maxD = d;
maxEdge = 1;
}
d = qPts[2].distanceToSqd(qPts[0]);
if (d > maxD) {
maxD = d;
maxEdge = 2;
}
// We could have a tolerance here, not sure if it would improve anything
if (maxD > 0) {
// Set the matrix to give (u = 0, v = distance_to_line)
GrVec lineVec = qPts[(maxEdge + 1)%3] - qPts[maxEdge];
// when looking from the point 0 down the line we want positive
// distances to be to the left. This matches the non-degenerate
// case.
lineVec.setOrthog(lineVec, GrPoint::kLeft_Side);
lineVec.dot(qPts[0]);
// first row
fM[0] = 0;
fM[1] = 0;
fM[2] = 0;
// second row
fM[3] = lineVec.fX;
fM[4] = lineVec.fY;
fM[5] = -lineVec.dot(qPts[maxEdge]);
} else {
// It's a point. It should cover zero area. Just set the matrix such
// that (u, v) will always be far away from the quad.
fM[0] = 0; fM[1] = 0; fM[2] = 100.f;
fM[3] = 0; fM[4] = 0; fM[5] = 100.f;
}
} else {
m.postConcat(UVpts);
// The matrix should not have perspective.
SkDEBUGCODE(static const SkScalar gTOL = SkFloatToScalar(1.f / 100.f));
GrAssert(SkScalarAbs(m.get(SkMatrix::kMPersp0)) < gTOL);
GrAssert(SkScalarAbs(m.get(SkMatrix::kMPersp1)) < gTOL);
// It may not be normalized to have 1.0 in the bottom right
float m33 = m.get(SkMatrix::kMPersp2);
if (1.f != m33) {
m33 = 1.f / m33;
fM[0] = m33 * m.get(SkMatrix::kMScaleX);
fM[1] = m33 * m.get(SkMatrix::kMSkewX);
fM[2] = m33 * m.get(SkMatrix::kMTransX);
fM[3] = m33 * m.get(SkMatrix::kMSkewY);
fM[4] = m33 * m.get(SkMatrix::kMScaleY);
fM[5] = m33 * m.get(SkMatrix::kMTransY);
} else {
fM[0] = m.get(SkMatrix::kMScaleX);
fM[1] = m.get(SkMatrix::kMSkewX);
fM[2] = m.get(SkMatrix::kMTransX);
fM[3] = m.get(SkMatrix::kMSkewY);
fM[4] = m.get(SkMatrix::kMScaleY);
fM[5] = m.get(SkMatrix::kMTransY);
}
}
}
namespace {
// a is the first control point of the cubic.
// ab is the vector from a to the second control point.
// dc is the vector from the fourth to the third control point.
// d is the fourth control point.
// p is the candidate quadratic control point.
// this assumes that the cubic doesn't inflect and is simple
bool is_point_within_cubic_tangents(const SkPoint& a,
const SkVector& ab,
const SkVector& dc,
const SkPoint& d,
SkPath::Direction dir,
const SkPoint p) {
SkVector ap = p - a;
SkScalar apXab = ap.cross(ab);
if (SkPath::kCW_Direction == dir) {
if (apXab > 0) {
return false;
}
} else {
GrAssert(SkPath::kCCW_Direction == dir);
if (apXab < 0) {
return false;
}
}
SkVector dp = p - d;
SkScalar dpXdc = dp.cross(dc);
if (SkPath::kCW_Direction == dir) {
if (dpXdc < 0) {
return false;
}
} else {
GrAssert(SkPath::kCCW_Direction == dir);
if (dpXdc > 0) {
return false;
}
}
return true;
}
void convert_noninflect_cubic_to_quads(const SkPoint p[4],
SkScalar toleranceSqd,
bool constrainWithinTangents,
SkPath::Direction dir,
SkTArray<SkPoint, true>* quads,
int sublevel = 0) {
// Notation: Point a is always p[0]. Point b is p[1] unless p[1] == p[0], in which case it is
// p[2]. Point d is always p[3]. Point c is p[2] unless p[2] == p[3], in which case it is p[1].
SkVector ab = p[1] - p[0];
SkVector dc = p[2] - p[3];
if (ab.isZero()) {
if (dc.isZero()) {
SkPoint* degQuad = quads->push_back_n(3);
degQuad[0] = p[0];
degQuad[1] = p[0];
degQuad[2] = p[3];
return;
}
ab = p[2] - p[0];
}
if (dc.isZero()) {
dc = p[1] - p[3];
}
// When the ab and cd tangents are nearly parallel with vector from d to a the constraint that
// the quad point falls between the tangents becomes hard to enforce and we are likely to hit
// the max subdivision count. However, in this case the cubic is approaching a line and the
// accuracy of the quad point isn't so important. We check if the two middle cubic control
// points are very close to the baseline vector. If so then we just pick quadratic points on the
// control polygon.
if (constrainWithinTangents) {
SkVector da = p[0] - p[3];
SkScalar invDALengthSqd = da.lengthSqd();
if (invDALengthSqd > SK_ScalarNearlyZero) {
invDALengthSqd = SkScalarInvert(invDALengthSqd);
// cross(ab, da)^2/length(da)^2 == sqd distance from b to line from d to a.
// same goed for point c using vector cd.
SkScalar detABSqd = ab.cross(da);
detABSqd = SkScalarSquare(detABSqd);
SkScalar detDCSqd = dc.cross(da);
detDCSqd = SkScalarSquare(detDCSqd);
if (SkScalarMul(detABSqd, invDALengthSqd) < toleranceSqd &&
SkScalarMul(detDCSqd, invDALengthSqd) < toleranceSqd) {
SkPoint b = p[0] + ab;
SkPoint c = p[3] + dc;
SkPoint mid = b + c;
mid.scale(SK_ScalarHalf);
// Insert two quadratics to cover the case when ab points away from d and/or dc
// points away from a.
if (SkVector::DotProduct(da, dc) < 0 || SkVector::DotProduct(ab,da) > 0) {
SkPoint* qpts = quads->push_back_n(6);
qpts[0] = p[0];
qpts[1] = b;
qpts[2] = mid;
qpts[3] = mid;
qpts[4] = c;
qpts[5] = p[3];
} else {
SkPoint* qpts = quads->push_back_n(3);
qpts[0] = p[0];
qpts[1] = mid;
qpts[2] = p[3];
}
return;
}
}
}
static const SkScalar kLengthScale = 3 * SK_Scalar1 / 2;
static const int kMaxSubdivs = 10;
ab.scale(kLengthScale);
dc.scale(kLengthScale);
// e0 and e1 are extrapolations along vectors ab and dc.
SkVector c0 = p[0];
c0 += ab;
SkVector c1 = p[3];
c1 += dc;
SkScalar dSqd = sublevel > kMaxSubdivs ? 0 : c0.distanceToSqd(c1);
if (dSqd < toleranceSqd) {
SkPoint cAvg = c0;
cAvg += c1;
cAvg.scale(SK_ScalarHalf);
bool subdivide = false;
if (constrainWithinTangents &&
!is_point_within_cubic_tangents(p[0], ab, dc, p[3], dir, cAvg)) {
// choose a new cAvg that is the intersection of the two tangent lines.
ab.setOrthog(ab);
SkScalar z0 = -ab.dot(p[0]);
dc.setOrthog(dc);
SkScalar z1 = -dc.dot(p[3]);
cAvg.fX = SkScalarMul(ab.fY, z1) - SkScalarMul(z0, dc.fY);
cAvg.fY = SkScalarMul(z0, dc.fX) - SkScalarMul(ab.fX, z1);
SkScalar z = SkScalarMul(ab.fX, dc.fY) - SkScalarMul(ab.fY, dc.fX);
z = SkScalarInvert(z);
cAvg.fX *= z;
cAvg.fY *= z;
if (sublevel <= kMaxSubdivs) {
SkScalar d0Sqd = c0.distanceToSqd(cAvg);
SkScalar d1Sqd = c1.distanceToSqd(cAvg);
// We need to subdivide if d0 + d1 > tolerance but we have the sqd values. We know
// the distances and tolerance can't be negative.
// (d0 + d1)^2 > toleranceSqd
// d0Sqd + 2*d0*d1 + d1Sqd > toleranceSqd
SkScalar d0d1 = SkScalarSqrt(SkScalarMul(d0Sqd, d1Sqd));
subdivide = 2 * d0d1 + d0Sqd + d1Sqd > toleranceSqd;
}
}
if (!subdivide) {
SkPoint* pts = quads->push_back_n(3);
pts[0] = p[0];
pts[1] = cAvg;
pts[2] = p[3];
return;
}
}
SkPoint choppedPts[7];
SkChopCubicAtHalf(p, choppedPts);
convert_noninflect_cubic_to_quads(choppedPts + 0,
toleranceSqd,
constrainWithinTangents,
dir,
quads,
sublevel + 1);
convert_noninflect_cubic_to_quads(choppedPts + 3,
toleranceSqd,
constrainWithinTangents,
dir,
quads,
sublevel + 1);
}
}
void GrPathUtils::convertCubicToQuads(const GrPoint p[4],
SkScalar tolScale,
bool constrainWithinTangents,
SkPath::Direction dir,
SkTArray<SkPoint, true>* quads) {
SkPoint chopped[10];
int count = SkChopCubicAtInflections(p, chopped);
// base tolerance is 1 pixel.
static const SkScalar kTolerance = SK_Scalar1;
const SkScalar tolSqd = SkScalarSquare(SkScalarMul(tolScale, kTolerance));
for (int i = 0; i < count; ++i) {
SkPoint* cubic = chopped + 3*i;
convert_noninflect_cubic_to_quads(cubic, tolSqd, constrainWithinTangents, dir, quads);
}
}