static void bloat_quad(const SkPoint qpts[3], const SkMatrix* toDevice,
const SkMatrix* toSrc, BezierVertex verts[kQuadNumVertices]) {
SkASSERT(!toDevice == !toSrc);
// original quad is specified by tri a,b,c
SkPoint a = qpts[0];
SkPoint b = qpts[1];
SkPoint c = qpts[2];
if (toDevice) {
toDevice->mapPoints(&a, 1);
toDevice->mapPoints(&b, 1);
toDevice->mapPoints(&c, 1);
}
// make a new poly where we replace a and c by a 1-pixel wide edges orthog
// to edges ab and bc:
//
// before | after
// | b0
// b |
// |
// | a0 c0
// a c | a1 c1
//
// edges a0->b0 and b0->c0 are parallel to original edges a->b and b->c,
// respectively.
BezierVertex& a0 = verts[0];
BezierVertex& a1 = verts[1];
BezierVertex& b0 = verts[2];
BezierVertex& c0 = verts[3];
BezierVertex& c1 = verts[4];
SkVector ab = b;
ab -= a;
SkVector ac = c;
ac -= a;
SkVector cb = b;
cb -= c;
// We should have already handled degenerates
SkASSERT(ab.length() > 0 && cb.length() > 0);
ab.normalize();
SkVector abN;
abN.setOrthog(ab, SkVector::kLeft_Side);
if (abN.dot(ac) > 0) {
abN.negate();
}
cb.normalize();
SkVector cbN;
cbN.setOrthog(cb, SkVector::kLeft_Side);
if (cbN.dot(ac) < 0) {
cbN.negate();
}
a0.fPos = a;
a0.fPos += abN;
a1.fPos = a;
a1.fPos -= abN;
c0.fPos = c;
c0.fPos += cbN;
c1.fPos = c;
c1.fPos -= cbN;
intersect_lines(a0.fPos, abN, c0.fPos, cbN, &b0.fPos);
if (toSrc) {
toSrc->mapPointsWithStride(&verts[0].fPos, sizeof(BezierVertex), kQuadNumVertices);
}
}
void GrPathUtils::QuadUVMatrix::set(const SkPoint qPts[3]) {
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]
// And control_pts = [x0 x1 x2]
// [y0 y1 y2]
// [1 1 1 ]
// We invert the control pt matrix and post concat to both sides to get M.
// Using the known form of the control point matrix and the result, we can
// optimize and improve precision.
double x0 = qPts[0].fX;
double y0 = qPts[0].fY;
double x1 = qPts[1].fX;
double y1 = qPts[1].fY;
double x2 = qPts[2].fX;
double y2 = qPts[2].fY;
double det = x0*y1 - y0*x1 + x2*y0 - y2*x0 + x1*y2 - y1*x2;
if (!sk_float_isfinite(det)
|| SkScalarNearlyZero((float)det, SK_ScalarNearlyZero * SK_ScalarNearlyZero)) {
// 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)
SkVector 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, SkPoint::kLeft_Side);
// 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 {
double scale = 1.0/det;
// compute adjugate matrix
double a2, a3, a4, a5, a6, a7, a8;
a2 = x1*y2-x2*y1;
a3 = y2-y0;
a4 = x0-x2;
a5 = x2*y0-x0*y2;
a6 = y0-y1;
a7 = x1-x0;
a8 = x0*y1-x1*y0;
// this performs the uv_pts*adjugate(control_pts) multiply,
// then does the scale by 1/det afterwards to improve precision
m[SkMatrix::kMScaleX] = (float)((0.5*a3 + a6)*scale);
m[SkMatrix::kMSkewX] = (float)((0.5*a4 + a7)*scale);
m[SkMatrix::kMTransX] = (float)((0.5*a5 + a8)*scale);
m[SkMatrix::kMSkewY] = (float)(a6*scale);
m[SkMatrix::kMScaleY] = (float)(a7*scale);
m[SkMatrix::kMTransY] = (float)(a8*scale);
// kMPersp0 & kMPersp1 should algebraically be zero
m[SkMatrix::kMPersp0] = 0.0f;
m[SkMatrix::kMPersp1] = 0.0f;
m[SkMatrix::kMPersp2] = (float)((a2 + a5 + a8)*scale);
// 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);
}
}
}