SkDPoint SkDQuad::subDivide(const SkDPoint& a, const SkDPoint& c, double t1, double t2) const {
SkASSERT(t1 != t2);
SkDPoint b;
SkDQuad sub = subDivide(t1, t2);
SkDLine b0 = {{a, sub[1] + (a - sub[0])}};
SkDLine b1 = {{c, sub[1] + (c - sub[2])}};
SkIntersections i;
i.intersectRay(b0, b1);
if (i.used() == 1 && i[0][0] >= 0 && i[1][0] >= 0) {
b = i.pt(0);
} else {
SkASSERT(i.used() <= 2);
b = SkDPoint::Mid(b0[1], b1[1]);
}
if (t1 == 0 || t2 == 0) {
align(0, &b);
}
if (t1 == 1 || t2 == 1) {
align(2, &b);
}
if (AlmostBequalUlps(b.fX, a.fX)) {
b.fX = a.fX;
} else if (AlmostBequalUlps(b.fX, c.fX)) {
b.fX = c.fX;
}
if (AlmostBequalUlps(b.fY, a.fY)) {
b.fY = a.fY;
} else if (AlmostBequalUlps(b.fY, c.fY)) {
b.fY = c.fY;
}
return b;
}
void SkDCubic::subDivide(const SkDPoint& a, const SkDPoint& d,
double t1, double t2, SkDPoint dst[2]) const {
SkASSERT(t1 != t2);
// this approach assumes that the control points computed directly are accurate enough
SkDCubic sub = subDivide(t1, t2);
dst[0] = sub[1] + (a - sub[0]);
dst[1] = sub[2] + (d - sub[3]);
if (t1 == 0 || t2 == 0) {
align(0, 1, t1 == 0 ? &dst[0] : &dst[1]);
}
if (t1 == 1 || t2 == 1) {
align(3, 2, t1 == 1 ? &dst[0] : &dst[1]);
}
if (AlmostBequalUlps(dst[0].fX, a.fX)) {
dst[0].fX = a.fX;
}
if (AlmostBequalUlps(dst[0].fY, a.fY)) {
dst[0].fY = a.fY;
}
if (AlmostBequalUlps(dst[1].fX, d.fX)) {
dst[1].fX = d.fX;
}
if (AlmostBequalUlps(dst[1].fY, d.fY)) {
dst[1].fY = d.fY;
}
}
void SkDCubic::subDivide(const SkDPoint& a, const SkDPoint& d,
double t1, double t2, SkDPoint dst[2]) const {
SkASSERT(t1 != t2);
#if 0
double ex = interp_cubic_coords(&fPts[0].fX, (t1 * 2 + t2) / 3);
double ey = interp_cubic_coords(&fPts[0].fY, (t1 * 2 + t2) / 3);
double fx = interp_cubic_coords(&fPts[0].fX, (t1 + t2 * 2) / 3);
double fy = interp_cubic_coords(&fPts[0].fY, (t1 + t2 * 2) / 3);
double mx = ex * 27 - a.fX * 8 - d.fX;
double my = ey * 27 - a.fY * 8 - d.fY;
double nx = fx * 27 - a.fX - d.fX * 8;
double ny = fy * 27 - a.fY - d.fY * 8;
/* bx = */ dst[0].fX = (mx * 2 - nx) / 18;
/* by = */ dst[0].fY = (my * 2 - ny) / 18;
/* cx = */ dst[1].fX = (nx * 2 - mx) / 18;
/* cy = */ dst[1].fY = (ny * 2 - my) / 18;
#else
// this approach assumes that the control points computed directly are accurate enough
SkDCubic sub = subDivide(t1, t2);
dst[0] = sub[1] + (a - sub[0]);
dst[1] = sub[2] + (d - sub[3]);
#endif
if (t1 == 0 || t2 == 0) {
align(0, 1, t1 == 0 ? &dst[0] : &dst[1]);
}
if (t1 == 1 || t2 == 1) {
align(3, 2, t1 == 1 ? &dst[0] : &dst[1]);
}
if (AlmostBequalUlps(dst[0].fX, a.fX)) {
dst[0].fX = a.fX;
}
if (AlmostBequalUlps(dst[0].fY, a.fY)) {
dst[0].fY = a.fY;
}
if (AlmostBequalUlps(dst[1].fX, d.fX)) {
dst[1].fX = d.fX;
}
if (AlmostBequalUlps(dst[1].fY, d.fY)) {
dst[1].fY = d.fY;
}
}
SkDPoint SkDQuad::subDivide(const SkDPoint& a, const SkDPoint& c, double t1, double t2) const {
SkASSERT(t1 != t2);
SkDPoint b;
#if 0
// this approach assumes that the control point computed directly is accurate enough
double dx = interp_quad_coords(&fPts[0].fX, (t1 + t2) / 2);
double dy = interp_quad_coords(&fPts[0].fY, (t1 + t2) / 2);
b.fX = 2 * dx - (a.fX + c.fX) / 2;
b.fY = 2 * dy - (a.fY + c.fY) / 2;
#else
SkDQuad sub = subDivide(t1, t2);
SkDLine b0 = {{a, sub[1] + (a - sub[0])}};
SkDLine b1 = {{c, sub[1] + (c - sub[2])}};
SkIntersections i;
i.intersectRay(b0, b1);
if (i.used() == 1 && i[0][0] >= 0 && i[1][0] >= 0) {
b = i.pt(0);
} else {
SkASSERT(i.used() <= 2);
b = SkDPoint::Mid(b0[1], b1[1]);
}
#endif
if (t1 == 0 || t2 == 0) {
align(0, &b);
}
if (t1 == 1 || t2 == 1) {
align(2, &b);
}
if (AlmostBequalUlps(b.fX, a.fX)) {
b.fX = a.fX;
} else if (AlmostBequalUlps(b.fX, c.fX)) {
b.fX = c.fX;
}
if (AlmostBequalUlps(b.fY, a.fY)) {
b.fY = a.fY;
} else if (AlmostBequalUlps(b.fY, c.fY)) {
b.fY = c.fY;
}
return b;
}
double SkDLine::NearPointV(const SkDPoint& xy, double top, double bottom, double x) {
if (!AlmostBequalUlps(xy.fX, x)) {
return -1;
}
if (!AlmostBetweenUlps(top, xy.fY, bottom)) {
return -1;
}
double t = (xy.fY - top) / (bottom - top);
t = SkPinT(t);
SkASSERT(between(0, t, 1));
double realPtY = (1 - t) * top + t * bottom;
SkDVector distU = {xy.fX - x, xy.fY - realPtY};
double distSq = distU.fX * distU.fX + distU.fY * distU.fY;
double dist = sqrt(distSq); // OPTIMIZATION: can we compare against distSq instead ?
double tiniest = SkTMin(SkTMin(x, top), bottom);
double largest = SkTMax(SkTMax(x, top), bottom);
largest = SkTMax(largest, -tiniest);
if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
return -1;
}
return t;
}
double SkDLine::NearPointH(const SkDPoint& xy, double left, double right, double y) {
if (!AlmostBequalUlps(xy.fY, y)) {
return -1;
}
if (!AlmostBetweenUlps(left, xy.fX, right)) {
return -1;
}
double t = (xy.fX - left) / (right - left);
t = SkPinT(t);
SkASSERT(between(0, t, 1));
double realPtX = (1 - t) * left + t * right;
SkDVector distU = {xy.fY - y, xy.fX - realPtX};
double distSq = distU.fX * distU.fX + distU.fY * distU.fY;
double dist = sqrt(distSq); // OPTIMIZATION: can we compare against distSq instead ?
double tiniest = SkTMin(SkTMin(y, left), right);
double largest = SkTMax(SkTMax(y, left), right);
largest = SkTMax(largest, -tiniest);
if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
return -1;
}
return t;
}