SkDQuadPair SkDQuad::chopAt(double t) const
{
SkDQuadPair dst;
interp_quad_coords(&fPts[0].fX, &dst.pts[0].fX, t);
interp_quad_coords(&fPts[0].fY, &dst.pts[0].fY, t);
return dst;
}
void SkChopQuadAt(const SkPoint src[3], SkPoint dst[5], SkScalar t)
{
SkASSERT(t > 0 && t < SK_Scalar1);
interp_quad_coords(&src[0].fX, &dst[0].fX, t);
interp_quad_coords(&src[0].fY, &dst[0].fY, t);
}
static int check_linear(const Quadratic& quad, Quadratic& reduction,
int minX, int maxX, int minY, int maxY) {
int startIndex = 0;
int endIndex = 2;
while (quad[startIndex].approximatelyEqual(quad[endIndex])) {
--endIndex;
if (endIndex == 0) {
printf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
assert(0);
}
}
if (!isLinear(quad, startIndex, endIndex)) {
return 0;
}
// four are colinear: return line formed by outside
reduction[0] = quad[0];
reduction[1] = quad[2];
int sameSide;
bool useX = quad[maxX].x - quad[minX].x >= quad[maxY].y - quad[minY].y;
if (useX) {
sameSide = sign(quad[0].x - quad[1].x) + sign(quad[2].x - quad[1].x);
} else {
sameSide = sign(quad[0].y - quad[1].y) + sign(quad[2].y - quad[1].y);
}
if ((sameSide & 3) != 2) {
return 2;
}
double tValue;
int root;
if (useX) {
root = findExtrema(quad[0].x, quad[1].x, quad[2].x, &tValue);
} else {
root = findExtrema(quad[0].y, quad[1].y, quad[2].y, &tValue);
}
if (root) {
_Point extrema;
extrema.x = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
extrema.y = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
// sameSide > 0 means mid is smaller than either [0] or [2], so replace smaller
int replace;
if (useX) {
if (extrema.x < quad[0].x ^ extrema.x < quad[2].x) {
return 2;
}
replace = (extrema.x < quad[0].x | extrema.x < quad[2].x)
^ (quad[0].x < quad[2].x);
} else {
if (extrema.y < quad[0].y ^ extrema.y < quad[2].y) {
return 2;
}
replace = (extrema.y < quad[0].y | extrema.y < quad[2].y)
^ (quad[0].y < quad[2].y);
}
reduction[replace] = extrema;
}
return 2;
}
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;
}
static int horizontal_line(const Quadratic& quad, Quadratic& reduction) {
double tValue;
reduction[0] = quad[0];
reduction[1] = quad[2];
int smaller = reduction[1].x > reduction[0].x;
int larger = smaller ^ 1;
if (findExtrema(quad[0].x, quad[1].x, quad[2].x, &tValue)) {
double xExtrema = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
if (reduction[smaller].x > xExtrema) {
reduction[smaller].x = xExtrema;
} else if (reduction[larger].x < xExtrema) {
reduction[larger].x = xExtrema;
}
}
return 2;
}
static int vertical_line(const Quadratic& quad, Quadratic& reduction) {
double tValue;
reduction[0] = quad[0];
reduction[1] = quad[2];
int smaller = reduction[1].y > reduction[0].y;
int larger = smaller ^ 1;
if (findExtrema(quad[0].y, quad[1].y, quad[2].y, &tValue)) {
double yExtrema = interp_quad_coords(quad[0].y, quad[1].y, quad[2].y, tValue);
if (reduction[smaller].y > yExtrema) {
reduction[smaller].y = yExtrema;
} else if (reduction[larger].y < yExtrema) {
reduction[larger].y = yExtrema;
}
}
return 2;
}
// OPTIMIZE : special case either or both of t1 = 0, t2 = 1
SkDQuad SkDQuad::subDivide(double t1, double t2) const {
SkDQuad dst;
double ax = dst[0].fX = interp_quad_coords(&fPts[0].fX, t1);
double ay = dst[0].fY = interp_quad_coords(&fPts[0].fY, t1);
double dx = interp_quad_coords(&fPts[0].fX, (t1 + t2) / 2);
double dy = interp_quad_coords(&fPts[0].fY, (t1 + t2) / 2);
double cx = dst[2].fX = interp_quad_coords(&fPts[0].fX, t2);
double cy = dst[2].fY = interp_quad_coords(&fPts[0].fY, t2);
/* bx = */ dst[1].fX = 2 * dx - (ax + cx) / 2;
/* by = */ dst[1].fY = 2 * dy - (ay + cy) / 2;
return dst;
}
