void QNanoPainter::quadTo(const QPointF &controlPoint, const QPointF &endPoint)
{
quadTo(controlPoint.x(), controlPoint.y(), endPoint.x(), endPoint.y());
}
void WPainterPath::quadTo(const WPointF& c, const WPointF& endPoint)
{
quadTo(c.x(), c.y(), endPoint.x(), endPoint.y());
}
/* genEllipticPath:
* Approximate an elliptical arc via Beziers of given degree
* threshold indicates quality of approximation
* if isSlice is true, the path begins and ends with line segments
* to the center of the ellipse.
* Returned path must be freed by the caller.
*/
static Ppolyline_t *genEllipticPath(ellipse_t * ep, int degree,
double threshold, boolean isSlice)
{
double dEta;
double etaB;
double cosEtaB;
double sinEtaB;
double aCosEtaB;
double bSinEtaB;
double aSinEtaB;
double bCosEtaB;
double xB;
double yB;
double xBDot;
double yBDot;
double t;
double alpha;
Ppolyline_t *path = NEW(Ppolyline_t);
// find the number of Bezier curves needed
boolean found = FALSE;
int i, n = 1;
while ((!found) && (n < 1024)) {
double dEta = (ep->eta2 - ep->eta1) / n;
if (dEta <= 0.5 * M_PI) {
double etaB = ep->eta1;
found = TRUE;
for (i = 0; found && (i < n); ++i) {
double etaA = etaB;
etaB += dEta;
found =
(estimateError(ep, degree, etaA, etaB) <= threshold);
}
}
n = n << 1;
}
dEta = (ep->eta2 - ep->eta1) / n;
etaB = ep->eta1;
cosEtaB = cos(etaB);
sinEtaB = sin(etaB);
aCosEtaB = ep->a * cosEtaB;
bSinEtaB = ep->b * sinEtaB;
aSinEtaB = ep->a * sinEtaB;
bCosEtaB = ep->b * cosEtaB;
xB = ep->cx + aCosEtaB * ep->cosTheta - bSinEtaB * ep->sinTheta;
yB = ep->cy + aCosEtaB * ep->sinTheta + bSinEtaB * ep->cosTheta;
xBDot = -aSinEtaB * ep->cosTheta - bCosEtaB * ep->sinTheta;
yBDot = -aSinEtaB * ep->sinTheta + bCosEtaB * ep->cosTheta;
if (isSlice) {
moveTo(path, ep->cx, ep->cy);
lineTo(path, xB, yB);
} else {
moveTo(path, xB, yB);
}
t = tan(0.5 * dEta);
alpha = sin(dEta) * (sqrt(4 + 3 * t * t) - 1) / 3;
for (i = 0; i < n; ++i) {
double xA = xB;
double yA = yB;
double xADot = xBDot;
double yADot = yBDot;
etaB += dEta;
cosEtaB = cos(etaB);
sinEtaB = sin(etaB);
aCosEtaB = ep->a * cosEtaB;
bSinEtaB = ep->b * sinEtaB;
aSinEtaB = ep->a * sinEtaB;
bCosEtaB = ep->b * cosEtaB;
xB = ep->cx + aCosEtaB * ep->cosTheta - bSinEtaB * ep->sinTheta;
yB = ep->cy + aCosEtaB * ep->sinTheta + bSinEtaB * ep->cosTheta;
xBDot = -aSinEtaB * ep->cosTheta - bCosEtaB * ep->sinTheta;
yBDot = -aSinEtaB * ep->sinTheta + bCosEtaB * ep->cosTheta;
if (degree == 1) {
lineTo(path, xB, yB);
#if DO_QUAD
} else if (degree == 2) {
double k = (yBDot * (xB - xA) - xBDot * (yB - yA))
/ (xADot * yBDot - yADot * xBDot);
quadTo(path, (xA + k * xADot), (yA + k * yADot), xB, yB);
#endif
} else {
curveTo(path, (xA + alpha * xADot), (yA + alpha * yADot),
(xB - alpha * xBDot), (yB - alpha * yBDot), xB, yB);
}
}
endPath(path, isSlice);
return path;
}
