/**
* \return List of bezier spline segments which together represent this curve.
*/
QList<RSpline> RSpline::getBezierSegments() const {
// spline is a single bezier segment:
if (countControlPoints()==getDegree()+1) {
return QList<RSpline>() << *this;
}
updateInternal();
QList<RSpline> ret;
#ifndef R_NO_OPENNURBS
ON_NurbsCurve* dup = dynamic_cast<ON_NurbsCurve*>(curve.DuplicateCurve());
if (dup==NULL) {
return ret;
}
dup->MakePiecewiseBezier();
for (int i=0; i<=dup->CVCount() - dup->Order(); ++i) {
ON_BezierCurve bc;
if (!dup->ConvertSpanToBezier(i, bc)) {
continue;
}
QList<RVector> ctrlPts;
for (int cpi=0; cpi<bc.CVCount(); cpi++) {
ON_3dPoint onp;
bc.GetCV(cpi, onp);
ctrlPts.append(RVector(onp.x, onp.y, onp.z));
}
ret.append(RSpline(ctrlPts, degree));
}
delete dup;
#endif
return ret;
}
/**
* Cubic bezier approximation of a circular arc centered at the origin,
* from (radians) a1 to a2, where a2-a1 < pi/2. The arc's radius is r.
*
* Returns an spline approximation.
*
* This algorithm is based on the approach described in:
* A. Riškus, "Approximation of a Cubic Bezier Curve by Circular Arcs and Vice Versa,"
* Information Technology and Control, 35(4), 2006 pp. 371-378.
*/
RSpline RSpline::createBezierFromSmallArc(double r, double a1, double a2) {
// Compute all four points for an arc that subtends the same total angle
// but is centered on the X-axis
double a = (a2 - a1) / 2.0; //
double x4 = r * cos(a);
double y4 = r * sin(a);
double x1 = x4;
double y1 = -y4;
//double k = 0.552284749831;
//double k = 4.0/3.0*(sqrt(2.0)-1.0);
//double f = k * tan(a);
double q1 = x1*x1 + y1*y1;
double q2 = q1 + x1*x4 + y1*y4;
double k2 = 4/3 * (sqrt(2 * q1 * q2) - q2) / (x1 * y4 - y1 * x4);
double x2 = x1 - k2 * y1;
double y2 = y1 + k2 * x1;
//double x2 = x1 + f * y4;
//double y2 = y1 + f * x4;
double x3 = x2;
double y3 = -y2;
// Find the arc points actual locations by computing x1,y1 and x4,y4
// and rotating the control points by a + a1
double ar = a + a1;
double cos_ar = cos(ar);
double sin_ar = sin(ar);
QList<RVector> ctrlPts;
ctrlPts
<< RVector(
r * cos(a1),
r * sin(a1)
)
<< RVector(
x2 * cos_ar - y2 * sin_ar,
x2 * sin_ar + y2 * cos_ar
)
<< RVector(
x3 * cos_ar - y3 * sin_ar,
x3 * sin_ar + y3 * cos_ar
)
<< RVector(
r * cos(a2),
r * sin(a2)
);
// qDebug() << "ctrlPts: " << ctrlPts[0];
// qDebug() << "ctrlPts: " << ctrlPts[1];
// qDebug() << "ctrlPts: " << ctrlPts[2];
// qDebug() << "ctrlPts: " << ctrlPts[3];
return RSpline(ctrlPts, 2);
}