/**
* \return List of splines which approximate the given arc.
*/
QList<RSpline> RSpline::createSplinesFromArc(const RArc& arc) {
RArc a = arc;
if (a.isReversed()) {
a.reverse();
}
double startAngle = RMath::getNormalizedAngle(a.getStartAngle());
double endAngle = RMath::getNormalizedAngle(a.getEndAngle());
if (a.isFullCircle()) {
startAngle = 0.0;
endAngle = 2*M_PI;
}
// normalize startAngle, endAngle to [-2PI, 2PI]
double twoPI = M_PI * 2;
//double startAngle = RMath::getNormalizedAngle(a.getStartAngle());
//double endAngle = RMath::getNormalizedAngle(a.getEndAngle());
if (startAngle>endAngle) {
startAngle-=2*M_PI;
}
double radius = a.getRadius();
double EPSILON = 0.00001;
// Compute the sequence of arc curves, up to PI/2 at a time. Total arc angle
// is less than 2PI.
QList<RSpline> curves;
double piOverTwo = M_PI_2;
double segmentationAngle = piOverTwo/4;
//double segmentationAngle = M_PI/8;
double sgn = (startAngle < endAngle) ? +1 : -1;
double a1 = startAngle;
for (double totalAngle = qMin(twoPI, qAbs(endAngle - startAngle)); totalAngle > EPSILON; ) {
double a2 = a1 + sgn * qMin(totalAngle, segmentationAngle);
RSpline sp = RSpline::createBezierFromSmallArc(radius, a1, a2);
sp.move(a.getCenter());
curves.append(sp);
totalAngle -= qAbs(a2 - a1);
a1 = a2;
}
return curves;
}
void RExporter::exportArcSegment(const RArc& arc, bool allowForZeroLength) {
if (allowForZeroLength && arc.isFullCircle()) {
exportLineSegment(RLine(arc.getStartPoint(), arc.getEndPoint()), arc.getDirection1());
return;
}
double segmentLength;
if (pixelSizeHint>0.0) {
// approximate arc with segments with the length of 2 pixels:
segmentLength = pixelSizeHint * 2;
}
else {
segmentLength = arc.getRadius() / 40.0;
}
// avoid a segment length of 0:
if (segmentLength<1.0e-4) {
segmentLength = 1.0e-4;
}
double a1 = arc.getStartAngle();
double a2 = arc.getEndAngle();
RVector center = arc.getCenter();
double radius = arc.getRadius();
double aStep;
if (radius<1.0e-3) {
aStep = 0.1;
}
else {
aStep = segmentLength / radius;
if (aStep>1.0) {
aStep = 1.0;
}
double minAStep = RSettings::getMinArcAngleStep();
if (draftMode) {
minAStep *= 4;
}
if (aStep<minAStep) {
aStep = minAStep;
}
}
RVector prev = arc.getStartPoint();
RVector ci;
double a;
if (!arc.isReversed()) {
// Arc Counterclockwise:
if(a1>a2-RS::AngleTolerance) {
a2+=2*M_PI;
}
for (a=a1+aStep; a<=a2; a+=aStep) {
ci.x = center.x + cos(a) * radius;
ci.y = center.y + sin(a) * radius;
exportLineSegment(RLine(prev, ci), a+M_PI_2);
prev = ci;
}
} else {
// Arc Clockwise:
if (a1<a2+RS::AngleTolerance) {
a2-=2*M_PI;
}
for (a=a1-aStep; a>=a2; a-=aStep) {
ci.x = center.x + cos(a) * radius;
ci.y = center.y + sin(a) * radius;
exportLineSegment(RLine(prev, ci), a+M_PI_2);
prev = ci;
}
}
this->exportLineSegment(RLine(prev, arc.getEndPoint()), arc.getEndAngle()+M_PI_2);
}