QList<RVector> RShape::getIntersectionPointsAE(const RArc& arc1,
const REllipse& ellipse2, bool limited) {
QList<RVector> candidates =
RShape::getIntersectionPointsCE(
RCircle(arc1.getCenter(), arc1.getRadius()),
ellipse2);
if (!limited) {
return candidates;
}
QList<RVector> res;
for (int i=0; i<candidates.count(); i++) {
RVector c = candidates[i];
if (arc1.isOnShape(c)) {
if (!ellipse2.isFullEllipse()) {
double a1 = ellipse2.getCenter().getAngleTo(ellipse2.getStartPoint());
double a2 = ellipse2.getCenter().getAngleTo(ellipse2.getEndPoint());
double a = ellipse2.getCenter().getAngleTo(c);
if (!RMath::isAngleBetween(a, a1, a2, ellipse2.isReversed())) {
continue;
}
}
res.append(c);
}
}
return res;
}
void REllipseEntity::setShape(const REllipse& e) {
data.setCenter(e.getCenter());
data.setMajorPoint(e.getMajorPoint());
data.setRatio(e.getRatio());
data.setStartParam(e.getStartParam());
data.setEndParam(e.getEndParam());
data.setReversed(e.isReversed());
}
/**
* Exports an ellipse with the current attributes.
* \todo switch from line based interpolation to arcs.
*/
void RExporter::exportEllipse(const REllipse& ellipse, double offset) {
if (ellipse.getMajorRadius()<RS::PointTolerance ||
ellipse.getMinorRadius()<RS::PointTolerance) {
return;
}
RPolyline polyline;
RVector cp = ellipse.getCenter();
double radius1 = ellipse.getMajorRadius();
double radius2 = ellipse.getMinorRadius();
double angle = ellipse.getAngle();
double a1 = ellipse.getStartParam();
double a2 = ellipse.getEndParam();
bool reversed = ellipse.isReversed();
double aStep; // Angle Step (rad)
double a; // Current Angle (rad)
aStep=0.05;
RVector vp;
RVector vc(cp.x, cp.y);
vp.set(cp.x+cos(a1)*radius1,
cp.y+sin(a1)*radius2);
vp.rotate(angle, vc);
polyline.appendVertex(vp);
if (!reversed) {
// Arc Counterclockwise:
if (a1>a2-RS::AngleTolerance) {
a2+=2*M_PI;
}
for(a=a1+aStep; a<=a2; a+=aStep) {
vp.set(cp.x+cos(a)*radius1,
cp.y+sin(a)*radius2);
vp.rotate(angle, vc);
polyline.appendVertex(vp);
}
} else {
// Arc Clockwise:
if (a1<a2+RS::AngleTolerance) {
a2-=2*M_PI;
}
for(a=a1-aStep; a>=a2; a-=aStep) {
vp.set(cp.x+cos(a)*radius1,
cp.y+sin(a)*radius2);
vp.rotate(angle, vc);
polyline.appendVertex(vp);
}
}
vp.set(cp.x+cos(a2)*radius1,
cp.y+sin(a2)*radius2);
vp.rotate(angle, vc);
polyline.appendVertex(vp);
exportPolyline(polyline, offset);
}
QList<RVector> RShape::getIntersectionPointsEE(const REllipse& ellipse1, const REllipse& ellipse2, bool limited) {
QList<RVector> candidates = getIntersectionPointsEE(ellipse1, ellipse2);
if (!limited) {
return candidates;
}
QList<RVector> ret;
for (int i=0; i<candidates.length(); i++) {
RVector c = candidates[i];
bool onShape = true;
double a1 = ellipse1.getCenter().getAngleTo(ellipse1.getStartPoint());
double a2 = ellipse1.getCenter().getAngleTo(ellipse1.getEndPoint());
double a = ellipse1.getCenter().getAngleTo(c);
if (!RMath::isAngleBetween(a, a1, a2, ellipse1.isReversed())) {
// qDebug() << "1) angle NOT between: "
// << " a: " << RMath::rad2deg(a)
// << " a1: " << RMath::rad2deg(a1)
// << " a2: " << RMath::rad2deg(a2)
// << " r: " << ellipse1.isReversed();
//ret.append(c);
onShape = false;
}
a1 = ellipse2.getCenter().getAngleTo(ellipse2.getStartPoint());
a2 = ellipse2.getCenter().getAngleTo(ellipse2.getEndPoint());
a = ellipse2.getCenter().getAngleTo(c);
if (!RMath::isAngleBetween(a, a1, a2, ellipse2.isReversed())) {
// qDebug() << "2) angle NOT between: "
// << " a: " << RMath::rad2deg(a)
// << " a1: " << RMath::rad2deg(a1)
// << " a2: " << RMath::rad2deg(a2)
// << " r: " << ellipse2.isReversed();
//ret.append(c);
onShape = false;
}
if (onShape) {
ret.append(c);
}
}
return ret;
}
QList<RVector> RShape::getIntersectionPointsLE(const RLine& line1,
const REllipse& ellipse2, bool limited) {
QList<RVector> res;
// find out if line1 is (almost) a tangent:
QList<RLine> tangents = ellipse2.getTangents(line1.getMiddlePoint());
for (int i=0; i<tangents.length(); i++) {
double a = tangents[i].getAngle();
double ad1 = fabs(RMath::getAngleDifference180(a, line1.getDirection1()));
double ad2 = fabs(RMath::getAngleDifference180(a, line1.getDirection2()));
if (ad1 < 1.0e-2 || ad2 < 1.0e-2) {
res.append(tangents[i].getEndPoint());
// no need to continue: max. one tangent possible:
return res;
}
}
// rotate into normal position:
double ang = ellipse2.getAngle();
double rx = ellipse2.getMajorRadius();
double ry = ellipse2.getMinorRadius();
RVector center = ellipse2.getCenter();
RVector a1 = line1.getStartPoint();
a1.rotate(-ang, center);
RVector a2 = line1.getEndPoint();
a2.rotate(-ang, center);
RVector origin = a1;
RVector dir = a2-a1;
RVector diff = origin - center;
RVector mDir = RVector(dir.x/(rx*rx), dir.y/(ry*ry));
RVector mDiff = RVector(diff.x/(rx*rx), diff.y/(ry*ry));
double a = RVector::getDotProduct(dir, mDir);
double b = RVector::getDotProduct(dir, mDiff);
double c = RVector::getDotProduct(diff, mDiff) - 1.0;
double d = b*b - a*c;
RVector res1 = RVector::invalid;
RVector res2 = RVector::invalid;
if (d < 0) {
// no solution
} else if ( d > 0 ) {
double root = sqrt(d);
double t_a = (-b - root) / a;
double t_b = (-b + root) / a;
res1 = a1.getLerp(a2, t_a).rotate(ang, center);
res2 = a1.getLerp(a2, t_b).rotate(ang, center);
} else {
double t = -b/a;
if ( 0 <= t && t <= 1 ) {
// one solution:
res1 = a1.getLerp(a2, t).rotate(ang, center);
} else {
// no solution
}
}
if (res1.isValid()) {
if (!limited || (line1.isOnShape(res1) && ellipse2.isOnShape(res1))) {
res.append(res1);
}
}
if (res2.isValid()) {
if (!limited || (line1.isOnShape(res2) && ellipse2.isOnShape(res2))) {
res.append(res2);
}
}
return res;
}
