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;
}
