/**
* @return One or two intersection points between given entities.
*/
RS_VectorSolutions RS_Information::getIntersectionArcArc(RS_Entity const* e1,
RS_Entity const* e2) {
RS_VectorSolutions ret;
if (!(e1 && e2)) return ret;
if(e1->rtti() != RS2::EntityArc && e1->rtti() != RS2::EntityCircle)
return ret;
if(e2->rtti() != RS2::EntityArc && e2->rtti() != RS2::EntityCircle)
return ret;
RS_Vector c1 = e1->getCenter();
RS_Vector c2 = e2->getCenter();
double r1 = e1->getRadius();
double r2 = e2->getRadius();
RS_Vector u = c2 - c1;
// concentric
if (u.magnitude()<1.0e-6) {
return ret;
}
RS_Vector v = RS_Vector(u.y, -u.x);
double s, t1, t2, term;
s = 1.0/2.0 * ((r1*r1 - r2*r2)/(RS_Math::pow(u.magnitude(), 2.0)) + 1.0);
term = (r1*r1)/(RS_Math::pow(u.magnitude(), 2.0)) - s*s;
// no intersection:
if (term<0.0) {
ret = RS_VectorSolutions();
}
// one or two intersections:
else {
t1 = sqrt(term);
t2 = -sqrt(term);
bool tangent = false;
RS_Vector sol1 = c1 + u*s + v*t1;
RS_Vector sol2 = c1 + u*s + v*t2;
if (sol1.distanceTo(sol2)<1.0e-4) {
sol2 = RS_Vector(false);
ret = RS_VectorSolutions({sol1});
tangent = true;
} else {
ret = RS_VectorSolutions({sol1, sol2});
}
ret.setTangent(tangent);
}
return ret;
}
/**
* @return One or two intersection points between given entities.
*/
RS_VectorSolutions RS_Information::getIntersectionLineArc(RS_Line* line,
RS_Arc* arc) {
RS_VectorSolutions ret;
if (line==NULL || arc==NULL) {
return ret;
}
double dist=0.0;
RS_Vector nearest;
nearest = line->getNearestPointOnEntity(arc->getCenter(), false, &dist);
// special case: arc touches line (tangent):
if (fabs(dist - arc->getRadius()) < 1.0e-4) {
ret = RS_VectorSolutions(nearest);
ret.setTangent(true);
return ret;
}
RS_Vector p = line->getStartpoint();
RS_Vector d = line->getEndpoint() - line->getStartpoint();
if (d.magnitude()<1.0e-6) {
return ret;
}
RS_Vector c = arc->getCenter();
double r = arc->getRadius();
RS_Vector delta = p - c;
// root term:
double term = RS_Math::pow(RS_Vector::dotP(d, delta), 2.0)
- RS_Math::pow(d.magnitude(), 2.0)
* (RS_Math::pow(delta.magnitude(), 2.0) - RS_Math::pow(r, 2.0));
// no intersection:
if (term<0.0) {
RS_VectorSolutions s;
ret = s;
}
// one or two intersections:
else {
double t1 = (- RS_Vector::dotP(d, delta) + sqrt(term))
/ RS_Math::pow(d.magnitude(), 2.0);
double t2;
bool tangent = false;
// only one intersection:
if (fabs(term)<RS_TOLERANCE) {
t2 = t1;
tangent = true;
}
// two intersections
else {
t2 = (-RS_Vector::dotP(d, delta) - sqrt(term))
/ RS_Math::pow(d.magnitude(), 2.0);
}
RS_Vector sol1;
RS_Vector sol2(false);
sol1 = p + d * t1;
if (!tangent) {
sol2 = p + d * t2;
}
ret = RS_VectorSolutions(sol1, sol2);
ret.setTangent(tangent);
}
return ret;
}
/**
* @return One or two intersection points between given entities.
*/
RS_VectorSolutions RS_Information::getIntersectionLineArc(RS_Line* line,
RS_Arc* arc) {
RS_VectorSolutions ret;
if (!(line && arc)) return ret;
double dist=0.0;
RS_Vector nearest;
nearest = line->getNearestPointOnEntity(arc->getCenter(), false, &dist);
// special case: arc touches line (tangent):
if (nearest.valid && fabs(dist - arc->getRadius()) < 1.0e-4) {
ret = RS_VectorSolutions({nearest});
ret.setTangent(true);
return ret;
}
RS_Vector p = line->getStartpoint();
RS_Vector d = line->getEndpoint() - line->getStartpoint();
double d2=d.squared();
RS_Vector c = arc->getCenter();
double r = arc->getRadius();
RS_Vector delta = p - c;
if (d2<RS_TOLERANCE2) {
//line too short, still check the whether the line touches the arc
if ( fabs(delta.squared() - r*r) < 2.*RS_TOLERANCE*r ){
return RS_VectorSolutions({line->getMiddlePoint()});
}
return ret;
}
//intersection
// solution = p + t d;
//| p -c+ t d|^2 = r^2
// |d|^2 t^2 + 2 (p-c).d t + |p-c|^2 -r^2 = 0
double a1 = RS_Vector::dotP(delta,d);
double term1 = a1*a1 - d2*(delta.squared()-r*r);
// std::cout<<" discriminant= "<<term1<<std::endl;
if( term1 < - RS_TOLERANCE) {
// std::cout<<"no intersection\n";
return ret;
}else{
term1=fabs(term1);
// std::cout<< "term1="<<term1 <<" threshold: "<< RS_TOLERANCE * d2 <<std::endl;
if( term1 < RS_TOLERANCE * d2 ) {
//tangential;
// ret=RS_VectorSolutions(p - d*(a1/d2));
ret=RS_VectorSolutions({line->getNearestPointOnEntity(c, false)});
ret.setTangent(true);
// std::cout<<"Tangential point: "<<ret<<std::endl;
return ret;
}
double t = sqrt(fabs(term1));
//two intersections
return RS_VectorSolutions({ p + d*(t-a1)/d2, p -d*(t+a1)/d2});
}
// // root term:
// term1 = r*r - delta.squared() + term1*term1/d.squared();
// double term = RS_Math::pow(RS_Vector::dotP(d, delta), 2.0)
// - RS_Math::pow(d.magnitude(), 2.0)
// * (RS_Math::pow(delta.magnitude(), 2.0) - RS_Math::pow(r, 2.0));
// std::cout<<"old term= "<<term<<"\tnew term= "<<term1<<std::endl;
// // no intersection:
// if (term<0.0) {
// ret = RS_VectorSolutions() ;
// }
// // one or two intersections:
// else {
// double t1 = (- RS_Vector::dotP(d, delta) + sqrt(term))
// / RS_Math::pow(d.magnitude(), 2.0);
// double t2;
// bool tangent = false;
// // only one intersection:
// if (fabs(term)<RS_TOLERANCE) {
// t2 = t1;
// tangent = true;
// }
// // two intersections
// else {
// t2 = (-RS_Vector::dotP(d, delta) - sqrt(term))
// / RS_Math::pow(d.magnitude(), 2.0);
// }
// RS_Vector sol1;
// RS_Vector sol2(false);
// sol1 = p + d * t1;
// if (!tangent) {
// sol2 = p + d * t2;
// }
// ret = RS_VectorSolutions(sol1, sol2);
// ret.setTangent(tangent);
// }
// std::cout<<"ret= "<<ret<<std::endl;
// return ret;
}
