Vect2 Vect2::intersect_pt(const Vect2& s0, const Vect2& v0, const Vect2& s1, const Vect2& v1) {
if (Util::almost_equals(v0.det(v1),0.0)) {
//fpln(" $$$$$$$$ ERROR $$$$$$$$$");
return Vect2::INVALID();
} else {
Vect2 delta = s1.Sub(s0);
double ss = delta.det(v1)/v0.det(v1);
return s0.Add(v0.Scal(ss));
}
}
std::pair<Vect2,double> VectFuns::intersection(const Vect2& so, const Vect2& vo, const Vect2& si, const Vect2& vi) {
Vect2 ds = si.Sub(so);
if (vo.det(vi) == 0) {
//f.pln(" $$$ intersection: lines are parallel");
return std::pair<Vect2,double>(Vect2::ZERO(), NaN);
}
double tt = ds.det(vi)/vo.det(vi);
Vect2 intersec = so.Add(vo.Scal(tt));
return std::pair<Vect2,double>(intersec,tt);
}
/**
* Computes 2D intersection point of two lines, but also finds z component (projected by time from line 1)
* @param s0 starting point of line 1
* @param v0 direction vector for line 1
* @param s1 starting point of line 2
* @param v1 direction vector of line 2
* @return Pair (2-dimensional point of intersection with 3D projection, relative time of intersection, relative to the so3)
* If the lines are parallel, this returns the pair (0,NaN).
*/
double VectFuns::timeOfIntersection(const Vect3& so3, const Velocity& vo3, const Vect3& si3, const Velocity& vi3) {
Vect2 so = so3.vect2();
Vect2 vo = vo3.vect2();
Vect2 si = si3.vect2();
Vect2 vi = vi3.vect2();
Vect2 ds = si.Sub(so);
if (vo.det(vi) == 0) {
//f.pln(" $$$ intersection: lines are parallel");
return NaN;
}
double tt = ds.det(vi)/vo.det(vi);
//f.pln(" $$$ intersection: tt = "+tt);
return tt;
}
/**
* Computes 2D intersection point of two lines, but also finds z component (projected by time from line 1)
* @param s0 starting point of line 1
* @param v0 direction vector for line 1
* @param s1 starting point of line 2
* @param v1 direction vector of line 2
* @return Pair (2-dimensional point of intersection with 3D projection, relative time of intersection, relative to the so3)
* If the lines are parallel, this returns the pair (0,NaN).
*/
std::pair<Vect3,double> VectFuns::intersection(const Vect3& so3, const Velocity& vo3, const Vect3& si3, const Velocity& vi3) {
Vect2 so = so3.vect2();
Vect2 vo = vo3.vect2();
Vect2 si = si3.vect2();
Vect2 vi = vi3.vect2();
Vect2 ds = si.Sub(so);
if (vo.det(vi) == 0) {
//f.pln(" $$$ intersection: lines are parallel");
return std::pair<Vect3,double>(Vect3::ZERO(), NaN);
}
double tt = ds.det(vi)/vo.det(vi);
//f.pln(" $$$ intersection: tt = "+tt);
Vect3 intersec = so3.Add(vo3.Scal(tt));
double nZ = intersec.z;
double maxZ = Util::max(so3.z,si3.z);
double minZ = Util::min(so3.z,si3.z);
if (nZ > maxZ) nZ = maxZ;
if (nZ < minZ) nZ = minZ;
return std::pair<Vect3,double>(intersec.mkZ(nZ),tt);
}
