std::pair<Vect3,double> VectFuns::intersectionAvgZ(const Vect3& so1, const Vect3& so2, double dto, const Vect3& si1, const Vect3& si2) {
Velocity vo3 = Velocity::genVel(so1, so2, dto);
Velocity vi3 = Velocity::genVel(si1, si2, dto); // its ok to use any time here, all times are relative to so
std::pair<Vect3,double> iP = intersection(so1,vo3,si1,vi3);
Vect3 interSec = iP.first;
double do1 = distanceH(so1,interSec);
double do2 = distanceH(so2,interSec);
double alt_o = so1.z;
if (do2 < do1) alt_o = so2.z;
double di1 = distanceH(si1,interSec);
double di2 = distanceH(si2,interSec);
double alt_i = si1.z;
if (di2 < di1) alt_i = si2.z;
double nZ = (alt_o + alt_i)/2.0;
return std::pair<Vect3,double>(interSec.mkZ(nZ),iP.second);
}
/**
* 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);
}
