/// <summary>
/// This method calculates the distance to a Line L
/// The parameter Lam1 can be taken to calculate the point, which has the lowest distance to
/// the other Line L . Nearest1 = Value(Lam1).
/// The parameter Lam2 can be taken to calculate the point of L , which has the lowest distance to
/// the Linetype this. Nearest2 = L.Value(Lam2).
/// </summary>
/// <param name="L">The other LineType</param>
/// <param name="Lam1">Paramter which belongs to this line : Nearest1 = Value(Lam1)</param>
/// <param name="Lam2">Paramter which belongs to the Line L: Nearest2 = L.Value(Lam2)</param>
/// <param name="Nearest1">The point on the Line, which has the smallest distance to the Line L</param>
/// <param name="Nearest2">The point on the Line L, which has the smallest distance </param>
/// <returns>Returns the distance to the line L</returns>
public double Distance(LineType L, out double Lam1, out double Lam2, out xyz Nearest1, out xyz Nearest2)
{
xyz PQ = L.P.sub(P);
double PQV = PQ.Scalarproduct(Direction);
double PQW = PQ.Scalarproduct(L.Direction);
double vv = Direction.Scalarproduct(Direction);
double ww = L.Direction.Scalarproduct(L.Direction);
double vw = L.Direction.Scalarproduct(Direction);
double Det = vv * ww - vw * vw;
if (Det == 0)// parallele
{
xyz n = PQ.cross(Direction).cross(Direction).normalized();
double result = PQ.Scalarproduct(n);
Nearest2 = P.add(n.mul(result));
Nearest1 = P;
Lam1 = 0;
Lam2 = L.Direction.normalized().Scalarproduct(Nearest2.sub(L.P));
return(System.Math.Abs(result));
}
else
{
Lam1 = (PQV * ww - PQW * vw) / Det;
Lam2 = -(PQW * vv - PQV * vw) / Det;
Nearest1 = P.add(Direction.mul(Lam1));
Nearest2 = L.P.add(L.Direction.mul(Lam2));
return(Nearest1.dist(Nearest2));
}
}
