/// <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)); } }
/// <summary> /// Calculates the relative coordinates from point. /// The base is assumed to be normalized /// The invert method is <see cref="Absolut"/>. /// </summary> /// <param name="P">Point</param> /// <returns>returns the coordinates relative to the base</returns> public xyz Relativ(xyz P) { if ((System.Math.Abs(BaseX * BaseY) < double.Epsilon) && (System.Math.Abs(BaseX * BaseZ) < double.Epsilon) && (System.Math.Abs(BaseZ * BaseY) < double.Epsilon) ) // Orthogonal { xyz d = P.sub(BaseO); return(new xyz(d.Scalarproduct(BaseX.normalized()), d.Scalarproduct(BaseY.normalized()), d.Scalarproduct(BaseZ.normalized()))); } P = P - BaseO; double Det = xyz.dot(BaseX, BaseY, BaseZ); if (System.Math.Abs(Det) < 0.0000000000000000001) { xyz d = P.sub(BaseO); return(new xyz(d.Scalarproduct(BaseX), d.Scalarproduct(BaseY), d.Scalarproduct(BaseZ))); } else { } return(new xyz(xyz.dot(P, BaseY, BaseZ) / Det, xyz.dot(BaseX, P, BaseZ) / Det, xyz.dot(BaseX, BaseY, P) / Det)); }
/// <summary> /// Calculate the cross point with a line. /// </summary> /// <param name="aLine">A line which intersects the plane</param> /// <param name="Lam">Is a parameter, which determines the crosspoint</param> /// <param name="pt">Is the cross point</param> /// <returns>returns true, if there is a crosspoint.</returns> /// <example><code> /// //the following snippet shows the meaning of lam /// Plane p = new Plane( new xyz(0, 0, 0), new xyz(1, 5, 5)); /// LineType l = new LineType( new xyz (3,-1,3), new xyz(2, 1, 5)); /// if (p.Cross(l, out Lam, out pt)) /// { /// // you can also get p through the following /// pt = l.P + l.Direction*lam; /// } /// </code></example> public bool Cross(LineType aLine, out double Lam, out xyz pt) { pt = aLine.P; Lam = -1; xyz Direction = aLine.Direction.normalized(); double En = Direction.Scalarproduct(NormalUnit); if (System.Math.Abs(En) < Utils.epsilon) { return(false); } xyz OP = aLine.P; OP = OP.sub(P); Lam = -OP.Scalarproduct(NormalUnit) / En; pt = pt.add(Direction.mul(Lam)); Lam /= (aLine.P - aLine.Q).length(); return(true); }