/// <summary>
/// This method calculates the distance to a point Pt.
/// The parameter Lam can be used to calculate the nearest point of the LineType, which is
/// also returned by the outvalue Nearest
/// </summary>
/// <param name="Pt">Point to calculate the distance to the LineType</param>
/// <param name="Lam">Parameter to calculate the nearest point</param>
/// <param name="Nearest">Point on the Line, with the lowest distance to Pt</param>
/// <returns>Returns the distance from the line to the point Pt</returns>
public double Distance(xyz Pt, out double Lam, out xyz Nearest)
{
if (Utils.Equals(Direction.length(), 0))
{
Lam = 0;
Nearest = P;
return(Pt.dist(P));
}
Lam = Direction.normalized().Scalarproduct(Pt.sub(P)) / Direction.length();
Nearest = P.add(Direction.mul(Lam));
return(Nearest.dist(Pt));
}
/// <summary>
/// Calculates the absolute coordinates of the point, whose coordinates are related to the Base.
/// The base is assumed to be normalized.
/// The invert method is <see cref="Relativ"/>.
/// </summary>
/// <param name="pt">Point</param>
/// <returns>returns the absolut coordinates in a worldbase</returns>
public xyz Absolut(xyz pt)
{
//xyz d=pt.sub(BaseO);
if ((!Utils.Equals(BaseX.length(), 1f)) || (!Utils.Equals(BaseY.length(), 1f)) || (!Utils.Equals(BaseZ.length(), 1f)))
{
}
return(BaseO.add(BaseX.mul(pt.x)).add(BaseY.mul(pt.y)).add(BaseZ.mul(pt.z)));
}
/// <summary>
/// Calculates the cross product over all xyzArray by adding the cross products.
/// If the Loxyz is plane then cross is a normal of this plane?
/// </summary>
/// <returns>Return the cross product over all xyzArrays contained in it</returns>
public xyz cross()
{
xyz result = new xyz(0, 0, 0);
for (int i = 0; i < Count; i++)
{
result = result.add(this[i].cross());
}
return(result);
}
/// <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);
}