/// <summary>
/// Returns the projection of a point on the line defined with two other points.
/// When the projection is out of the segment, then the closest extremity is returned.
/// </summary>
/// <exception cref="ArgumentNullException">None of the arguments can be null.</exception>
/// <exception cref="ArgumentException">P1 and P2 must be different.</exception>
/// <param name="Pt">Point to project.</param>
/// <param name="P1">First point of the line.</param>
/// <param name="P2">Second point of the line.</param>
/// <returns>The projected point if it is on the segment / The closest extremity otherwise.</returns>
public static Point3D ProjectOnLine(Point3D Pt, Point3D P1, Point3D P2)
{
if (Pt == null || P1 == null || P2 == null)
{
throw new ArgumentNullException("None of the arguments can be null.");
}
if (P1.Equals(P2))
{
throw new ArgumentException("P1 and P2 must be different.");
}
Vector3D VLine = new Vector3D(P1, P2);
Vector3D V1Pt = new Vector3D(P1, Pt);
Vector3D Translation = VLine * (VLine | V1Pt) / VLine.SquareNorm;
Point3D Projection = P1 + Translation;
Vector3D V1Pjt = new Vector3D(P1, Projection);
double D1 = V1Pjt | VLine;
if (D1 < 0)
{
return(P1);
}
Vector3D V2Pjt = new Vector3D(P2, Projection);
double D2 = V2Pjt | VLine;
if (D2 > 0)
{
return(P2);
}
return(Projection);
}
/// <summary>
/// Returns the projection of a point on the line defined with two other points.
/// When the projection is out of the segment, then the closest extremity is returned.
/// </summary>
/// <exception cref="ArgumentNullException">None of the arguments can be null.</exception>
/// <exception cref="ArgumentException">P1 and P2 must be different.</exception>
/// <param name="Pt">Point to project.</param>
/// <param name="P1">First point of the line.</param>
/// <param name="P2">Second point of the line.</param>
/// <returns>The projected point if it is on the segment / The closest extremity otherwise.</returns>
public static Point3D ProjectOnLine(Point3D Pt, Point3D P1, Point3D P2)
{
if ( Pt==null || P1==null || P2==null ) throw new ArgumentNullException("None of the arguments can be null.");
if ( P1.Equals(P2) ) throw new ArgumentException("P1 and P2 must be different.");
Vector3D VLine = new Vector3D(P1, P2);
Vector3D V1Pt = new Vector3D(P1, Pt);
Vector3D Translation = VLine*(VLine|V1Pt)/VLine.SquareNorm;
Point3D Projection = P1+Translation;
Vector3D V1Pjt = new Vector3D(P1, Projection);
double D1 = V1Pjt|VLine;
if ( D1<0 ) return P1;
Vector3D V2Pjt = new Vector3D(P2, Projection);
double D2 = V2Pjt|VLine;
if ( D2>0 ) return P2;
return Projection;
}
