/// <summary>
/// Computes the distance from a point p to a line segment AB.
/// Note: NON-ROBUST!
/// </summary>
/// <param name="p">The point to compute the distance for.</param>
/// <param name="A">One point of the line.</param>
/// <param name="B">Another point of the line (must be different to A).</param>
/// <returns> The distance from p to line segment AB.</returns>
public static double DistancePointLine(Coordinate2D p, Coordinate2D A, Coordinate2D B)
{
// if start = end, then just compute distance to one of the endpoints
if (A.X == B.X && A.Y == B.Y)
{
return(p.CartesianDistance(A));
}
// otherwise use comp.graphics.algorithms Frequently Asked Questions method
/*(1) AC dot AB
* r = ---------
||AB||^2
* r has the following meaning:
* r=0 Point = A
* r=1 Point = B
* r<0 Point is on the backward extension of AB
* r>1 Point is on the forward extension of AB
* 0<r<1 Point is interior to AB
*/
var len2 = ((B.X - A.X) * (B.X - A.X) + (B.Y - A.Y) * (B.Y - A.Y));
var r = ((p.X - A.X) * (B.X - A.X) + (p.Y - A.Y) * (B.Y - A.Y)) / len2;
if (r <= 0.0)
{
return(p.CartesianDistance(A));
}
if (r >= 1.0)
{
return(p.CartesianDistance(B));
}
/*(2)
* (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
* s = -----------------------------
* Curve^2
* Then the distance from C to Point = |s|*Curve.
* This is the same calculation as {@link #distancePointLinePerpendicular}.
* Unrolled here for performance.
*/
var s = ((A.Y - p.Y) * (B.X - A.X) - (A.X - p.X) * (B.Y - A.Y)) / len2;
return(Math.Abs(s) * Math.Sqrt(len2));
}
