/// <summary>
/// Computes the distance from a line segment AB to a line segment CD
/// <para/>
/// Note: NON-ROBUST!
/// </summary>
/// <param name="A">The first point of the first line</param>
/// <param name="B">The second point of the first line (must be different to A)</param>
/// <param name="C">The first point of the second line</param>
/// <param name="D">The second point of the second line (must be different to C)</param>
/// <returns>The distance from a line segment AB to a line segment CD</returns>
public static double SegmentToSegment(Coordinate A, Coordinate B,
Coordinate C, Coordinate D)
{
// check for zero-length segments
if (A.Equals(B))
{
return(DistanceComputer.PointToSegment(A, C, D));
}
if (C.Equals(D))
{
return(DistanceComputer.PointToSegment(D, A, B));
}
// AB and CD are line segments
/*
* from comp.graphics.algo
*
* Solving the above for r and s yields
*
* (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
* r = ----------------------------- (eqn 1)
* (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
*
* (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
* s = ----------------------------- (eqn 2)
* (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
*
* Let P be the position vector of the
* intersection point, then
* P=A+r(B-A) or
* Px=Ax+r(Bx-Ax)
* Py=Ay+r(By-Ay)
* By examining the values of r & s, you can also determine some other limiting
* conditions:
* If 0<=r<=1 & 0<=s<=1, intersection exists
* r<0 or r>1 or s<0 or s>1 line segments do not intersect
* If the denominator in eqn 1 is zero, AB & CD are parallel
* If the numerator in eqn 1 is also zero, AB & CD are collinear.
*/
var noIntersection = false;
if (!Envelope.Intersects(A, B, C, D))
{
noIntersection = true;
}
else
{
double denom = (B.X - A.X) * (D.Y - C.Y) - (B.Y - A.Y) * (D.X - C.X);
if (denom == 0)
{
noIntersection = true;
}
else
{
double r_num = (A.Y - C.Y) * (D.X - C.X) - (A.X - C.X) * (D.Y - C.Y);
double s_num = (A.Y - C.Y) * (B.X - A.X) - (A.X - C.X) * (B.Y - A.Y);
double s = s_num / denom;
double r = r_num / denom;
if ((r < 0) || (r > 1) || (s < 0) || (s > 1))
{
noIntersection = true;
}
}
}
if (noIntersection)
{
return(MathUtil.Min(
DistanceComputer.PointToSegment(A, C, D),
DistanceComputer.PointToSegment(B, C, D),
DistanceComputer.PointToSegment(C, A, B),
DistanceComputer.PointToSegment(D, A, B)));
}
// segments intersect
return(0.0);
}
public static double DistancePointLine(Coordinate p, Coordinate A, Coordinate B)
{
return(DistanceComputer.PointToSegment(p, A, B));
}