Rash thoughts about .NET, C#, F# and Dynamics NAV.

In one of my next postings I will show a algorithm, that calculates line segment intersections. As a prerequisite we need an algorithm, which calculates the intersection of two lines. In this post I will consider the following intersection of two lines in the euclidean plan:

We can write this as an equation system with two variables and two equations:

• Ax + r (Bx – Ax) = Cx + s (Dx – Cx)
• Ay + r (By – Ay) = Cy + s (Dy – Cy)

After solving this system we can calculate the intersection:

• Px = Ax + r (Bx – Ax)
• Py = Ay + r (By – Ay)

Putting this all together we can derive the following F#-code:

let calcIntersection (A:Location, B:Location, C:Location, D:Location) =
  let (Ax,Ay,Bx,By,Cx,Cy,Dx,Dy) =
     (A.XPos, A.YPos, B.XPos, B.YPos, C.XPos, C.YPos, D.XPos, D.YPos)
  let d = (Bx-Ax)*(Dy-Cy)-(By-Ay)*(Dx-Cx)  

  if  d = 0 then
    // parallel lines ==> no intersection in euclidean plane
    None
  else
    let q = (Ay-Cy)*(Dx-Cx)-(Ax-Cx)*(Dy-Cy) 
    let r = q / d
    let p = (Ay-Cy)*(Bx-Ax)-(Ax-Cx)*(By-Ay)
    let s = p / d

    if r < 0. or r > 1. or s < 0. or s > 1. then
      None // intersection is not within the line segments
    else
      Some(
        (Ax+r*(Bx-Ax)),  // Px
        (Ay+r*(By-Ay)))  // Py

Remarks:

1. If one given line degenerates into a point, then the algorithm gives no intersection.
2. If the given lines are parallel, then the algorithm gives no intersection, even if the lines have an overlap.