Find if point lays on line segment

Question

I have line segment defined by two points A(x1,y1,z1) and B(x2,y2,z2) and point p(x,y,z). How can I check if the point lays on the line segment?

Answer 1

Here's some C# code for the 2D case:

public static bool PointOnLineSegment(PointD pt1, PointD pt2, PointD pt, double epsilon = 0.001)
{
  if (pt.X - Math.Max(pt1.X, pt2.X) > epsilon || 
      Math.Min(pt1.X, pt2.X) - pt.X > epsilon || 
      pt.Y - Math.Max(pt1.Y, pt2.Y) > epsilon || 
      Math.Min(pt1.Y, pt2.Y) - pt.Y > epsilon)
    return false;

  if (Math.Abs(pt2.X - pt1.X) < epsilon)
    return Math.Abs(pt1.X - pt.X) < epsilon || Math.Abs(pt2.X - pt.X) < epsilon;
  if (Math.Abs(pt2.Y - pt1.Y) < epsilon)
    return Math.Abs(pt1.Y - pt.Y) < epsilon || Math.Abs(pt2.Y - pt.Y) < epsilon;

  double x = pt1.X + (pt.Y - pt1.Y) * (pt2.X - pt1.X) / (pt2.Y - pt1.Y);
  double y = pt1.Y + (pt.X - pt1.X) * (pt2.Y - pt1.Y) / (pt2.X - pt1.X);

  return Math.Abs(pt.X - x) < epsilon || Math.Abs(pt.Y - y) < epsilon;
}