How to know if a line intersects a plane in C#?

Question

I have two points (a line segment) and a rectangle. I would like to know how to calculate if the line segment intersects the rectangle.

Answer 1

using System;

public class ThreeDVector

{

public static void Main(string[] args)

{

var ray = new ThreeDVector(0.0, -1.0, -1.0);

var rayPoint = new ThreeDVector(0.0, 0.0, 11.0);

var plane = new ThreeDVector(0.0, 0.0, 3.0);

var planePoint = new ThreeDVector(0.0, 0.0, 4.0);

Console.WriteLine("Intersection of the plane occurs at {0}", ThreeDVector.FindIntersection(ray, rayPoint, plane, planePoint));

}

private double x;

private double y;

private double z;

public ThreeDVector(double x, double y, double z)

{

this.x = x;

this.y = y;

this.z = z;

}

public static ThreeDVector operator +(ThreeDVector a, ThreeDVector b)

{

return new ThreeDVector(a.x + b.x, a.y + b.y, a.z + b.z);

}

public static ThreeDVector operator -(ThreeDVector a, ThreeDVector b)

{

return new ThreeDVector(a.x - b.x, a.y - b.y, a.z - b.z);

}

public static ThreeDVector operator *(ThreeDVector a, double b)

{

return new ThreeDVector(a.x * b, a.y * b, a.z * b);

}

public double Point(ThreeDVector a)

{

return this.x * a.x + this.y * a.y + this.z * a.z;

}

public static ThreeDVector FindIntersection(ThreeDVector ray, ThreeDVector rayPoint, ThreeDVector plane, ThreeDVector planePoint)

{

return rayPoint - ray * ((rayPoint - planePoint).Point(plane) / ray.Point(plane));

}

public override string ToString()

{

return string.Format("({0:F}, {1:F}, {2:F})", this.x, this.y, this.z);

}

}