Rectangle Ray Intersection

Question

Im making a simple Ray Traycer in C#. And for my viewport I have a rectangle class.

public class Rectangle3D
{
    public readonly Point3D Point1;
    public readonly Point3D Point2;
    public readonly Point3D Point3;
    public readonly Point3D Point4;

    public Rectangle3D(Point3D point1, Point3D point2, Point3D point3, Point3D point4)
    {
        this.Point1 = point1;
        this.Point2 = point2;
        this.Point3 = point3;
        this.Point4 = point4;
    }

    public Point3D FindCrossPoint(Ray ray)
    {
        //Intersection
    }

how would I go about writing this function. Help is much appreciated. P.S Point3D has all the needed functions. Such as cross,normalize etc...

I tried representing a rectangle through triangles and then testing collision but that way to complicated really fast. And I didn't say for you guys to write the code I asked, how should I write it. Trust me I'm not trying to be lazy even if it does look like that. I'm also really naïve to this field. Thank you. — Armen Aghajanyan, Jul 20 '13 at 02:04
I did line-line intersection in 3D. But I don't understand how to do this for a rectangle — Armen Aghajanyan, Jul 20 '13 at 02:10
okay... so I understand how to solve the equation above. But how do you find a plane from 4 points? P.S Never learned this in school. I'm just 15 — Armen Aghajanyan, Jul 20 '13 at 02:23

Eric Lippert · Accepted Answer · 2013-07-20T02:45:17.140

All right, let's put this in the form of an answer instead of all those comments.

Break your problem down into sub-problems:

1) Find the plane that the rectangle lies on, in the form Ax+By+Cz+D=0 Two methods:

Method one:

Find the equations of two orthogonal lines; the edges of the rectangle will be orthogonal by definition.
Given two orthogonal lines, figure out how to get the equation of the plane the lines define, in the form Ax+By+Cz+D=0.

Some hints here:

Suppose the two orthogonal lines were both going through the origin. Make them vectors. What is the meaning of the cross product of those two vectors?
What is the relationship between the cross product vector and the plane you're seeking? Specifically, what is the relationship between the cross product vector, and the constants A, B and C?

Method two:

Pick three of the points on the rectangle that do not lie in a line; obviously any three corners will do. Substitute those points in for x, y, z in Ax+By+Cz+D=0 to make three new equations; solve those equations for A, B, C and D.

2) Once you have the equation of the plane, work out the intersection of the plane with the ray.

3) Now that you have the intersection point -- if it exists, remember, the ray might be parallel to the plane or might be entirely in the plane -- check to see if the intersection point is inside the rectangle.

Hint: this is a special case of the more general problem of "is this point inside a polygon".

Rectangle Ray Intersection

1 Answers1