Rectangle Ray Intersection [closed]

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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...

Answer 1

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".