Building a ray tracer is simple. First we start with a convenient vector algebra library.

class Vector3D {
    public float x, y, z;

    // constructors
    public Vector3D( ) { }
    public Vector3D(float x, float y, float z);
    public Vector3D(Vector3D v);

    // methods
    public float dot(Vector3D B);                         // this with B
    public float dot(float Bx, float By, float Bz);       // B spelled out
    public static float dot(Vector3D A, Vector3D B);      // A dot B

    public Vector3D cross(Vector3D B);                    // this with B
    public Vector3D cross(float Bx, float By, float Bz);  // B spelled out
    public static Vector3D cross(Vector3D A, Vector3D B); // A cross B

    public float length( );                               // of this
    public static float length(Vector3D A);               // of A

    public void normalize( );                             // makes this unit length
    public static Vector3D normalize(Vector3D A);         // makes A unit length

    public String toString();                             // convert to a string
}