Design of The Geometry2D Class

Details

Vectors of Different Size:

If these methods are passed vectors with more than two elements they must ignore all "irrelevant" elements. That is, you must assume that they are filled-out with "garbage".

Side Effects:

The methods in this class must NOT change the parameters they are passed.

The area() Method:

This class must include an implementation of the following method:

    /**
     * Compute the area of a triangle from its three vertices
     *
     * The verteces can be assumed to be ordered correctly
     * (i.e., obey the right-hand rule)
     * 
     * @param a  The first vertex
     * @param b  The second vertex
     * @param c  The third vertex
     */
    public static double area(double[] a, double[] b, double[] c)
  

The intersect() Method:

This class must include an implementation of the following method:

    /**
     * Find the intersection of two lines
     *
     * This method returns null if the lines are parallel.
     * Otherwise, it returns the (convex combination) weights 
     * that define the intersection point.  Letting
     * alpha denote the weight for line 0 and 
     * beta denote the weight for line 1, the intersection
     * point is given by:
     *
     *    x: alpha*p[0] + (1-alpha)*q[0]
     *    y: alpha*p[1] + (1-alpha)*q[1]
     *
     * and or:
     *
     *    x: beta*r[0] + (1-beta)*s[0]
     *    y: beta*r[1] + (1-beta)*s[1]
     *
     * If alpha is in [0, 1] then the intersection point is
     * within the line segment from p to q.  Similarly, 
     * if beta is in [0, 1] then the intersection point is 
     * within the line segment from r to s.
     *
     * @param p  One endpoint of the line from p to q
     * @param q  The other endpoint of the line from p to q
     * @param r  One endpoint of the line from r to s
     * @param s  The other endpoint of  the line from r to s
     * @return   The weights (alpha,beta) or null if the lines are parallel
     */
    public static double[] intersect(double[] p, double[] q,
                                     double[] r, double[] s)