One approach to measuring the similarity between two compact manifolds is to find the smallest amount that one manifold must be stretched to map diffeomorphically onto the other. Since the diffeomorphisms that realize this minimal stretching are examples of harmonic maps, applying this approach requires that we find a way to construct energy-minimizing harmonic maps between real-world objects. In this talk, we present our progress in developing a penalty-function method for constructing harmonic maps between manifolds known only by point clouds. Since the penalty functions are the most novel element in this method, we describe these functions in some detail.