  This paper is a companion paper to [Lipman and Daubechies 2011]. We provide
numerical procedures and algorithms for computing the alignment of and distance
between two disk type surfaces. We provide a convergence analysis of the
discrete approximation to the arising mass-transportation problems. We
furthermore generalize the framework to support sphere-type surfaces, and prove
a result connecting this distance to local geodesic distortion. Lastly, we
provide numerical experiments on several surfaces' datasets and compare to
state of the art method.
