Spherical Parameterization of Marching Cubes IsoSurfaces Based upon Nearest Neighbor Coordinates

We present some new methods for parameterizing the triangle mesh surface (TMS) which result from the Marching Cubes (MC) algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sphere. We take advantage of some special properties of the TMS resulting from the MC algorithm to obtain simple, computational efficient representations of the nearest neighbor coordinates and utilize these coordinates in the characterization of the parameterization by means of systems of equations which are solved iteratively. Examples and comparisons are presented. This work is supported by the US Army Research Office under contract W911NF-05-1-0301 and the US National Science Foundation.