Spherical Parameterization of Marching Cubes IsoSurfaces Based upon Nearest Neighbor Coordinates

We present some new methods for parameterizing thetriangle mesh surface (TMS) which result from the Marching Cubes (MC)algorithm. The methods apply to surfaces of genus zero and theparameter domain is a unit sphere. We take advantage of some specialproperties of the TMS resulting from the MC algorithm to obtain simple,computational efficient representations of the nearest neighborcoordinates and utilize these coordinates in the characterization ofthe parameterization by means of systems of equations which are solvediteratively. Examples and comparisons are presented.