Parameterizing marching cubes isosurfaces with natural neighbor coordinates

Authors:
Gregory M. Nielson;Liyan Zhang;Kun Lee;Adam Huang
Affiliations:
Arizona State University, Tempe, AZ;Nanjing University of Aeronautics and Astronautics, Nanjing, China;Handong Global University, Pohang, Kyungbuk, South Korea;National Taiwan University Hospital, Taipei, Taiwan
Venue:
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Year:
2008

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Abstract

The triangular mesh surfaces (TMS) which result form the Marching Cubes (MC) algorithm have some unique and special properties not shared by general TMS. We exploit some of these properties in the development of some new, effective and efficient methods for parameterizing these surfaces. The parameterization consists of a planar triangulation which is isomorphic (maps one-to-one) to the triangular mesh. The parameterization is computed as the solution of a sparse linear system of equations which is based upon the fact that locally the MC surfaces are functions (height-fields). The coefficients of the linear system utilize natural neighbor coordinates (NNC) which depend upon Dirchlet tessellations. While the use of NNC for general TMS can be somewhat computationally expensive and is often done procedurally, for the present case of MC surfaces, we are able to obtain simple and explicit formulas which lead to efficient computational algorithms.