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.
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Nielson, G.M., Zhang, L., Lee, K., Huang, A. (2008). Parameterizing Marching Cubes Isosurfaces with Natural Neighbor Coordinates. In: Chen, F., Jüttler, B. (eds) Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, vol 4975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79246-8_24
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DOI: https://doi.org/10.1007/978-3-540-79246-8_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79245-1
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