Parameterizing marching cubes isosurfaces with natural neighbor coordinates

Gregory M. Nielson, Liyan Zhang, Kun Lee, Adam Huang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations


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.

Original languageEnglish
Title of host publicationAdvances in Geometric Modeling and Processing - 5th International Conference, GMP 2008, Proceedings
PublisherSpringer Verlag
Number of pages14
ISBN (Print)3540792457, 9783540792451
StatePublished - 2008
Event5th International Conference on Geometric Modeling and Processing, GMP 2008 - Hangzhou, China
Duration: 23 Apr 200825 Apr 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4975 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference5th International Conference on Geometric Modeling and Processing, GMP 2008


  • Marching Cubes
  • Natural Neighbor Coordinates
  • Parameterization


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