Contouring 1- and 2-manifolds in arbitrary dimensions

Joon Kyung Seong, Gershon Elber, Myung Soo Kim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)


We propose an algorithm for contouring k-manifolds (k = 1,2) embedded in an arbitrary n-dimensional space. We assume (n-k) geometric constraints are represented as polynomial equations in n variables. The common zero-set of these (n-k) equations is computed as a 1- or 2-manifold, respectively, for k = 1 or k = 2. In the case of 1-manifolds, this framework is a generalization of techniques for contouring regular intersection curves between two implicitlydefined surfaces of the form F(x,y,z) = G(x,y,z) = 0. Moreover, in the case of 2-manifolds, the algorithm is similar to techniques for contouring iso-surfaces of the form F(x, y, z) = 0, where n = 3 and only one (= 3 -2) constraint is provided. By extending the Dual Contouring technique to higher dimensions, we approximate the simultaneous zero-set as a piecewise linear 1- or 2-manifold. There are numerous applications for this technique in data visualization and modeling, including the processing of various geometric constraints for freeform objects, and the computation of convex hulls, bisectors, blendings and sweeps.

Original languageEnglish
Title of host publicationProceedings - International Conference on Shape Modeling and Applications, SMI'05
PublisherIEEE Computer Society
Number of pages10
ISBN (Print)076952379X, 9780769523798
Publication statusPublished - 2005
Externally publishedYes
EventInternational Conference on Shape Modeling and Applications, SMI'05 - Cambridge, MA, United States
Duration: 2005 Jun 132005 Jun 17

Publication series

NameProceedings - International Conference on Shape Modeling and Applications, SMI'05


OtherInternational Conference on Shape Modeling and Applications, SMI'05
Country/TerritoryUnited States
CityCambridge, MA

ASJC Scopus subject areas

  • Engineering(all)


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