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Vertex configurations and their relationship on orthogonal pseudo-polyhedra

Marzal, J., Xie, H. and Fung, C.C. (2011) Vertex configurations and their relationship on orthogonal pseudo-polyhedra. Proceedings of World Academy of Science, Engineering and Technology, 77 . pp. 1-8.

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    Abstract

    Vertex configuration for a vertex in an orthogonal pseudo-polyhedron is an identity of a vertex that is determined by the number of edges, dihedral angles, and non-manifold properties meeting at the vertex. There are up to sixteen vertex configurations for any orthogonal pseudo-polyhedron (OPP). Understanding the relationship between these vertex configurations will give us insight into the structure of an OPP and help us design better algorithms for many 3-dimensional geometric problems. In this paper, 16 vertex configurations for OPP are described first. This is followed by a number of formulas giving insight into the relationship between different vertex configurations in an OPP. These formulas will be useful as an extension of orthogonal polyhedra usefulness on pattern analysis in 3D-digital images.

    Publication Type: Journal Article
    Murdoch Affiliation: School of Information Technology
    Publisher: World Academy of Science, Engineering and Technology
    Copyright: Licensed under a Creative Commons License
    URI: http://researchrepository.murdoch.edu.au/id/eprint/4773
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