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Vertex Configurations and Their Relationship on Orthogonal Pseudo-Polyhedra
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1083579Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1109
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