Subdivision algorithms and the kernel of a polyhedron
type: Item
instance of: scholarly article
title: Subdivision algorithms and the kernel of a polyhedron
zbMATH Open document ID: 0764.52004
DOI: 10.1007/BF02293056
author: Michael Kallay
author: Richard J. Gardner
published in: Discrete \& Computational Geometry
publication date: 1992-12-17T00:00:00Z
full work available at URL: https://eudml.org/doc/131228
review text: The Fejes-Tóth kernel of a complex polytope is the limiting set obtained when iteratively taking the convex hull of the midpoints of all edges (midpoint process). It is shown that in dimension 3 this kernel has no 2-dimensional faces, that the centroids of all facets obtained during the iterations is dense in the kernel's boundary, and that this boundary may not be twice continuously differentiable. The midpoint process is related to smoothing techniques used in CAD, thereby indicating limits to the smoothing obtained by such techniques in dimension 3. For another smoothing process defined by DOO, it is shown that the corresponding kernel may be nonconvex.
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 68U07
zbMATH DE Number: 77886
zbMATH Keywords: 3-polytopes
zbMATH Keywords: smoothing algorithm
zbMATH Keywords: Fejes-Tóth kernel
zbMATH Keywords: CAD
reviewed by: Frank Plastria
MaRDI profile type: Publication
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OpenAlex ID: W2073048911
description: scientific article; zbMATH DE number 77886