Tetrahedral meshes from planar cross-sections
type: Item
instance of: scholarly article
title: Tetrahedral meshes from planar cross-sections
zbMATH Open document ID: 0981.74081
DOI: 10.1016/S0045-7825(99)00030-4
author: Chandrajit L. Bajaj
author: Edward J. Coyle
author: Kwun-Nan Lin
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2001-01-18T00:00:00Z
review text: Conclusion: We present a new approach to build a three-dimensional triangular mesh from planar contours. There are two main contributions in this paper. The first contribution is the characterization, prevention, and postprocessing of untetrahedralizable parts. The tetrahedralizability characterization of a general polyhedron is shown to be NP-complete. Under reasonable constraints on degenerate problem domain, we characterize this problem based on a group operator, and develop a rule to reduce the chance of generating untetrahedralizable remaining parts. The characterization also helps the postprocessing of untetrahedralizable parts if they occur. The second contribution is an algorithm to reduce a non-prismatoid into one or more prismatoids. This algorithm is guaranteed to work on the non-prismatoids generated by a surface construction program.
Mathematics Subject Classification ID: 74S99
Mathematics Subject Classification ID: 74L15
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 1442938
zbMATH Keywords: reduction of non-prismatoids
zbMATH Keywords: three-dimensional triangular mesh
zbMATH Keywords: untetrahedralizable part
zbMATH Keywords: tetrahedralizability
zbMATH Keywords: group operator
zbMATH Keywords: postprocessing
zbMATH Keywords: surface construction program
MaRDI profile type: Publication
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full work available at URL: s0045-7825(99)00030-4
OpenAlex ID: W2074709057
description: scientific article; zbMATH DE number 1442938