Edgewise subdivision of a simplex
type: Item
instance of: scholarly article
title: Edgewise subdivision of a simplex
zbMATH Open document ID: 0968.51016
published in: Discrete \& Computational Geometry
publication date: 2001-09-11T00:00:00Z
review text: The main result of the paper is that, for every positive integer \(k\), every \(d\)-dimensional simplex can be decomposed into \(k^d\) simplices of dimension \(d\), all of the same volume and shape characteristics. The approach is based on an algebraic description of a simplex. The elementary model is very effective in the detailed analysis of the algorithm employed to construct a subdivision of a simplex, and is very convenient for computer representation of simplices and subdivisions. It is worth mentioning that the same model can be used to decompose a simplex into Cartesian product of simplices [see \textit{D. R. Grayson}, K-Theory 3, No. 3, 247-260 (1989; Zbl 0701.18007)]. The construction has been also used by \textit{T. N. T. Goodman} and \textit{J. Peters} [Comput. Aided Geom. Des. 12, No. 1, 53-65 (1995; Zbl 0875.68829)] to design smooth manifolds.
reviewed by: Mihai Cipu
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 68U07
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 1545822
zbMATH Keywords: simplex
zbMATH Keywords: subdivision of a simplex
zbMATH Keywords: barycentric coordinates
author: Herbert Edelsbrunner
author: Daniel R. Grayson
MaRDI profile type: Publication
full work available at URL: s004540010063
OpenAlex ID: W4231444415
DOI: 10.1007/S004540010063
description: scientific article; zbMATH DE number 1545822