Representing geometric structures in \(d\) dimensions: Topology and order
type: Item
instance of: scholarly article
title: Representing geometric structures in \(d\) dimensions: Topology and order
zbMATH Open document ID: 0783.68129
DOI: 10.1007/BF02189330
author: Erik Brisson
published in: Discrete \& Computational Geometry
publication date: 1993-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/131254
review text: The work investigates data structures for representing and manipulating \(d\)-dimensional geometric objects for arbitrary \(d\geq 1\). A class of geometric objects is defined, the `subdivided \(d\)-manifolds', which is large enough to encompass many applications. A new representation is given for such objects, the `cell-tuple structure', which provides direct access to topological structure, ordering information among cells, the topological dual, and boundaries. The cell-tuple structure gives a simple, uniform representation of subdivided manifolds which unifies the existing work in the field and provides intuitive clarity in all dimensions. The dual subdivision, and boundaries, are represented consistently. The work has direct applications in solid modeling, computer graphics, and computational geometry.
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 203063
zbMATH Keywords: subdivided \(d\)-manifolds
zbMATH Keywords: cell-tuple structure
MaRDI profile type: Publication
cites work: Q3814809
cites work: A Representation of 2-dimensional Pseudomanifolds and its use in the Design of a Linear-Time Shelling Algorithm
cites work: On tilings of the plane
cites work: Q3772828
cites work: Constructing Arrangements of Lines and Hyperplanes with Applications
cites work: The classification of quasi-regular polyhedra of genus 2
cites work: Q5547252
cites work: Primitives for the manipulation of general subdivisions and the computation of Voronoi
cites work: Two-Dimensional Voronoi Diagrams in the L p -Metric
cites work: Q3800058
cites work: Topological models for boundary representation: A comparison with \(n\)- dimensional generalized maps
cites work: Q5607712
cites work: Q3267404
cites work: Finding the intersection of two convex polyhedra
cites work: Q4064159
cites work: Q3827224
cites work: Convex hulls of finite sets of points in two and three dimensions
cites work: Constructive non-regularized geometry
cites work: Incidence graphs of convex polytopes
cites work: THE PROBLEM OF DISCRIMINATING ALGORITHMICALLY THE STANDARD THREE-DIMENSIONAL SPHERE
description: scientific article; zbMATH DE number 203063