Towards a topology for computational geometry
type: Item
instance of: scholarly article
title: Towards a topology for computational geometry
zbMATH Open document ID: 0824.65150
DOI: 10.1016/0010-4485(95)91141-7
author: Sean Michael Barker
published in: CAD. Computer-Aided Design
publication date: 1995-07-24T00:00:00Z
review text: The author notes that computations in finite precision can lead to impossible solutions, in particular in intersection problems that are close to singular. He proposes to deal with the problem in two steps. The first is to use different criteria for identifying two points or asserting their distinctness; another approach to the same problem is to consider the identification of two points as a fuzzy problem. The second step is to use halfspaces to test for compatible topologies (at least for computational problems of linear geometry). An unanswered problem is the construction of an algorithm that suggests coherent solutions in case the halfspace test turns up an inconsistency in the computed numbers.
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 777941
zbMATH Keywords: computational geometry
zbMATH Keywords: intersection problems
zbMATH Keywords: fuzzy problem
zbMATH Keywords: compatible topologies
zbMATH Keywords: linear geometry
zbMATH Keywords: algorithm
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
full work available at URL: 0010-4485(95)91141-7
OpenAlex ID: W1966053830
description: scientific article; zbMATH DE number 777941