Foundation of a computable solid modelling.
type: Item
instance of: scholarly article
title: Foundation of a computable solid modelling.
zbMATH Open document ID: 1042.68111
DOI: 10.1016/S0304-3975(01)00091-3
author: Abbas Edalat
author: A. Lieutier
published in: Theoretical Computer Science
publication date: 2002-07-31T00:00:00Z
review text: Solid modelling and computational geometry are based on classical topology and geometry in which the basic predicates and operations, such as membership, subset inclusion, union and intersection, are not continuous and therefore not computable. But a sound computational framework for solids and geometry can only be built in a framework with computable predicates and operations. In practice, correctness of algorithms in computational geometry is usually proved using the unrealistic Real RAM machine model of computation, which allows comparison of real numbers, with the undesirable result that correct algorithms, when implemented, turn into unreliable programs. Here, we use a domain-theoretic approach to recursive analysis to develop the basis of an effective and realistic framework for solid modelling. This framework is equipped with a well defined and realistic notion of computability which reflects the observable properties of real solids. The basic predicates and operations on solids are computable in this model which admits regular and non-regular sets and supports a design methodology for actual robust algorithms. Moreover, the model is able to capture the uncertainties of input data in actual CAD situations.
Mathematics Subject Classification ID: 68U07
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 1774166
zbMATH Keywords: Solid modelling
zbMATH Keywords: Robustness
zbMATH Keywords: Model of computation
zbMATH Keywords: Domain theory
zbMATH Keywords: Turing computability
describes a project that uses: GCLC
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1774166