Domain representations of partial functions, with applications to spatial objects and constructive volume geometry.
type: Item
instance of: scholarly article
title: Domain representations of partial functions, with applications to spatial objects and constructive volume geometry.
zbMATH Open document ID: 1042.68108
DOI: 10.1016/S0304-3975(01)00065-2
author: John V. Tucker
author: Jens Blanck
author: Viggo Stoltenberg-Hansen
published in: Theoretical Computer Science
publication date: 2002-07-31T00:00:00Z
review text: A partial spatial object is a partial map from space to data. Data types of partial spatial objects are modelled by topological algebras of partial maps and are the foundation for a high level approach to volume graphics called Constructive Volume Geometry (CVG), where space and data are subspaces of \(n\)-dimensional Euclidean space. We investigate the computability of partial spatial object data types, in general and in volume graphics, using the theory of effective domain representations for topological algebras. The basic mathematical problem considered is to classify which partial functions between topological spaces can be represented by total continuous functions between given domain representations of the spaces. We prove theorems about partial functions on regular Hausdorff spaces and their domain representations, and apply the results to partial spatial objects and CVG algebras.
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 1774161
zbMATH Keywords: Effective domains
zbMATH Keywords: Topological spaces
zbMATH Keywords: Partial functions
zbMATH Keywords: Volume graphics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1774161