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The algebraic specification of spatial data types with applications to constructive volume geometry. / KENNETH JOHNSON

Swansea University Author: KENNETH JOHNSON

Abstract

Spatial objects are modelled as total functions, mapping a topological space of points to a topological algebra of data attributes. High-level operations on these spatial objects form algebras of spatial objects, which model spatial data types. This thesis presents a comprehensive account of the the...

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Published: 2007
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42232
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spelling 2020-09-03T09:58:32.1894324 v2 42232 2018-08-02 The algebraic specification of spatial data types with applications to constructive volume geometry. f4bf38850e7c1f0208dac9a587ad4c57 KENNETH JOHNSON KENNETH JOHNSON true false 2018-08-02 Spatial objects are modelled as total functions, mapping a topological space of points to a topological algebra of data attributes. High-level operations on these spatial objects form algebras of spatial objects, which model spatial data types. This thesis presents a comprehensive account of the theory of spatial data types. The motivation behind the general theory is Constructive Volume Geometry (CVG). CVG is an algebraic framework for the specification, representation and manipulation of graphics objects in 3D. By using scalar fields as the basic building blocks, CVG gives an abstract representation of spatial objects, with the goal of unifying the many representations of objects used in 3D computer graphics today. The general theory developed in this thesis unifies discrete and continuous spatial data, and the many examples where such data is used - from computer graphics to hardware design. Such a theory is built from the algebraic and topological properties of spatial data types. We examine algebraic laws, approximation methods, and finiteness and computability for general spatial data types. We show how to apply the general theory to modelling (i) hardware and (ii) CVG. We pose the question "Which spatial objects can be represented in the algebraic framework developed for spatial data types?". To answer such a question, we analyse the expressive power of our algebraic framework. Applying our results to the CVG framework yields a new result: We show any CVG spatial object can be approximated by way of CVG terms, to arbitrary accuracy. E-Thesis Computer science. 31 12 2007 2007-12-31 COLLEGE NANME COLLEGE CODE Swansea University Doctoral Ph.D 2020-09-03T09:58:32.1894324 2018-08-02T16:24:28.5109848 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science KENNETH JOHNSON 1 0042232-02082018162438.pdf 10797940.pdf 2018-08-02T16:24:38.4170000 Output 5939748 application/pdf E-Thesis true 2018-08-02T00:00:00.0000000 false
title The algebraic specification of spatial data types with applications to constructive volume geometry.
spellingShingle The algebraic specification of spatial data types with applications to constructive volume geometry.
KENNETH JOHNSON
title_short The algebraic specification of spatial data types with applications to constructive volume geometry.
title_full The algebraic specification of spatial data types with applications to constructive volume geometry.
title_fullStr The algebraic specification of spatial data types with applications to constructive volume geometry.
title_full_unstemmed The algebraic specification of spatial data types with applications to constructive volume geometry.
title_sort The algebraic specification of spatial data types with applications to constructive volume geometry.
author_id_str_mv f4bf38850e7c1f0208dac9a587ad4c57
author_id_fullname_str_mv f4bf38850e7c1f0208dac9a587ad4c57_***_KENNETH JOHNSON
author KENNETH JOHNSON
author2 KENNETH JOHNSON
format E-Thesis
publishDate 2007
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description Spatial objects are modelled as total functions, mapping a topological space of points to a topological algebra of data attributes. High-level operations on these spatial objects form algebras of spatial objects, which model spatial data types. This thesis presents a comprehensive account of the theory of spatial data types. The motivation behind the general theory is Constructive Volume Geometry (CVG). CVG is an algebraic framework for the specification, representation and manipulation of graphics objects in 3D. By using scalar fields as the basic building blocks, CVG gives an abstract representation of spatial objects, with the goal of unifying the many representations of objects used in 3D computer graphics today. The general theory developed in this thesis unifies discrete and continuous spatial data, and the many examples where such data is used - from computer graphics to hardware design. Such a theory is built from the algebraic and topological properties of spatial data types. We examine algebraic laws, approximation methods, and finiteness and computability for general spatial data types. We show how to apply the general theory to modelling (i) hardware and (ii) CVG. We pose the question "Which spatial objects can be represented in the algebraic framework developed for spatial data types?". To answer such a question, we analyse the expressive power of our algebraic framework. Applying our results to the CVG framework yields a new result: We show any CVG spatial object can be approximated by way of CVG terms, to arbitrary accuracy.
published_date 2007-12-31T03:52:34Z
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score 11.012678

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