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A topological model for a 3-dimensional spatial information system

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Pigot, SP 1995 , 'A topological model for a 3-dimensional spatial information system', PhD thesis, University of Tasmania.

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Abstract

This thesis proposes the topological theory necessary to extend the conventional
topological models used in geographic information systems (GIS), computer-aided
design (CAD) and computational geometry, to a 3-dirnensional spatial information
system (SIS) which supports query and analysis of spatial relationships.
To encompass a wide range of applications and minirniz.e fragmentation, we define a
spatial object as a cell complex, where each k-cell is homeomorphic to a Euclidean kmanifold
with one or more subdivided (k-1)-manifold boundary cycles. The sirnplicial
and regular cell complexes currently used in topology and many spatial information
systems, are restricted forms of these generaliz.ed regular cell complexes.
Spatial relationships between the cells of the generalized regular cell complex are
expressed 4i terms of their boundary and coboundary cells. To support query and
traversal of the neighborhood of any cell via orderings of its cobounding cells, we
embed the generalized regular k-cell complex in a Euclidean n-manifold which we
represent as a 'world' n-cell.
Spatial relationships between spatial objects can be expressed in terms of the boundary
and co boundary relations between the cells of another complex formed from the union
of the generalized regular cell complexes. If this complex is embedded in a Euclidean nmanifold,
then co bounding cells may also be ordered. The cells of this complex have
'singular manifold' or 'pseudomanifold' boundary cycles, which we classify into three
primitive types using identification spaces. The cell complex is known as the generaliz.ed
singular cell complex - generalized regular, regular and simplicial complexes are
restricted forms of this complex.
To represent these cell complexes, we extend the implicit cell-tuple of Brisson (1990)
since it encapsulates the boundary-coboundary relations and the ordering information.
Topological operators are defined to construct spatial objects. Since the set of spatial
objects has few restrictions, we define topological operators which consistently
construct both subdivided manifolds and manifolds with boundary, from the strong
deformation retract of a manifold with boundary. The theory underlying these operators
is based on combinatorial homotopy. Generic versions of these topological construction
operators can then be used to join these subdivided manifolds or manifolds with
boundary, to form the generalized regular cell complex.

Item Type: Thesis - PhD
Authors/Creators:Pigot, SP
Keywords: Geographic information systems, Topological spaces
Copyright Holders: The Author
Copyright Information:

Copyright 1995 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

Additional Information:

Includes bibliographical references (p. 219-228). Thesis (Ph.D.)--University of Tasmania, 1996

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