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Computer Application
Data Retrieval
Geographic Information System
Qualitative Spatial Reasoning
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Connectivity in the regular polytope representation
Connectivity in the regular polytope representation,10.1007/s1070700900943,Geoinformatica,Rodney James Thompson,Peter van Oosterom
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Connectivity in the regular polytope representation
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Citations: 3
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Rodney James Thompson
,
Peter van Oosterom
In order to be able to draw inferences about real world phenomena from a representation expressed in a digital computer, it is essential that the representation should have a rigorously correct algebraic structure. It is also desirable that the underlying algebra be familiar, and provide a close modelling of those phenomena. The fundamental problem addressed in this paper is that, since computers do not support realnumber arithmetic, the algebraic behaviour of the representation may not be correct, and cannot directly model a mathematical abstraction of space based on real numbers. This paper describes a basis for the robust geometrical construction of spatial objects in computer applications using a complex called the "Regular Polytope". In contrast to most other
spatial data
types, this definition supports a rigorous logic within a finite digital arithmetic. The definition of connectivity proves to be nontrivial, and alternatives are investigated. It is shown that these alternatives satisfy the relations of a
region connection calculus
(RCC) as used for qualitative spatial reasoning, and thus introduce the rigor of that reasoning to geographical information systems. They also form what can reasonably be termed a "Finite Boolean Connection Algebra". The rigorous and closed nature of the algebra ensures that these primitive functions and predicates can be combined to any desired level of complexity, and thus provide a useful toolkit for
data retrieval
and analysis. The paper argues for a model with two and threedimensional objects that have been coded in Java and which implement a full set of topological and connectivity functions which is shown to be complete and rigorous.
Journal:
Geoinformatica
, vol. 15, no. 2, pp. 223246, 2011
DOI:
10.1007/s1070700900943
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References
(24)
Proofs of Assertions in the Investigation of the Regular Polytope
(
Citations: 6
)
Rod Thompson
Published in 2005.
An introduction to the theory of spatial object modelling for GIS
(
Citations: 98
)
M. Molenaar
Published in 1998.
Verifiable Implementations of Geometric Algorithms Using Finite Precision Arithmetic
(
Citations: 118
)
Victor J. Milenkovic
Journal:
Artificial Intelligence  AI
, vol. 37, no. 13, pp. 377401, 1988
Cartographic Errors Symptomatic of Underlying Algebra Problems
(
Citations: 35
)
W. R. Franklin
Published in 1984.
Spatial Data Types for Database Systems, Finite Resolution Geometry for Geographic Information Systems
(
Citations: 52
)
Markus Schneider
Published in 1997.
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Citations
(3)
Mathematically provable correct implementation of integrated 2D and 3D representations
(
Citations: 2
)
Rodney Thompson
,
Peter van Oosterom
Chapter 15 Mathematically provable correct implementation of integrated 2D and 3D representations
Rodney Thompson
,
Peter van Oosterom
Integrated Representation of (Potentially Unbounded) 2D and 3D Spatial Objects for Rigorously Correct Query and Manipulation
Rodney James Thompson
,
Peter van Oosterom