The data type of spatial objects

Kenneth Harold Anthony Johnson; John V Tucker

doi:10.1007/s00165-011-0182-7

The data type of spatial objects

Kenneth Harold Anthony Johnson, John V Tucker

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

A spatial object consists of data assigned to points in a space. Spatial objects, such as memory states and three dimensional graphical scenes, are diverse and ubiquitous in computing. We develop a general theory of spatial objects by modelling abstract data types of spatial objects as topological algebras of functions. One useful algebra is that of continuous functions, with operations derived from operations on space and data, and equipped with the compact-open topology. Terms are used as abstract syntax for defining spatial objects and conditional equational specifications are used for reasoning. We pose a completeness problem: Given a selection of operations on spatial objects, do the terms approximate all the spatial objects to arbitrary accuracy? We give some general methods for solving the problem and consider their application to spatial objects with real number attributes.

Original language	English
Pages (from-to)	189-218
Number of pages	30
Journal	Formal Aspects of Computing
Volume	25
Issue number	2
DOIs	https://doi.org/10.1007/s00165-011-0182-7
Publication status	Published - Mar 2013

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The data type of spatial objects

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