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A Conceptual Framework for Modelling Spatial Relations

Abstract : The models of spatial relations have stimulated great interest among researchers in spatial databases from the nineties. We can distinguish three different levels of representation where we can identify spatial relations: a purely geometric one, where objects are represented as point-sets and relations can be formally defined in mathematical terms; a computational level, where objects are represented as spatial data types and relations are calculated using spatial operators; a user level, where objects and relations correspond to the concepts of user context. From a geometric point of view, we can consider a categorization of spatial relations in three groups: topological, projective, and metric. This dissertation proposes both a general framework for modelling qualitative spatial relations and presents new developments for projective relations. By providing a formal mathematical framework to a qualitative description of relations, the models are of great research interest in geographic information science. The most important geometric property that has been taken into account is the collinearity of three points. The importance of this property is such that it influences the whole approach, making ternary relations the formal basis of the models. We have developed algorithms to calculate the relations from a vector data structure and a reasoning system on ternary projective relations. We also extended the model to the three-dimensional space and the sphere. From a user perspective, projective relations should consider context information, combining them with reference systems to avoid ambiguities in the meaning of the relation.
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https://hal.archives-ouvertes.fr/hal-01459695
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Submitted on : Tuesday, February 7, 2017 - 1:48:20 PM
Last modification on : Tuesday, June 1, 2021 - 2:08:02 PM

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  • HAL Id : hal-01459695, version 1

Citation

Eliseo Clementini. A Conceptual Framework for Modelling Spatial Relations. 2009. ⟨hal-01459695⟩

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