線分演算と区域演算 : 時間と空間の操作の一手法

概要

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Time and space are two basic ontologies of representation of the physical world. This paper addresses an engineering perspective on how to reason about temporally and spatially qualified information. Two systems of calculi are proposed, one for temporal reasoning and the other for spatial reasoning. A segment is defined mathematically as a half-open real interval so that it can either be represented as a pair of quantitative endpoints, or determined by referring to other segments. The segment calculus defines operations to compute new segments from existing segments using quantitative endpoints or qualitative order relations. On the other hand, a region is a two-dimensional rectangular space modeled by its two orthogonal sides (segments) or by its spatial relations to other regions. The region calculus provides methods for handling regions based on their quantitative information or their qualitative relations. The utility and validity of the two calculi are proven through their applications to two mechanical engineering problems, one involving product processing scheduling and the other involving qualitative kinematic simulation.
一般社団法人日本機械学会の論文
1996-05-25