Cardinal direction relations in 3D space

Authors:
Juan Chen;Dayou Liu;Haiyang Jia;Changhai Zhang
Affiliations:
College of Computer Science and Technology, Jilin University, Changchun, China and Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Chan ...;College of Computer Science and Technology, Jilin University, Changchun, China and Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Chan ...;College of Computer Science and Technology, Jilin University, Changchun, China and Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Chan ...;College of Computer Science and Technology, Jilin University, Changchun, China and Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Chan ...
Venue:
KSEM'07 Proceedings of the 2nd international conference on Knowledge science, engineering and management
Year:
2007

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Abstract

The existing 3D direction models approximate spatial objects either as a point or as a minimal bounding block, which decrease the descriptive capability and precision. Considering the influence of object's shape, this paper extends the planar cardinal direction (CD) into 3D space and obtains a new model called TCD (three-dimensional cardinal direction). Base on the smallest cubic TCD relations and original relations, explain the correlations between basic TCD relations and block algebra. Then according to the results in block algebra, two novel ways to compute the inverse and composition of basic TCD relations are proposed. And an O(n4) algorithm to check the consistency of a set of basic TCD constraints over simple blocks is given.