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(n 4) algorithm to check the consistency of a set of basic TCD constraints over simple blocks is given.
Supported by NSFC Major Research Program 60496321, Basic Theory and Core Techniques of Non Canonical Knowledge; National Natural Science Foundation of China under Grant Nos. 60373098, 60573073, 60603030 the National High-Tech Research and Development Plan of China under Grant No. 2003AA118020, the Major Program of Science and Technology Development Plan of Jilin Province under Grant No. 20020303, the Science and Technology Development Plan of Jilin Province under Grant No. 20030523.
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Chen, J., Liu, D., Jia, H., Zhang, C. (2007). Cardinal Direction Relations in 3D Space. In: Zhang, Z., Siekmann, J. (eds) Knowledge Science, Engineering and Management. KSEM 2007. Lecture Notes in Computer Science(), vol 4798. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76719-0_69
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DOI: https://doi.org/10.1007/978-3-540-76719-0_69
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