Research on Combinational Reasoning of Directional Relations Based on Double Projections Model in Three-Dimensional Space
The xoy and xoz planes are divided into nine areas in three-dimensional space respectively by the MBR (Minimum Bounding Rectangle), which are produced by the reference objects’ projection to their planes. The intersecting situations between the projection of target objects and the two of reference objects are expressed by two 3×3 matrices. Then, a directional relations matrix model based on double projections is put forward. A combinational reasoning method is proposed by using the computational performance of matrices based on this model. Moreover, a combinational reasoning experiment is given and the result matches the reality.
Wenya Tian and Linli Xu
Y. S. Liu and W. J. Gu, "Research on Combinational Reasoning of Directional Relations Based on Double Projections Model in Three-Dimensional Space", Advanced Materials Research, Vol. 186, pp. 61-65, 2011