On the Connection Between the Projection and the Extension of a Parallelotope |
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Authors: | Á. G. Horváth |
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Affiliation: | (1) Budapest University of Technology and Economics, Hungary |
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Abstract: | This paper presents a result concerning the connection between the parallel projection P v,H of a parallelotope P along the direction v (into a transversal hyperplane H) and the extension P + S(v), meaning the Minkowski sum of P and the segment S(v) = {λv | −1 ≤ λ ≤ 1}. A sublattice L v of the lattice of translations of P associated to the direction v is defined. It is proved that the extension P + S(v) is a parallelotope if and only if the parallel projection P v,H is a parallelotope with respect to the lattice of translations L v,H , which is the projection of the lattice L v along the direction v into the hyperplane H. |
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Keywords: | 2000 Mathematics Subject Classification: 52B12 52C22 |
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