Successive Determination and Verification of Polytopes by their X-Rays
Identifieur interne : 001979 ( Istex/Curation ); précédent : 001978; suivant : 001980Successive Determination and Verification of Polytopes by their X-Rays
Auteurs : R. J. Gardner [États-Unis] ; Peter Gritzmann [Allemagne]Source :
- Journal of the London Mathematical Society [ 0024-6107 ] ; 1994-10.
Abstract
It is shown that each convex polytope P in 𝔼d can be verified by ([d/(d–k)] + 1) k-dimensional X-rays. This means that P is uniquely determined by these X-rays and the choice of the direction of each X-ray depends only on P. Examples are constructed to show that in general this number cannot be reduced. Further, it is shown that each convex polytope P in 𝔼3 can be successively determined by only two one-dimensional X-rays. This means that P is uniquely determined by one X-ray taken in an arbitrary direction together with another whose direction depends only on the first X-ray. The results extend those for the case d = 2 of Giering and of Edelsbrunner and Skiena.
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DOI: 10.1112/jlms/50.2.375
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