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Generalized Functionality for Arithmetic Discrete Planes

Valerie Berthe 1 Christophe Fiorio 1 Damien Jamet 1
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The discrete plane P(a,b,c,mu,omega) is the set of points (x,y,z) in Z^3 satisfying 0 =< ax+by+cz + mu < omega. In the case omega =max (|a|,|b|,|c|), the discrete plane is said naive and is well-known to be functional on a coordinate plane. The aim of our paper is to extend the notion of functionality to a larger family of arithmetic discrete planes by introducing a suitable orthogonal projection direction (alpha,beta,gamma) satisfying alpha a + beta b + gamma c =omega. We then apply this functionality property to the enumeration of some local configurations, that is, the (m,n)-cubes such as introduced in [VitChas99].
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Submitted on : Tuesday, March 29, 2011 - 10:59:39 AM
Last modification on : Thursday, May 24, 2018 - 3:59:21 PM
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Valerie Berthe, Christophe Fiorio, Damien Jamet. Generalized Functionality for Arithmetic Discrete Planes. DGCI: Discrete Geometrey for Computer Imagery, Apr 2005, Poitiers, France. pp.276-286, ⟨10.1007/978-3-540-31965-8_26⟩. ⟨hal-00580571⟩



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