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An elementary digital plane recognition algorithm

Yan Gérard 1 Isabelle Debled-Rennesson 2 Paul Zimmermann 3
2 ADAGE - Applying discrete algorithms to genomics
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : A naive digital plane is a subset of points $(x,y,z) \in \mathbb{Z} ^3$ verifying $h\leq ax+by+cz < h+\rm{ max }\{ | a|,|b|,|c| \}$ where $(a,b,c,h)\in \mathbb{Z} ^4 $. Given a finite unstructured subset of $\mathbb{Z} ^3$, the problem of the digital plane recognition is to determine whether there exists a naive digital plane containing it. This question is rather classical in the field of digital geometry (also called discrete geometry). We suggest in this paper a new algorithm to solve it. Its asymptotic complexity is bounded by $O( n^7)$ but its behavior seems to be linear in practice. It uses an original strategy of optimization in a set of triangular facets (triangles). The code is short and elementary (less than 300 lines) and available on \url{http://www.loria.fr/~debled/plane}.
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https://hal.inria.fr/inria-00100057
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Submitted on : Tuesday, September 26, 2006 - 10:13:44 AM
Last modification on : Monday, August 9, 2021 - 2:52:41 PM

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Yan Gérard, Isabelle Debled-Rennesson, Paul Zimmermann. An elementary digital plane recognition algorithm. Discrete Applied Mathematics, Elsevier, 2005, 151 (1-3), pp.169-183. ⟨10.1016/j.dam.2005.02.026⟩. ⟨inria-00100057⟩

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