An elementary digital plane recognition algorithm - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Applied Mathematics Year : 2005

An elementary digital plane recognition algorithm


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{}.

Dates and versions

inria-00100057 , version 1 (26-09-2006)



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



Gmail Facebook X LinkedIn More