Minimal enclosing parallelepiped in 3D

Frédéric Vivien (1) , Nicolas Wicker (1)

1 REMAP - Regularity and massive parallel computing

We investigate the problem of finding a minimal volume parallelepiped enclosing a given set of n three-dimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n^6). Experiments show that in practice our quickest algorithm runs in O(n^2) (at least for $n \leq 10^5$n 10^5). We also present our application in structural biology.

Mots clés: BIOINFORMATIC; ALGORITHMIC GEOMETRY; PARALLELEPIPED

Domaines: Autre [cs.OH]

Frédéric Vivien, Nicolas Wicker. Minimal enclosing parallelepiped in 3D. [Research Report] RR-4685, LIP RR-2002-49, INRIA, LIP. 2002. ⟨inria-00071901⟩