Minimal enclosing parallelepiped in 3D

Authors:
Frédéric Vivien;Nicolas Wicker
Affiliations:
INRIA--LIP, École normale supérieure de Lyon, Lyon, France;IGBMC, Université Louis Pasteur, Strasbourg, France
Venue:
Computational Geometry: Theory and Applications
Year:
2004

Citing 3
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Abstract

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(n6). Experiments show that in practice our quickest algorithm runs in O(n2) (at least for n ≤ 105). We also present our application in structural biology.