Minimal enclosing parallelepiped in 3D

We investigate the problem of finding a minimal volume parallelepiped enclosing a given set of n threedimensional 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. 2004 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2004
• Where: COMGEO
• Authors: Frédéric Vivien, Nicolas Wicker
• Keywords: Applied Computing, COMGEO 2004, Minimal Volume, Parallelepiped Enclosing, Threedimensional Points