Decomposition of a Three-Dimensional Discrete Object Surface into Discrete Plane Pieces

Authors:
Isabelle Sivignon;Florent Dupont;Jean-Marc Chassery
Affiliations:
Laboratoire LIS, 961 rue de la Houille Blanche, Domaine Universitaire - BP46, 38402 Saint Martin D’Héres Cedex, France;Laboratoire LIRIS, 8 Boulevard Niels Bohr, 69622 Villeurbanne Cedex, France;Laboratoire LIS, 961 rue de la Houille Blanche, Domaine Universitaire - BP46, 38402 Saint Martin D’Héres Cedex, France
Venue:
Algorithmica
Year:
2003

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Abstract

This paper deals with the polyhedrization of discrete volumes. The aim is to do a reversible transformation from a discrete volume to a Euclidean polyhedron, i.e. such that the discretization of the Euclidean volume is exactly the initial discrete volume. We propose a new polynomial algorithm to split the surface of any discrete volume into pieces of naive discrete planes with well-defined shape properties, and present a study of the time complexity as well as a study of the influence of the voxel tracking order during the execution of this algorithm.