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

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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.

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Correspondence to Isabelle Sivignon or Florent Dupont or Jean-Marc Chassery.

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Sivignon, I., Dupont, F. & Chassery, J. Decomposition of a Three-Dimensional Discrete Object Surface into Discrete Plane Pieces. Algorithmica 38, 25–43 (2004). https://doi.org/10.1007/s00453-003-1041-6

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  • Discrete volumes
  • Digital plane recognition
  • Surface
  • Polyhedrization