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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.

Abstract. An invertible Euclidean reconstruction method for a 2D curve is proposed. Hints on an extension to 3D are provided. The framework of this method is the discrete analytical geometry. The reconstruction result is more compact than classical methods such as the Marching Cubes. The notions of discrete cusps and patches are introduced.