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Detection of Constrictions on Closed Polyhedral Surfaces

Franck Hétroy 1 Dominique Attali 2
1 EVASION - Virtual environments for animation and image synthesis of natural objects
GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : We define constrictions on a surface as simple closed geodesic curves, i.e. curves whose length is locally minimal. They can be of great interests in order to cut the surface in smaller parts. In this paper, we present a method to detect constrictions on closed triangulated surfaces. Our algorithm is based on a progressive approach. First, the surface is simplified by repeated edge collapses. The simplification continues until we detect an edge whose collapse would change the topology of the surface. It happens when three edges of the surface form a triangle that does not belong to the surface. The three edges define what we call a seed curve and are used to initialize the search of a constriction. Secondly, the constriction is progressively constructed by incrementally refining the simplified surface until the initial surface is retrieved. At each step of this refinement process, the constriction is updated. Some experimental results are provided.
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https://hal.inria.fr/inria-00001144
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Franck Hétroy, Dominique Attali. Detection of Constrictions on Closed Polyhedral Surfaces. Eurographics/IEEE TCVG Visualisation Symposium, G.-P. Bonneau, S. Hahmann, C. Hansen, May 2003, Grenoble, France, France. pp.67-74. ⟨inria-00001144⟩

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