Detection of constrictions on closed polyhedral surfaces

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Date
2003
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
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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@inproceedings{
:10.2312/VisSym/VisSym03/067-074
, booktitle = {
Eurographics / IEEE VGTC Symposium on Visualization
}, editor = {
G.-P. Bonneau and S. Hahmann and C. D. Hansen
}, title = {{
Detection of constrictions on closed polyhedral surfaces
}}, author = {
Hétroy, F.
and
Attali, D.
}, year = {
2003
}, publisher = {
The Eurographics Association
}, ISSN = {
1727-5296
}, ISBN = {
3-905673-01-0
}, DOI = {
/10.2312/VisSym/VisSym03/067-074
} }
Citation