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Meshes Preserving Minimum Feature Size

Author(s)
Aloupis, Greg; Demaine, Erik D.; Demaine, Martin L.; Dujmovic, Vida; Iacono, John
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Abstract
The minimum feature size of a planar straight-line graph is the minimum distance between a vertex and a nonincident edge. When such a graph is partitioned into a mesh, the degradation is the ratio of original to final minimum feature size. For an n-vertex input, we give a triangulation (meshing) algorithm that limits degradation to only a constant factor, as long as Steiner points are allowed on the sides of triangles. If such Steiner points are not allowed, our algorithm realizes \ensuremathO(lgn) degradation. This addresses a 14-year-old open problem by Bern, Dobkin, and Eppstein.
Date issued
2012
URI
http://hdl.handle.net/1721.1/86202
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Computational Geometry
Publisher
Springer-Verlag
Citation
Aloupis, Greg, Erik D. Demaine, Martin L. Demaine, Vida Dujmovic, and John Iacono. “Meshes Preserving Minimum Feature Size.” Lecture Notes in Computer Science (2012): 258–273.
Version: Author's final manuscript
ISBN
978-3-642-34190-8
978-3-642-34191-5
ISSN
0302-9743
1611-3349

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