Meshes Preserving Minimum Feature Size
Author(s)Aloupis, Greg; Demaine, Erik D.; Demaine, Martin L.; Dujmovic, Vida; Iacono, John
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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.
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