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Abstract: We show that any PSLG with v vertices can be triangulated with no angle larger than 7=8 by adding O(v 2 log v) Steiner points in O(v 2 log 2 v) time. We first triangulate the PSLG with an arbitrary constrained triangulation and then refine that triangulation by adding additional vertices and edges. We follow a lazy strategy of starting from an obtuse angle and exploring the triangulation in search of a sequence of Steiner points that will satisfy a local angle condition. Explorations may... (Update)
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BibTeX entry: (Update)
S. Mitchell. Refining a triangulation of a planar straight-line graph to eliminate large angles. Proc. 34 th Annual IEEE Symposium on Foundation of Computer Science (FOCS). Pages 583---591, 1993. http://citeseer.ist.psu.edu/mitchell93refining.html More
@inproceedings{ mitchell93refining,
author = "Scott A. Mitchell",
title = "Refining a Triangulation of a Planar Straight-Line Graph to Eliminate Large Angles",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "583-591",
year = "1993",
url = "citeseer.ist.psu.edu/mitchell93refining.html" }
Citations (may not include all citations):88 the angle condition in the finite element method (context) - Babuska, Aziz - 1976
38 A New and Simple Algorithm for Quality 2-Dimensional Mesh Ge.. (context) - Ruppert - 1993
29 Linear-Size Non-Obtuse Triangulation of Polygons - Bern, Mitchell et al. - 1993
29 Computing in Euclidean Geometry (context) - Bern, Eppstein et al. - 1992
27 Polynomial-Size Nonobtuse Triangulations of Polygons - Bern, Eppstein - 1991
20 Triangulating polygons without large angles - Bern, Dobkin et al. - 1991
10 Computer aided surface representation and design (context) - Barnhill - 1983
10 Time Algorithm for the MinMax Angle Triangulation (context) - Edelsbrunner, Tan et al. - 1990
10 Approximating the MinimumWeight Triangulation - Eppstein - 1992
4 Finding a Covering Triangulation Whose Maximum Angle is Prov.. - Mitchell - 1993
3 A Discussion on the Triangulation Refinement Problem (context) - Rivara - 1993
1 st IEEE Symposium on Foundations of Computer Science (context) - Bern, Eppstein et al. - 1990
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://endo.sandia.gov/~samitch/csstuff/csguide.html): More
Cardinality Bounds for Triangulations with Bounded Minimum Angle - Mitchell (1994) (Correct)
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