CiteSeerX — Polynomial-Size Nonobtuse Triangulation Of Polygons

Polynomial-Size Nonobtuse Triangulation Of Polygons (1992) [26 citations — 8 self]

Popular Tags

No tags have been applied to this document.

BibTeX | Add To MetaCart

@MISC{Bern92polynomial-sizenonobtuse,
    author = {Marshall Bern and David Eppstein},
    title = {Polynomial-Size Nonobtuse Triangulation Of Polygons},
    year = {1992}
}

Bookmarks

OpenURL

Abstract:

We describe methods for triangulating polygonal regions of the plane so that no triangle has a large angle. Our main result is that a polygon with n sides can be triangulated with O(n 2 ) nonobtuse triangles. We also show that any triangulation (without Steiner points) of a simple polygon has a refinement with O(n 4 ) nonobtuse triangles. Finally we show that a triangulation whose dual is a path has a refinement with only O(n 2 ) nonobtuse triangles. Keywords: Computational geometry, mesh generation, triangulation, angle condition. 1. Introduction One of the classical motivations for problems in computational geometry has been automatic mesh generation for finite element methods. In particular, mesh generation has motivated a number of triangulation algorithms, such as finding a triangulation that minimizes the maximum angle. 1 A triangulation algorithm takes a geometric input, typically a point set or polygonal region, and produces an output that is a triangulation of ...

Citations

92	Two algorithms for constructing the Delaunay triangulation – Lee, Schachter - 1980
55	Generalized Delaunay triangulation for planar graphs – Lee, Lin - 1986
50	Locally equiangular triangulations – SIBSON - 1977
31	Condition of finite element matrices generated from nonuniform meshes – Fried - 1972
31	Nonobtuse triangulation of polygons – Baker, Grosse, et al. - 1988
28	An Upper Bound for Conforming Delaunay Triangulations – Edelsbrunner, Tan - 1993
27	Constrained Delaunay triangulations. Algorithmica, 4(1):97– 108 – Chew - 1989
26	Edge insertion for optimal triangulations – Bern, Edelsbrunner, et al. - 1993
23	Learning with a Helpful Teacher – Salzberg, Delcher, et al. - 1991
23	1991], Triangulating polygons without large angles, preprint – Bern, Dobkin, et al.
19	On the angle condition in the finite element method – Babuˇska, Aziz - 1976
16	Globally-equiangular triangulations of co-circular points in O(n log n) time – Mount, Saalfeld - 1988
14	A Polynomial Time Algorithm for the Minmax Angle Triangulation – Edelsbrunner, Tan, et al. - 1990
9	The farthest point Delaunay triangulation minimizes angles – Eppstein
6	Drawing the planar dual – Bern, Gilbert - 1992
4	Provably good mesh generation. 31st – Bern, Eppstein, et al. - 1990
3	The dissection of a polygon into nearly equilateral triangles – Gerver - 1984