Parallel Construction of Quadtrees and Quality Triangulations

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Parallel Construction of Quadtrees and Quality Triangulations (1993)

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by Marshall Bern , David Eppstein , Shang-Hua Teng

Venue:	In Proc. 3rd Workshop Algorithms Data Struct
Citations:	71 - 8 self

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@INPROCEEDINGS{Bern93parallelconstruction,
    author = {Marshall Bern and David Eppstein and Shang-Hua Teng},
    title = {Parallel Construction of Quadtrees and Quality Triangulations},
    booktitle = {In Proc. 3rd Workshop Algorithms Data Struct},
    year = {1993},
    pages = {188--199},
    publisher = {Springer-Verlag}
}

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Abstract

We describe e#cient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtree-based finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straight-line graphs, using O(n+k/ log n) processors, where n measures input size and k output size. 1 Introduction A crucial preprocessing step for the finite element method is mesh generation, and the most general and versatile type of two-dimensional mesh is an unstructured triangular mesh. Such a mesh is simply a triangulation of the input domain (e.g., a polygon), along with some extra vertices, called Steiner points. Not all triangulations, however, serve equally well; numerical and discretization error depend on the quality of the triangulation, meaning the shapes and sizes of triangles. A typical quality guarantee gives a lower bound on the minimum angle in the triangulation. Baker et al. [2] first proved the existence of quality triangulations for ...

Keyphrases

quality triangulation parallel construction two-dimensional mesh cient pram algorithm mesh generation quadtree-based finite element mesh input domain extra vertex unbalanced quadtrees output size versatile type typical quality guarantee finite element method unstructured triangular mesh crucial preprocessing step minimum angle steiner point discretization error planar straight-line graph

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