Abstract
We give an algorithm for triangulatingn-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than π/2. The number of triangles in the triangulation is onlyO(n), improving a previous bound ofO(n 2), and the running time isO(n log2 n). The basic technique used in the algorithm, recursive subdivision by disks, is new and may have wider application in mesh generation. We also report on an implementation of our algorithm.
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The research of S. Mitchell was supported by the Applied Mathematical Sciences program, U.S. Department of Energy Research and by the U.S. Department of Energy under Contract DE-AC04-76DP00789. J. Ruppert's work was performed while he was at the NASA Ames Research Center as an employee of Computer Sciences Corporation, under NASA Contrast NAS 2-12961.
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Bern, M., Michell, S. & Ruppert, J. Linear-size nonobtuse triangulation of polygons. Discrete & Computational Geometry 14, 411–428 (1995). https://doi.org/10.1007/BF02570715
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DOI: https://doi.org/10.1007/BF02570715