Linear-size nonobtuse triangulation of polygons

  • Authors:
  • Marshall Bern;Scott Mitchell;Jim Ruppert

  • Affiliations:
  • Xerox Palo Alto Research Center, 3333 Coyote Hill Rd., Palo, Alto, CA;Applied and Numerical Mathematics Dept., Sandia National Laboratories, Albuquerque, NM;NASA Ames Research Center, M/S T27A-1, Moffett Field, CA

  • Venue:
  • SCG '94 Proceedings of the tenth annual symposium on Computational geometry
  • Year:
  • 1994

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Abstract

We give an algorithm for triangulating n-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than &pgr;/2. The number of triangles in the triangulation is only O(n), improving a previous bound of O(n2), and the worst-case running time is O(nlog2n). 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.