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Gilbert. Provably good mesh generation. J. Comput. Syst. Sci. 48 (1994), 384–409. [2] J. Ruppert. A new and simple algorithm for quality 2-dimensional mesh generation. Report UCB/CSD 92/694, Comput. Sci. , Univ. California, Berkeley, California, 1992. [3] J. Ruppert. A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J. Algorithms 18 (1995), 548–585. Exercise collection The credit assignment reflects a subjective assessment of difficulty. A typical question can be answered by using knowledge of the material combined with some thought and analysis.

Extended Voronoi diagrams Just as for ordinary Delaunay triangulations, every constrained Delaunay triangulation has a dual Voronoi diagram, but in a surface that is more complicated than the Euclidean plane. Imagine R2 is a sheet of paper, 0 , with the points of S and the line segments in L drawn on it. For each i ∈ L, we cut 0 open along i and glue another sheet i , which is also cut open along i . The gluing is done around i such that every traveler who crosses i switches from 0 to i and vice versa.

Constrained Delaunay triangulations. In “Proc. 3rd Ann. Sympos. Comput. ,” 1987, 215–222. [2] D. T. Lee and A. K. Lin. Generalized Delaunay triangulations for planar graphs. Discrete Comput. Geom. 1 (1986), 201–217. [3] J. Nievergelt and F. P. Preparata. Plane-sweep algorithms for intersecting geometric figures. Comm. ACM 25 (1982), 739–747. [4] R. Seidel. Constrained Delaunay triangulations and Voronoi diagrams with obstacles. In “1978–1988 Ten Years IIG,” 1988, 178–191. 2 Delaunay refinement This section demonstrates the use of Delaunay triangulations in constructing triangle meshes in the plane.

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Advanced scientific computing (B673) by Meglicki Z.

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