An upper bound for conforming Delaunay triangulations

A plane geometric graphC in ℝ2conforms to another such graphG if each edge ofG is the union of some edges ofC. It is proved that, for everyG withn vertices andm edges, there is a completion of a Delaunay triangulation ofO(m2n) points that conforms toG. The algorithm that constructs the points is also described.

[1]  C. Lawson.  Software for C1 Surface Interpolation , 1977 .

[2]  D. T. Lee,et al.  Generalized delaunay triangulation for planar graphs , 1986, Discret. Comput. Geom..

[3]  Jean-Daniel Boissonnat,et al.  Shape reconstruction from planar cross sections , 1988, Comput. Vis. Graph. Image Process..

[4]  D. T. Lee,et al.  Visibility of a simple polygon , 1983, Comput. Vis. Graph. Image Process..

[5]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[6]  V. T. Rajan.  Optimality of the Delaunay triangulation in ℝd , 1994, Discret. Comput. Geom..

[7]  B. Joe,et al.  Corrections to Lee's visibility polygon algorithm , 1987, BIT.

[8]  David Eppstein,et al.  Provably Good Mesh Generation , 1994, J. Comput. Syst. Sci..

[9]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[10]  David Eppstein,et al.  Polynomial-size nonobtuse triangulation of polygons , 1991, SCG '91.

[11]  Olivier D. Faugeras,et al.  Representing stereo data with the Delaunay triangulation , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[12]  J. Cavendish.  Automatic triangulation of arbitrary planar domains for the finite element method , 1974 .

[13]  Nickolas S. Sapidis,et al.  Delaunay triangulation of arbitrarily shaped planar domains , 1991, Comput. Aided Geom. Des..

[14]  Amr A. Oloufa,et al.  Triangulation Applications in Volume Calculation , 1991 .

[15]  V. T. Rajan,et al.  Optimality of the Delaunay triangulation in Rd , 1991, SCG '91.

[16]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[17]  David Avis,et al.  A Linear Algorithm for Computing the Visibility Polygon from a Point , 1981, J. Algorithms.

[18]  Elefterios A. Melissaratos,et al.  Coping with inconsistencies: a new approach to produce quality triangulations of polygonal domains with holes , 1992, SCG '92.

[19]  Samuel Rippa,et al.  Minimal roughness property of the Delaunay triangulation , 1990, Comput. Aided Geom. Des..

[20]  Tiow Seng Tan,et al.  An upper bound for conforming Delaunay triangulations , 1992, SCG '92.

[21]  Robin Sibson,et al.  Locally Equiangular Triangulations , 1978, Comput. J..

[22]  R. B. Simpson,et al.  On optimal interpolation triangle incidences , 1989 .

[23]  David Eppstein,et al.  Triangulating polygons without large angles , 1992, SCG '92.

[24]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[25]  Georges Voronoi.  Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .

[26]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .