A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

The foundation of delaunay triangulation and constrained delaunay triangulation is the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generating constrained delaunay triangulation in two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation of constrained delaunay triangulation is showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

[1]  L. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi , 1985, TOGS.

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

[3]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

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

[5]  Rex A. Dwyer.  Higher-dimensional voronoi diagrams in linear expected time , 1989, SCG '89.

[6]  L. Chew.  Constrained Delaunay Triangulations (eng) , 1989 .

[7]  Leonidas J. Guibas,et al.  Randomized Incremental Construction of Delaunay and Voronoi Diagrams , 1990, ICALP.

[8]  Leila De Floriani,et al.  An on-line algorithm for constrained Delaunay triangulation , 1992, CVGIP Graph. Model. Image Process..

[9]  Les A. Piegl,et al.  Delaunay triangulation using a uniform grid , 1993, IEEE Computer Graphics and Applications.

[10]  S. Sloan.  A fast algorithm for generating constrained delaunay triangulations , 1993 .

[11]  Robert L. Scot Drysdale,et al.  A comparison of sequential Delaunay triangulation algorithms , 1995, SCG '95.

[12]  Ernst P. Mücke,et al.  Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations , 1996, SCG '96.

[13]  Marc Vigo Anglada,et al.  An improved incremental algorithm for constructing restricted delaunay triangulations , 1997, Comput. Graph..

[14]  Borut Zalik,et al.  Improvements to randomized incremental Delaunay insertion , 2002, Comput. Graph..

[15]  Borut Zalik,et al.  An incremental construction algorithm for Delaunay triangulation using the nearest-point paradigm , 2003, Int. J. Geogr. Inf. Sci..

[16]  D. T. Lee,et al.  Two algorithms for constructing a Delaunay triangulation , 1980, International Journal of Computer & Information Sciences.

[17]  L. Chew.  Constrained Delaunay triangulations , 1987, SCG '87.

[18]  Les A. Piegl,et al.  Algorithm for constrained delaunay triangulation , 2005, The Visual Computer.

[19]  Rex A. Dwyer.  A faster divide-and-conquer algorithm for constructing delaunay triangulations , 1987, Algorithmica.