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Delaunay Triangulation Using a Uniform Grid
May/June 1993 (vol. 13 no. 3)
pp. 36-47

An algorithm for triangulating 2-D data points that is based on a uniform grid structure and a triangulation strategy that builds triangles in a circular fashion is discussed. The triangulation strategy lets the algorithm eliminate points from the internal data structure and decreases the time used to find points to form triangles, given an edge. The algorithm has a tested linear time complexity that significantly improves on that of other methods. As a by-product, the algorithm produces the convex hull of the data set at no extra cost. Two ways to compute the convex hull using the algorithm are presented. The first is based on the edge list and the second is based on the grid structure.

1. G. Voronoi. "Nouvelles applications des paramätres continusàla théorie des formes quadratiques. Premier Mémoire: Sur quelques proprieteés des formes quadratiques positives parfaites,"J. reine angewandte Mathematik, Vol. 133, 1907, pp. 97-178.
2. B. Delaunay, "Neue Darstellung der geometrischen Krystallographie,"Zeitschrift Krystallographie, Vol. 84, 1932, pp. 109-149.
3. F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: Springer-Verlag, 1985.
4. H. Edelsbrunner,Algorithms in Combinatorial Geometry, Springer-Verlag, New York, 1987.
5. P.J. Green and R. Sibson, "Computing Dirichlet Tessellations in the Plane,"Computer J., Vol. 21, No. 2, Feb. 1978, pp. 168-173.
6. R. Sibson, "Locally Equiangular Triangulations,"Computer J., Vol. 21, No. 3, March, pp. 243-245.|Au: Year?|
7. A. Bowyer, "Computing Dirichlet Tessellations,"Computer J., Vol. 24, No. 2, Feb. 1981, pp. 162-166.
8. D.F. Watson, "Computing then-dimensional Delaunay Tessellation with Applications to Voronoi Polytopes,"Computer J., Vol. 24, No. 2, Feb. 1981, pp. 167-172.
9. D.T. Lee and B.J. Schachter, "Two Algorithms for Constructing Delaunay Triangulation,"Int'l J. Computer and Information Science, Vol. 9, No. 3, 1980, pp. 219-242.
10. L. Guibas and J. Stolfi, "Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams,"ACM Trans. Graphics, Vol. 4, No. 2, April 1985, pp. 74-123.
11. L. Guibas, D.E. Knuth, and M. Sharir, "Randomized Incremental Construction of Delaunay and Voronoi Diagrams," Tech. Report 481. Computer Science Dept., Courant Inst. of Mathematical Sciences, New York Univ., 1990.
12. A.R. Forrest, "Computational Geometry and Software Engineering: Towards a Geometric Computing Environment," inTechniques for Computer Graphics, D.F. Rogers and R.A. Earnshaw, eds., Springer-Verlag, New York, 1987, pp. 23-37.

Citation:
Tsung-Pao Fang, Les A. Piegl, "Delaunay Triangulation Using a Uniform Grid," IEEE Computer Graphics and Applications, vol. 13, no. 3, pp. 36-47, May-June 1993, doi:10.1109/38.210490
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