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Issue No.05 - September (1995 vol.15)
pp: 62-69
A direct algorithm for computing the Delaunay triangulation in three dimensions is presented. The algorithm uses a 3D cell data structure to preprocess the data, a range searching procedure to find Delaunay points quickly, and a shelling mechanism to put tetrahedra together in such a way that completeness and correctness are guaranteed. A face and an edge lists are used to govern the triangulation process. The convex hull can also be computed at no extra cost.
Delaunay triangulation
Tsung-Pao Fang, Les A. Piegl, "Delaunay Triangulation in Three Dimensions", IEEE Computer Graphics and Applications, vol.15, no. 5, pp. 62-69, September 1995, doi:10.1109/38.403829
1. F.P. Preparata and M.I. Shamos, Computational Geometry. Springer-Verlag, 1985.
2. H. Edelsbrunner, Algorithms in Combinatorical Geometry. EATCS Monographs in Computer Science, Berlin: Springer, 1987.
3. J. O'Rourke, Computational Geometry in C. Cambridge Univ. Press, 1993.
4. A. Okabe, B. Boots, and K. Sugihara, Spatial Tesselations—Concepts and Applications of Voronoi Diagrams. Chichester: Wiley, 1992.
5. F. Aurenhammer, "Voronoi Diagrams: A Survey of a Fundamental Geometric Data Structure," ACM Computing Surveys, vol. 23, no. 3, 1991, pp. 345-405.
6. A. Bowyer, “Computing Dirichlet Tessellations,” The Computer J., Vol. 24, No. 2, 1981, pp. 162-166.
7. D. F. Watson, “Computing then-Dimensional Delaunay Tessellation with Applications to Voronoi Polytopes,” The Computer J., Vol. 24, No. 2, 1981, pp. 167-172.
8. M. Tanemura, T. Ogawa, and N. Ogita, “A New Algorithm for Three-Dimensional Voronoi Tessellation,” J. Computational Physics, Vol. 51, No. 2, 1983, pp. 191-207.
9. D.A. Field, “Implementing Watson’s Algorithm in Three Dimensions,” Proc. 2nd Symp. Computational Geometry, ACM Press, New York, 1986, pp. 246-259.
10. R.A. Dwyer, “Higher-Dimensional Voronoi Diagrams in Linear Expected Time,” Proc. 5th Symp. on Computational Geometry, ACM Press, New York, 1989, pp. 326-333.
11. T.K. Dey, “Delaunay Triangulations in Three Dimensions with Finite Precision Arithmetic,” Computer Aided Geometric Design, Vol. 9, 1992, pp. 457-470.
12. T.-P. Fang and L.A. Piegl, "Delaunay Triangulation Using a Uniform Grid," IEEE Computer Graphics and Applications, pp. 36-47, 1993.
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