Abstract
This paper presents a new incremental insertion algorithm for constructing a Delaunay triangulation. Firstly, the nearest point is found in order to speed up the location of a triangle containing a currently inserted point. A hash table and 1–3 deterministic skip lists, combined with a walking strategy, are used for this task. The obtained algorithm is compared with the most popular Delaunay triangulation algorithms. The algorithm has the following attractive features: it is fast and practically independent of the distribution of input points, it is not memory demanding, and it is numerically stable and easy to implement.
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de Berg M, van Kreveld M, Overmars M, Schwarzkopf O (1997) Computational geometry: algorithms and applications. Springer, Berlin Heidelberg, New York
Dwyer RA (1987) A faster divide-and-conquer algorithm for constructing Delaunay triangulations. Algorithmica 2(2):137–151
Edelsbrunner H, Seidel R (1986) Voronoi diagrams and arrangements. Discrete Comput Geom 1(1):25–44
Fang T-P, Piegl L (1992) Algorithm for Delaunay triangulation and convex–hull computation using a sparse matrix. Comput Aided Des 24(8):425–436
Fang T-P, Piegl L (1993) Delaunay triangulation using a uniform grid. Comput Graph Appl 13(3):36–47
Fortune S (1987) A sweep-line algorithm for Voronoi diagrams. Algorithmica 2:153–174
Guibas L, Stolfi J (1985) Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans Graph 4:75–123
Guibas L, Knuth D, Sharir M (1992) Randomised incremental construction of Delaunay and Voronoi diagrams. Algorithmica 7:381–413
Huang C-W, Shih T-Y (1998) Improvements on Sloan’s algorithm for constructing Delaunay triangulations. Comput Geosci 24(2):193–196
Kolingerová I, Žalik B (2002) Improvements to randomized incremental Delaunay insertion. Comput Graph J 26(3):477–490
Lawson CL (1977) Software for C1 Surface Interpolation. In: Price JR (ed) Mathematical Software III. Academic, New York, pp 161–194
Lee DT, Schachter BJ (1980) Two algorithms for constructing a Delaunay triangulation. Int J Comput Inf Sci 9(3):219–242
Mücke EP, Saias I, Zhu B (1996) Fast-randomized point location without preprocessing and two- and three-dimensional Delaunay triangulations. In: Computational Geometry ’96. ACM Press, Philadelphia, pp 274–283
Munro JI, Papadakis T, Sedgewick R (1992) Deterministic skip lists. In: Proceedings of the 3rd ACM-SIAM symposium on discrete algorithms, pp 367–375
Pugh W (1990) Skip lists: a probabilistic alternative to balanced trees. Commun ACM 33(6):668–676
Shewchuk JR (1996) Triangle: engineering a 2D quality mesh generator and Delaunay triangulator. In: 1st workshop on applied computational geometry. Association of Computing Machinery, Philadelphia, pp 124–133
Shewchuk JR (2001) http://www-2.cs.cmu.edu/∼quake/triangle.html A two–dimensional quality mesh generator and delaunay triangulator. Accessed 1 February 2003
Sloan SW (1987) A fast algorithm constructing Delaunay triangulations in the plane. Adv Eng Softw Workstat 9(1):34–55
Su P, Drysdale RLS (1995) A comparison of sequential Delaunay triangulation algorithms. In: Proceedings of the 11th annual symposium on computational geometry. ACM Press, New York, pp 61–70
Žalik B, Kolingerová I (2003) An incremental construction algorithm for Delaunay triangulation using the nearest-point paradigm. Int J Geograph Inf Sci 17(2):119–138
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Zadravec, M., Žalik, B. An almost distribution-independent incremental Delaunay triangulation algorithm. Visual Comput 21, 384–396 (2005). https://doi.org/10.1007/s00371-005-0293-3
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DOI: https://doi.org/10.1007/s00371-005-0293-3