Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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Acceleration of Delaunay Refinement Algorithm by Geometric Hashing

기하학적 해싱을 이용한 딜러니 개선 알고리듬의 가속화

  • Kim, Donguk (Dept. of Industrial and Management Engineering, Gangneung-Wonju National University)
  • 김동욱 (강릉원주대학교 산업경영공학과)
  • Received : 2017.01.19
  • Accepted : 2017.04.01
  • Published : 2017.06.01
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Abstract

Delaunay refinement algorithm is a classical method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. It computes the Delaunay triangulation for given points and edges to obtain an initial solution, and update the triangulation by inserting steiner points one by one to get an improved quality triangulation. This process repeats until it satisfies given quality criteria. The efficiency of the algorithm depends on the criteria and point insertion method. In this paper, we propose a method to accelerate the Delaunay refinement algorithm by applying geometric hashing technique called bucketing when inserting a new steiner point so that it can localize necessary computation. We have tested the proposed method with a few types of data sets, and the experimental result shows strong linear time behavior.

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References

  1. Okabe, A., Boots, B., Sugihara, K. and Chiu, S.N., 2000, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edition, Chichester, John Wiley & Sons.
  2. Lee, K., 1999, Principles of CAD/CAM/CAE Systems, Addison-Wesley.
  3. Chew, L.P., 1989, Guaranteed-Quality Triangular Meshes, Technical Report TR-89-983, Cornell University.
  4. Ruppert, J., 1995, A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation, Journal of Algorithms, 18(3), pp.548-585. https://doi.org/10.1006/jagm.1995.1021
  5. Shewchuk, J.R., 2012, Lecture Notes on Delaunay Mesh Generation, Univ. of California at Berkeley
  6. Shewchuk, J.R., 2002, Delaunay Refinement Algorithms for Triangular Mesh Generation, Computational Geometry: Theory and Applications, 22, pp.21-74. https://doi.org/10.1016/S0925-7721(01)00047-5
  7. Chew, L.P., 1993, Guaranteed-Quality Mesh Generation for Curved Surfaces, Proceedings of the 9th Annual Symposium on Computational Geometry, pp.274-280.
  8. Kim, D., Cho, Y., and Kim, D.-S., 2006, Two Algorithms for Constructing the Voronoi Diagram for 3D Spheres and Applications to Protein Structure Analysis, Transactions of the Society of CAD/CAM Engineers, 11(2), pp.97-106.
  9. Kim, J., Cho, Y., Kim, D. and Kim, D.-S., 2014, Voronoi Diagrams, Quasi-triangulations, and Betacomplexes for Disks in R2: The Theory and Implementation in BetaConcept, Journal of Computational Design and Engineering, 1(2), pp.79-87. https://doi.org/10.7315/JCDE.2014.008

Cited by

  1. Triangulation of Voronoi Faces of Sphere Voronoi Diagram using Delaunay Refinement Algorithm vol.41, pp.4, 2018, https://doi.org/10.11627/jkise.2018.41.4.123