한국CDE학회논문집 (Korean Journal of Computational Design and Engineering)

  • 제14권4호
  • /
  • Pages.217-224
  • /
  • 2009
  • /
  • 2508-4003(pISSN)
  • /
  • 2508-402X(eISSN)
한국CDE학회 (Society for Computational Design and Engineering)
권호 표지

배열기반 데이터 구조를 이용한 간략한 divide-and-conquer 삼각화 알고리즘

A Compact Divide-and-conquer Algorithm for Delaunay Triangulation with an Array-based Data Structure

  • 양상욱 (중앙대학교 미래신기술연구소) ;
  • 최영 (중앙대학교 기계공학부)
  • 발행 : 2009.08.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Most divide-and-conquer implementations for Delaunay triangulation utilize quad-edge or winged-edge data structure since triangles are frequently deleted and created during the merge process. How-ever, the proposed divide-and-conquer algorithm utilizes the array based data structure that is much simpler than the quad-edge data structure and requires less memory allocation. The proposed algorithm has two important features. Firstly, the information of space partitioning is represented as a permutation vector sequence in a vertices array, thus no additional data is required for the space partitioning. The permutation vector represents adaptively divided regions in two dimensions. The two-dimensional partitioning of the space is more efficient than one-dimensional partitioning in the merge process. Secondly, there is no deletion of edge in merge process and thus no bookkeeping of complex intermediate state for topology change is necessary. The algorithm is described in a compact manner with the proposed data structures and operators so that it can be easily implemented with computational efficiency.

키워드

참고문헌

  1. O'Rouke, J., Computational Geometry in C 2nd Ed., Cambridge University press, 1998
  2. Shamos, M. I. and Hoey, D., 'Closest-point Problems', Proceedings of the 16th Annual IEEE Sympostum on FOCS, pp. 151-162, 1975 https://doi.org/10.1109/SFCS.1975.8
  3. Lee, D. T. and Schachter, B. J., 'Two Algorithms for Constructing a Delaunay Triangulation', Int. J Comput. Inf. Sci., Vol. 9, pp. 219-242, 1980 https://doi.org/10.1007/BF00977785
  4. Guibas, L. and Stolfi, J., 'Primitives for the Manipulation of General Subdivisions and the Computation ofVoronoi Diagrams', ACM Transactions on Graphics, Vol. 4, No.2, pp. 75-123, April 1985
  5. Ohya, T., Iri, M. and Murota, K., 'A Fast Voronoidiagram Algorithm with Quaternary Tree Bucketing', Information Processing Letters, Vol. 18, pp. 227-31, 1984 https://doi.org/10.1016/0020-0190(84)90116-9
  6. Maus, A., 'Delaunay Triangulations and the Convex Hull of n Points in Expected Linear Time', BIT 24, pp. 151-163, 1984 https://doi.org/10.1007/BF01937482
  7. Dwyer, R. A., 'A Simple Divide-and-Conquer Algorithm for Constructing Delaunay Triangulations in O(n log log n) Expected Time', ACM Symposium on Computational Geometry, pp. 276-284, 1986 https://doi.org/10.1145/10515.10545
  8. Finkel, R. A. and Bentley, J. L., 'Quad Trees: A Data Structure for Retrieval on Composite Key', Acta Informatica, Vol. 4, No.1, pp. 1-9, 1974 https://doi.org/10.1007/BF00288933
  9. Adam, B., Elbaz, M. and Spehner, J. C., 'Construction du diagramme de Delaunay dans Ie plan en utilisant les melanges de tris', Quatriemes Jourmees de I'AFIG, Dijon, pp. 215-223, 1996
  10. Lemaire, C. and Moreau, J. M., 'A Probabilistic Result on Multi-dimensional Delaunay Triangulations, and Its Application to the 2D Case', Computational Geometry, Vol. 17, No. 1-2, pp. 69-96, October 2000 https://doi.org/10.1016/S0925-7721(00)00017-1
  11. Katajainen, J. and Koppinen, M., 'Constructing Delaunay Triangulations by Merging Buckets in Quadtree Order', Fundamenta Informaticae, Vol. 11, No.3, pp. 275-288, 1988
  12. Boissonnat, J. D. and Teiliaud, M., 'On the Randomized Construction of the Delaunay Tree', Theoretical Computer Science, Vol. 112, pp. 339-54, 1993 https://doi.org/10.1016/0304-3975(93)90024-N
  13. Kim, D. S., Kim, D., Cho, Y. and Sugihara, K., 'Quasi-triangulation and Interworld Data Structure in Three Dimensions', Computer-Aided Design, Vol. 38, No.7, pp. 808-819, 2006 https://doi.org/10.1016/j.cad.2006.04.008
  14. Yang, S. W., Choi, Y. and Lee, H. C., 'CAD Data Visualization on Mobile Devices Using Sequential Constrained Delaunay Triangulation', ComputerAided Design, Vol. 41, No.5, pp. 375-384, 2009 https://doi.org/10.1016/j.cad.2008.08.005
  15. 양상욱, '들로네 삼각화를 위한 간결한 알고리즘 및 CAD 가시화 적용 연구,' 박사학위논문, 중앙대학교, 2008. 12
  16. Bentley, J. L., 'Multidimensional Binary Search Trees Used for Associative Searching', Communications of ACM, Vol. 18, pp. 509-17, 1975 https://doi.org/10.1145/361002.361007
  17. Bentley, J. L., 'Multidimensional Binary Search Tree in Database Applications', IEEE Transactions on Software Engineering, Vol. se-5, No.4, pp. 333-340, 1979 https://doi.org/10.1109/TSE.1979.234200
  18. Ohya, T., Iri, M. and Murota, M., 'Improvements of the Incremental Method for the Voronoi Diagram with Computational Comparison of Various Algorithms', J. Oper. Res. Soc. Japan, Vol. 27, pp. 306-336, 1984
  19. Anglada, M. V., 'An Improved Incremental Algorithm for Constructing Restricted Delaunay Triangulations', Computers & Graphics, Vol. 21, No.2, pp.215-23, 1997 https://doi.org/10.1016/S0097-8493(96)00085-4