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

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

  • 양상욱 (중앙대학교 미래신기술연구소) ;
  • 최영 (중앙대학교 기계공학부)
  • Published : 2009.08.31

Abstract

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.

Keywords

References

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