Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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Two Algorithms for Constructing the Voronoi Diagram for 3D Spheres and Applications to Protein Structure Analysis

삼차원 구의 보로노이 다이어그램 계산을 위한 두 가지 알고리듬 및 단백질구조채석에의 응용

  • 김동욱 (한양대학교 Voronoi Diagram 연구단) ;
  • 조영송 (한양대학교 Voronoi Diagram 연구단) ;
  • 김덕수 (한양대학교 산업공학과)
  • Published : 2006.04.01
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Abstract

Voronoi diagrams have been known for numerous important applications in science and engineering including CAD/CAM. Especially, the Voronoi diagram for 3D spheres has been known as very useful tool to analyze spatial structural properties of molecules or materials modeled by a set of spherical atoms. In this paper, we present two algorithms, the edge-tracing algorithm and the region-expansion algorithm, for constructing the Voronoi diagram of 3D spheres and applications to protein structure analysis. The basic scheme of the edge-tracing algorithm is to follow Voronoi edges until the construction is completed in O(mn) time in the worst-case, where m and n are the numbers of edges and spheres, respectively. On the other hand, the region-expansion algorithm constructs the desired Voronoi diagram by expanding Voronoi regions for one sphere after another via a series of topology operations, starting from the ordinary Voronoi diagram for the centers of spheres. It turns out that the region-expansion algorithm also has the worst-case time complexity of O(mn). The Voronoi diagram for 3D spheres can play key roles in various analyses of protein structures such as the pocket recognition, molecular surface construction, and protein-protein interaction interface construction.

Keywords

References

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