Anomalies in quasi-triangulations and beta-complexes of spherical atoms in molecules

Authors:
Deok-Soo Kim;Youngsong Cho;Joonghyun Ryu;Jae-Kwan Kim;Donguk Kim
Affiliations:
Voronoi Diagram Research Center, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, South Korea and Department of Industrial Engineering, Hanyang University, 17 Haengdang-dong, Se ...;Voronoi Diagram Research Center, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, South Korea;Voronoi Diagram Research Center, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, South Korea;Voronoi Diagram Research Center, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, South Korea;Department of Industrial, Information, and Management Engineering, Gangneung-Wonju National University, Gangneung, Gangwon-do, South Korea
Venue:
Computer-Aided Design
Year:
2013

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Abstract

The beta-complex is the most compact and efficient representation of molecular structure as it stores the precise proximity among spherical atoms in molecules. Thus, the beta-complex is a powerful tool for solving otherwise difficult shape-related problems in molecular biology. However, to use the beta-complex properly, it is necessary to correctly understand the anomalies of both the quasi-triangulation and the beta-complex. In this paper, we present the details of the anomaly of the beta-complex in relation to the quasi-triangulation. With a proper understanding of anomaly theory, seemingly complicated application problems related to the geometry and topology among spherical balls can be correctly and efficiently solved in rather straightforward computational procedures. We present the theory with examples in both R^2 and R^3.