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An efficient algorithm for three-dimensional Β-complex and Β-shape via a quasi-triangulation

Authors
Seo, JeongyeonCho, YoungsongKim, DongukKim, Deok-So
Issue Date
Jun-2007
Publisher
SPM
Keywords
��-complex; ��-shape; ��-complex; ��-shape; Complex; Quasi-triangulation; Voronoi diagram of spheres
Citation
Proceedings - SPM 2007: ACM Symposium on Solid and Physical Modeling, pp.323 - 328
Indexed
SCOPUS
Journal Title
Proceedings - SPM 2007: ACM Symposium on Solid and Physical Modeling
Start Page
323
End Page
328
URI
https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/179996
DOI
10.1145/1236246.1236292
ISSN
0000-0000
Abstract
The concept of a Β-shape has been recently proposed by extending the concept of the well-known α-shape. Since the Β-shape takes full consideration of the Euclidean geometry of spherical particles, it is better suited than the (weighted) α-shape for applications using spatial queries on the system of variable sized spheres based on the Euclidean distance metric. In this paper, we present an efficient and elegant algorithm which computers a Β-shape from a quasi-triangulation in O(log m + k) time in the worst case, where the quasi-triangulation has m simplicies and the boundary of Β-shape consists of k simplicies. We believe that the Β-shape and Β-complex for a set of variable sized spheres (such as the atoms in a protein) will be very useful in the near future since the precise and efficient analysis of molecular structure can be conveniently facilitated by using these structures.
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