Manifoldization of beta-shapes in O(n) time
- Authors
- Kim, Deok-Soo; Lee, Changhee; Cho, Youngsong; Kim, Donguk
- Issue Date
- Apr-2010
- Publisher
- ELSEVIER SCI LTD
- Keywords
- beta-shape; beta-complex; Voronoi diagram of spheres; Quasi-triangulation; Topology; Mesh; Non-manifold; Protein structure
- Citation
- COMPUTER-AIDED DESIGN, v.42, no.4, pp.322 - 339
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMPUTER-AIDED DESIGN
- Volume
- 42
- Number
- 4
- Start Page
- 322
- End Page
- 339
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/175190
- DOI
- 10.1016/j.cad.2009.12.005
- ISSN
- 0010-4485
- Abstract
- The beta-shape and the beta-complex are recently announced geometric constructs which facilitate efficient reasoning about the proximity among spherical particles in three-dimensional space. They have proven to be very useful for the structural analysis of bio-molecules such as proteins. Being non-manifold, however, the topology traversal on the boundary of the beta-shape is inconvenient for reasoning about the surface structure of a sphere set. In this paper, we present an algorithm to transform a beta-shape from being non-manifold to manifold without altering any of the geometric characteristics of the model. After locating the simplexes where the non-manifoldness is defined on the beta-shape, the algorithm augments the beta-complex which corresponds to the beta-shape so that all the non-manifoldness is resolved on such simplexes. The algorithm runs in O(n) time, without any floating-point operation, in the worst case for protein models where n is the number of spherical atoms. We also provide some experimental results obtained from real protein models available from the Protein Data Bank.
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