Abstract
Libraries are available for the power diagram and the ordinary Voronoi diagram of points upon which application programs can be easily built. However, its counterpart for the Voronoi diagram of spheres does not exist despite of enormous applications, particularly those in molecular worlds. In this paper, we present the BULL! library which abbreviates “Beta Universe Library Liberandam!” for computing the Voronoi diagram of spheres, transforming it to the quasi-triangulation, and extracting the beta-complex. Being an engine library implemented in the standard C++, application programmers can simply call API-functions of BULL! to build application programs correctly, efficiently, and easily. The BULL! engine is designed so that the application programs developed by embedding API-functions are completely independent of the future modifications of the engine.
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References
Voronoi Diagram Research Center, http://voronoi.hanyang.ac.kr/
Aurenhammer, F.: Power diagrams: Properties, algorithms and applications. SIAM Journal on Computing 16, 78–96 (1987)
Aurenhammer, F.: Voronoi diagrams – a survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)
Cho, Y., Kim, D., Kim, D.S.: Topology representation for the Voronoi diagram of 3D spheres. International Journal of CAD/CAM 5(1), 59–68 (2005), http://www.ijcc.org
Edelsbrunner, H., Mücke, E.P.: Three-dimensional alpha shapes. ACM Transactions on Graphics 13(1), 43–72 (1994)
Kim, D.S., Cho, Y., Kim, D.: Euclidean Voronoi diagram of 3D balls and its computation via tracing edges. Computer-Aided Design 37(13), 1412–1424 (2005)
Kim, D.S., Cho, Y., Sugihara, K.: Quasi-worlds and quasi-operators on quasi-triangulations. Computer-Aided Design 42(10), 874–888 (2010)
Kim, D.S., Cho, Y., Sugihara, K., Ryu, J., Kim, D.: Three-dimensional beta-shapes and beta-complexes via quasi-triangulation. Computer-Aided Design 42(10), 911–929 (2010)
Kim, D.S., Kim, D., Cho, Y., Sugihara, K.: Quasi-triangulation and interworld data structure in three dimensions. Computer-Aided Design 38(7), 808–819 (2006)
Kim, D.S., Kim, J.K., Cho, Y., Kim, C.M.: Querying simplexes in quasi-triangulation. Computer-Aided Design 44(2), 85–98 (2012)
Kim, D., Kim, D.S.: Region-expansion for the Voronoi diagram of 3D spheres. Computer-Aided Design 38(5), 417–430 (2006)
Kim, J.K., Cho, Y., Kim, D., Kim, D.S.: Voronoi diagrams, quasi-triangulations, and beta-complexes for disks in ℝ2: The theory and implementation in BetaConcept. Journal of Computational Design and Engineering 1(2), 78–86 (2014)
Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edn. John Wiley & Sons, Chichester (1999)
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Kim, DS. et al. (2014). BULL! - The Molecular Geometry Engine Based on Voronoi Diagram, Quasi-Triangulation, and Beta-Complex. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_33
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DOI: https://doi.org/10.1007/978-3-662-44199-2_33
Publisher Name: Springer, Berlin, Heidelberg
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