Molecular Geometry and BULL!

Geometric properties are critical for the function of molecules consisting of atoms which are usually modeled as a set of spheres in 3D. We propose "Molecular Geometry" which is a theoretical framework of computational understanding of the geometry of molecules in the claim that most, hopefully all, molecular structure problems can be effectively and efficiently facilitated by the "geometrization" of the problem at hand. We also report BULL!, the molecular geometry engine based on the Voronoi diagram of spheres, the quasi-triangulation, and the beta-complex. Being a program implemented in C++, application programmers can simply call API-functions of BULL! to create application programs correctly, efficiently, and conveniently. The BULL! engine, which will be freely available from the Voronoi Diagram Research Center at Hanyang University, is designed so that application programs are completely independent of future modifications and improvements.

[1]  Deok-Soo Kim,et al.  Molecular surfaces on proteins via beta shapes , 2007, Comput. Aided Des..

[2]  Deok-Soo Kim,et al.  Querying simplexes in quasi-triangulation , 2012, Comput. Aided Des..

[3]  Deok-Soo Kim,et al.  Edge-tracing algorithm for euclidean voronoi diagram of 3d spheres , 2004, CCCG.

[4]  Donguk Kim,et al.  Topology Representation for the Voronoi Diagram of 3D Spheres , 2009 .

[5]  Deok-Soo Kim,et al.  QTF: Quasi-triangulation file format , 2012, Comput. Aided Des..

[6]  Deok-Soo Kim,et al.  Voronoi diagrams, quasi-triangulations, and beta-complexes for disks in R2: the theory and implementation in BetaConcept , 2014, J. Comput. Des. Eng..

[7]  M Kokkinidis,et al.  A correlation between the loss of hydrophobic core packing interactions and protein stability. , 1999, Journal of molecular biology.

[8]  Deok-Soo Kim,et al.  Quasi-triangulation and interworld data structure in three dimensions , 2006, Comput. Aided Des..

[9]  Deok-Soo Kim,et al.  Quasi-worlds and quasi-operators on quasi-triangulations , 2010, Comput. Aided Des..

[10]  Deok-Soo Kim,et al.  Region-expansion for the Voronoi diagram of 3D spheres , 2006, Comput. Aided Des..

[11]  Deok-Soo Kim,et al.  Three-dimensional beta-shapes and beta-complexes via quasi-triangulation , 2010, Comput. Aided Des..

[12]  Franz Aurenhammer,et al.  Power Diagrams: Properties, Algorithms and Applications , 1987, SIAM J. Comput..

[13]  Deok-Soo Kim,et al.  BetaVoid: Molecular voids via beta‐complexes and Voronoi diagrams , 2014, Proteins.

[14]  Atsuyuki Okabe,et al.  Spatial Tessellations: Concepts and Applications of Voronoi Diagrams , 1992, Wiley Series in Probability and Mathematical Statistics.

[15]  Kunwoo Lee,et al.  Principles of CAD/CAM/CAE Systems , 1999 .

[16]  Deok-Soo Kim,et al.  Euclidean Voronoi diagram of 3D balls and its computation via tracing edges , 2005, Comput. Aided Des..

[17]  Deok-Soo Kim,et al.  Triangulation of molecular surfaces , 2009, Comput. Aided Des..

[18]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.