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이목원(Mokwon Lee),차제현(Jehyun Cha),송찬영(Chanyoung Song),김재관(Jae-Kwan Kim),조영송(Youngsong Cho),유중현(Joonghyun Ryu),김덕수(Deok-Soo Kim) (사)한국CDE학회 2014 한국 CAD/CAM 학회 학술발표회 논문집 Vol.2014 No.8
Voronoi diagrams are useful for reasoning spatial properties among particles. In particular, the Voronoi diagram of circles in 2D is important on its own and has many applications. And also it is meaningful for extending to that of spheres in 3D. In this paper, we propose a new algorithm for construction of Voronoi diagram of circles. This algorithm constructs the Voronoi diagram by adding a new circle to the already constructed one and then changing the topology influenced by the new circle. The approach using topology uses logical computations instead of numerical computations. That reduces the number of numerical errors.
BetaConcpet 프로그램: 2 차원 평면의 Voronoi diagram, 쌍대구조 그리고 콤플렉스
김재관(Jae-Kwan Kim),이목원(Mokwon Lee),차제현(Jehyun Cha),송찬영(Youngsong Song),조영송(Youngsong Cho),유중현(Joonghyun Ryu),김덕수(Deok-Soo Kim) (사)한국CDE학회 2014 한국 CAD/CAM 학회 학술발표회 논문집 Vol.2014 No.8
Voronoi diagrams are powerful for solving spatial problems among particles with different sizes.Voronoi diagram of atoms has proven its power for solving various fields of different disciplines, particularly molecular biology/material science problems, in an unified framework. Beta-complex is a generalization of alpha-complex and they share similarities and dissimilarities. This paper presents the BetaConcept program which facilitates easy understanding of the powerful capability of the Voronoi diagram, its dual structure, and the beta-complex in the plane. BetaConcept is a Windows program with a graphic user interface written in the standard C++ language and is freely available at the Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).
조영송(Youngsong Cho),김재관(Jae-Kwan Kim),유중현(Joonghyun Ryu),이목원(Mokwon Lee),차제현(Jehyun Cha),송찬영(Chanyoung Song),김덕수(Deok-Soo Kim) (사)한국CDE학회 2014 한국 CAD/CAM 학회 학술발표회 논문집 Vol.2014 No.8
Geometric properties are critical for the function of molecules consisting of atoms with different radii which are usually modeled as spheres in 3D. “Molecular Geometry” is a theoretical framework of computational understanding of the geometry of molecules in the claim that most molecular structure problems can be effectively and efficiently facilitated by the “geometrization” of the problem into that among spheres in 3D whose solution can be easily found via “geometry kernel”. In this paper, we 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! is designed compatibly so that application programs are completely independent of future modifications and improvements. The BULL! engine will be freely available from the Voronoi Diagram Research Center at Hanyang University.