Real-time Triangulation of Molecular Surfaces Joonghyun Ryu 1 , Rhohun Park 1 , Jeongyeon Seo 2 , Chongmin Kim 2 , Hyun Chan Lee 3 , and Deok-Soo Kim 2 1 Voronoi Diagram Research Center, Hanyang University 17 Haengdang-dong, Seongdong-gu Seoul 133-791, Korea {jhryu, rhpark}@voronoi.hanyang.ac.kr 2 Department of Industrial Engineering, Hanyang University 17 Haengdang-dong, Seongdong-gu Seoul 133-791, Korea {jyseo, cmkim}@voronoi.hanyang.ac.kr, dskim@hanyang.ac.kr 3 Department of Industrial Engineering , Hongik University Sangsu-dong, 72-1. Mapo-gu, Seoul, Korea hclee@wow.hongik.ac.kr Abstract. Protein consists of a set of atoms. Given a protein, the molec- ular surface of the protein is defined with respect to a probe approximat- ing a solvent molecule. This paper presents an efficient, as efficient as the realtime, algorithm to triangulate the blending surfaces which is the most critical subset of a molecular surface. For the quick evaluation of points on the surface, the proposed algorithm uses masks which are similar in their concepts to those in subdivision surfaces. More fundamentally, the proposed algorithm takes advantage of the concise representation of topology among atoms stored in the β-shape which is indeed used in the computation of the blending surface itself. Given blending surfaces and the corresponding β-shape, the proposed algorithm triangulates the blending surfaces in O(c · m) time in the worst case, where m is the number of boundary atoms in the protein and c is the number of point evaluations on a patch in the blending surface. Key words: a protein, a molecular surface, β-shape, a Voronoi diagram of atoms 1 Introduction It has been generally agreed that the structure of molecule is one of the most important factors which determines the functions of a molecule. Hence, studies have been conducted to analyze the structure of a molecule. Molecular surface is an important example of molecular structure. Protein consists of a set of atoms where the atoms are usually modelled by spherical balls. Since a protein is usually solvated and the interaction between a protein and solvent molecules is important, we build a protein model in the solvent so that the interaction can be conveniently analyzed. A solvent molecule is usually approximated by a spherical ball, called a probe, which encloses a solvent molecule. This approximation is due to geometric as well as stochastic