Computational geometry: an introduction
Computational geometry: an introduction
Introduction to Solid Modeling
Introduction to Solid Modeling
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Spheres, molecules, and hidden surface removal
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
NURBS based B-rep models for macromolecules and their properties
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Principles of CAD/CAM/CAE Systems
Principles of CAD/CAM/CAE Systems
Computing Smooth Molecular Surfaces
IEEE Computer Graphics and Applications
Dynamic maintenance and visualization of molecular surfaces
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Defining, Computing, and Visualizing Molecular Interfaces
VIS '95 Proceedings of the 6th conference on Visualization '95
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Pocket recognition on a protein using euclidean voronoi diagram of atoms
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
A β-shape from the Voronoi diagram of atoms for protein structure analysis
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
An efficient algorithm for three-dimensional β-complex and β-shape via a quasi-triangulation
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Triangulation of molecular surfaces
Computer-Aided Design
Computer-Aided Design
A sweepline algorithm for Euclidean Voronoi diagram of circles
Computer-Aided Design
Kernel modeling for molecular surfaces using a uniform solution
Computer-Aided Design
Manifoldization of β-shapes in O(n) time
Computer-Aided Design
Manifoldization of β-shapes by topology operators
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Real-time triangulation of molecular surfaces
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Topologies of surfaces on molecules and their computation in O(n) time
Computer-Aided Design
Quasi-worlds and quasi-operators on quasi-triangulations
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
Molecular surface mesh generation by filtering electron density map
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Protein-ligand docking based on beta-shape
Transactions on computational science IX
Protein-ligand docking based on beta-shape
Transactions on computational science IX
Querying simplexes in quasi-triangulation
Computer-Aided Design
QTF: Quasi-triangulation file format
Computer-Aided Design
Geometry guided crystal phase transition pathway search
Computer-Aided Design
Anomalies in quasi-triangulations and beta-complexes of spherical atoms in molecules
Computer-Aided Design
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A protein consists of linearly combined amino acids via peptide bonds, and an amino acid consists of atoms. It is known that the geometric structure of a protein is the primary factor which determines the functions of the protein. Given the atomic complex of a protein, one of the most important geometric structures of a protein is its molecular surface since this distinguishes between the interior and exterior of the protein and plays an important role in protein folding, docking, interactions between proteins, and other functions. This paper presents an algorithm for the precise and efficient computation of the molecular surface of a protein, using a recently proposed geometric construct called the @b-shape based on the Voronoi diagram of atoms in a protein. Given a Voronoi diagram of atoms, based on the Euclidean distance from the atom surfaces, the proposed algorithm first computes the @b-shape with an appropriate sized probe. Then, the molecular surface is computed by employing a blending operation on the atomic complex of the protein. In this paper, it is also shown that for a given Voronoi diagram of atoms, the multiple molecular surfaces can be computed by using various sized probes.