Introduction to Solid Modeling
Introduction to Solid Modeling
Journal of Computational Chemistry
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
Principles of CAD/CAM/CAE Systems
Principles of CAD/CAM/CAE Systems
A 3D Molecular Surface Representation Supporting Neighborhood Queries
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
Dynamic maintenance of molecular surfaces under conformational changes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
An algebraic spline model of molecular surfaces
Proceedings of the 2007 ACM symposium on Solid and physical modeling
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
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Triangulation of molecular surfaces
Computer-Aided Design
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Quality meshing of implicit solvation models of biomolecular structures
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
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
Manifoldization of β-shapes 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
Euclidean voronoi diagrams of 3d spheres: their construction and related problems from biochemistry
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Visualization and analysis of protein structures using euclidean voronoi diagram of atoms
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
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As the molecular shape determines the functions of a molecule, understanding molecular shapes is important for understanding the biological system of life and thus for designing drugs. To properly define a molecular shape, the definition and computation of the boundary or the surface of a molecule is the most fundamental information. Assuming the hard sphere model of atoms in a molecule, the van der Waals surface, the molecular surface (Connolly surface), and the offset surface (Lee-Richards surface) are the most common surfaces defined on a molecule in biochemistry and molecular biology. In this paper, we present important observations related to the topologies of the three types of surface on molecules and their relationships. We find that the topologies of all three surface types can be computed in O(m) time, and that the topology of one surface can be transformed to the topology of another in O(m) time, both in the worst case, where m represents the number of simplexes on the boundary of a @b-shape. The observations are made based on the recently announced theory of the @b-shape, which can be efficiently computed from the quasi-triangulation, the dual of the Voronoi diagram of a molecule.