A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
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
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
NURBS based B-rep models for macromolecules and their properties
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Digital Principles and Applications
Digital Principles and Applications
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
Weighted alpha shapes
Guaranteed Quality Triangulation of Molecular Skin Surfaces
VIS '04 Proceedings of the conference on Visualization '04
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
\beta-shape Based Computation of Blending Surfaces on a Molecule
ISVD '07 Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
Manifoldization of β-shapes in O(n) time
Computer-Aided Design
Topologies of surfaces on molecules and their computation in O(n) time
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
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
Accelerated visualization of dynamic molecular surfaces
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
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Given a molecule, which consists of a set of atoms, a molecular surface is defined for a spherical probe approximating a solvent molecule. Molecular surface is used for both the visualization of the molecule and the computation of various molecular properties such as the area and volume of a protein, which are important for studying problems such as protein docking and folding. In this paper, we present an O(n) time algorithm, in the worst case, for triangulating molecular surface based on the combinatorial information provided by the @b-shape of the molecule with n atoms. The proposed algorithm takes advantage of the concise representation of topology among atoms stored in the @b-shape. A molecular surface consists of two parts: a blending surface consisting of blending patches and a (solvent) contact surface consisting of (solvent) contact patches. For each blending patch, the algorithm uses compact masks for the construction of a triangular mesh in O(c^') time in the worst case, where c^' is the number of point evaluations on the blending patch. For each contact patch, the algorithm uses a template, for each atom type, for the triangulation of the boundary of the atom. Then, the triangular mesh is trimmed off by hyperplanes where each hyperplane corresponds to an arc of the boundary of the contact patch. The triangulation of a contact patch takes O(c^'') time in the worst case, where c^'' is the number of point evaluations on the boundary of an atom. Since there are at most O(n) patches, the worst case time complexity is O(n). The proposed algorithm also handles internal voids and guarantees the watertightness of the produced triangular mesh of a molecular surface. In addition, the level-of-detail is easily achieved as a by-product of the proposed scheme. The proposed algorithm is fully implemented and statistics from experiments are also collected.