Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Journal of Computational Chemistry
Rational cubic circular arcs and their application in CAD
Computers in Industry
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
Fast and robust computation of molecular surfaces
Proceedings of the eleventh 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
A perturbation scheme for spherical arrangements with application to molecular modeling
Computational Geometry: Theory and Applications - special issue on applied computational geometry
Real-Time Rendering
Dynamic maintenance and visualization of molecular surfaces
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Weighted alpha shapes
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
\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 Representation of Molecular Surfaces
IEEE Computer Graphics and Applications
Computer-Aided Design
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In this paper, a rational Bezier surface is proposed as a uniform approach to modeling all three types of molecular surfaces (MS): the van der Waals surface (vdWS), solvent accessible surface (SAS) and solvent excluded surface (SES). Each molecular surface can be divided into molecular patches, which can be defined by their boundary arcs. The solution consists of three steps: topology modeling, boundary modeling and surface modeling. Firstly, using a weighted @a-shape, topology modeling creates two networks to describe the neighboring relationship of the molecular atoms. Secondly, boundary modeling derives all boundary arcs from the networks. Thirdly, surface modeling constructs all three types of molecular surfaces patch-by-patch, based on the networks and the boundary arcs. For an SES, the singularity is specially treated to avoid self-intersections. Instead of approximation, this proposed solution can produce precise shapes of molecular surfaces. Since rational Bezier representation is much simpler than a trimmed non-uniform rational B-spline surface (NURBS), computational load can be significantly saved when dealing with molecular surfaces. It is also possible to utilize the hardware acceleration for tessellation and rendering of a rational Bezier surface. CAGD kernel modelers typically use NURBSs as a uniform representation to handle different types of free-form surface. This research indicates that rational Bezier representation, more specifically, a bi-cubic or 2x4 rational Bezier surface, is sufficient for kernel modeling of molecular surfaces and related applications.