Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Voronoi diagrams over dynamic scenes
Discrete Applied Mathematics
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Animating soft substances with implicit surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fast and robust computation of molecular surfaces
Proceedings of the eleventh annual symposium on Computational geometry
Representation and computation of Boolean combinations of sculptured models
Proceedings of the eleventh annual symposium on Computational geometry
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
Splitting a complex of convex polytopes in any dimension
Proceedings of the twelfth annual symposium on Computational geometry
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
Near-quadratic bounds for the L1 Voronoi diagram of moving points
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
NURBS based B-rep models for macromolecules and their properties
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
Voronoi Diagrams of Moving Points in Higher Dimensional Spaces
SWAT '92 Proceedings of the Third Scandinavian Workshop on Algorithm Theory
Smooth Surfaces for Multi-Scale Shape Representation
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
Geometric Techniques for Molecular Shape Analysis
Geometric Techniques for Molecular Shape Analysis
On the definition and the construction of pockets in macromolecules
On the definition and the construction of pockets in macromolecules
Fast analytical computation of Richards's smooth molecular surface
VIS '93 Proceedings of the 4th conference on Visualization '93
TexMol: Interactive Visual Exploration of Large Flexible Multi-Component Molecular Complexes
VIS '04 Proceedings of the conference on Visualization '04
Dynamic maintenance of molecular surfaces under conformational changes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Geometric modeling applications in rational drug design: a survey
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
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
Geometry-guided computation of 3D electrostatics for large biomolecules
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Meshing skin surfaces with certified topology
Computational Geometry: Theory and Applications
Periodic surface modeling for computer aided nano design
Computer-Aided Design
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Triangulation of molecular surfaces
Computer-Aided Design
Higher-order level-set method and its application in biomolecular surfaces construction
Journal of Computer Science and Technology
A dynamic data structure for flexible molecular maintenance and informatics
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Feature-based crystal construction in computer-aided nano-design
Computer-Aided Design
Geometric modeling applications in rational drug design: a survey
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
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
Geometry-guided computation of 3D electrostatics for large biomolecules
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Computer-Aided Design
Interaction interfaces in proteins via the Voronoi diagram of atoms
Computer-Aided Design
Kernel modeling for molecular surfaces using a uniform solution
Computer-Aided Design
Real-time triangulation of molecular surfaces
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Multi-level grid algorithms for faster molecular energetics
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Molecular surface mesh generation by filtering electron density map
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Adaptive skin meshes coarsening for biomolecular simulation
Computer Aided Geometric Design
Power diagrams and intersection detection
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
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
Improved maintenance of molecular surfaces using dynamic graph connectivity
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Geometric modeling of nano structures with periodic surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Geometry guided crystal phase transition pathway search
Computer-Aided Design
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Molecular surface computations are often necessary in order to perform synthetic drug design. A critical step in this process is the computation and update of an exact boundary representation for the molecular surface (e.g. the Lee--Richards surface). In this paper we introduce efficient techniques for computing a molecular surface boundary representation as a set of non-uniform rational B-splines patches. This representation introduces for molecules the same geometric data structure used in the solid modeling community and enables immediate access to a wide range of modeling operations and techniques. Furthermore, this allows the use of any general solid modeling or visualization system as a molecular modeling interface. However, using such a representation in a molecular modeling environment raises several efficiency and update constraints, especially in a dynamic setting. For example, changes in the probe radius result in both geometric and topological changes to the set of patches. Our techniques provide the option of trading accuracy of the representation for the efficiency of the computation, while still tracking the changes in the set of patches. In particular, we discuss two main classes of dynamic updates: one that keeps the topology of the molecular configuration fixed, and a more complicated case were the topology may be updated continuously. In general the generated output surface is represented in a format that can be loaded into standard solid modeling systems. It can also be directly triangulated or rendered, possibly at different levels of resolution, by a standard graphics library such as OpenGL without any additional effort.