Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
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
On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Voronoi diagram of a circle set from Voronoi diagram of a point set: topology
Computer Aided Geometric Design
Voronoi diagram of a circle set from Voronoi diagram of a point set: geometry
Computer Aided Geometric Design
Principles of CAD/CAM/CAE Systems
Principles of CAD/CAM/CAE Systems
Blending quadric surfaces with piecewise algebraic surfaces
Graphical Models
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic maintenance and visualization of molecular surfaces
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space
Computer Aided Geometric Design
Weighted alpha shapes
Proximity and applications in general metrics
Proximity and applications in general metrics
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
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
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
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
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
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
QTF: Quasi-triangulation file format
Computer-Aided Design
Technical Section: Efficient construction of the Čech complex
Computers and Graphics
Protein structure optimization by side-chain positioning via beta-complex
Journal of Global Optimization
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The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mucke introduced the concept of @a-shape based on the Delaunay triangulation of a point set. In this paper, we present the theory of @b-shape for a set of three-dimensional spheres as the generalization of the well-known @a-shape for a set of points. The proposed @b-shape fully accounts for the size differences among spheres and therefore it is more appropriate for the efficient and correct solution for applications in biological systems such as proteins. Once the Voronoi diagram of spheres is given, the corresponding @b-shape can be efficiently constructed and various geometric computations on the sphere complex can be efficiently and correctly performed. It turns out that many important problems in biological systems such as proteins can be easily solved via the Voronoi diagram of atoms in proteins and @b-shapes transformed from the Voronoi diagram.