Data structures and network algorithms
Data structures and network algorithms
Molecular docking using shape descriptors
Journal of Computational Chemistry
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Algorithmic geometry
A perturbation scheme for spherical arrangements with application to molecular modeling
Computational Geometry: Theory and Applications - special issue on applied computational geometry
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Dynamic maintenance of molecular surfaces under conformational changes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Computing the volume of a union of balls: A certified algorithm
ACM Transactions on Mathematical Software (TOMS)
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Balls and spheres are the simplest modeling primitives after affine ones, which accounts for their ubiquitousness in Computer Science and Applied Mathematics. Amongst the many applications, we may cite their prevalence when it comes to modeling our ambient 3D space, or to handle molecular shapes using Van der Waals models. If most of the applications developed so far are based upon simple geometric tests between balls, in particular the intersection test, a number of applications would obviously benefit from finer pieces of information. Consider a sphere S"0 and a list of circles on it, each such circle stemming from the intersection between S"0 and another sphere, say S"i. Also assume that S"i has an accompanying ball B"i. This paper develops an integrated framework, based on the generalization of the Bentley-Ottmann algorithm to the spherical setting, to (i) compute the exact arrangement of circles on S"0 (ii) construct in a single pass the half-edge data structure encoding the arrangement induced by the circles (iii) report the covering list of each face of this arrangement, i.e. the list of balls containing it. As an illustration, the covering lists are used as the building block of a geometric optimization algorithm aiming at selecting diverse conformational ensembles for flexible protein-protein docking.