Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Triangulating the surface of a molecule
Discrete Applied Mathematics - Special volume on computational molecular biology
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Weighted alpha shapes
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Computing the arrangement of circles on a sphere, with applications in structural biology
Computational Geometry: Theory and Applications
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
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Balls and spheres are amongst the simplest 3D modeling primitives, and computing the volume of a union of balls is an elementary problem. Although a number of strategies addressing this problem have been investigated in several communities, we are not aware of any robust algorithm, and present the first such algorithm. Our calculation relies on the decomposition of the volume of the union into convex regions, namely the restrictions of the balls to their regions in the power diagram. Theoretically, we establish a formula for the volume of a restriction, based on Gauss' divergence theorem. The proof being constructive, we develop the associated algorithm. On the implementation side, we carefully analyse the predicates and constructions involved in the volume calculation, and present a certified implementation relying on interval arithmetic. The result is certified in the sense that the exact volume belongs to the interval computed. Experimental results are presented on hand-crafted models illustrating various difficulties, as well as on the 58,898 models found in the tenth of July 2009 release of the Protein Data Bank.