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Given a quasi-triangulation, the dual structure of the Voronoi diagram of a molecule, querying its simplexes of a particular bounding state for the spherical probe of a given radius occurs frequently. The β-complex and the β-shape are such examples with various applications for reasoning the spatial structure of molecules. While such simplexes can be found by linearly scanning all simplexes in the...
The proximity and topology among particles are often the most important factor for understanding the spatial structure of particles. Reasoning the morphological structure of molecules and reconstructing a surface from a point set are examples where proximity among particles is important. Traditionally, the Voronoi diagram of points, the power diagram, the Delaunay triangulation, and the regular triangulation,...
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