The topic of this chapter, Voronoi diagrams, di ers from other areas of computational
geometry, in that its origin dates back to the 17th century. In his book on the principles of …

Efficient algorithms are described for computing topological, combinatorial, and metric
properties of the union of finitely many balls in ℝd. These algorithms are based on a …

A systematic study of random Laguerre tessellations, weighted generalisations of the well-
known Voronoi tessellations, is presented. We prove that every normal tessellation with …

Modeling a crystal as a periodic point set, we present a fingerprint consisting of density
functions that facilitates the efficient search for new materials and material properties. We …

This paper is the second part of a broader survey of computational convexity, an area of
mathematics that has crystallized around a variety of results, problems and applications …

An algorithm for the exact calculation of the overlap volume of a sphere and a tetrahedron,
wedge, or hexahedron is described. The method can be used to determine the exact local …

Improvements to the classical inclusion-exclusion identity are developed. There are two
main results: an abstract combinatoric result and a concrete geometric result. In the abstract …

Balls and spheres are amongst the simplest 3 D modeling primitives, and computing the
volume of a union of balls is an elementary problem. Although a number of strategies …

In this article we derive a complete characterization of the Solvent Excluded Surface (SES)
for molecular systems including a complete characterization of singularities of the surface …

The computational effort of biomolecular simulations can be significantly reduced by means
of implicit solvent models in which the energy generally contains a correction depending on …