YVINEC , Mariette

A polyhedron is any set that can be obtained from the open halfspaces by a finite number of set complement and set intersection operations. We give an efficient and complete algorithm for intersecting two three-dimensional polyhedra, one of which is convex. The algorithm is efficient in the sense that its running time is bounded by the size of...

Anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions, with elements elongated along prescribed directions. Anisotropic trian-gulations are known to be well suited for interpolation of functions or solving PDEs. Assuming that the anisotropic shape requirements for mesh elements are given through a metric...

Geometric and topological inference deals with the retrieval of information about a geometric object that is only known through a finite set of possibly noisy sample points. Geometric and topological inference employs many tools from Computational Geometry and Applied Topology. It has connections to Manifold Learning and provides the...

Underwater range scanning techniques are starting to gain interest in underwater exploration, providing new tools to represent the seafloor. These scans (often) acquired by underwater robots usually result in an unstructured point cloud, but given the common downward-looking or forward-looking configuration of these sensors with respect to the...

CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (CGAL). It generates isotropic simplicial meshes -- surface triangular meshes or volume tetrahedral meshes -- from input surfaces, 3D domains as well as 3D multi-domains, with or without sharp features. The underlying meshing algorithm relies on...

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We present an algorithm which computes the convex hull of a set of spheres in dimension d in time O(n^ceil(d/2)+n log n). It is worst case optimal in three dimensions and in even dimensions. The same method can also be used to compute the convex hull of a set of n homethetic objects of Ed. If the complexity of each object is constant, the time...

We propose a method to evaluate signs of $2\times 2$ and $3\times 3$ determinants with $b$-bit integer entries using only $b$ and $(b+1)$-bit arithmetic respectively. This algorithm has numerous applications in geometric computation and provides a general and practical approach to robustness. The algorithm has been implemented and experimental...

The electrostatic potential in the neighborhood of a biomolecule can be computed thanks to the non-linear divergence-form elliptic Poisson-Boltzmann PDE. Dedicated Monte-Carlo methods have been developed to solve its linearized version (see e.g.Bossy et al 2009, Mascagni & Simonov 2004}). These algorithms combine walk on spheres techniques and...