Section: New Software and Platforms

CGAL Periodic Triangulations and Meshes

The CGAL library offers a package to compute the 3D periodic Delaunay triangulation of a point set in ${ℝ}^3$, more precisely the Delaunay triangulation of a point set in the 3-dimensional flat torus with cubic domain [30] . The package has been used in various fields. (see http://www.cgal.org/projects.html )

We have been extending this package in three directions:

First, a few new small functions have been added to the Delaunay triangulation class and integrated in CGAL 4.7.

We have developed and documented some new classes allowing to compute weighted periodic Delaunay triangulations. They have been submitted to the CGAL editorial board and accepted for inclusion in CGAL . The code still needs some polishing, and the testsuite must be completed, before a public distribution in CGAL .

We have continued our work to use this package together with the 3D mesh generation package of CGAL [29] , in order to propose a construction of meshes of periodic volumes. Although last year's preliminary results were already convincing [32] , [33] , the work is not ready yet for being submitted to CGAL : the code requires to be completed, documented, and extensively tested.

• Contact: Monique Teillaud

• In collaboration with Aymeric Pellé (Geometrica project-team)

• This work was done in the framework of the Inria ADT (Action de Développement Technologique) OrbiCGAL http://www.loria.fr/~teillaud/ADT-OrbiCGAL/