The GEOMETRICA group

from INRIA is currently exploring theoretical and computational aspects of surface reconstruction, applied differential geometry (with theoretical guarantees, proofs of convergence), shape approximation with meshes (sampling, interpolation, meshing, isotropic/anisotropic surface remeshing), geometry compression, related data structures and analysis of algorithms. We propose CGAL as a research development platform for training, research and integration of the results.

CGAL

is a C++ library of geometric algorithms designed to provide robust, efficient, flexible and easy to use implementations of geometric algorithms. CGAL aims to make most of the advanced solutions proposed in the field of computational geometry available to users in industry and application area. The library consists of three parts:

• The kernel includes basic geometric data types and operations,
• The basic library includes a large number of geometric data structures and algorithms, such as convex hull and (Delaunay) triangulation algorithms,
• The support library includes STL extensions, supports for different number types, and interfaces to other packages, e.g. for visualisation, and I/O.

The GALAAD group

is working on algebraic-geometric problems related to shape modeling. Its interest includes representations of shapes by parametric or implicit equations, conversion and approximation questions, in particular meshing algebraic surfaces and related problems for the treatment of these models such as intersection, topology, singularity analysis. These questions involve algebraic methods, for the resolution of polynomial equations, at the border between symbolic and numeric computation. A special emphasis in our work is given on certified computation. We propose the library SYNAPS as a software support for training, research and integration of results on algebraic questions related to shape modeling.