By geometric modeling, we mean essentially the passage from continuous to discrete and vice versa. The topics related to this subject constitute an original and new axis of the UR. The (Surface) modeling is to be considered here in the sense of queries related to mesh generation algorithms. In particular, the presence of certain geometric characteristics ensures approximation and quality properties. Furthermore, we are interested in the modeling, in the classical sense, of mechanical structures, here nanostructures, and we look at some reconstruction problems from discrete data (reverse engineering and geometric control). These points can be broken down into :
  • Construction of topological skeleton of CAD surfaces.

    This step is necessary to obtain a conformal assembly of surface tiles before generating a quality mesh.

  • Representation or second-order geometric approximation of CAD surfaces.

    This order is essential for the generation of meshes with faithful respect to geometry.

  • Extraction of geometric features from CAD surfaces,

    in particular ridge lines, to improve the geometric quality of meshes without explicitly considering geometric curvatures.

  • Geometric modeling of granular structures (innovative materials).

    This involves extending the methodology to take into account the anisotropy of materials.

  • 3D reconstruction from a point cloud.

    The focus will be on the identification and faithful reconstruction of geometric singularities (sharp edges and corners) in mechanical parts, since traditional methods do not generally treat these cases.

  • 3D reconstruction from digital images.

    This is a special case of 3D reconstruction in which the scan is performed without "contact" (probes or rays) with the object.

  • Continuous surface model from discrete surface

    leading to adaptive surface re-meshing, fluid-structure interaction, shape optimization and fictitious domains.

It should be noted that these studies have important (and/or indirect) spin-offs effects on generic surface meshing methods and, in the opposite direction, rely on conventional (sometimes hijacked) meshing tools.