Objective "3D geometric objects play a central role in many industrial processes (modeling, scientific visualisation, numerical simulation). However, since the raw output of acquisition mechanisms cannot be used directly in these processes, converting a real object into its numerical counterpart still involves a great deal of user intervention. Geometry Processing is a recently emerged, highly competitive scientific domain that studies this type of problems. The author of this proposal contributed to this domain at its origin, and developped several parameterization algorithms, that construct a ""geometric coordinate system"" attached to the object. This facilitates converting from one representation to another. For instance, it is possible to convert a mesh model into a piecewise bi-cubic surface (much easier to manipulate in Computer Aided Design packages). In a certain sense, this retreives an ""equation"" of the geometry. One can also say that this constructs an *abstraction* of the geometry. Once the geometry is abstracted, re-instancing it into alternative representations is made easier. In this project, we propose to attack the problem from a new angle, and climb one more level of abstraction. In more general terms, a geometric coordinates system corresponds to a *function basis*. Thus, we consider the more general problem of constructing a *dynamic function basis* attached to the object. This abstract forms makes the meaningful parameters appear, and provides the user with new ""knobs"" to interact with the geometry. The formalism that we use combines aspects from finite element modeling, differential geometry, spectral geometry, topology and numerical optimization. We plan to develop applications for processing and optimimizing the representation of both static 3D objets, animated 3D objets, images and videos." Fields of science natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometry Keywords PDE dynamic function bases eigenfunctions geometry processing mesh parameterization Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE5 - ERC Starting Grant - Materials and Synthesis Call for proposal ERC-2007-StG See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE EU contribution € 1 100 000,00 Address DOMAINE DE VOLUCEAU ROCQUENCOURT 78153 Le Chesnay Cedex France See on map Region Ile-de-France Ile-de-France Yvelines Activity type Research Organisations Administrative Contact Armelle Demange (Ms.) Principal investigator Bruno Eric Emmanuel Levy (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE France EU contribution € 1 100 000,00 Address DOMAINE DE VOLUCEAU ROCQUENCOURT 78153 Le Chesnay Cedex See on map Region Ile-de-France Ile-de-France Yvelines Activity type Research Organisations Administrative Contact Armelle Demange (Ms.) Principal investigator Bruno Eric Emmanuel Levy (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
