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numerical geometric abstraction : from bits to equations

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."

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
Address
Domaine De Voluceau Rocquencourt
78153 Le Chesnay Cedex
France
Activity type
Research Organisations
EU contribution
€ 1 100 000
Principal investigator
Bruno Eric Emmanuel Levy (Dr.)
Administrative Contact
Armelle Demange (Ms.)

Beneficiaries (1)

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE
France
EU contribution
€ 1 100 000
Address
Domaine De Voluceau Rocquencourt
78153 Le Chesnay Cedex
Activity type
Research Organisations
Principal investigator
Bruno Eric Emmanuel Levy (Dr.)
Administrative Contact
Armelle Demange (Ms.)