CAD Research team

Computer Aided Design

Team presentation

CAD is one of the projects run within the LIAMA Consortium, as a cooperation Project between INRIA and Tsinghua University. This Project is focused on Geometry Modeling and Mathematics of Curves and Surfaces.

Research themes

In many applications, from design to engineering or re-engineering processes, numerical simulations, shapes are first described in term of Parametric Surfaces. The pioneering work in this domain was the theory of Bézier curves and surfaces (theory of polynomial curves and surfaces in Bernstein form), later combined with B-spline methods. Differential Geometry is also an important scientific foundation for Geometry Modeling. Differential geometry is based largely of the pioneering work of L. Euler (1707-1783), C. Monge (1746-1818) and C.F. Gauss (1777-1855). One of their concerns was the description of local curves and surface properties such as parametric continuities. These concepts are also of interest in modern computer-aided geometry design.

Today, Non-Uniform Rational B-Spline (NURBS) have become the standard curves and surfaces description in the field of CAD. NURBS have many advantages due to their simple representation, but there are many computational problems with NURBS: intersection, merging, blending, etc.

Our contributions address the most important problems related on the parametric surfaces representation: geometry precision, i.e. continuity, operations, quality of parametric mesh, control points net optimization, etc. Most of these contributions are tested on industrial unsolved problems both with Chinese or French industrial companies.

International and industrial relations

CAD is supported by the NSF China, System@tic, Spring Technology and EADS.

Keywords: Geometry Modeling Mathematics of Curves and surfaces

Research teams of the same theme :

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