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Abstract

The main interests of the project are computational geometry and geometric issues in robotics. The research is motivated by the many applications domains, and most notably robotics, that requires to solve geometric problems efficiently.

The goal of our work in computational geometry is three-fold: to design new algorithms, to build a library of geometric algorithms, to apply our techniques to various application domains.

New algorithms deal mainly with some optimization problems in geometry: set stabbing and covering, optimal triangulations and constrained shortest paths.

Special efforts have been devoted this year to geometric computing. This work is supported by the ESPRIT LTR project CGAL in joint collaboration with six other groups in Europe. The main problems considered this year are the specification and the development of the kernel of the library, and robustness issues.

Regarding applications, we work on surface reconstruction in Geology within the GEOFRANCE3D project, on satellite layout in collaboration with MATRA MARCONI SPACE and on the simulation of large telecommunication networks in collaboration with the MISTRAL project in the context of a CNET contract.

The research on parallel robots has been pursued. The main goals are to simplify the computation of the direct kinematics and to provide tools for designing such manipulators. New aplications of this work to car suspensions and machine tools have also been studied.