## Section:
Software2>
### Axel , a geometric modeler for algebraic objects3>

Participants : Anaïs Ducoffe, Bernard Mourrain, Meriadeg Perrinel.

computational algebraic geometry, curve, implicit equation, intersection, parameterisation, resolution, surface, singularity, topology

We are developing a software called Axel (Algebraic Software-Components for gEometric modeLing) dedicated to algebraic methods for curves and surfaces. Many algorithms in geometric modeling require a combination of geometric and algebraic tools. Aiming at the development of reliable and efficient implementations, Axel provides a framework for such combination of tools, involving symbolic and numeric computations.

The software contains data structures and functionalities related to algebraic models used in geometric modeling, such as polynomial parameterisation, B-Spline, implicit curves and surfaces. It provides algorithms for the treatment of such geometric objects, such as tools for computing intersection points of curves or surfaces, detecting and computing self-intersection points of parameterized surfaces, implicitization, for computing the topology of implicit curves, for meshing implicit (singular) surfaces, etc.

The developments related to isogeometric analysis have been integrated as dedicated plugins. Optimisation techniques and solvers for partial differential equations developed by R. Duvigneau (OPALE) have been connected.

A new version of the algebraic-geometric modelers is developed by Meriadeg Perinnel to connect it to the platform Dtk in order to provide a better modularity and a better interface to existing computation facilities and geometric rendering interface.

The package is distributed as binary packages for Linux as well as for MacOSX. It is hosted at Inria's gforge (http://gforge.inria.fr ) and referenced by many leading software websites such as http://apple.com . The first version of the software has been downloaded more than 15000 times, since it is available.

Collaboration with Gang Xu (Hangzhou Dianzi University, China), Julien Wintz (Dream).