## Section: Software

### Axel , a geometric modeler for algebraic objects

Participants : Angelos Mantzaflaris, Bernard Mourrain [ contact person ] , Gang Xu.

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.

Applications contain 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.

This package is now distributed as binary packages for Linux as well as for MacOSX. It is hosted at the 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.

Collaborators: Stéphane Chau, Jean-Pascal Pavone and Julien Wintz.