## Section: Software

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

### Axel, a geometric modeler for algebraic objects

Participants : Bernard Mourrain, Jean-Pascal Pavone, Julien Wintz [ contact person ] .

See axel web site: http://www-sop.inria.fr/galaad/logiciels/axel/ .

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 application 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.

This package is now distributed as binary packages as well for linux as for MacOSX, see http://www-sop.inria.fr/galaad/axel/ .