# Project : galaad

## Section: Software

Keywords : curve, surface, parameterisation, implicit equation, topology, singularity, intersection, algebra, resolution.

### axel, a module for curves and surfaces

Participants : Grégory Gatellier, Bernard Mourrain, Jean-Pascal Pavone, Olivier Ruatta, Jean-Pierre Técourt.

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

We are developing a module 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 library 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 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 library is connected to external libraries such as synaps for algebraic tools such as polynomial solvers or cgal (Geometric Algorithms Library) for classical computational geometry ingredients. Some components of the library are connected to industrial CAGD software. Many functionalities of the library are also available through the computer algebra system mathemagix, as dynamic binary libraries.