Section: Software

CGAL: Computational Geometry Algorithms Library

Participants : Sylvain Lazard, Luis Peñaranda, Marc Pouget.

Born as a European project, CGAL (http://www.cgal.org ) has become the standard library for computational geometry. It offers easy access to efficient and reliable geometric algorithms in the form of a C++ library. CGAL is used in various areas needing geometric computation, such as: computer graphics, scientific visualization, computer aided design and modeling, geographic information systems, molecular biology, medical imaging, robotics and motion planning, mesh generation, numerical methods...

M. Pouget is co-author and maintainer, with F. Cazals from INRIA Sophia Antipolis - Méditerranée (ABS team), of two packages released in the version (3.3) of the library. These packages belong to the geometry processing part, they enable the Approximation of Ridges and Umbilics   [45] and the Estimation of Local Differential Properties   [46] on triangulated surface meshes.

In computational geometry, many problems lead to standard, though difficult, algebraic questions such as computing the real roots of a system of equations, computing the sign of a polynomial at the roots of a system, or determining the dimension of a set of solutions. we want to make state-of-the-art algebraic software more accessible to the computational geometry community, in particular, through the computational geometric library CGAL. On this line, S. Lazard and L. Peñaranda proposed an extension to the already existing Number Types package. It consists in adding a multiple-precision floating-point arithmetic, and the corresponding interval arithmetic; these number types are based on the libraries MPFR and MPFI. They also developed a model of the Univariate Algebraic Kernel concept for algebraic computations. This package improves, for instance, the efficiency of the computation of arrangements of polynomial functions in CGAL [28] . This implementation uses the RS library developed by F. Rouillier at INRIA Paris - Rocquencourt (SALSA) for isolating real roots of polynomials. All these packages have been reviewed and accepted or tentatively accepted by the editorial board of CGAL and should be released next year.