Overall Objectives
Research Program
Application Domains
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: New Software and Platforms

CGAL, the Computational Geometry Algorithms Library

Participants : Jean-Daniel Boissonnat, Olivier Devillers, Marc Glisse, Aymeric Pellé, Monique Teillaud, Mariette Yvinec.

With the collaboration of Pierre Alliez, Hervé Brönnimann, Manuel Caroli, Pedro Machado Manhães de Castro, Frédéric Cazals, Frank Da, Christophe Delage, Andreas Fabri, Julia Flötotto, Philippe Guigue, Michael Hemmer, Samuel Hornus, Clément Jamin, Menelaos Karavelas, Sébastien Loriot, Abdelkrim Mebarki, Naceur Meskini, Andreas Meyer, Sylvain Pion, Marc Pouget, François Rebufat, Laurent Rineau, Laurent Saboret, Stéphane Tayeb, Jane Tournois, Radu Ursu, and Camille Wormser

cgal is a C++ library of geometric algorithms and data structures. Its development has been initially funded and further supported by several European projects (CGAL, GALIA, ECG, ACS, AIM@SHAPE) since 1996. The long term partners of the project are research teams from the following institutes: Inria Sophia Antipolis - Méditerranée, Max-Planck Institut Saarbrücken, ETH Zürich, Tel Aviv University, together with several others. In 2003, cgal became an Open Source project (under the LGPL and QPL licenses).

The transfer and diffusion of cgal in industry is achieved through the company Geometry Factory ( ). Geometry Factory is a Born of Inria company, founded by Andreas Fabri in January 2003. The goal of this company is to pursue the development of the library and to offer services in connection with cgal (maintenance, support, teaching, advice). Geometry Factory is a link between the researchers from the computational geometry community and the industrial users.

The aim of the cgal project is to create a platform for geometric computing supporting usage in both industry and academia. The main design goals are genericity, numerical robustness, efficiency and ease of use. These goals are enforced by a review of all submissions managed by an editorial board. As the focus is on fundamental geometric algorithms and data structures, the target application domains are numerous: from geological modeling to medical images, from antenna placement to geographic information systems, etc.

The cgal library consists of a kernel, a list of algorithmic packages, and a support library. The kernel is made of classes that represent elementary geometric objects (points, vectors, lines, segments, planes, simplices, isothetic boxes, circles, spheres, circular arcs...), as well as affine transformations and a number of predicates and geometric constructions over these objects. These classes exist in dimensions 2 and 3 (static dimension) and d (dynamic dimension). Using the template mechanism, each class can be instantiated following several representation modes: one can choose between Cartesian or homogeneous coordinates, use different number types to store the coordinates, and use reference counting or not. The kernel also provides some robustness features using some specifically-devised arithmetic (interval arithmetic, multi-precision arithmetic, static filters...).

A number of packages provide geometric data structures as well as algorithms. The data structures are polygons, polyhedra, triangulations, planar maps, arrangements and various search structures (segment trees, d-dimensional trees...). Algorithms are provided to compute convex hulls, Voronoi diagrams, Boolean operations on polygons, solve certain optimization problems (linear, quadratic, generalized of linear type). Through class and function templates, these algorithms can be used either with the kernel objects or with user-defined geometric classes provided they match a documented interface.

Finally, the support library provides random generators, and interfacing code with other libraries, tools, or file formats (ASCII files, QT or LEDA Windows, OpenGL, Open Inventor, Postscript, Geomview...). Partial interfaces with Python, scilab and the Ipe drawing editor are now also available.

Geometrica is particularly involved in general maintenance, in the arithmetic issues that arise in the treatment of robustness issues, in the kernel, in triangulation packages and their close applications such as alpha shapes, in mesh generation and related packages. Two researchers of Geometrica are members of the cgal Editorial Board, whose main responsibilities are the control of the quality of cgal , making decisions about technical matters, coordinating communication and promotion of cgal .

cgal is about 700,000 lines of code and supports various platforms: GCC (Linux, Mac OS X, Cygwin...), Visual C++ (Windows), Intel C++. A new version of cgal is released twice a year, and it is downloaded about 10000 times a year. Moreover, cgal is directly available as packages for the Debian, Ubuntu and Fedora Linux distributions.

More numbers about cgal : there are now 12 editors in the editorial board, with approximately 20 additional developers. The user discussion mailing-list has more than 1000 subscribers with a relatively high traffic of 5-10 mails a day. The announcement mailing-list has more than 3000 subscribers.

High-dimensional kernel Epick_d

Participant : Marc Glisse.

We implemented a new high-dimensional kernel taking advantage of the progress that was made in dimensions 2 and 3. It is meant to be used with a reimplementation of high-dimensional triangulations (in progress).

Number type Mpzf

Participant : Marc Glisse.

We added a new exact ring number type that can represent all finite double floating-point numbers. It makes building a Delaunay triangulation 8 times faster than with earlier cgal releases in some degenerate cases.

CGALmesh: a Generic Framework for Delaunay Mesh Generation

Participants : Jean-Daniel Boissonnat, Mariette Yvinec.

In collaboration with Pierre Alliez (EPI Titane), ClémentJamin (EPI Titane)

CGALmesh is the mesh generation software package of the Computational Geometry Algorithm Library (cgal ). It generates isotropic simplicial meshes – surface triangular meshes or volume tetrahedral meshes – from input surfaces, 3D domains as well as 3D multi-domains, with or without sharp features. The underlying meshing algorithm relies on restricted Delaunay triangulations to approximate domains and surfaces, and on Delaunay refinement to ensure both approximation accuracy and mesh quality. CGALmesh provides guarantees on approximation quality as well as on the size and shape of the mesh elements. It provides four optional mesh optimization algorithms to further improve the mesh quality. A distinctive property of CGALmesh is its high flexibility with respect to the input domain representation. Such a flexibility is achieved through a careful software design, gathering into a single abstract concept, denoted by the oracle, all required interface features between the meshing engine and the input domain. We already provide oracles for domains defined by polyhedral and implicit surfaces. [27] [53]

Periodic Meshes

Participants : Aymeric Pellé, Monique Teillaud.

There is a growing need for a 3D periodic mesh generator for various fields, such as material engineering or modeling of nano-structures. We are writing a software package answering this need, and which will be made publicly available in the open source library cgal . The software is based on the cgal 3D volume mesh generator package and the cgal 3D periodic triangulations package. [42] [63]