Geometric computing plays a central role in most engineering activities: geometric modelling, computer aided design and manufacturing, computer graphics and virtual reality, scientific visualization, geographic information systems, molecular biology, fluid mechanics, and robotics are just a few well-known examples. The rapid advances in visualization systems, networking facilities and 3D sensing and imaging make geometric computing both dominant and more demanding concerning effective algorithmic solutions.

Computational geometry emerged as a discipline in the seventies and
has met with considerable success in resolving the asymptotic
complexity of basic geometric problems including data structures,
convex hulls, triangulations, Voronoi diagrams, geometric arrangements
and geometric optimisation. However, in the mid-nineties, it was
recognized that the applicability in practice of the computational
geometry techniques was far from satisfactory and a vigorous effort
has been undertaken to make computational geometry more effective.
The prisme project together with several partners in Europe took
a prominent role in this research and in the development of a large
library of computational geometry algorithms, cgal.

geometrica aims at pursuing further the effort in this direction and
at building upon the initial success. Its focus is on effective
computational geometry with special emphasis on curves and surfaces.
This is a challenging research area with a huge number of potential
applications in almost all application domains involving geometric computing.

The overall objective of the project is to give effective computational geometry for curves and surfaces solid mathematical and algorithmic foundations, to provide solutions to key problems and to validate our theoretical advances through extensive experimental research and the development of software packages that could serve as steps towards a standard for safe and effective geometric computing.

The research conducted by geometrica focuses on three main directions:

- design and analysis of geometric algorithms for curves, surfaces and triangulations

- robust computation and advanced programming,

- shape approximation, surface reconstruction and compression.

geometrica intends to revisit the field of computational geometry in order
to understand how structures that are well-known for linear objects
behave when defined on curves and surfaces. We are especially
interested in extending the theory of Voronoi diagrams beyond the
affine case. This research includes to study the mathematical
properties of these structures and to design algorithms to construct
them. To ensure the effectiveness of our algorithms, we precisely
specify what are the basic numerical primitives that need to be
performed, and consider tradeoffs between the complexity of the
algorithms (i.e. the number of primitive calls), and the complexity of
the primitives and their numerical stability. Working out carefully
the robustness issues is a central objective of geometrica (see below).

Decomposing a complex shape in basic simple elements such as triangles
or tetrahedra is a first step for many purposes, starting from
visualization and going to more complex modeling such as meshing for
finite elements method. Triangulations are a fundamental
structure in this respect. Triangulations and, in particular,
Delaunay triangulations have been extensively studied by the
Computational Geometry community: the algorithmic and combinatorial
issues are mostly solved in the plane. The situation is different in
higher dimensions, and even in three dimensional space, many questions
remain open.

A first question is related to the combinatorial complexity of the Delaunay triangulation in 3-dimensional space. It is well known that this size can be quadratic, but examples of such behavior seem quite artificial and work has been done to prove sub-quadratic behaviors under realistic hypotheses.

Constrained triangulations are triangulations that include
some given sets of edges and triangles. A typical case is to include
the boundary of some polyhedral domain. Computing a constrained
triangulation is more difficult than just triangulating a set of
points, and it is NP-hard to decide if such a triangulation exists.
Adding points to the original set is then required to help
triangulating while respecting the constraints or to obtain well
shaped tetrahedra. Designing efficient algorithms, with certified
results and a controlled number of added points for such purposes is
an active area of research geometrica investigates.

An implementation of a geometric algorithm is called robust if
it produces a valid output for all inputs. Geometric programs are
notorious for their non-robustness due to two reasons: (1) Geometric
algorithms are designed for a model of computation where real numbers
are dealt with exactly and (2) geometric algorithms are frequently
only formulated for inputs in general position. As a result,
implementations may crash or produce nonsensical output. This is
observed in all commercial cad-systems.

The importance of robustness in geometric computations was recognized
for a long time, but significant progress was made only in recent
years. geometrica held a central role in this process, including
advances regarding the exact computation paradigm. In this
paradigm, robustness is achieved by a combination of three methods:
exact arithmetic, dedicated arithmetic and
controlled rounding.

In addition to pursuing research on robust geometric computation,
geometrica is an active member of a European consortium that develops
a large library named cgal. This library makes extensive use of
generic programming techniques and is both a unique tool to perform
experimental research in Computational Geometry and a comprehensive
library for Geometric Computing. A startup company has been launched
in January 2003 to commercialize components from cgal and to offer
services for geometric applications.

Complex shapes are
ubiquitous in robotics (configuration spaces), computer graphics
(animation models) or physical simulations (fluid models, molecular
systems). In all these cases, no natural shape space is
available or when such spaces exist they are not easily dealt with.
When it comes to performing calculations, the objects under study must
be discretized. On the other hand, several application areas such as
Computer Aided Geometric Design or medical imaging require
reconstructing

The questions afore-mentioned fall in the realm of geometric
approximation theory, a topic geometrica is actively involved in. More
precisely, the generation of samples, the definition of differential
quantities (e.g. curvatures) in a discrete setting, the geometric and
topological control of approximations, as well as multi-scale
representations are investigated. Connected topics of interest are
also the progressive transmission of models over networks and their
compression.

Surface mesh generation and surface reconstruction have received a
great deal of attention by researchers in various areas ranging from
computer graphics through numerical analysis to computational
geometry. However, work in these areas has been mostly heuristic and
the first theoretical foundations have been established only recently.
Quality mesh generation amounts to finding a partition of a domain
into linear elements (mostly triangles or quadrilaterals) with
topological and geometric properties. Typically, one wants to
construct a piece-wise linear (PL) approximation with the ``same''
topology as the original surface (same topology may have several
meanings). In some contexts, one wants to simplify the topology in a
controlled way. Regarding the geometric distance between the surface
and its PL approximation, different measures must be considered:
Hausdorff distance, errors on normals, curvatures, areas etc. In
addition, the shape, angles or size of the elements must match certain
criteria. We call remeshing the techniques involved when the
input domain to be discretized is itself discrete. The input mesh is
often highly irregular and non-uniform, since it typically comes as
the output of a surface reconstruction algorithm applied to a point
cloud obtained from a scanning device. Many geometry processing
algorithms (e.g. smoothing, compression) benefit from remeshing,
combined with uniform or curvature-adapted sampling. geometrica intends to
contribute to all aspects of this matter, both in theory and in
practice.

Modeling 3D shapes is required for all visualization applications where interactivity is key since the observer can change the viewpoint and get an immediate feedback. This interactivity enhances the descriptive power of the medium significantly. For example, visualization of complex molecules help drug designers to understand their structure. Multimedia applications also involve interactive visualization and include e-commerce (companies can present their product realistically), 3D games, animation and special effects in motion pictures. The uses of geometric modeling also cover the spectrum of engineering, computer-aided design and manufacture applications (CAD/CAM). More and more stages of the industrial development and production pipeline are now performed by simulation, the geometric modeling for simulation having received more attention in recent years due to the increased performance of numerical simulation packages. Another emerging application of geometric modeling with high impact is medical visualization and simulation.

In a broad sense, shape reconstruction consists of creating digital
models of real objects from points. Example application areas where
such a process is involved are Computer Aided Geometric Design (making
a car model from a clay mockup), medical imaging (reconstructing an
organ from medical data), geology (modeling underground strata from
seismic data), or cultural heritage projects (making models of ancient
and or fragile models or places). The availability of precise and fast
scanning devices has also made the reproduction of real objects more
effective such that additional fields of applications are coming into
reach. The members of geometrica have a long experience in shape
reconstruction and contributed several original methods based upon the
Delaunay and Voronoi diagrams.

Two of the most prominent challenges of the post-genomic era are to understand the molecular machinery of the cell and to develop new drug design strategies. These key challenges require the determination, understanding and exploitation of the three-dimensional structure of several classes of molecules (nucleic acids, proteins, drugs), as well as the elucidation of the interaction mechanisms between these molecules.

These challenges clearly involve aspects from biology, chemistry, physics, mathematics and computer science. For this latter discipline, while the historical focus has been on text and pattern matching related algorithms, the amount of structural data now available calls for geometric methods. At a macro-scopic scale, the classification of protein shapes, as well as the analysis of molecular complexes requires shape description and matching algorithms. At a finer scale, molecular dynamics and force fields require efficient data-structures to represent solvent models, as well as reliable meshes so as to solve the Poisson-Boltzmann equation.

Meshes are the basic tools for scientific computation. Unstructured
meshes allow to mesh complex shapes and to refine locally the mesh,
which may be required because of the geometry or in order to increase
the precision of the computation. geometrica contributes to 2D and 3D
meshes, and also to surface meshes. The methods are mostly based on
Delaunay triangulations, Voronoi diagrams and their variants. Affine
diagrams are well-suited for volume element methods. Non affine
diagrams are especially important in the context of anisotropic
meshes. Anisotropic quadrilateral meshes are also of interest.

The emerging demand for visualizing and simulating 3D geometric data
in networked environments has motivated research on representations
for such data. Slow networks require data compression to reduce the
latency, and progressive representations to transform 3D objects into
streams manageable by the networks. The members of geometrica have
contributed several original compression methods for surface and
volume meshes. We investigate both single-rate and progressive
compression depending on whether the model is intended to be decoded
during, or only after, the transmission. The case of progressive
compression is in fact closely related both to approximation and
information theory, aiming for the best trade-off between data size
and approximation accuracy (the so-called rate-distortion
tradeoff). We now cast this problem into the one of shape
compression.

cgal is a C++ library of geometric algorithms developed initially within
two European projects (project ESPRIT IV LTR CGAL december 97 - june
98, project ESPRIT IV LTR GALIA november 99 - august 00) by a
consortium of eight research teams from the following institutes:
Universiteit Utrecht, Max-Planck Institut Saarbrücken, INRIA Sophia
Antipolis, ETH Zürich, Tel Aviv University, Freie Universität Berlin,
Universität Halle, RISC Linz. The goal of cgal is to make the
solutions offered by the computational geometry community available to
the industrial world and applied domains.

The cgal library consists in a kernel, a basic library and a support
library. The kernel is made of classes that represent elementary
geometric objects (points, vectors, lines, segments, planes,
simplices, isothetic boxes...), 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

The basic library provides a number of geometric data structures as
well as algorithms. The data structures are polygons, polyhedra,
triangulations, planar maps, arrangements and various search
structures (segment trees,

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...).

geometrica is particularly involved in the arithmetic issues that arise in
the treatment of robustness issues, the kernel, triangulation packages and
their close applications such as alpha shapes, general maintainance...

cgal is about 400,000 lines of code and supports various platforms: GCC
(Linux, Solaris, Irix, Cygwin...), MipsPro (IRIX), SunPro (Solaris),
Visual C++ (Windows), Intel C++... Version 3.0 has been released on
november 6th, 2003. The previous release, cgal 2.4, has been
downloaded 9000 times from our web site, during the 18 months period
where it was the main version.

In collaboration with Frank Da and Andreas Fabri.

The surface reconstruction algorithm developed by David Cohen-Steiner and
Frank Da using cgal is available as a web service. Via the web,
the user uploads the point cloud data set to the server and obtains a Vrml file of the reconstructed surface, which gets visualized in the browser
of the user. This allows the user to get a first impression of the algorithm
to see if it fits the needs, before contacting Inria for obtaining an
executable, learning how to call the program, etc. At the same time it allows
us to collect real-world data sets to test and improve our algorithms.

In collaboration with Menelaos Karavelas, University of Notre Dame (USA).

This work results in a dynamic algorithm for the construction of
the Euclidean Voronoi diagram of a set of convex objects
in the plane

In collaboration with Menelaos Karavelas, University of Notre Dame (USA).

This work is a continuation of the work done last year on Voronoi
diagrams of spheres. We introduce a new type of Voronoi diagrams
called Möbius diagram

The construction of Möbius diagrams in the plane has been
implemented

In collaboration with Dominique Attali (ENSIEG-LIS) and André Lieutier (Dassault Systèmes).

It is well known that the number of faces of the Delaunay triangulation of

The case of points distributed on a surface is of great practical
importance in reverse engineering since most surface reconstruction
algorithms first construct the Delaunay triangulation of a set of
points measured on a surface. The time complexity of those methods
therefore crucially depends on the complexity of the triangulation of
points scattered over a surface in

Several results have been obtained recently. In particular, Attali and
Boissonnat proved last year a deterministic linear bound for the
polyhedral case. In smooth surface. We prove that
the complexity of the Delaunay triangulation of a generic
surface is

One way to address robustness issues in geometric algorithms is to
follow the exact computation paradigm that asks to evaluate all
predicates exactly. Recent work has proved that this approach can be
made very efficient for most single geometric algorithms. However, in
some applications, it is necessary to embed the result in some
representable space (say the grid of floating numbers) : we are then
faced with the problem of rounding the result in accordance with the
computed (possibly in an exact way) combinatorial output. This issue
is especially critical when several algorithms are cascaded,
i.e. when the output of an algorithm is used as input for another
algorithm in a repeated way. For such use, one needs to round
intermediate results while preserving some geometric properties. We
have developed algorithms for boolean operations on polygons in the
plane with guarantees on the inclusion between the true result and the
rounded result and also guarantees on the distance and the number of
vertices of the rounded result

cgal now has a 2D visualization tool based on the Qt software from TrollTech.
It has been chosen because of the portability feature (Windows/Unix).
All 2D cgal packages now have at least one demonstration program based on
this tool.

Support for the Windows platform has been considerably improved in
cgal 3.0. In particular, the newest version of the Visual C++
compiler is supported. The user has now access to a standard
installation tool Install Shield, and the use of the integrated
development environment provided by Microsoft Developer Studio has
been greatly facilitated.

Several applications from Computer Vision, Computer Graphics, Computer
Aided Design or Computational Geometry require estimating local
differential quantities from either a point cloud or a mesh sampled
over a smooth curve or surface. In

On the way to using jets, the question of estimating differential
properties is recasted into the more general framework of multivariate
interpolation / approximation, a well-studied problem in numerical
analysis. On a theoretical perspective, we prove several convergence
results when the samples get denser. For curves and surfaces, these
results involve asymptotic estimates with convergence rates depending
upon the degree of the jet used. For the particular case of curves, an
error bound is also derived. To the best of our knowledge, these
results are among the first ones providing accurate estimates for
differential quantities of order three and more. On the algorithmic
side, we solve the interpolation/approximation problem using
Vandermonde systems. Experimental results for surfaces of

A first report

In a second report

In collaboration with Gert Vegter (University of Groningen).

Implicit equations are a popular way to encode geometric objects. Typical examples are CSG models, where objects are defined as results of boolean operations on simple geometric primitives. Given an implicit surface, associated geometric objects of interest, such as contour generators, are also defined by implicit equations. Another advantage of implicit representations is that they allow for efficient blending of surfaces, with obvious applications in CAD or metamorphosis. Finally, this type of representation is also relevant to other scientific fields, such as level sets methods or density estimation.

However, most graphical algorithms, and especially those implemented in hardware, cannot process implicit surfaces directly, and require that a piecewise linear approximation of the considered surface has been computed beforehand. As a consequence, polygonalization of implicit surfaces has been widely studied in the literature (e.g. the celebrated marching cube algorithm).

In

The notion of

We introduce the notion of loose

In

With this new concept of point sample, we can build an algorithm that is able to mesh smooth closed surfaces with topological and geometric guarantees. Examples of algebraic surfaces meshed with the algorithm are illustrated in Figure . An example of a point set surface is shown in Figure .

Examples of quality-guaranteed meshes of algebraic surfaces

Surface reconstruction algorithms produce piece-wise linear
approximations of a surface

In collaboration with M. Isenburg (University of North Carolina at Chapell Hill) and É. Colin de Verdière (École Normale Supérieure, Paris).

In

In collaboration with B. Lévy (Loria, Nancy) and M. Desbrun (University of Southern California).

In

In collaboration with V. Surazhsky and C. Gotsman (Technion, Haifa, Israel).

We present a method for isotropic remeshing of arbitrary genus
surfaces

In collaboration with F. Chazal, Mathematics Department, Université de Bourgogne, France.

Docking is the process by which two or several molecules form a
complex. Docking involves the geometry of the molecular surfaces, as
well as chemical and energetical considerations. In the mid-eighties,
Connolly proposed a docking algorithm matching surface knobs
with surface depressions. Knobs and depressions refer to the
extrema of the Connolly function, which is defined as
follows. Given a surface

We recast the notions of knob and depression of the Connolly function
in the framework of Morse theory for functions defined over
two-dimensional manifolds

In collaboration with M. Isenburg, University of North Carolina at Chapell Hill.

Unstructured hexahedral volume meshes are of particular interest for
visualization and simulation applications. They allow regular tiling
of the three-dimensional space and show good numerical behavior in
finite element computations. Beside such appealing properties, volume
meshes take huge amount of space when stored in a raw format. In this
paper we present a technique for encoding connectivity and geometry of
unstructured hexahedral volume meshes

In collaboration with M. Isenburg (University of North Carolina at Chapell Hill) and S. Valette (INSA Lyon).

The fast development of the Internet allows transmission of geometric
models. Among various representations, meshes provide effective means
to model complex shapes. Since they often require a huge amount of
data for storage and/or transmission in a raw data format, many
algorithms have been proposed to compress them efficiently. In a
survey paper

In collaboration with P.-M. Gandoin and M. Trentini (École Polytechnique and ENST).

Based on previous work described in Pierre-Marie Gandoin thesis, we
have experimented a compression scheme for an application visualizing
several objects with transmission of data on the internet

In collaboration with C. Gotsman (Technion, Haifa, Israel).

3D meshes are widely used in graphic and simulation applications for
approximating 3D objects. When representing complex shapes in a raw
data format, meshes consume a large amount of space. Applications
calling for compact storage and fast transmission of 3D meshes have
motivated the multitude of algorithms developed to efficiently
compress these datasets. In this paper we survey recent developments
in compression of 3D surface meshes. We survey the main ideas and
intuition behind techniques for single-rate and progressive mesh
coding. Where possible, we discuss the theoretical results obtained
on the asymptotic behavior and the optimality of the approach. We also list
some open questions and directions of future
research

In this work, we are designing a compression algorithm dedicated to polygons, and with extremely fast decompression speed and low memory requirement, since the targeted application has to run on low speed processor such as PDA.

We have experimented with several compression schemes and compared
them together. The best result has been obtained with the combination of
various techniques depending on the context (mainly the polygon size).
For the basic level of compression, we succeed to reach almost the
same compression rate as arithmetic coding but without its expensive
cost using a collection of Huffman's trees

The Cgal library is developed by a European consortium. In order to
achieve the transfer and diffusion of Cgal, a start-up called Geometry
Factory has been founded in January 2003 by Andreas Fabri
(

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 users.

It offers licenses to interested companies, and provides support. There are contracts in various domains such as CAD/CAM, medical applications, GIS, computer vision...

First customers are from various application areas : geophysical modelling (IFP, Midland Valley Exploration), geographic information systems (Leica Geosystems), location based services (TruePosition), image processing (Toshiba, BAE), digital maps (Durch Topographic Service).

During the creation process, we realized in particular that it was very
important to offer better support in Cgal for the Windows/Visual C++
platform. Radu Ursu got an ODL position to work on these aspects. He now
works part time for Geometry Factory.

Benomad is a start-up devoted to software for geometric data,
and in particular geographic data on PDA
(

One of the goals of Benomad was to have the software running on PDAs. For processors with such a low computational power, state of the art compression algorithms, e.g. arithmetic coding, were too expensive. We have developed a geometric coder inspired by standard geometric coding techniques to reduce the problem to a word coding problem. Then by a careful use of Huffman coding, we almost reach the compression ratio of the best algorithms which are much more computationally demanding.

Also involved: Xavier Cavin and Nicolas Rey (ISA project, LORIA), Bernard Maigret and Christophe Chipot (CNRS Nancy).

Given a cell receptor involved in a given disease, Virtual Screening (VS) is the computational process aiming at selecting good drug candidates for that receptor. As opposed to High Throuput Screening which consists of performing wet chemistry experiments to qualify potential drugs, VS has the advantage of being cheaper and faster (more candidate molecules tested). Unfortunately, the effectiveness of VS depends upon the quality of the score functions used, and a VS process usually involves three filters —coarse, medium, fine, each being more accurate and more time consuming than its predecessor.

The Protein-Protein Docking ARC aims at contributing to the
state-of-the-art VS methods. The focus is on improving coarse filters
using more efficient molecular representations

ARC telegeo (Geometry and Telecommunications) :

The objective of telegeo is a two-years coordinated research
effort, carried out by a total of 26 people at inria
Sophia-Antipolis, Loria Nancy, irisa Rennes, enst
Paris and insa Lyon, aimed at facilitating geometry processing
and compression for applications to heterogeneous
networks. Accomplishments of the action include (i) a prototypical
client-server software for progressive transmission of triangle
meshes

The geometrica seminar :

The geometrica seminar featured presentations from the following visiting
scientists:

– Christian Mercat, Technical University of Berlin

– Jean-Jacques Risler, Institut de Mathématiques, Paris 6

– Frédéric Chazal, Université de Bourgogne

– Boris Thibert, Institut Girard Desargues, Lyon

– Mark Moll, Rice University, USA

– François Cayre, ENST Paris

– Mahmoud Melkemi, Université Claude Bernard, Lyon

– Anders Adamson, Technische Universität Darmstadt

inria is the coordinating site
of this project. J-D. Boissonnat is the project leader and
M. Teillaud (galaad) the technical coordinator.

– Acronym : ECG, numéro IST-2000-26473

– Title : Effective Computational Geometry for Curves and Surfaces.

– Specific program : IST

– RTD (FET Open)

– Starting date : may 1st, 2001 - Duration : 3 years

– Participation mode of Inria : Coordinator

– Other participants : ETH (Zürich), Freie Universität (Berlin), Rijksuniversiteit (Groningen), Max Plank Institute (Sarrebruck), Tel Aviv University.

– Abstract : Effective processing of curved objects in computational geometry. Geometric algorithms for curves and surfaces, algebraic issues, robustness issues, geometric approximation.

The web site of the project includes a detailled description of the objectives
and all results

- J-D. Boissonnat is a member of the editorial board of
Theoretical Computer Science,
Algorithmica,
International Journal of Computational Geometry and Applications,
Computational Geometry : Theory and Applications, and
The Visual Computer

- He also co-edited the book Algorithmic Foundations of Robotics V, Springer 2003.

- M. Yvinec is a member of the editorial board of
Journal of Discrete Algorithms.

- S. Pion is co-editor of a special issue of
Computational Geometry : Theory and Applications on robustness issues.

- S. Pion and M. Yvinec are members of the CGAL editorial board.

- Jean-Daniel Boissonnat was on the program committee of ESA 2003 (European Symposium on Algorithms) held in Budapest, September 2003.

- Jean-Daniel Boissonnat and Frédéric Cazals were members of the program committee of the Symposium on Geometry Processing, held in Aachen, June 2003.

- Olivier Devillers was a member of the program committee of the ACM Symposium on Computational Geometry, held in San Diego, June 2003.

- Mariette Yvinec organized the workshop Journées de Geométrie Algorithmique, JGA03, in Giens, 14-19 september 2003.

- Olivier Devillers and Pierre Alliez organized the Workshop for Geometry Compression in Sophia-Antipolis in november 2003.

- Jean-Daniel Boissonnat was a member of the PhD thesis committees of Franck Hetroy (INPG), Nicolas Ray (université de Nancy 2), Boris Thibert (université Claude Bernard).

- Jean-Daniel Boissonnat was a member of the habilitation committee of M. Melkemi (université Claude Bernard).

- Frédéric Cazals was a member of the PhD thesis committee of Cédric
Chappuis, University of Compiègne, France. Thesis title:
Optimisation inverse de maillages surfaciques de pièces
mécaniques par interpolation diffuse.

- Mariette Yvinec was a member of the PhD thesis committee of
Francois Lepage, University of Nancy. Thesis title:
Génération de maillages tridimensionnels pour la simulation
des phénomènes physiques en géosciences.

- Mariette Yvinec was a member of the PhD thesis committee of
David Ledez, University of Nancy. Thesis title:
Modélisation d'objets naturels par formulation implicite.

Jean-Daniel Boissonnat is

- chairman of the Comité des Projets of INRIA Sophia-Antipolis.

- member of the Commission d'Evaluation of INRIA.

- member of the scientific committee of ENS-Lyon.

- member of the AFIT advisory board (Association Française d'Informatique Théorique).

- Jean-Daniel Boissonnat was a member of the selection committee of INRIA Lorraine and INRIA Sophia-Antipolis.

- Frédéric Cazals is member of the « Commission de spécialistes » of the Mathematics Department of the University of Bourgogne, Dijon, France.

- Olivier Devillers is chairman of the « Comité des utilisateurs des moyens informatiques de l'INRIA Sophia-Antipolis » (CUMI).

- Olivier Devillers is member of the committee for « détachements » at INRIA Sophia-Antipolis.

- Sylvain Pion is a member of the « Commission du Développement Logiciel » (CDL) at INRIA Sophia-Antipolis.

The geometrica project maintains on its web site a collection of
comprehensive sheets about the subjects presented in this report, as
well as downloadable software.

A surface reconstruction service is also available (see section ).

- J-D. Boissonnat co-chairs with D. Lazard (Paris 6) the option « Géométrie et Calcul Formel » of the DEA d'algorithmique de Paris.

- Olivier Devillers is chairman of the DEA : « Images and vision » at Nice Sophia-Antipolis University.

- Olivier Devillers is professor « Chargé de cours » at École Polytechnique.

- DEA Algorithmique, Paris, (2003-2004), Cours de tronc commun : Géométrie Algorithmique (24h) (J.-D. Boissonnat)

- DEA Algorithmique, Paris, Filière Géométrie et Calcul Formel, Triangulations, maillages et modélisation géométrique, 20h, (J-D. Boissonnat et M. Yvinec)

- DEA Imagerie Vision Robotique (Grenoble), Introduction to Differential Geometry, 6h (F. Cazals)

- Ecole Centrale Paris, Computational Geometry and Molecular Modeling, 7h, (F. Cazals)

- École Polytechnique (Palaiseau), Computational Geometry and Image Synthesis, 30h (O. Devillers).

- École Polytechnique (Palaiseau), Basis of computer science, 60h (O. Devillers).

- ISIA (Sophia-Antipolis), Computational Geometry, 10h (O. Devillers).

- ESSI (Sophia-Antipolis), Computational Geometry, 10h (O. Devillers).

- Maîtrise Informatique (Nice), Computational Geometry, 16h (O. Devillers, J. Flötotto).

- DEA Images et Vision (Sophia-Antipolis), From Computational Geometry to Geometric Computing, 15h (O. Devillers).

Internship proposals can be seen on the web at

- Christophe Delage, Möbius diagrams in the plane, Stage de DEA, ENS-Lyon

- Mathieu Monnier, Compressing vectorial data,
Third year internship at École Polytechnique.

- Marie Samozino, Largeur locale
Stage de DEA Images Vision, Université de Nice

- Luca Castelli,
Compression et entropie d'objets pour la synthèse d'images
en cotutelle avec l'École Polytechnique.

- David Cohen-Steiner,
Echantillonnage de surfaces,
École Polytechnique.

- Christophe Delage, Non affine Voronoi diagrams, ENS-Lyon.

- Thomas Lewiner,
Computational Topology and Applications in Molecular Modeling,
École Polytechnique.

- Steve Oudot,
Maillages de surfaces,
École Polytechnique.

- Marc Pouget,
Computational Differential Geometry,
université de Nice-Sophia Antipolis.

- Laurent Rineau,
Maillages tétraédriques,
Université de Paris VI.

- Marie Samozino,
Filtrage, simplification et représentation multirésolution
d'objets géométriques reconstruits, Université de Nice-Sophia
Antipolis.

- Julia Flötotto, A coordinate system associated to a point cloud
issued from a manifold: definition, properties and applications,
University of Nice-Sophia Antipolis

- Philippe Guigue, Constructions géométriques à précision fixée,
Université de Nice-Sophia Antipolis

P. Alliez visited C. Gotsman at the TECHNION in March-April 2003 concerning joint work on compression, parameterization, and remeshing.

S. Pion visited I. Z. Emiris at the University of Athens in November
2003 concerning work on algebraic and implementation issues for geometric
predicates on curved objects (collaboration with Galaad).

Members of the project presented articles at conferences. The reader can refer to the bibliography to obtain the corresponding list.

Moreover, they made presentations during the following events :

- Invited talk at Journées Nationales de Calcul Formel, Quelques résultats récents sur le calcul des diagrammes de Voronoï, (J-D. Boissonnat).

- ALEA'03, January 2003, CIRM, Randomized jumplists: a jump-and-walk dictionary data-structure, (F. Cazals).

- DIMACS Workshop on Surface Reconstruction, May 2003, DIMACS, Point clouds, Surface Reconstruction, and Differential Geometry: two selected topics, (F. Cazals).

- « Journées de géométrie algorithmique », Sep 2003, Giens France

Compression de modèles géométriques (Olivier Devillers and Pierre Alliez)

Approximation de surfaces - deuxième étape : à propos des r-échantillons (Steve Oudot)

Estimation des Quantités Différentielles par Ajustement Polynomial des Jets Osculateurs (Marc Pouget)

Sur une Analyse des Formes Moléculaires basée sur le Complexe de Morse-Smale et la Fonction de Connolly (Frédéric Cazals)

- GMDG (Geometric Modeling and Differential Geometry), Sep 2003,
Erbach, Germany. Remeshing of surfaces (P. Alliez).

- ECG Workshop on Applications involving geometric algorithms with
curved objects, Sep 2003, Saarbruecken, Germany. Isotropic
Remeshing of Surfaces (P. Alliez).

- Workshop on geometry compression, November 2003, Anisotropic Polygonal Remeshing (P. Alliez); Canonical triangulation of a graph, with coding application (L. Castelli).

- SIAM Conference on Geometric Design and Computing, Seattle, November 2003, Sampling, meshing and interactive surface reconstruction (J-D. Boissonnat). Invited talk of the minisymposium on point set surfaces.