Starting in the eighties, the emerging computational geometry community has put
a lot of effort into designing and analyzing algorithms for geometric problems.
The most commonly used framework was to study
the worst-case theoretical complexity of geometric problems
involving linear objects (points, lines, polyhedra...) in
Euclidean spaces.
This so-called
*classical computational geometry* has some known
limitations:

Objects: dealing with objects only defined by linear equations.

Ambient space: considering only Euclidean spaces.

Complexity: worst-case complexities often do not capture realistic behaviour.

Dimension: complexities are often exponential in the dimension.

Robustness: ignoring degeneracies and rounding errors.

Even if these limitations have already got some attention from the
community ,
a quick look at the flagship conference SoCG

It should be stressed that, in this document, the notion of certified algorithms is to be understood with respect to robustness issues. In other words, certification does not refer to programs that are proven correct with the help of mechnical proof assistants such as Coq, but to algorithms that are proven correct on paper even in the presence of degeneracies and computer-induced numerical rounding errors.

We address several of the above limitations:

** $\u2022$ Non-linear computational geometry. **
Curved objects are ubiquitous in the world we live in. However,
despite this ubiquity and decades of research in several
communities, curved objects
are far
from being robustly and efficiently manipulated by geometric algorithms. Our work on, for instance,
quadric intersections and certified drawing of plane curves has proven that
dramatic improvements can be accomplished when the right mathematics and
computer science concepts
are put into motion. In this direction, many problems
are fundamental
and solutions have potential industrial impact in Computer Aided
Design and Robotics for instance.
Intersecting NURBS (Non-uniform rational basis spline) and meshing
singular surfaces in a certified manner
are important examples of such problems.

** $\u2022$ Non-Euclidean computational geometry. **
Triangulations are central
geometric data structures in many areas of science and
engineering. Traditionally, their study has been limited to the
Euclidean setting. Needs for triangulations in non-Euclidean settings have emerged in many areas
dealing with objects whose sizes range from the
nuclear to the astrophysical scale, and both in academia and in industry.
It has become timely to extend the traditional focus on

** $\u2022$ Probability in computational geometry. **
The design of efficient algorithms is driven by the analysis of their
complexity. Traditionally, worst-case input and sometimes uniform distributions
are considered and many results in these settings have had a great influence on
the domain.
Nowadays, it is necessary to be more subtle and to prove new results in between these two extreme settings.
For instance, smoothed analysis, which was introduced for the simplex algorithm and which we applied successfully to
convex hulls, proves that
such promising alternatives exist.

As mentioned above, curved objects are ubiquitous in real world problems and in computer science and, despite this fact, there are very few problems on curved objects that admit robust and efficient algorithmic solutions without first discretizing the curved objects into meshes. Meshing curved objects induces a loss of accuracy which is sometimes not an issue but which can also be most problematic depending on the application. In addition, discretization induces a combinatorial explosion which could cause a loss in efficiency compared to a direct solution on the curved objects (as our work on quadrics has demonstrated with flying colors , , , , ). But it is also crucial to know that even the process of computing meshes that approximate curved objects is far from being resolved. As a matter of fact there is no algorithm capable of computing in practice meshes with certified topology of even rather simple singular 3D surfaces, due to the high constants in the theoretical complexity and the difficulty of handling degenerate cases. Even in 2D, meshing an algebraic curve with the correct topology, that is in other words producing a correct drawing of the curve (without knowing where the domain of interest is), is a very difficult problem on which we have recently made important contributions , , .

It is thus to be understood that producing practical robust and efficient algorithmic solutions to geometric problems on curved objects is a challenge on all and even the most basic problems. The basicness and fundamentality of two problems we mentioned above on the intersection of 3D quadrics and on the drawing in a topologically certified way of plane algebraic curves show rather well that the domain is still in its infancy. And it should be stressed that these two sets of results were not anecdotical but flagship results produced during the lifetime of the Vegas team.

There are many
problems in this theme that are expected to have high long-term
impacts. Intersecting NURBS (Non-uniform rational basis spline) in a certified way is an important problem in computer-aided design and
manufacturing. As hinted above, meshing objects in a certified way is important
when topology matters.
The 2D case, that is essentially drawing plane curves with the correct topology,
is a fundamental
problem with far-reaching applications in research or R&D.
Notice that on such elementary problems it is often difficult to predict the
reach of the applications; as an example, we were astonished by the scope of the applications of our
software on 3D quadric intersection

Triangulations, in particular Delaunay triangulations, in the
*Euclidean space* *et al.*
). Some members of Gamble have been contributing to these algorithmic advances
(see, e.g. , , , ); they have also
contributed robust and efficient triangulation packages through the
state-of-the-art Computational Geometry Algorithms Library
Cgal,

It is fair to say that little has been done on non-Euclidean spaces,
in spite of the large number of questions raised by application
domains. Needs for simulations or modeling in a variety of
domains *flat torus*, quotient of

Interestingly, even for the simple case of triangulations on the *sphere*, the software
packages that are
currently
available are far from offering satisfactory solutions in terms of
robustness and efficiency .

Moreover, while our solution for computing triangulations in
hyperbolic spaces can be considered as ultimate , the case
of *hyperbolic manifolds* has hardly been explored. Hyperbolic manifolds are
quotients of a hyperbolic space by some group of hyperbolic
isometries. Their triangulations can be seen as hyperbolic
periodic triangulations. Periodic hyperbolic triangulations and
meshes appear for instance in geometric modeling
, neuromathematics , or physics
. Even the simplest possible case (a surface
homeomorphic to the torus with two
handles)
shows strong mathematical
difficulties , .

In most computational geometry papers, algorithms are analyzed in the worst-case setting. This often yields too pessimistic complexities that arise only in pathological situations that are unlikely to occur in practice. On the other hand, probabilistic geometry provides analyses with great precision , , , but using hypotheses with much more randomness than in most realistic situations. We are developing new algorithmic designs improving state-of-the-art performance in random settings that are not overly simplified and that can thus reflect many realistic situations.

Twelve years ago, smooth analysis was introduced by Spielman and Teng analyzing the simplex algorithm by averaging on some noise on the data (and they won the Gödel prize). In essence, this analysis smoothes the complexity around worst-case situations, thus avoiding pathological scenarios but without considering unrealistic randomness. In that sense, this method makes a bridge between full randomness and worst case situations by tuning the noise intensity. The analysis of computational geometry algorithms within this framework is still embryonic. To illustrate the difficulty of the problem, we started working in 2009 on the smooth analysis of the size of the convex hull of a point set, arguably the simplest computational geometry data structure; then, only one very rough result from 2004 existed and we only obtained in 2015 breakthrough results, but still not definitive , , .

Another example of problem of different flavor concerns Delaunay triangulations, which are rather ubiquitous in computational geometry. When Delaunay triangulations are computed for reconstructing meshes from point clouds coming from 3D scanners, the worst-case scenario is, again, too pessimistic and the full randomness hypothesis is clearly not adapted. Some results exist for “good samplings of generic surfaces” but the big result that everybody wishes for is an analysis for random samples (without the extra assumptions hidden in the “good” sampling) of possibly non-generic surfaces.

Trade-offs between full randomness and worst case may also appear in other forms such as dependent distributions, or random distributions conditioned to be in some special configurations. Simulating these kinds of geometric distributions is currently out of reach for more than a few hundred points although it has practical applications in physics or networks.

Many domains of science can benefit from the results developed
by Gamble.
Curves and surfaces are ubiquitous in all sciences to
understand and interpret raw data as well as experimental results.
Still, the non-linear problems we address are rather basic and
fundamental, and it is often difficult to predict the impact of
solutions in that area.
The short-term industrial impact is likely to be small because, on basic
problems, industries have used ad hoc solutions for decades and have thus got
used to it.
The example of our work on quadric intersection is typical: even though we were
fully convinced that intersecting 3D quadrics is such an elementary/fundamental problem that it
ought to be useful, we were the first to be astonished by the scope of the applications of our
software

The fact that several of our pieces of software for computing non-Euclidean triangulations have already been requested by users long before they become public is a good sign for their wide future impact once in Cgal. This will not come as a surprise, since most of the questions that we have been studying followed from discussions with researchers outside computer science and pure mathematics. Such researchers are either users of our algorithms and software, or we meet them in workshops. Let us only mention a few names here. We have already referred above to our collaboration with Rien van de Weijgaert , (astrophysicist, Groningen, NL). Michael Schindler (theoretical physicist, ENSPCI, CNRS, France) is using our prototype software for 3D periodic weighted triangulations. Stephen Hyde and Vanessa Robins (applied mathematics and physics at Australian National University) have recently signed a software license agreement with Inria that allows their group to use our prototype for 3D periodic meshing. Olivier Faugeras (neuromathematics, Inria Sophia Antipolis) had come to us and mentioned his needs for good meshes of the Bolza surface before we started to study them. Such contacts are very important both to get feedback about our research and to help us choose problems that are relevant for applications. These problems are at the same time challenging from the mathematical and algorithmic points of view. Note that our research and our software are generic, i.e., we are studying fundamental geometric questions, which do not depend on any specific application. This recipe has made the sucess of the Cgal library.

Probabilistic models for geometric data are widely used to model various situations ranging from cell phone distribution to quantum mechanics. The impact of our work on probabilistic distributions is twofold. On the one hand, our studies of properties of geometric objects built on such distributions will yield a better understanding of the above phenomena and has potential impact in many scientific domains. On the other hand, our work on simulations of probabilistic distributions will be used by other teams, more maths oriented, to study these distributions.

Given a set of possibly intersecting polygons in 3D, we presented a breakthrough result on the problem of computing a set of interior-disjoint triangles whose geometry is close to that of the input and such that the output vertices have coordinates of fixed precision, typically integers or floating-point numbers of bounded precision (eg. int, float, double). This problem is important in academic and industrial contexts because many 3D digital models contain self intersections and many applications require models without self intersections. Despite the theoretical and practical relevance of this problem, there was almost no literature on the subject and we presented its first satisfactory solution .

*Topology and geometry of planar algebraic curves*

Keywords: Topology - Curve plotting - Geometric computing

Functional Description: Isotop is a Maple software for computing the topology of an algebraic plane curve, that is, for computing an arrangement of polylines isotopic to the input curve. This problem is a necessary key step for computing arrangements of algebraic curves and has also applications for curve plotting. This software has been developed since 2007 in collaboration with F. Rouillier from Inria Paris - Rocquencourt.

News Of The Year: In 2018, an engineer from Inria Nancy (Benjamin Dexheimer) finished the implementation of the web server to improve the diffusion of our software.

Participants: Luis Penaranda, Marc Pouget and Sylvain Lazard

Contact: Marc Pouget

Publications: Rational Univariate Representations of Bivariate Systems and Applications - Separating Linear Forms for Bivariate Systems - On The Topology of Planar Algebraic Curves - New bivariate system solver and topology of algebraic curves - Improved algorithm for computing separating linear forms for bivariate systems - Solving bivariate systems using Rational Univariate Representations - On the topology of planar algebraic curves - On the topology of real algebraic plane curves - Bivariate triangular decompositions in the presence of asymptotes - Separating linear forms and Rational Univariate Representations of bivariate systems

Keywords: Numerical solver - Polynomial or analytical systems

Scientific Description: The goal underlying the developpement of RealSolver is the ability to solve large polynomial systems with certified results using adaptive multi-precision arithmetic for efficiency.

The software is based on a classic branch and bound algorithm using interval arithmetic: an initial box is subdivided until its sub-boxes are certified to contain either no solution or a unique solution of the input system. Evaluation is performed with a centered evaluation at order two, and existence and uniqueness of solutions is verified thanks to the Krawczyk operator.

RealSolver uses two implementations of interval arithmetic: the C++ boost library that provides a fast arithmetic when double precision is enough, and otherwise the C mpfi library that allows to work in arbitrary precision. Considering the subdivision process as a breadth first search in a tree, the boost interval arithmetic is used as deeply as possible before a new subdivision process using higher precision arithmetic is performed on the remaining forest.

The software is can be interfaced with sage and the library Fast_Polynomial that allows to solve systems of polynomials that are large in terms of degree, number of monomials and bit-size of coefficients.

Functional Description: The software RealSolver solves square systems of analytic equations on a compact subset of a real space. RealSolver is a subdivision solver using interval arithmetic and multiprecision arithmetic to achieve certified results. If the arithmetic precision required to isolate solutions is known, it can be given as an input parameter of the process, otherwise the precision is increased on-the-fly. In particular, RealSolver can be interfaced with the Fast_Polynomial library (https://bil.inria.fr/en/software/view/2423/tab#lA) to solve polynomial systems that are large in terms of degree, number of monomials and bit-size of coefficients.

News Of The Year: In 2018, Mohamed Eissa was recruited on a FastTrack contract for porting the code to python.

Contact: Rémi Imbach

Keywords: Geometry - Delaunay triangulation - Hyperbolic space

Functional Description: This package implements the construction of Delaunay triangulations in the Poincaré disk model.

News Of The Year: This package has been submitted to the CGAL Editorial Board for future integration into the library.

Participants: Mikhail Bogdanov, Olivier Devillers, Iordan Iordanov and Monique Teillaud

Contact: Monique Teillaud

Publication: Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical

URL: https://

Keywords: Geometry - Delaunay triangulation - Hyperbolic space

Functional Description: This module implements the computation of Delaunay triangulations of the Bolza surface.

News Of The Year: This package has been submitted to the CGAL Editorial Board for future integration into the library.

Authors: Iordan Iordanov and Monique Teillaud

Contact: Monique Teillaud

Publication: Implementing Delaunay Triangulations of the Bolza Surface

URL: https://

Keywords: Flat torus - CGAL - Geometry - Delaunay triangulation - Mesh generation - Tetrahedral mesh - Mesh

Functional Description: This package of CGAL (Computational Geometry Algorithms Library http://www.cgal.org) allows to build and handle volumic meshes of shapes described through implicit functional boundaries over the 3D flat torus whose fundamental domain is a cube.

News Of The Year: This new package has been released in CGAL 4.13

Participants: Mikhail Bogdanov, Aymeric Pellé, Mael Rouxel-Labbe and Monique Teillaud

Contact: Monique Teillaud

Publications: CGAL periodic volume mesh generator - Periodic meshes for the CGAL library

URL: https://

Consider a plane curve

*In collaboration with Ranjan Jha, Damien Chablat,
Luc Baron and Fabrice Rouillier.*

We have worked on extending our previous results on the computation of Delaunay triangulations of the Bolza surface (see also the section New Software above), which is the most symmetric surface of genus 2. Elaborating further on previous work , we are now considering symmetric hyperbolic surfaces of higher genus, for which we study mathematical properties that allow us to propose algorithms .

*In collaboration with Gert Vegter and
Matthijs Ebbens (University of Groningen).*

Let

*In collaboration with Nicolas Chenavier (Université du Littoral Côte d'Opale).*

The complexity of the Delaunay triangulation of

Let

*In collaboration with Philippe Duchon (LABRI) and Marc Glisse
(project team *
Datashape
*).*

Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but since it is not a generic situation, this difficulty is usually handled by using a (symbolic or explicit) perturbation. As an alternative, we proposed to define a canonical triangulation for a set of concyclic points by using a max-min angle characterization of Delaunay triangulations. This point of view leads to a well defined and unique triangulation as long as there are no symmetric quadruples of points. This unique triangulation can be computed in quasi-linear time by a very simple algorithm .

*In collaboration with Hugo Parlier and Jean-Marc Schlenker
(University of Luxembourg).*

A geometric graph

*In collaboration with Nicolas Bonichon (Labri), Prosenjit Bose, Jean-Lou De Carufel, Michiel Smid and Daryl Hill (Carleton University)*

We completed an extended version of a work published at SoCG 2015, in
which we apply ideas from the theory of limits of dense combinatorial
structures to study order types, which are combinatorial encodings of
finite point sets. Using flag algebras we obtain new numerical results
on the Erdös problem of finding the minimal density of 5-or
6-tuples in convex position in an arbitrary point set, and also an
inequality expressing the difficulty of sampling order types
uniformly. Next we establish results on the analytic representation of
limits of order types by planar measures. Our main result is a
rigidity theorem: we show that if sampling two measures induce the
same probability distribution on order types, then these measures are
projectively equivalent provided the support of at least one of them
has non-empty interior. We also show that some condition on the
Hausdorff dimension of the support is necessary to obtain projective
rigidity and we construct limits of order types that cannot be
represented by a planar measure. Returning to combinatorial geometry
we relate the regularity of this analytic representation to the
aforementioned problem of Erdös on the density of

*In collaboration with
Alfredo Hubard
(Laboratoire d'Informatique Gaspard-Monge)
Rémi De Joannis de Verclos
(Radboud university, Nijmegen)
Jean-Sébastien Sereni
(CNRS)
Jan Volec
(Department of Mathematics and Computer Science, Emory University)
*

Let

*In collaboration with William J. Lenhart (Williams College, USA).*

We show that any outerplanar graph admits a planar straight-line drawing such that the length ratio
of the longest to the shortest edges is strictly less than 2.
This result is tight in the sense that for any

*In collaboration with William J. Lenhart (Williams College, USA) and
Giuseppe Liotta (Università di Perugia, Italy).*

Company: WATERLOO MAPLE INC

Duration: 2 years

Participants: Gamble and Ouragan Inria teams

Abstract: A two-years licence and cooperation agreement was signed on April 1st, 2018 between WATERLOO MAPLE INC., Ontario, Canada (represented by Laurent Bernardin, its Executive Vice President Products and Solutions) and Inria. On the Inria side, this contract involves the teams GAMBLE and OURAGAN (Paris), and it is coordinated by Fabrice Rouillier (OURAGAN).

F. Rouillier and GAMBLE are the developers of the ISOTOP software for the computation of topology of curves. One objective of the contract is to transfer a version of ISOTOP to WATERLOO MAPLE INC.

Company: GeometryFactory

Duration: permanent

Participants: Inria and GeometryFactory

Abstract: Cgal packages developed in Gamble are commercialized by GeometryFactory.

We organized, with colleagues of the mathematics department (Institut Elie Cartan Nancy) a regular working group about geometry and probability.

Project title: Singular Curves and Surfaces Topology

Duration: March 2014 – August 2018

Coordinators: Guillaume Moroz 60%, and Marc Pouget 40%

Abstract: The objective of the young-researcher ANR grant SingCAST was to intertwine further symbolic/numeric approaches to compute efficiently solution sets of polynomial systems with topological and geometrical guarantees in singular cases. We focused on two applications: the visualization of algebraic curves and surfaces and the mechanical design of robots. We developed dedicated symbolic-numerical methods that take advantage of the structure of the associated polynomial systems that cannot be handled by purely symbolic or numerical methods.

The project had a total budget of 100k€.
Project website:
https://

Project title: Structures on Surfaces

Duration: 4 years

Starting Date: April 1st, 2018

Coordinator: Monique Teillaud

Participants:

Gamble project-team, Inria.

LIGM (Laboratoire d'Informatique Gaspard Monge), Université Paris-Est Marne-la-Vallée. Local Coordinator: Éric Colin de Verdière.

RMATH (Mathematics Research Unit), University of Luxembourg. National Coordinator: Hugo Parlier

SoS is co-funded by ANR (ANR-17-CE40-0033) and FNR (INTER/ANR/16/11554412/SoS) as a PRCI (Projet de Recherche Collaborative Internationale).

The central theme of this project is the study of geometric and combinatorial structures related to surfaces and their moduli. Even though they work on common themes, there is a real gap between communities working in geometric topology and computational geometry and SoS aims to create a long lasting bridge between them. Beyond a common interest, techniques from both ends are relevant and the potential gain in perspective from long-term collaborations is truly thrilling.

In particular, SoS aims to extend the scope of computational geometry, a field at the interface between mathematics and computer science that develops algorithms for geometric problems, to a variety of unexplored contexts. During the last two decades, research in computational geometry has gained wide impact through CGAL, the Computational Geometry Algorithms Library. In parallel, the needs for non-Euclidean geometries are arising, e.g., in geometric modeling, neuromathematics, or physics. Our goal is to develop computational geometry for some of these non-Euclidean spaces and make these developments readily available for users in academy and industry.

To reach this aim, SoS will follow an interdisciplinary approach, gathering researchers whose expertise cover a large range of mathematics, algorithms and software. A mathematical study of the objects considered will be performed, together with the design of algorithms when applicable. Algorithms will be analyzed both in theory and in practice after prototype implementations, which will be improved whenever it makes sense to target longer-term integration into CGAL.

Our main objects of study will be Delaunay triangulations and circle patterns on surfaces, polyhedral geometry, and systems of disjoint curves and graphs on surfaces.

Project website:
https://

Project title: Analyse et Simulation Probabilistes d'Algorithmes Géométriques

Duration: 4 years

Starting date: January 1st, 2018

Coordinator: Olivier Devillers

Participants:

Gamble project-team, Inria.

Labri (Laboratoire Bordelais de Recherche en Informatique), Université de Bordeaux. Local Coordinator: Philippe Duchon.

Laboratoire de Mathématiques Raphaël Salem, Université de Rouen. Local Coordinator: Pierre Calka.

LAMA (Laboratoire d'Analyse et de Mathématiques Appliquées), Université Paris-Est Marne-la-Vallée. Local Coordinator: Matthieu Fradelizi

Abstract: ASPAG projet is funded by ANR undered number ANR-17-CE40-0017 .

The analysis and processing of geometric data has become routine in a variety of human activities ranging from computer-aided design in manufacturing to the tracking of animal trajectories in ecology or geographic information systems in GPS navigation devices. Geometric algorithms and probabilistic geometric models are crucial to the treatment of all this geometric data, yet the current available knowledge is in various ways much too limited: many models are far from matching real data, and the analyses are not always relevant in practical contexts. One of the reasons for this state of affairs is that the breadth of expertise required is spread among different scientific communities (computational geometry, analysis of algorithms and stochastic geometry) that historically had very little interaction. The Aspag project brings together experts of these communities to address the problem of geometric data. We will more specifically work on the following three interdependent directions.

(1) Dependent point sets: One of the main issues of most models is the core assumption that the data points are independent and follow the same underlying distribution. Although this may be relevant in some contexts, the independence assumption is too strong for many applications.

(2) Simulation of geometric structures: The phenomena studied in (1) involve intricate random geometric structures subject to new models or constraints. A natural first step would be to build up our understanding and identify plausible conjectures through simulation. Perhaps surprisingly, the tools for an effective simulation of such complex geometric systems still need to be developed.

(3) Understanding geometric algorithms: the analysis of algorithm is an essential step in assessing the strengths and weaknesses of algorithmic principles, and is crucial to guide the choices made when designing a complex data processing pipeline. Any analysis must strike a balance between realism and tractability; the current analyses of many geometric algorithms are notoriously unrealistic. Aside from the purely scientific objectives, one of the main goals of Aspag is to bring the communities closer in the long term. As a consequence, the funding of the project is crucial to ensure that the members of the consortium will be able to interact on a very regular basis, a necessary condition for significant progress on the above challenges.

Project website:
https://

*Embeds* is a bilateral, two-year project funded by the PHC
Barrande program. It is joint between various french locations (Paris
Est, Grenoble and, since september 2018, Nancy) and Charles University
(Prague). The PI are Xavier Goaoc and Martin Tancer. It started in
2015 for two years, and was renewed in 2017 for two more years
(5kE/year on the french side to support travels).

Starting Date: January 1st, 2017.

Duration: 2 years.

Xavier Goaoc was appointed *junior member* of the Institut
Universitaire de France, a grant supporting a reduction in teaching
duties and funding.

Starting Date: October 1st, 2014.

Duration: 5 years.

Title: Triangulation and Random Incremental Paths

International Partner: Carleton University (Canada) - Prosenjit Bose

Start year: 2018

The two teams are specialists of Delaunay triangulation with a focus on computation algorithms on the French side and routing on the Canadian side. We plan to attack several problems where the two teams are complementary: - Stretch factor of the Delaunay triangulation in 3D. - Probabilistic analysis of Theta-graphs and Yao-graphs. - Smoothed analysis of a walk in Delaunay triangulation. - Walking in/on surfaces. - Routing in non-Euclidean spaces.

Title: ASsociate Team On Non-ISH euclIdeaN Geometry

International Partner: University of Groningen (Netherlands) - Institute of Systems Science - Gert Vegter

Start year: 2017

See also: https://

Some research directions in computational geometry have hardly been explored. The spaces in which most algorithms have been designed are the Euclidean spaces

Gert Vegter spent three weeks in Gamble in the framework of the Astonishing associate team.

Jean-Lou De Carufel and Prosenjit Bose spent one week in Gamble in the framework of the TRIP associate team.

Martin Tancer, Vojta Kalusza and Pavel Paták, from Charles University (Prague), spent one week each in Gamble. They were supported by the PHC program EMBEDS II.

Olivier Devillers spent two weeks at the Computational Geometry Lab
of Carleton University http://

Charles Duménil spent one month at the Computational Geometry Lab
of Carleton University http://

Monique Teillaud and Iordan Iordanov spent one month at Johann Bernouilli Institute for Mathematics and Computer Science of the University of Groningen in the framework of the Astonishing associate team.

Sylvain Lazard organized with S. Whitesides (Victoria University) the 17th Workshop on Computational Geometry at the Bellairs Research Institute of McGill University in Feb. (1 week workshop on invitation).

Olivier Devillers and Xavier Goaoc co-organized the Aspag Prospective workshop, April 8-12 2018 in Arcachon.

Monique Teillaud is chairing the Steering Committee of the Symposium on Computational Geometry (SoCG).

Monique Teillaud was a member of the program committee of the European Workshop on Computational Geometry.

All members of the team are regular reviewers for the conferences of our
field, namely the *Symposium on Computational Geometry* (SoCG) and the
*International Symposium on Symbolic and Algebraic Computation* (ISSAC)
and also SODA, CCCG, EuroCG.

Monique Teillaud is a managing editor of JoCG, *Journal of
Computational Geometry* and a member of the editorial board of IJCGA,
*International Journal of Computational Geometry and Applications*.

Marc Pouget and Monique Teillaud are members of the Cgal editorial board.

All members of the team are regular reviewers for the journals of our
field, namely *Discrete and Computational Geometry* (DCG),
*Computational Geometry. Theory and Applications* (CGTA), *Journal
of Computational Geometry* (JoCG), *International Journal on
Computational Geometry and Applications* (IJCGA), *Journal on
Symbolic Computations* (JSC), *SIAM Journal on Computing* (SICOMP),
*Mathematics in Computer Science* (MCS), etc.

Monique Teillaud was a member of the Scientific Board of the *Société Informatique
de France* (SIF) until July.

Sylvain Lazard was the laboratory delegate in a prof (PR) hiring committee at Lorraine Univ. (IUT Charlemagne & Loria).

Monique Teillaud chaired the hiring committee for young researchers (CRCN) of Inria Bordeaux - Sud Ouest.

L. Dupont is the secretary of *Commission Pédagogique
Nationale Carrières Sociales / Information-Communication / Métiers du Multimédia
et de l'Internet*.

M. Teillaud is a member of the working group for the BIL,
*Base d'Information des Logiciels* of Inria.

O. Devillers: Elected member to *Pole AM2I* the council that
gathers labs in mathematics, computer science, and control theory at
*Université de Lorraine*.

L. Dupont: Head of the Bachelor diploma
*Licence Professionnelle Animation des Communautés et
Réseaux Socionumériques*, Université de Lorraine.
Responsible of Fablab of IUT Charlemagne, Univerasité de
Lorraine (since 2018, November).
Member of *Comité Information Edition Scientifique* of
LORIA.

S. Lazard: Head of the PhD and Post-doc hiring committee for Inria
Nancy-Grand Est (since 2009).
Member of the *Bureau de la mention informatique* of the *École
Doctorale IAEM* (since 2009).
Head of the *Mission Jeunes Chercheurs* for Inria national.
Head of the Department Algo at LORIA (since 2014).
Member of the *Conseil Scientifique* of LORIA (since 2014).

G. Moroz:
Member of the *Comité des utilisateurs des moyens informatiques*.
Member of the CDT, *Commission de développement technologique*, of Inria Nancy - Grand Est.

M. Pouget is elected at the *Comité de centre*, and is
secretary of the board of *AGOS-Nancy*.

M. Teillaud joined the *Conseil de Laboratoire* of LORIA in
May. She was a member of the BCP, *Bureau du Comité des
Projets* of Inria Nancy - Grand Est until end November.

X. Goaoc is a member of the council of the *Fédération Charles Hermite* since sep. 2018.

M. Teillaud is maintaining the Computational Geometry Web Pages
http://

Licence: Charles Duménil, *Algorithmique et programmation avancée*, 32h, M2, Université de Lorraine, France.

Licence: Laurent Dupont, *Algorithmique*, 15h, L1, Université de Lorraine, France.

Licence: Laurent Dupont, *Web development*, 100h, L2, Université de Lorraine, France.

Licence: Laurent Dupont, *Traitement Numérique du Signal*, 20h, L2, Université de Lorraine, France.

Licence: Laurent Dupont *Web devloppment and Social networks* 100h L3, Université de Lorraine, France.

Licence: Iordan Iordanov, *Algorithmique et Programmation*, 64h, L1, Université de Lorraine, France.

Licence: Iordan Iordanov, *Systèmes de gestion de bases de données*, 20h, L2, Université de Lorraine, France.

Licence: Iordan Iordanov, *Algorithmique et développement web*, 28h, L2, Université de Lorraine, France.

Licence: Iordan Iordanov, *Programmation objet et événementielle*, 16h, L3, Université de Lorraine, France.

Licence: Sylvain Lazard, *Algorithms and Complexity*, 25h, L3, Université de Lorraine, France.

Master: Marc Pouget, *Introduction to computational geometry*, 10.5h, M2, École Nationale Supérieure de Géologie, France.

Licence: Galatée Hemery, *Programmation*, 64h, L3, École des Mines de Nancy, France.

Master: Vincent Despré, *Algorithmique*, 72h, M1, Polytech Nancy, France.

Master: Vincent Despré, *Systèmes distribués*, 20h, M1, Polytech Nancy, France.

Master: Olivier Devillers, *Modèles d'environnements,
planification de trajectoires*, 18h, M2 AVR, Université de Lorraine.
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Master: Olivier Devillers and Marc Pouget, *Computational Geometry*, 24h (academic year 2018-19), M2 Informatique, ENS Lyon
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Master : Xavier Goaoc, *Algorithms and data structures*, 31.5 HETD (academic year 2018-19), M1, École des Mines de Nancy, France

Master : Xavier Goaoc, *Computer architecture*, 31.5 HETD, M1 (academic year 2018-19), École des Mines de Nancy, France

PhD in progress: Sény Diatta, Complexité du calcul de la topologie d'une courbe dans l'espace et d'une surface, started in Nov. 2014, supervised by Daouda Niang Diatta, Marie-Françoise Roy and Guillaume Moroz.

PhD in progress: Charles Duménil, Probabilistic analysis of geometric structures, started in Oct. 2016, supervised by Olivier Devillers.

PhD in progress: Iordan Iordanov, Triangulations of Hyperbolic Manifolds, started in Jan. 2016, supervised by Monique Teillaud.

PhD in progress: George Krait, Topology of singular curves and surfaces, applications to visualization and robotics, started in Nov. 2017, supervised by Sylvain Lazard, Guillaume Moroz and Marc Pouget.

PhD in progress: Galatée Hemery, Algorithmic and geometric aspects of inclusion-exclusion, started in Sep. 2018 , supervised by Xavier Goaoc and Éric Colin de Verdière (UPEM).

PhD in progress: Fernand Kuiebove Pefireko, Simulation of random geometric structures, started in Oct. 2018 , supervised by Olivier Devillers.

O. Devillers was the president of the PhD committee of Tuong-Bach Nguyen (Université de Grenoble).

S. Lazard was a reviewer for the HDR of Yukiko Kenmochi (Université de Marnes-la-Vallée).

G. Moroz was a member of the PhD committee of Guillaume Rance (Université Paris-Sud).

G. Moroz is member of the Mathematics Olympiades committee of the Nancy-Metz academy.

L. Dupont participated in several events of popularization of computer science:

Math en Jeans, March 30th, popularization of computer science for high-school students.

ISN day, March 22th, adult continuing education of computer science for high-school teachers.

FabLab14, July 13th, popularization of computer science, general audience.

Ada Lovelace Day 2018, october 9 : popularization of computer science for female high-school students.