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 splines) 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.

** $\u2022$ Discrete geometric structures. ** Many
geometric algorithms work, explicitly or implicitly, over discrete
structures such as graphs, hypergraphs, lattices that are
induced by the geometric input data. For example, convex hulls or
straight-line graph drawing are essentially based on orientation
predicates, and therefore operate on the so-called

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.
Part of the difficulty comes from the unintuitive fact that the structure of an algebraic
object can be quite
complicated, as depicted in the Whitney umbrella (see Figure ), surface of
equation

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 anecdotal but flagship results produced during the lifetime of the Vegas team (the team preceding Gamble).

There are many
problems in this theme that are expected to have high long-term
impacts. Intersecting NURBS (Non-uniform rational basis splines) 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 whose impact extends far
beyond computational geometry.
Application fields include particle physics, fluid dynamics, shape
matching, image processing, geometry processing, computer graphics,
computer vision, shape reconstruction, mesh generation, virtual
worlds, geophysics, and medical
imaging.

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 case of the Bolza surface (a surface
of genus 2, whose fundamental domain is the regular octagon in the
hyperbolic plane) shows 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 a 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.

Our work on discrete geometric structures develops in several directions, each one probing a different type of structure. Although these objects appear unrelated at first sight, they can be tackled by the same set of probabilistic and topological tools.

A first research topic is the study of *Order types.* Order types
are combinatorial encodings of finite (planar) point sets, recording
for each triple of points the orientation (clockwise or
counterclockwise) of the triangle they form. This already determines
properties such as convex hulls or half-space depths, and the
behaviour of algorithms based on orientation predicates. These
properties for all (infinitely many)

A second research topic is the study of *Embedded graphs and
simplicial complexes.* Many topological structures can be
effectively discretized, for instance combinatorial maps record
homotopy classes of embedded graphs and simplicial complexes represent
a large class of topological spaces. This raises many structural and
algorithmic questions on these discrete structures; for example, given
a closed walk in an embedded graph, can we find a cycle of the graph
homotopic to that walk? (The complexity status of that problem is
unknown.) Going in the other direction, some purely discrete
structures can be given an associated topological space that reveals
some of their properties (*e.g.* the Nerve theorem for
intersection patterns). An open problem is for instance to obtain
fractional Helly theorems for set system of bounded topological
complexity.

Another research topic is that of *Sparse inclusion-exclusion formulas.*
For any family of sets

where

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 had already been requested by users long before they become public in Cgal is a good sign for their wide future impact. 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. Rien van de Weijgaert , (astrophysicist, Groningen, NL) and Michael Schindler (theoretical physicist, ENSPCI, CNRS, France) used our software for 3D periodic weighted triangulations. Stephen Hyde and Vanessa Robins (applied mathematics and physics at Australian National University) used our package 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.

We are happy to report that some of our past work appeared this year
in highly visible journals. Our proof that deciding
*shellability* of simplicial complexes, a problem that was open
for 40 years, was published in the Journal of the
ACM , and our survey on *combinatorial
geometry and topology and their applications* was published in the
Bulletin of the AMS .

Keywords: Geometry - Delaunay triangulation - Hyperbolic space

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

News Of The Year: Integration into CGAL 4.14

Authors: Iordan Iordanov and Monique Teillaud

Contact: Monique Teillaud

Publication: Implementing Delaunay Triangulations of the Bolza Surface

URL: https://

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: Integration into CGAL 4.14

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: Numerical solver - Visualization - Polynomial equations

Functional Description: Clenshaw is a mixed C and python library that provides computation and plotting functions for the solutions of polynomial equations in the Taylor or the Chebyshev basis. The library is optimized for machine double precision and for numerically well-conditioned polynomials. In particular, it can find the roots of polynomials with random coefficients of degree one million.

Contact: Guillaume Moroz

Keywords: Visualization - Curve plotting - Implicit surface - Polynomial equations

Functional Description: Voxelize is a C++ software to visualize the solutions of polynomial equations and inequalities. The software is optimized for high degree curves and surfaces. Internally, polynomials and sets of boxes are stored in the Compressed Sparse Fiber format. The output is either a mesh or a union of boxes written in the standard 3D file format ply.

Release Functional Description: This is the first published version.

Contact: Guillaume Moroz

*In collaboration with R. Imbach and C. Yap (Courant Institute of
Mathematical Sciences, New York University, USA).*

We are interested in computing the topology of plane singular curves. For this, the singular points must be isolated. Numerical methods for isolating singular points are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. In this setting, we show that the singularities can be encoded by a regular square system whose isolation can be certified by numerical methods. This type of curves appears naturally in robotics applications and scientific visualization. This work was presented at the EuroCG'19 Conference .

Computing efficiently the singularities of surfaces embedded in

*In collaboration with Sény Diatta (University Assane Seck of Ziguinchor,
Senegal)*

In approximation theory, it is standard to approximate functions by
polynomials expressed in the Chebyshev basis. Evaluating a polynomial

We present the SIROPA Maple Library which has been designed to study serial and parallel manipulators at the conception level. We show how modern algorithms in Computer Algebra can be used to study the workspace, the joint space but also the existence of some physical capabilities w.r.t. to some design parameters left as degree of freedom for the designer of the robot. This work was presented at the Maple Conference 2019 .

*In collaboration with Philippe Wenger, Damien Chablat
(Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004)
and Fabrice Rouillier (project team *
Ouragan
*)*

We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a closed hyperbolic surface is connected. We give upper bounds on the number of edge flips that are necessary to transform any geometric triangulation on such a surface into a Delaunay triangulation .

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

The geometric intersection number of a curve on a surface is the minimal number of self-intersections of any homotopic curve, i.e. of any curve obtained by continuous deformation. Given a curve

*In collaboration with Francis Lazarus (University of Grenoble).*

We study online routing algorithms on the

*In collaboration with Prosenjit Bose (University Carleton) and
JeanLou De Carufel (University of Ottawa)*

The complexity of the 3D-Delaunay triangulation (tetrahedralization)
of

Let

*In collaboration with Philippe Duchon (Université de Bordeaux) and Marc Glisse (project team *
Datashape
*).*

Randomized incremental construction (RIC) is one of the most important
paradigms for building geometric data structures. Clarkson and Shor
developed a general theory that led to numerous algorithms that are
both simple and efficient in theory and in practice. Randomized
incremental constructions are most of the time space and time optimal
in the worst-case, as exemplified by the construction of convex hulls,
Delaunay triangulations and arrangements of line segments. However,
the worst-case scenario occurs rarely in practice and we would like
to understand how RIC behaves when the input is nice in the sense that
the associated output is significantly smaller than in the
worst-case. For example, it is known that the Delaunay triangulations
of nicely distributed points on polyhedral surfaces in

*In collaboration with Jean-Daniel Boissonnat, Kunal Dutta and Marc Glisse (project team *
Datashape
*).*

We examine how the measure and the number of vertices of the convex
hull of a random sample of

*In collaboration with
Imre Barany (Rényi Institute of Mathematics)
Matthieu Fradelizi (Laboratoire d'Analyse et de Mathématiques Appliquées)
Alfredo Hubard (Laboratoire d'Informatique Gaspard-Monge)
Günter Rote (Institut für Informatik, Berlin)*

We study how a single value of the shatter function of a set system restricts its asymptotic growth. Along the way, we refute a conjecture of Bondy and Hajnal which generalizes Sauer's Lemma.

We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We explore their connections and emphasize their broad impact in application areas such as game theory, graph theory, mathematical optimization, computational geometry, etc.

We prove that for every

We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in

Let

We show that converting Apollonius and Laguerre diagrams from an
already built Voronoi diagram of a set of n points in 2D
requires at least

*In collaboration with Kevin Buchin (TU Eindhoven), Pedro de
Castro (University Pernanbuco), and Menelaos Karavelas (University Heraklion).*

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.

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: The ASPAG projet is funded by ANR under 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 algorithms 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://

Project title: MIN-MAX

Duration: 4 years

Starting date: 2019

Coordinator: Stéphane Sabourau (Université Paris-Est Créteil)

Participants:

Université Paris Est Créteil, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA). Local coordinator: Stéphane Sabourau

Université de Tours, Institut Denis Poisson. Local coordinator: Laurent Mazet. This node includes two participants from Nancy, Benoît Daniel (IECL) and Xavier Goaoc (Loria, Gamble).

Abstract: The MinMax projet is funded by ANR under number ANR-19-CE40-0014

This collaborative research project aims to bring together researchers from various areas – namely, geometry and topology, minimal surface theory and geometric analysis, and computational geometry and algorithms – to work on a precise theme around min-max constructions and waist estimates.

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 (Institution - Laboratory - Researcher):

Carleton University (Canada) - CGLab - 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 un non-Euclidean spaces.

Title: ASsociate Team On Non-ISH euclIdeaN Geometry

International Partner (Institution - Laboratory - Researcher):

University of Groningen (Netherlands) - Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence - 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 (University of Groningen, NL) spent two weeks in Gamble in the context of the Astonishing associate team.

Matthijs Ebbens (University of Groningen, NL) spent one week in Gamble in the context of the Astonishing associate team.

Hugo Parlier (University of Luxembourg) spent two days in Gamble in the context of the ANR project SoS.

Erin Wolf Chambers (Saint Louis University, USA) spent two days in Gamble

Vanessa Robins (Australian National University) spent two days in Gamble

Andreas Holmsen (KAIST, South Korea) and Zuzanna Patáková (IST Austria, Vienna) spent a week in Gamble

Olivier Devillers and Monique Teilaud spent one week in June at the Computational Geometry Lab
of Carleton University http://

Vincent Despré spent a total of three week during 2019 at the Mathematical Research Unit of the University of Luxembourg in the context of the ANR SoS project.

Sylvain Lazard spent two weeks in September at the Computational Geometry Lab
of Carleton University http://

Monique Teillaud spent two weeks at Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence of the University of Groningen in the context of the Astonishing associate team.

Monique Teillaud spent two days at University of Luxembourg in the context of the ANR SoS project

Xavier Goaoc spent one week at UNAM Queretaro, in Mexico.

Sylvain Lazard organized with S. Whitesides (Victoria University) the 18th Workshop on Computational Geometry at the Bellairs Research Institute of McGill University in Feb. (1 week workshop on invitation).

Olivier Devillers organized the Trip-Aspag Mini-workshop on routing in triangulations, October 21-25 in Nancy.

Guillaume Moroz was in the program committee of the Maple Conference 2019

Xavier Goaoc was on the organizing committee of the Rouen probability meeting

Xavier Goaoc was on the program committee of the Iranian conference on Computational geometry

Xavier Goaoc was on the scientific committee of the Séminaire Francilien de Géométrie Algorithmique et Combinatoire

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),
*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.

Olivier Devillers and Monique Teillaud gave talks at the workshop New Horizons in Computational Geometry and Topology

Monique Teillaud gave a talk at the Celebration for the CNRS Silver medal of Claire Mathieu

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

Sylvain Lazard was vice chair of the hiring committee for researchers (CRCN) of Inria Nancy - Grand Est.

Monique Teillaud was a member of the hiring committee for a Professor position at Université Paris Est Marne-la-Vallée.

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 is
responsible of Fablab of IUT Charlemagne, Univerasité de
Lorraine (since 2018, November).
Member of *Comité Information Edition Scientifique* of
LORIA.

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

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 (since 2018).
Head of the Department Algo at LORIA (since 2014).
Member of the *Conseil Scientifique* of LORIA (since 2014).

G. Moroz is
head of the *Comité des utilisateurs des moyens informatiques*
(since nov. 2019).
He is member of the CDT, *Commission de développement technologique*, of
Inria Nancy - Grand Est (since 2018).
He is member of the CLHSCT *Comité local d'hygiène, de sécurité et
des conditions de travail* of Inria Nancy - Grand Est (since jan. 2019).

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

M. Teillaud is “Chargée de Mission” as Scientific Advisor for
Technologic Development for Inria
Nancy-Grand Est. She is a member of the *Conseil de Laboratoire* of LORIA.

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

L. Dupont is the secretary of *Commission Pédagogique
Nationale Carrières Sociales / Information-Communication / Métiers du Multimédia
et de l'Internet* (2017-2022).

L. Dupont: Head of the Bachelor diploma
*Licence Professionnelle Animation des Communautés et
Réseaux Socionumériques*, Université de Lorraine.

Master: Olivier Devillers, *Modèles d'environnements,
planification de trajectoires*, 18h, M2 AVR, Université de Lorraine.
https://

Master: Vincent Despré, *Algorithmique*, 48h, M1, Polytech Nancy, France.

Master: Vincent Despré, *Programmation réseau*, 60h, M1, Polytech Nancy, France.

Master: Vincent Despré, *Architecture avancée*, 20h, M1, Polytech Nancy, France.

Master: Vincent Despré, *Architecture Java EE*, 72h, M1, Polytech Nancy, France.

Licence: Charles Duménil, *Algorithmique et programmation avancée*, 10h, M2, FST, Université de Lorraine, France.

Licence: Charles Duménil, *Décourverte de l'informatique*, 88h, L1, Polytech Nancy, Université de Lorraine, France.

Licence: Charles Duménil, *Logiciels scientifiques*, 8h, L3, Polytech Nancy, Université de Lorraine, France.

Licence: Laurent Dupont, *Web development*, 35h, L2, Université de Lorraine, France.

Licence: Laurent Dupont, *Web development*, 150h, L2, Université de Lorraine, France.

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

Licence: Xavier Goaoc, *Programmation*, 20 HETD, L3, École des Mines de Nancy, France.

Master: Xavier Goaoc, *Algorithms*, 32 HETD, M1, École des Mines de Nancy, France.

Master: Xavier Goaoc, *Computer architecture*, 32+24 HETD, M1, École des Mines de Nancy + Polytech Nancy, France.

Licence: Galatée Hemery, *Programmation*, 52 HETD, L3, École des Mines de Nancy, France.

Licence: Sylvain Lazard, *Algorithms and Complexity*, 20h, L3, Université de Lorraine, France.

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

PhD: Iordan Iordanov, Delaunay triangulations of a family of symmetric hyperbolic surfaces in practice, defended March 12th, supervised by Monique Teillaud .

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: 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: Nuwan Herath, Fast algorithm for the visualization of surfaces, started in Nov. 2019, supervised by Sylvain Lazard, Guillaume Moroz and Marc Pouget.

M. Teillaud was a member of the PhD committee of Iordan Iordanov (Université de Lorraine)

X. Goaoc was on the reading and defense committees of the habilitation defense of Arnau Padrol (IMJ, Université Paris Sorbonne)

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:

Day

ISN day, March 7th, adult continuing education of computer science for high-school teachers.

Atelier Google, April 13th, popularization of computer science, general audience.

Atelier Google, December 7th, popularization of computer science, general audience.