GAMBLE

GAMBLE - 2025

2025‌Activity reportProject-TeamGAMBLE‌‌

RNSR: 201722240E

Research center Inria Centre at Université‌ de Lorraine
In partnership‌ with:Université de Lorraine‌‌
Team name: Geometric Algorithms & Models Beyond the‌ Linear & Euclidean realm‌
In collaboration with:Laboratoire‌‌ lorrain de recherche en informatique et ses applications‌ (LORIA)

Creation of the‌ Project-Team: 2017 July 01‌‌

Each year, Inria research teams publish an Activity‌ Report presenting their work‌ and results over the‌‌ reporting period. These reports follow a common structure,‌ with some optional sections‌ depending on the specific‌‌ team. They typically begin‌ by outlining the overall objectives and research programme,‌ including the main research themes, goals, and methodological‌ approaches. They also describe the application domains targeted‌ by the team, highlighting the scientific or societal‌ contexts in which their work is situated.

The‌ reports then present the highlights of the year,‌ covering major scientific achievements, software developments, or teaching‌ contributions. When relevant, they include sections on software,‌ platforms, and open data, detailing the tools developed‌ and how they are shared. A substantial part‌ is dedicated to new results, where scientific contributions‌ are described in detail, often with subsections specifying‌ participants and associated keywords.

Finally, the Activity Report‌ addresses funding, contracts, partnerships, and collaborations at various‌ levels, from industrial agreements to international cooperations. It‌ also covers dissemination and teaching activities, such as‌ participation in scientific events, outreach, and supervision. The‌ document concludes with a presentation of scientific production,‌ including major publications and those produced during the‌ year.

Keywords

Computer Science and Digital Science

A5.5.1.‌ Geometrical modeling
A5.10.1. Design
A7.1. Algorithms
A8.1. Discrete‌ mathematics, combinatorics
A8.3. Geometry, Topology
A8.4. Computer Algebra‌

1 Team‌ members, visitors, external collaborators

Research Scientists

Guillaume Moroz‌ [Team leader, INRIA, Researcher,‌ HDR]
Olivier Devillers [INRIA, Senior‌ Researcher, until Jun 2025, HDR]‌
Sylvain Lazard [INRIA, Senior Researcher,‌ HDR]
Marc Pouget [INRIA, Researcher‌, HDR]
Monique Teillaud [INRIA,‌ Senior Researcher, until Jun 2025, HDR‌]

Faculty Members

Vincent Despre [UL,‌ Associate Professor]
Laurent Dupont [UL,‌ Associate Professor]
Xavier Goaoc [UL,‌ Professor, HDR]
Alba Marina Malaga Sabogal‌ [UL, Associate Professor]

Post-Doctoral Fellow‌

Niloufar Fuladi [INRIA, Post-Doctoral Fellow,‌ until Aug 2025]

PhD Students

Yacine Abdelsadok‌ [LS2N, from Nov 2025]
Marguerite‌ Bin [UL]
Loïc Dubois [UNIV‌ GUSTAVE EIFFEL, until Aug 2025]
Camille‌ Lanuel [UL, from Oct 2025 until‌ Nov 2025]
Dorian Perrot [UL]‌
Gautier Schanzenbacher [UL, from Sep 2025‌]
Sarah Wajsbrot [UL]

Interns and‌ Apprentices

Marie Choquet [UL, Intern,‌ from Sep 2025]
Rachel Dufau-Sansot [UL‌, Intern, from Sep 2025]
Paul‌ Remy [UL, Intern, from Apr‌ 2025 until May 2025]
Yacine Rouina [‌INRIA, Intern, from Sep 2025]‌
Gautier Schanzenbacher [UL, Intern, from‌ Mar 2025 until Jun 2025]

Administrative Assistants‌

Antoinette Courrier [CNRS]
Sophie Drouot [‌INRIA]
Cecilia Olivier [INRIA]

External‌ Collaborators

Valentin Feray [CNRS, HDR]‌
Valencia-Pabon Mario [Université de Lorraine, Mario Valencia-Pabon is part of‌ the new team proposed‌ as a follow-up to‌‌ Gamble, HDR]
Monique Teillaud [INRIA‌, from Jul 2025‌, HDR]
Leo‌‌ Valque [GEOMETRY FACTORY]

Hirings and departures‌

An important change of‌ the year is the‌‌ retirement, in July, of Monique Teillaud and Olivier‌ Devillers, two senior members‌ of Gamble, including‌‌ its scientific leader. The team wishes them the‌ best in their future‌ projects. A new team-project‌‌ has been proposed in the Spring 2025.

The‌ team was also pleased‌ that two of its‌‌ candidates were ranked by the CRCN admissibility committee‌ and one by the‌ admission committee this year.‌‌ Unfortunately, the candidate was not hired due to‌ the unusual decision not‌ to fill one of‌‌ the two CRCN positions at the final stage‌ of the competition.

2‌ Overall objectives

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 46, a quick‌ look at the proceedings‌‌ of the flagship conference SoCG1 shows that‌ these topics still need‌ a big effort.

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 mechanical 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:

$•‌$ 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.

$•‌$ 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 ${ℝ‌}^{d}$ of computational geometry and encompass non-Euclidean spaces.‌

$•$ 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.

$•$ 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 order type of the‌ input point set. Order types are a subclass‌ of oriented matroids that remains poorly understood: for‌ instance, we do not even know how to‌ sample this space with reasonable bias. One of‌ our goals is to contribute to the development‌ of these foundations by better understanding these discrete‌ geometric structures.

3 Research program

3.1 Non-linear computational‌ geometry

Figure 1.a — Figure 1: Two views of the‌ Whitney umbrella (on the left, the “stick” of‌ the umbrella, i.e., the negative $z$ -axis, is‌ missing). Right picture from [Wikipedia], left picture‌ from [Lachaud et al.].

Figure 1.b — Figure 1: Two views of the‌ Whitney umbrella (on the left, the “stick” of‌ the umbrella, i.e., the negative $z$ -axis, is‌ missing). Right picture from [Wikipedia], left picture‌ from [Lachaud et al.].

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 55, 56, 54, 59‌, 64). 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 (that is auto-intersecting) 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 1),‌ the surface with equation‌ $x^{2} = {y‌‌}^{2} z$ whose origin (the “special” point of‌ the surface) is a‌ vertex of the arrangement‌‌ induced by the surface while the singular locus‌ is simply the whole‌ $z$ -axis. 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 39,‌ 40, 14.‌‌

Thus 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 the 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 intersection‌2 which was used‌‌ by researchers in, for instance, photochemistry, computer vision,‌ statistics and mathematics.

3.2‌ Non-Euclidean computational geometry

Figure 2.a — Figure‌ 2: Left: 3D‌‌ mesh of a gyroid (triply periodic surface) 67‌. Right: Simulation of‌ a periodic Delaunay triangulation‌‌ of the hyperbolic plane 35.

Figure 2.b — Figure‌ 2: Left: 3D‌‌ mesh of a gyroid (triply periodic surface) 67‌. Right: Simulation of‌ a periodic Delaunay triangulation‌‌ of the hyperbolic plane 35.

Triangulations, in‌ particular Delaunay triangulations, in‌ the Euclidean space ${ℝ‌‌}^{d}$ have been extensively studied throughout the 20th‌ century and they are‌ still a very active‌‌ research topic. Their mathematical properties are now well‌ understood, many algorithms to‌ construct them have been‌‌ proposed and analyzed (see the book of Aurenhammer‌ et al.33).‌ Some members of Gamble‌‌ have been contributing to these algorithmic advances (see,‌ e.g. 38, 74‌, 53, 37‌‌); 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.‌3

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 domains4 ranging from the‌ infinitely small (nuclear matter, nano-structures, biological data) to‌ the infinitely large (astrophysics) have led us to‌ consider 3D periodic Delaunay triangulations, which can be‌ seen as Delaunay triangulations of the 3D flat‌ torus, i.e., the quotient of $ℝ^{3‌}$ under the action of some group of translations‌ 44. This work has already yielded a‌ fruitful collaboration with astrophysicists 60, 76 and‌ new collaborations with physicists are emerging. To the‌ best of our knowledge, our Cgal package 43‌ is the only publicly available software that computes‌ Delaunay triangulations of a 3D flat torus, in‌ the special case where the domain is cubic.‌ This case, although restrictive, is already useful.5‌ We have also generalized this algorithm to the‌ case of general $d$ -dimensional compact flat manifolds‌ 45. As far as non-compact manifolds are‌ concerned, past approaches, limited to the two-dimensional case,‌ have stayed theoretical 66.

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 42.

Moreover, while‌ our solution for computing triangulations in hyperbolic spaces‌ can be considered as ultimate 35, 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 70, neuromathematics 47, or‌ physics 71. 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 3612.‌

3.3 Probability in computational geometry

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 68‌, 69, 41, 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.

Sixteen years ago, smooth analysis was‌ introduced by Spielman and Teng analyzing the simplex‌ algorithm by averaging on some noise on the‌ data 73 (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 49 and‌ we only obtained in‌‌ 2015 breakthrough results, but still not definitive 52‌, 51, 58‌.

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” 32‌ 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. In particular,‌‌ simulating geometric distributions with repulsive properties, such as‌ the determinantal point process,‌ is currently out of‌‌ reach for more than a few hundred points‌ 61. Yet it‌ has practical applications in‌‌ physics to simulate particules with repulsion such as‌ electrons 65, to‌ simulate the distribution of‌‌ network antennas 34, or in machine learning‌ 63.

3.4 Discrete‌ geometric structures

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) $n$ -point sets can be‌ studied through the finitely‌ many order types of‌‌ size $n$ . Yet, this finite space is‌ poorly understood: its estimated‌ size leaves an exponential‌‌ margin of error, no method is known to‌ sample it without concentrating‌ on a vanishingly small‌‌ corner, the effect of pattern exclusion or VC‌ dimension-type restrictions are unknown.‌ These are all directions‌‌ we actively investigate.

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 systems of bounded topological complexity.‌

Another research topic is that of Sparse inclusion-exclusion‌ formulas. For any family of sets $A_{1‌}, A_{2}, ..., A_{n‌}$ , by the principle of inclusion-exclusion we have‌

1_{⋃_{i =﻿​﻿﻿ 1}^{n} A_{i​‌﻿﻿}} = \sum_{I \subseteq​​﻿﻿ {1, 2​​​‌, ..., n﻿​﻿﻿}} {(- 1​‌﻿﻿)}^{| I |​​﻿﻿ + 1} 1_{{⋂​​​‌}_{i \in I} {A﻿​﻿﻿}_{i}}

where ${1‌}_{X}$ is the indicator function of $X$ .‌ This formula is universal (it applies to any‌ family of sets) but its number of summands‌ grows exponentially with the number $n$ of sets.‌ When the sets are balls, the formula remains‌ true if the summation is restricted to the‌ regular triangulation; we proved that similar simplifications are‌ possible whenever the Venn diagram of the ${A‌}_{i}$ is sparse. There is much room for‌ improvements, both for general set systems and for‌ specific geometric settings. Another interesting problem is to‌ combine these simplifications with the inclusion-exclusion algorithms developed,‌ for instance, for graph coloring.

4 Application domains‌

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 6 (which was the‌ first and still is the only one —to‌ our knowledge— to compute robustly and efficiently the‌ intersection of 3D quadrics) which has been used‌ by researchers in, for instance, photochemistry, computer vision,‌ statistics, and mathematics. Our work on certified drawing‌ of plane (algebraic) curves falls in the same‌ category. It seems obvious that it is widely‌ useful to be able to draw curves correctly‌ (recall also that part of the problem is to determine where to‌ look in the plane)‌ but it is quite‌‌ hard to come up with specific examples of‌ fields where this is‌ relevant. A contrario, we‌‌ know that certified meshing is critical in mechanical-design‌ applications in robotics, which‌ is a non-obvious application‌‌ field. There, the singularities of a manipulator often‌ have degrees higher than‌ 10 and meshing the‌‌ singular locus in a certified way is currently‌ out of reach. As‌ a result, researchers in‌‌ robotics can only build physical prototypes for validating,‌ or not, the approximate‌ solutions given by non-certified‌‌ numerical algorithms.

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 60, 76‌‌ (astrophysicist, Groningen, NL) and Michael Schindler 72 (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 47 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.

5 Highlights of the year‌

A very positive highlight‌ of this year is‌‌ the nomination of Vincent Despré as junior member‌ of the Institut Universitaire‌ de France (IUF, promotion‌‌ 2025).

6 Latest software developments, platforms, open data‌

6.1 Latest software developments‌

6.1.1 CGAL Package: 2D‌‌ Triangulations on Hyperbolic Surfaces

Keyword:
Hyperbolic geometry
Functional‌ Description:
This package introduces‌ a data structure and‌‌ algorithms for triangulations of‌ closed orientable hyperbolic surfaces.
News of the Year:‌
First version.
URL:
https://doc.cgal.org/latest/Triangulation_on_hyperbolic_surface_2/index.html
Contact:
Marc Pouget

6.1.2‌ wdkroots

Name:
Weierstrass-Durand-Kerner roots
Keywords:
Complex number, Root,‌ Polynomial equations
Functional Description:

This code uses Durand-Kerner‌ (or Weierstrass) method to find polynomial complex roots‌ in double precision. The code has been written‌ to benefit from auto-vectorization, while reducing the risks‌ of overflow in floating-point arithmetic.

This component is‌ included in the main branch of the Flint‌ scientific computing library since the end of 2025.‌
News of the Year:
First version.
URL:
https://gitlab.inria.fr/gmoro/wdkroots‌
Contact:
Guillaume Moroz

6.1.3 3D SnapHeur

Name:
3D‌ SnapHeur
Keywords:
Mesh rounding, 3D modeling, Triangle-triangle intersection‌
Functional Description:

3D SnapHeur is a heuristic for‌ rounding 3D meshes or the vertices in a‌ soup of triangles in 3D, without creating self-intersections.‌ It is designed to robustly handle intersections in‌ complex 3D models.

The approach is presented and‌ evaluated in a publication by the authors in‌ the 2025 Symposium on Geometry Processing and has‌ been integrated into CGAL by Léo Valque in‌ the autorefine_triangle_soup CGAL function (https://doc.cgal.org/latest/Polygon_mesh_processing/group__PMP__corefinement__grp.html#gaf7747d676c459d9e5da9b13be7d12bb5).
News‌ of the Year:
First version.
URL:
https://gitlab.inria.fr/lazard/3d-snap-rounding
Publication:‌
hal-05242294
Contact:
Sylvain Lazard
Participants:
Sylvain Lazard, Leo‌ Valque
Partner:
Université de Lorraine

6.1.4 3D Snap‌ Rounding

Name:
3D Snap Rounding
Keywords:
Mesh rounding,‌ 3D modeling, Triangle-triangle intersection
Functional Description:
3D Snap‌ Rounding is a software for rounding 3D meshes‌ or the vertices in a soup of triangles‌ in 3D, without creating self-intersections. It is designed‌ to robustly handle intersections in complex 3D models.‌ and it is based on an exact (non-heuristic)‌ algorithm published in Léo Valque's 2024 PhD Thesis.‌
News of the Year:
First version.
Contact:
Sylvain‌ Lazard
Participants:
Sylvain Lazard, Leo Valque
Partner:
Université‌ de Lorraine

7 New results

7.1 Non-Linear Computational‌ Geometry

Participants: Laurent Dupont, Nuwan Herath Mudiyanselage‌, Sylvain Lazard, Guillaume Moroz, Marc‌ Pouget, Léo Valque.

7.1.1 On Arrangements‌ of Quadrics in Decomposing the Parameter Space of‌ 3D Digitized Rigid Motions

Computing the arrangement of‌ quadrics in 3D is a fundamental problem in‌ symbolic computation, with challenges arising when handling degenerate‌ cases and asymptotic critical values. State-of-the-art methods typically‌ require a generic change of coordinates to manage‌ these asymptotes, rendering certain problems intractable. A specific‌ instance of this challenge appears in digital geometry,‌ where comparing 3D shapes up to isometry requires‌ applying a 3D rigid motion on and mapping‌ the result back to , a process typically‌ achieved via a digitization operator. However, such motions‌ do not preserve the topology of digital objects,‌ making the analysis of digitized rigid motions crucial.‌ Our main contribution is the decomposition of the‌ 6D parameter space of digitized rigid motions for‌ image patches of radius up to three. This‌ problem reduces to computing the arrangement of up‌ to 741 quadrics, some of which are degenerate.‌ To address the computational challenges, we introduce and‌ implement a new algorithm for computing arrangements of quadrics in 3D, specifically‌ designed to handle degenerate‌ directions and asymptotic critical‌‌ values. This approach allows us to overcome the‌ limitations of existing methods,‌ making the problem tractable‌‌ in the context of digital geometry.

This result‌ was accepted in Journal‌ of Symbolic Computation 21‌‌.

In collaboration with Kacper Pluta, Yukiko Kenmochi,‌ Pascal Romon.

7.1.2 A‌ Subquadratic Algorithm for Computing‌‌ the $L_{1}$ -distance between Two Terrains

We‌ study the problem of‌ computing the $L_{1‌‌}$ -distance between two piecewise-linear bivariate functions $f$ and‌ $g$ , defined over‌ a common bounded domain‌‌ $𝕄 \subset ℝ^{2}$ , that is, computing‌ the quantity ${∥ f‌ - g ∥}_{1‌‌} = \int_{𝕄} | f (x,‌ y) - g‌ (x, y‌‌) | d x d y$ . If‌ $f$ and $g$ are‌ defined by linear interpolation‌‌ over triangulations $𝐓_{f}$ and $𝐓_{g}$ ,‌ respectively, of $𝕄$ with‌ a total of $n‌‌$ triangles, we show that ${∥ f - g‌ ∥}_{1}$ can be‌ computed in $\overset{˜‌‌}{O} (n^{(ω + 1) /‌ 2})$ time, where‌ $Θ (n^{ω‌‌})$ is the time required to multiply two‌ $n \times n$ matrices‌ and $\tilde{O}$ notation‌‌ hides polylogarithmic factors; this bound holds for the‌ currently best known value‌ of $ω$ , which‌‌ is approximately $2 . 37$ . The previously‌ best known algorithm for‌ computing ${∥ f -‌‌ g ∥}_{1}$ takes $Θ (n^{2‌})$ time in the‌ worst case.

More generally,‌‌ if the complexity of the overlay of ${𝐓‌}_{f}$ and $𝐓_{g‌}$ is $κ$ , then‌‌ the runtime of our algorithm is $\overset{˜‌}{O} (κ^{(ω‌ - 1) /‌‌ 2} n^{(3 - ω) /‌ 2})$ 23.‌ This article was accepted‌‌ at the conference SoCG 2025.

In collaboration with‌ Pankaj K. Agarwal and‌ Boris Aronov.

7.1.3 3D‌‌ snap rounding

Most algorithms for processing 3D polygonal‌ objects use fixed-precision coordinates‌ for both input and‌‌ output data. However, geometric operations often produce output‌ coordinates that require higher‌ precision than the input.‌‌ This discrepancy implies the need for rounding new‌ coordinates to match the‌ precision of the input,‌‌ while preserving the integrity of the model. The‌ critical problem we address‌ is the removal of‌‌ self-intersections in 3D models, achieved by subdividing faces‌ along their intersections and‌ rounding the resulting coordinates,‌‌ from their exact mathematical values to a fixed-precision‌ floating-point format, while ensuring‌ that the model remains‌‌ free from self-intersections. This problem is known as‌ the snap rounding problem.‌

We present in 22‌‌ a straightforward and robust heuristic for resolving this‌ problem. Our method takes‌ as input a soup‌‌ of triangles and outputs intersection-free models whose vertices‌ coordinates are all represented‌ with double-precision floating-point format.‌‌ We evaluated our approach thoroughly, considering a large‌ collection of meshes. In‌ particular, we can process‌‌ all the 4 524‌ models in Thingi10K 78 that contain self-intersections. This‌ outperforms previous state-of-the-art approaches: On the 527 models‌ of Thingi10K for which naive rounding fails, Zhou‌ et al.'s approach 77 is capable of handling‌ 91% of them, and Valque's 94% 75.‌ In terms of time efficiency, our approach handles‌ about 50k vertices per second on average, which‌ is faster to that of Zhou et al.‌ by a factor 1.4 on these non-trivial models‌ and is faster than that of Valque by‌ several order of magnitude.

7.2 Non-Euclidean Computational Geometry‌

Participants: Vincent Despré, Loïc Dubois, Camille‌ Lanuel, Alba Marina Málaga Sabogal, Marc‌ Pouget, Monique Teillaud.

7.2.1 A Discrete‌ Analog of Tutte's Barycentric Embeddings on Surfaces

Tutte's‌ celebrated barycentric embedding theorem describes a natural way‌ to build straight-5 line embeddings (crossing-free drawings) of‌ a (3-connected) planar graph: map the vertices of‌ the outer face to the vertices of a‌ convex polygon, and ensure that each remaining vertex‌ is in convex position, namely, a barycenter with‌ positive coefficients of its neighbors. Actually computing an‌ embedding then boils down to solving a system‌ of linear equations. A particularly appealing feature of‌ this method is the flexibility given by the‌ choice of the barycentric weights. Generalizations of Tutte's‌ theorem to surfaces of nonpositive curvature are known,‌ but due to their inherently continuous nature, they‌ do not lead to an algorithm. In this‌ paper 25, we propose a purely discrete‌ analog of Tutte's theorem for surfaces (with or‌ without boundary) of nonpositive curvature, based on the‌ recently introduced notion of reducing triangulations. We prove‌ a Tutte theorem in this setting: every drawing‌ homotopic to an embedding such that each vertex‌ is harmonious (a discrete analog of being in‌ convex position) is a weak embedding (arbitrarily close‌ to an embedding). We also provide a polynomial-time‌ algorithm to make an input drawing harmonious without‌ increasing the length of any edge, in a‌ similar way as a drawing can be put‌ in convex position without increasing the edge lengths.‌

In collaboration with Éric Colin de Verdière, Université‌ Gustave Eiffel.

7.2.2 $ϵ$ -Net Algorithm Implementation on‌ Hyperbolic Surface

We propose an implementation, using the‌ Cgal library, of an algorithm to compute $ϵ‌$ -nets on hyperbolic surfaces initially presented in 50‌. We describe the data structure, detail the‌ implemented algorithm and report experimental results on hyperbolic‌ surfaces of genus 2. The implementation differs from‌ the cited algorithm on several aspects. In particular,‌ we use a different data structure, using a‌ combinatorial map, to represent a triangulation of a‌ surface. Also for the critical step of locating‌ points on the surface, we use the visibility‌ walk and prove its termination in the hyperbolic‌ setting 26. This work is also a‌ chapter of the PhD thesis of Camille Lanuel‌ 27.

7.3 Discrete Geometric structures

Participants: Marguerite‌ Bin, Niloufar Fuladi, Xavier Goaoc, Sarah Wajsbrot, Mario‌ Valencia-Pabon.

7.3.1 Hitting‌ and Covering Affine Families‌‌ of Convex Polyhedra, with Applications to Robust Optimization‌

Geometric hitting set problems,‌ in which we seek‌‌ a smallest set of points that collectively hit‌ a given set of‌ ranges, are ubiquitous in‌‌ computational geometry. Most often, the set is discrete‌ and is given explicitly.‌ We propose new variants‌‌ of these problems, dealing with continuous families of‌ convex polyhedra, and show‌ that they capture decision‌‌ versions of the two-level finite adaptability problem in‌ robust optimization. We show‌ that these problems can‌‌ be solved in strongly polynomial time when the‌ size of the hitting/covering‌ set and the dimension‌‌ of the polyhedra and the parameter space are‌ constant. We also show‌ that the hitting set‌‌ problem can be solved in strongly quadratic time‌ for one-parameter families of‌ convex polyhedra in constant‌‌ dimension. This leads to new tractability results for‌ finite adaptability that are‌ the first ones with‌‌ so-called left-hand-side uncertainty, where the underlying problem is‌ non-linear.

This result was‌ accepted in the conference‌‌ Mathematical Foundation of Computer Science 24.

In‌ collaboration with Jean Cardinal.‌

7.3.2 An asymptotic rigidity‌‌ property from the realizability of chirotope extensions

Let‌ $P$ be a finite‌ full-dimensional point configuration in‌‌ $ℝ^{d}$ . We show that if a‌ point configuration $Q$ has‌ the property that all‌‌ finite chirotopes realizable by adding (generic) points to‌ $P$ are also realizable‌ by adding points to‌‌ $Q$ , then $P$ and $Q$ are equal‌ up to a direct‌ affine transform. We also‌‌ show that for any point configuration $P$ and‌ any $ϵ > 0‌$ , there is a‌‌ finite, (generic) extension $\hat{P}$ of $P$ with‌ the following property: if‌ another realization $Q$ of‌‌ the chirotope of $P$ can be extended so‌ as to realize the‌ chirotope of $\overset{^‌‌}{P}$ , then there exists a direct affine transform‌ that maps each point‌ of $Q$ within distance‌‌ $ϵ$ of the corresponding point of $P$ 30‌.

7.3.3 Intersection patterns‌ of set systems on‌‌ manifolds with slowly growing homological shatter functions

A‌ theorem of Matoušek asserts‌ that for any $k‌‌ \geq 2$ , any set system whose shatter‌ function is $o (‌ n^{k})$ enjoys‌‌ a fractional Helly theorem: in the $k$ -wise‌ intersection hypergraph, positive density‌ implies a linear-size clique.‌‌ Kalai and Meshulam conjectured a generalization of that‌ phenomenon to homological shatter‌ functions. It was verified‌‌ for set systems with bounded homological shatter functions‌ and ground set with‌ a forbidden homological minor‌‌ (which includes $ℝ^{d}$ by a homological analogue‌ of the van Kampen-Flores‌ theorem). We present two‌‌ contributions to this line of research:

We study‌ homological minors in certain‌ manifolds (possibly with boundary),‌‌ for which we prove analogues of the van‌ Kampen-Flores theorem and of‌ the Hanani-Tutte theorem.
We‌‌ introduce graded analogues of the Radon and Helly‌ numbers of set systems‌ and relate their growth‌‌ rate to the original‌ parameters. This allows to extend the verification of‌ the Kalai-Meshulam conjecture for sufficiently slowly growing homological‌ shatter functions.

In collaboration with Sergey Avvakumov.

7.3.4‌ Computing shortest closed curves on non-orientable surfaces

We‌ initiate the study of computing shortest non-separating simple‌ closed curves with some given topological properties on‌ non-orientable surfaces. While, for orientable surfaces, any two‌ non-separating simple closed curves are related by a‌ self-homeomorphism of the surface, and computing shortest such‌ curves has been vastly studied, for non-orientable ones‌ the classification of non-separating simple closed curves up‌ to ambient homeomorphism is subtler, depending on whether‌ the curve is one-sided or two-sided, and whether‌ it is orienting or not (whether it cuts‌ the surface into an orientable one). We prove‌ that computing a shortest orienting (weakly) simple closed‌ curve on a non-orientable combinatorial surface is NP-hard‌ but fixed-parameter tractable in the genus of the‌ surface. In contrast, we can compute a shortest‌ non-separating non-orienting (weakly) simple closed curve with given‌ sidedness in $g^{O (1)} n‌ log n$ time, where g is the genus‌ and n the size of the surface. For‌ these algorithms, we develop tools that can be‌ of independent interest, to compute a variation on‌ canonical systems of loops for non-orientable surfaces based‌ on the computation of an orienting curve, and‌ some covering spaces that are essentially quotients of‌ homology covers.

This result was accepted in the‌ Journal of Computational Geometry 18.

In collaboration‌ with Denys Bulavka and Éric Colin de Verdière.‌

7.3.5 A canonical tree decomposition for order types,‌ and some applications

We introduce and study a‌ notion of decomposition of planar point sets (or‌ rather of their chirotopes) as trees decorated by‌ smaller chirotopes. This decomposition is based on the‌ concept of mutually avoiding sets (which we rephrase‌ as modules), and adapts in some sense‌ the modular decomposition of graphs in the world‌ of chirotopes. The associated tree always exists and‌ is unique up to some appropriate constraints. We‌ also show how to compute the number of‌ triangulations of a chirotope efficiently, starting from its‌ tree and the (weighted) numbers of triangulations of‌ its parts.

This result was accepted in SIAM‌ Journal on Discrete Mathematics 17.

In collaboration‌ with Mathilde Bouvel, Florent Koechlin and Valenting Feray.‌

7.3.6 Computing Distances on Graph Associahedra Is Fixed-Parameter‌ Tractable

An elimination tree of a connected graph‌ G is a rooted tree on the vertices‌ of G obtained by choosing a root v‌ and recursing on the connected components of G-v‌ to obtain the subtrees of v. The graph‌ associahedron of G is a polytope whose vertices‌ correspond to elimination trees of G and whose‌ edges correspond to tree rotations, a natural operation‌ between elimination trees. These objects generalize associahedra, which‌ correspond to the case where G is a‌ path. Ito et al. 62 recently proved that‌ the problem of computing distances on graph associahedra is NP-hard. In this‌ paper we prove that‌ the problem, for a‌‌ general graph G, is fixed-parameter tractable parameterized by‌ the distance k. Prior‌ to our work, only‌‌ the case where G is a path was‌ known to be fixed-parameter‌ tractable. To prove our‌‌ result, we use a novel approach based on‌ a marking scheme that‌ restricts the search to‌‌ a set of vertices whose size is bounded‌ by a (large) function‌ of k.

This result‌‌ was accepted in the conference International Colloquium on‌ Automata, Languages and Programming‌ (ICALP) 48.

In‌‌ collaboration with Luís Felipe I. Cunha, Ignasi Sau‌ and Uéverton Souza.

7.3.7‌ Spectral properties of stellohedra‌‌

In this article we contribute to the analysis‌ of the spectral properties‌ of graph associahedra, providing‌‌ a lower bound for the second largest eigenvalue‌ of the graph associahedra‌ $A (G)‌‌$ of $G$ . Additionally, using equitable partitions, we‌ analyze the spectrum of‌ stellohedra $A (K‌‌ 1, n)$ , proving the existence‌ of an eigenvalue in‌ the interval $(n‌‌ - 2, n - 1]$ and‌ identifying two additional small‌ eigenvalues.

This result was‌‌ accepted in the conference Latin American Algorithms, Graphs,‌ and Optimization Symposium (LAGOS‌ 2025) 57.

In‌‌ collaboration with Ana Gargantini, Adrián Pastine and Pablo‌ Torres.

8 Bilateral‌ contracts and grants with‌‌ industry

8.1 Bilateral contracts with industry

8.1.1 Waterloo‌ Maple Inc.

Participants: Laurent‌ Dupont, Sylvain Lazard‌‌, Guillaume Moroz, Marc Pouget, Rémi‌ Imbach.

Company: Waterloo‌ Maple Inc.

Duration: 2‌‌ years, renewable

Participants: Gamble and Ouragan Inria teams‌

Abstract: A renewable 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. The transfer of a version‌ of Isotop to Waterloo‌ Maple Inc. should be‌‌ done on the long run.

This contract was‌ amended last year to‌ include the new software‌‌ hefroots for the isolation of the complex roots‌ of a univariate polynomial.‌ The transfer of hefroots‌‌ to Waterloo Maple Inc. started at the end‌ of 2021 with the‌ help of the independent‌‌ contractor Rémi Imbach. Rémi Imbach was then hired‌ for one year by‌ Inria through the ADT‌‌ program. This led to the inclusion of hefroots‌ in Maple 2023, and‌ to the development of‌‌ a improved software pwpoly included in Maple 2024.‌

8.1.2 GeometryFactory

Participants: Vincent‌ Despré, Loïc Dubois‌‌, Camille Lanuel, Marc Pouget, Monique‌ Teillaud.

Company: GeometryFactory‌

Duration: permanent

Participants: Inria‌‌ and GeometryFactory

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

9 Partnerships and‌‌ cooperations

9.1 International initiatives‌

9.1.1 Inria associate team not involved in an‌ IIL or an international program

ConforLux - Computational‌ Conformal Geometry

Participants: Vincent Despré, Marc Pouget‌, Alba Marina Malaga Sabogal, Dorian Perrot‌.

Title:
ConforLux
Duration:
2025 to 2027
Coordinators:‌
Marc Pouget and Jean-Marc Schlenker (University of Luxembourg)‌
Inria contact:
Marc Pouget
Summary:

ConforLux (Computational Conformal‌ Geometry) is a collaborative research initiative uniting the‌ Gamble project-team (Inria, France) and the research group‌ of Jean-Marc Schlenker (University of Luxembourg).

The project‌ operates at the frontier of theoretical mathematics and‌ computer science, focusing on Geometric Topology and Algorithmic‌ Geometry. The collaboration aims to leverage complementary expertise:‌ the mathematical depth of the Luxembourg group regarding‌ complex structures on surfaces, and the algorithmic expertise‌ of the Gamble team in designing data structures‌ and implementations for the CGAL library.

DIPPS -‌ Discrete models for Intersection Patterns and Point Sets‌

Participants: Xavier Goaoc, Niloufar Fuladi, Sarah‌ Wajsbrot, Marguerite Bin.

Title:
DIPPS
Duration:‌
2025 to 2027
Coordinators:
Xavier Goaoc and Andreas‌ Holmsen (KAIST)
Inria contact:
Xavier Goaoc
Summary:

DIPPS‌ is a collaborative research initiative uniting the Gamble‌ project-team (Inria, France) and the research group of‌ Andreas Holmsen (KAIST, South Korea).

The project brings‌ together 11 participants (including 3 members from other‌ institutions: Ponts et Chaussée, Université Gustave Eiffel, and‌ GIST). It tackles two established topics of discrete‌ and computational geometry: convexity spaces and order types.‌ The collaboration leverages the complementarity of the Korean‌ partners, who have strong connections to discrete mathematics‌ and extremal combinatorics, two topics under-represented in France,‌ and the French partners, who have strong connection‌ to algorithms.

9.2 International research visitors

9.2.1 Visits‌ of international scientists

Other international visits to the‌ team

Sergey Avvakumov

Status
Assistant professor
Institution of‌ origin:
Tel Aviv University
Country:
Israel
Dates:
April‌ (1 week)
Context of the visit:
Collaboration on‌ topological combinatorics
Mobility program/type of mobility:
research stay‌

Jean Cardinal

Status
professor
Institution of origin:
Université‌ libre de Bruxelles
Country:
Belgium
Dates:
December (2‌ weeks)
Context of the visit:
Seminar on geometric‌ algorithms
Mobility program/type of mobility:
Research stay /‌ Lecture

Otfried Cheong

Status
researcher
Institution of origin:‌
Scalgo / Bayreuth University
Country:
Germany
Dates:
October‌ (1 week)
Context of the visit:
Collaboration on‌ geometric computing
Mobility program/type of mobility:
research stay‌

Dohyeon Lee

Status
PhD student
Institution of origin:‌
KAIST
Country:
South Korea
Dates:
July 1–20
Context‌ of the visit:
Collaboration on discrete geometry
Mobility‌ program/type of mobility:
research stay (associate team DIPPS)‌

9.2.2 Visits to international teams

Research stays abroad‌

Niloufar Fuladi

Visited institution:
Institute for Basic Science‌ (IBS)
Country:
South Korea
Dates:
May – June‌ 2025 (2 months)
Context of the visit:
Research‌ visit to the Discrete Mathematics Group (DIMAG)
Mobility‌ program/type of mobility:
Associate team DIPPS

Sarah Wajsbrot‌

Visited institution:
Institute for Basic Science (IBS)
Country:‌
South Korea
Dates:
May – June 2025 (2‌ months)
Context of the visit:
Research visit to the Discrete Mathematics Group‌ (DIMAG)
Mobility program/type of‌ mobility:
DREAM mobility program‌‌ (Lorraine Université d'Excellence)

Marguerite Bin

Visited institution:
Centre‌ de Recerca Matemàtica (CRM)‌
Country:
Spain
Dates:
October‌‌ – November 2025 (2 months)
Context of the‌ visit:
Research School on‌ "Combinatorial Geometries & Geometric‌‌ Combinatorics"
Mobility program/type of mobility:
Doctoral school +‌ formation par la recherche‌ + invitation

Mario Valencia-Pabon‌‌

Visited institution:
University of Buenos Aires (UBA)
Country:‌
Argentina
Dates:
November 2025‌ (2 weeks)
Context of‌‌ the visit:
Research visit to the Graph Theory‌ and Combinatorial Optimization group‌
Mobility program/type of mobility:‌‌
International Research Project (IRP) SINFIN

9.3 National initiatives‌

9.3.1 ANR PRC

Participants:‌ Sylvain Lazard, Alba‌‌ Málaga Sabogal, Guillaume Moroz, Marc Pouget‌.

ANR StratMesh

Title:‌
StratMesh
Duration:
2025 to‌‌ 2029
Coordinator:
Guillaume Moroz (Inria)
Inria contact:
Guillaume‌ Moroz
Summary:

StratMesh aims‌ to develop provably-correct triangulation‌‌ algorithms for stratified spaces. Our focus is on‌ stratified spaces that are‌ the projection of smooth‌‌ manifolds, which arise in many applications such as‌ robotics, control theory, and‌ medial axis computation for‌‌ learning from geometric data.

The Gamble team members‌ are expert in computational‌ geometry. They contribute in‌‌ designing algorithmic methods for triangulating the varieties appearing‌ in robotics and control‌ theory.

9.3.2 ANR JCJC‌‌

Participants: Vincent Despré.

ANR Abysm

Title:
Abysm‌
Duration:
2024 to 2028‌
Coordinator:
Vincent Despré (Université‌‌ de Lorraine)
Inria contact:
Vincent Despré
Summary:
The‌ central theme of this‌ project is the study‌‌ of geometric and combinatorial structures related to hyperbolic‌ surfaces and their moduli‌ from an algorithmic point‌‌ of view. The needs for hyperbolic geometries are‌ arising, e.g., in crystallography,‌ in geometric modeling, neuromathematics,‌‌ or physics. The generic need regarding computer science‌ in all those examples‌ is clearly stated in‌‌ a very recent paper on Nature Communications: "Spaces‌ with negative curvature are‌ difficult to realize and‌‌ investigate experimentally". In order to solve this issue,‌ our goal is to‌ develop the study of‌‌ hyperbolic surfaces in computational geometry and make our‌ results readily available for‌ users. We intend to‌‌ design efficient and algorithms with precise data structures‌ to compute geometrical characteristics‌ of hyperbolic surfaces such‌‌ as the systole, the diameter and optimal pants‌ decompositions. We also want‌ to study the regularity‌‌ of the previous parameters while moving through the‌ Teichmüller and moduli spaces.‌ We plan to implement‌‌ our algorithms and make them publicly available to‌ users.

10 Dissemination

10.1‌ Promoting scientific activities

Member‌‌ of the organizing committees

Mario Valencia-Pabon was a‌ member of the program‌ committee of XIII Latin‌‌ American Algorithms, Graphs, and Optimization Symposium (LAGOS 2025)‌.

10.1.1 Scientific events:‌ selection

Reviewer

All members‌‌ of the team are regular reviewers for the‌ conferences of our field,‌ namely Symposium on Computational‌‌ Geometry (SoCG), European Symposium on Algorithms (ESA), Symposium‌ on Discrete Algorithms (SODA),‌ International Symposium on Symbolic‌‌ and Algebraic Computation (ISSAC).

10.1.2 Journal

Reviewer -‌ reviewing activities

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.

10.1.3‌ Software Project

Member of the Editorial Boards.

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

10.1.4 Leadership within the scientific‌ community

Guillaume Moroz was a coorganizer of the‌ Journées de Géométrie Algorithmique workshop in Roscoff. (October‌ 2025)

10.1.5 Research administration

Team members are involved‌ in various committees managing the scientific life of‌ the lab or at a national level.

Local‌

INRIA Commission Information et Édition Scientifique (Laurent‌ Dupont ),
INRIA Comité de centre (Xavier‌ Goaoc ),
LORIA Conseil scientifique (Sylvain Lazard‌ ),
LORIA associate director (Sylvain Lazard ),‌
École doctorale IAEM, Computer science board (co-chair, Xavier‌ Goaoc ; member, Sylvain Lazard ),
Conseil du‌ Pole scientifique Am2I of University of Lorraine (‌Xavier Goaoc )
INRIA Comité des utilisateurs des‌ moyens informatiques (chair, Guillaume Moroz )
INRIA Commission‌ de développement technologique (Guillaume Moroz ),
FSS‌ (Guillaume Moroz ),
INRIA and LORIA PhD‌ and postdoc hiring committee (Marc Pouget ),‌
Member of the mentoring committee at LORIA (‌Monique Teillaud ),
LORIA Conseil du laboratoire (‌Mario Valencia-Pabon )

National

INRIA Mission Jeunes Chercheurs‌ (chair, Sylvain Lazard ).

Hiring Committees

Xavier Goaoc‌ was vice-chair of the hiring committee for a‌ full professor position at LORIA and École des‌ Mines (Université de Lorraine).
Sylvain Lazard chaired the‌ hiring committee for a full professor position at‌ at LORIA and IUT Nancy-Charlemagne (Université de Lorraine).‌
Xavier Goaoc served on the "repyramidage" committees for‌ section CNU 27 at Sorbonne Université and Université‌ Montpellier.

10.2 Teaching - Supervision - Juries

10.2.1‌ Teaching Committees

Laurent Dupont : Head of the‌ Bachelor diploma Licence Professionnelle Animateur, Facilitateur de Tiers-lieux‌ Eco-Responsables, Université de Lorraine (not open this year)‌
Laurent Dupont : Responsible for the course "Création‌ Numérique" of the Bachelor (BUT) "Métiers du Multimédia‌ et de l'Internet"
Laurent Dupont : Responsible for‌ fablab "Charlylab" of I.U.T. Nancy-Charlemagne,
Xavier Goaoc is‌ the chair of the computer science department of‌ École des Mines de Nancy.
Xavier Goaoc is‌ a member of the Conseil d'administration de l'École‌ des Mines de Nancy.
Mario Valencia-Pabon is responsible‌ of the 5th year Polytech computer science engineering‌ internships.

10.2.2 Teaching

Licence: Vincent Despre , Algorithmique‌, 44h, L2 PEIP, Polytech Nancy, France.
Licence:‌ Vincent Despre , Programmation orientée objet, 84h,‌ L3 IA2R, Polytech Nancy, France. (web).
Licence:‌ Laurent Dupont , Web development, 45h, L1,‌ Université de Lorraine, France.
Licence: Laurent Dupont ,‌ Web development, 150h, L2, Université de Lorraine,‌ France.
Licence: Laurent Dupont , Web development,‌ 70h, L3, Université de Lorraine, France.
Licence: Laurent‌ Dupont , 3D printing and CAO 40h, L3,‌ Université de Lorraine, France.
Licence : Xavier Goaoc , Algorithms and complexity‌, 60 HETD, L3,‌ École des Mines de‌‌ Nancy, France.
Master: Xavier Goaoc , Computer architecture‌, 32 HETD, M1,‌ École des Mines de‌‌ Nancy, France.
Master: Xavier Goaoc , Introduction to‌ blockchains, 32 HETD,‌ M1, École des Mines‌‌ de Nancy, France.
Master: Xavier Goaoc , Réalité‌ augmentée et modèles géométriques‌ pour la vision,‌‌ 12h, M2 AVR, Université de Lorraine, France
Master:‌ Guillaume Moroz , Software‌ Engineering, 20h, M1,‌‌ École des Mines de Nancy, France.
Master: Marc‌ Pouget , Introduction to‌ computational geometry, 10.5h,‌‌ M2, École Nationale Supérieure de Géologie, France.
Licence:‌ Mario Valencia-Pabon , Conception‌ d'algorithmes, 44h, L3,‌‌ Polytech Nancy, France.
Licence: Mario Valencia-Pabon , Complexité‌ algorithmique, 23h, L3,‌ École des Mines de‌‌ Nancy, France.

10.2.3 Supervision

Master internship M1: Yacine‌ Rouina , Subdivision versus‌ suivi pour l'approximation de‌‌ surfaces Sept. 2025-Feb. 2026, supervised by Guillaume Moroz‌ and Marc Pouget .‌
Master internship M2: Gautier‌‌ Schanzenbacher , Geometry and triangulation of Hyperbolic surfaces,‌ Mar-Jun 2025, supervised by‌ Vincent Despre , Marc‌‌ Pouget , Julien Maubon (IECL) and Samuel Tapie‌ (IECL).
Master internship M2:‌ Rachel Dufau-Sansot , Shattering‌‌ sets of permutations, Sep 2025-Jan 2026, supervised by‌ Xavier Goaoc .
PhD‌ in progress: Gautier Schanzenbacher‌‌ , Systole, entropie et espace des modules des‌ surfaces hyperboliques de type‌ fini, started in Sept.‌‌ 2025, supervised by Vincent Despre , Marc Pouget‌ , Julien Maubon (IECL)‌ and Samuel Tapie (IECL).‌‌
PhD in progress: Marguerite Bin , Order types:‌ decomposition and complexity, started‌ in Sept. 2024, supervised‌‌ by Xavier Goaoc and Alfredo Hubard (LIGM, Université‌ Gustave Eiffel).
PhD in‌ progress: Dorian Perrot ,‌‌ Hyperbolic surfaces and computational geometry, started in Sept.‌ 2024, supervised by Vincent‌ Despre and Marc Pouget‌‌ .
PhD defended in Sep. 2025: Loïc Dubois‌ , Algorithms for Topological‌ and Metric Spaces, supervised‌‌ by Vincent Despre and Éric Colin de Verdière‌ (Marne la Vallée).
PhD‌ defended in Nov. 2025:‌‌ Camille Lanuel , Computing an $ε$ -net of‌ a hyperbolic surface, supervised‌ by Vincent Despre ,‌‌ Marc Pouget and Monique Teillaud .
PhD in‌ progress: Sarah Wajsbrot ,‌ Combinatorial convexity, its generalizations‌‌ and applications to optimization, started in Oct. 2023,‌ supervised by Xavier Goaoc‌ .
PhD in progress:‌‌ Yacine Abdelsadok , Characterization and analysis of the‌ singularity surfaces of cuspidal‌ 6r robots and tensegrity‌‌ robots, started in Nov. 2025, supervised by Guillaume‌ Moroz , Damien Chablat‌ and Philippe Wenger .‌‌

10.2.4 Juries

Xavier Goaoc chaired the PhD defense‌ committee of Nathan Claudet,‌ Université de Lorraine.
Xavier‌‌ Goaoc chaired the PhD defense committee of Anton‌ Medvedev, CNAM.
Xavier Goaoc‌ was on the reading‌‌ and defense committees of the PhD thesis of‌ Yann Marin, Université de‌ Montpellier.
Guillaume Moroz was‌‌ on the reading and defense committees of the‌ PhD thesis of Alexandre‌ Goyer, Université Paris-Saclay.

10.3‌‌ Popularization

10.3.1 Education

Olivier Devillers presented research career‌ in several different classes‌ in highschool within the‌‌ Chiche program.
Alba‌ Málaga Sabogal , Dorian Perrot and Paul Remy‌ have been invited to the festival Les Maths‌ Dans Tous Leurs États in Thionville (April, 24-25‌ 2025), to present the Hilbert slide.
Alba Málaga‌ is a member of the scientific board for‌ the association Les maths en scène and the‌ marraine for a high-school math student club in‌ Thionville, le labo Rosa Parks.
Guillaume Moroz‌ is member of the Olympiades committee of the‌ Académie Nancy-Metz.

10.3.2 Interventions

Laurent Dupont , Marc‌ Pouget , Dorian Perrot , Gautier Schanzenbacher organized‌ a workshop "Coloriage avec un crayon fin :‌ boostez vos courbes !" for the "Fête de‌ la science" in October 10-11 in Nancy.

11‌ Scientific production

11.1 Major publications

1 inproceedingsN.‌Nicolas Bonichon, P.Prosenjit Bose, J.-L.‌Jean-Lou De Carufel, V.Vincent Despré,‌ D.Darryl Hill and M.Michiel Smid.‌ Improved Routing on the Delaunay Triangulation.ESA‌ 2018 - 26th Annual European Symposium on Algorithms‌Helsinki, Finland2018HALDOI
2 articleL.‌Luca Castelli Aleardi and O.Olivier Devillers.‌ Array-based Compact Data Structures for Triangulations: Practical Solutions‌ with Theoretical Guarantees.Journal of Computational Geometry‌912018, 247-289HAL DOI
3‌ articleN.Nicolas Chenavier and O.Olivier Devillers‌. Stretch Factor in a Planar Poisson-Delaunay Triangulation‌ with a Large Intensity.Advances in Applied‌ Probability5012018, 35-56HAL DOI‌
4 inproceedingsV.Vincent Despré, J.-M.Jean-Marc‌ Schlenker and M.Monique Teillaud. Flipping Geometric‌ Triangulations on Hyperbolic Surfaces.SoCG 2020 -‌ 36th International Symposium on Computational GeometryZurich, Switzerland‌2020HAL DOI
5 articleO.Olivier Devillers‌, M.Menelaos Karavelas and M.Monique Teillaud‌. Qualitative Symbolic Perturbation: Two Applications of a‌ New Geometry-based Perturbation Framework.Journal of Computational‌ Geometry812017, 282--315HAL DOI‌
6 inproceedingsO.Olivier Devillers, S.Sylvain‌ Lazard and W.William Lenhart. 3D Snap‌ Rounding.Proceedings of the 34th International Symposium‌ on Computational GeometryBudapest, HungaryJune 2018,‌ 30:1--30:14HAL DOI
7 articleO.Olivier Devillers‌, S.Sylvain Lazard and W.William Lenhart‌. Rounding meshes in 3D.Discrete and‌ Computational GeometryApril 2020HAL DOI
8 article‌X.Xavier Goaoc, P.Pavel Paták,‌ Z.Zuzana Patáková, M.Martin Tancer and‌ U.Uli Wagner. Shellability is NP-complete.‌Journal of the ACM (JACM)6632019‌HAL DOI
9 inproceedingsX.Xavier Goaoc and‌ E.Emo Welzl. Convex Hulls of Random‌ Order Types.SoCG 2020 - 36th International‌ Symposium on Computational Geometry16436th International Symposium‌ on Computational Geometry (SoCG 2020)Best paper award‌Zürich / Virtual, Switzerland2020, 49:1--49:15HAL‌DOI
10 articleR.Rémi Imbach, G.‌Guillaume Moroz and M.Marc Pouget. Reliable‌ Location with Respect to the Projection of a‌ Smooth Space Curve.Reliable Computing262018, 13-55HAL
11‌ articleR.Rémi Imbach‌, M.Marc Pouget‌‌ and C.Chee Yap. Clustering Complex Zeros‌ of Triangular Systems of‌ Polynomials.Mathematics in‌‌ Computer ScienceJune 2020HAL DOI
12 inproceedings‌I.Iordan Iordanov and‌ M.Monique Teillaud.‌‌ Implementing Delaunay Triangulations of the Bolza Surface.‌33rd International Symposium on‌ Computational Geometry (SoCG 2017)‌‌Brisbane, AustraliaJuly 2017, 44:1--44:15HAL DOI‌back to text
13‌ articleR.Ranjan Jha‌‌, D.Damien Chablat, L.Luc Baron‌, F.Fabrice Rouillier‌ and G.Guillaume Moroz‌‌. Workspace, Joint space and Singularities of a‌ family of Delta-Like Robot‌.Mechanism and Machine‌‌ Theory127September 2018, 73-95HAL DOI‌
14 articleS.Sylvain‌ Lazard, M.Marc‌‌ Pouget and F.Fabrice Rouillier. Bivariate triangular‌ decompositions in the presence‌ of asymptotes.Journal‌‌ of Symbolic Computation822017, 123--133HAL‌DOI back to text‌
15 articleP.Pedro‌‌ Machado Manhães De Castro and O.Olivier Devillers‌. Expected Length of‌ the Voronoi Path in‌‌ a High Dimensional Poisson-Delaunay Triangulation.Discrete and‌ Computational Geometry601‌2018, 200--219HAL‌‌DOI
16 inproceedingsG.Guillaume Moroz. New‌ data structure for univariate‌ polynomial approximation and applications‌‌ to root isolation, numerical multipoint evaluation, and other‌ problems.2021 IEEE‌ 62nd Annual Symposimum on‌‌ Foundations of Computer Science (FOCS)FOCS 2021 -‌ 62nd Annual IEEE Symposimum‌ on Foundations of Computer‌‌ ScienceDenver, United StatesDecember 2021HAL DOI‌

11.2 Publications of the‌ year

International journals

17‌‌ articleM.Mathilde Bouvel, V.Valentin Féray‌, X.Xavier Goaoc‌ and F.Florent Koechlin‌‌. A canonical tree decomposition for order types,‌ and some applications.‌SIAM Journal on Discrete‌‌ Mathematics394October 2025, 2189-2241HAL‌DOI back to text‌
18 articleD.Denys‌‌ Bulavka, É.Éric Colin de Verdière and‌ N.Niloufar Fuladi.‌ Computing shortest closed curves‌‌ on non-orientable surfaces.Journal of Computational Geometry‌1622025,‌ 237-264HAL DOI back‌‌ to text
19 articleV.Vincent Despré,‌ B.Benedikt Kolbe,‌ H.Hugo Parlier and‌‌ M.Monique Teillaud. Computing a Dirichlet domain‌ for a hyperbolic surface‌.Journal of Computational‌‌ Geometry1522025, 40-56HAL DOI‌
20 articleR.Rémi‌ Imbach and G.Guillaume‌‌ Moroz. Fast evaluation and root finding for‌ polynomials with floating-point coefficients‌.Journal of Symbolic‌‌ Computation127March 2025, 102372HAL DOI‌
21 articleK.Kacper‌ Pluta, G.Guillaume‌‌ Moroz, Y.Yukiko Kenmochi and P.Pascal‌ Romon. On Arrangements‌ of Quadrics in Decomposing‌‌ the Parameter Space of 3D Digitized Rigid Motions‌.Journal of Symbolic‌ Computation131April 2025‌‌, 102447HAL DOIback to text
22‌ articleL.Léo Valque‌ and S.Sylvain Lazard‌‌. Resolving self‐intersections in 3D meshes while preserving‌ floating‐point coordinates.Computer‌ Graphics Forum445‌‌August 2025, e70197‌HAL DOI back to text

International peer-reviewed conferences‌

23 inproceedingsP. K.Pankaj K. Agarwal,‌ B.Boris Aronov, O.Olivier Devillers,‌ C.Christian Knauer and G.Guillaume Moroz.‌ A Subquadratic Algorithm for Computing the L1-distance between‌ Two Terrains.Leibniz International Proceedings in Informatics‌ (LIPIcs)Symposium on Computational Geometry (SoCG)41st International‌ Symposium on Computational Geometry (SoCG 2025)Kanazawa, Japan‌Schloss Dagstuhl – Leibniz-Zentrum für InformatikJune 2025‌, 4:1-4:17HAL DOIback to text
24‌ inproceedingsJ.Jean Cardinal, X.Xavier Goaoc‌ and S.Sarah Wajsbrot. Hitting and Covering‌ Affine Families of Convex Polyhedra, with Applications to‌ Robust Optimization.LIPIcs50th International Symposium on‌ Mathematical Foundations of Computer Science (MFCS 2025)345‌Warsaw, PolandSchloss Dagstuhl – Leibniz-Zentrum für Informatik‌2025, 33:1--33:18HALDOI back to text‌
25 inproceedingsÉ.Éric Colin de Verdière,‌ V.Vincent Despré and L.Loïc Dubois.‌ A Discrete Analog of Tutte's Barycentric Embeddings on‌ Surfaces.Proceedings of the 2025 Annual ACM-SIAM‌ Symposium on Discrete Algorithms (SODA)ACM-SIAM Symposium on‌ Discrete Algorithms (SODA)New Orleans, United States2025‌, 5114-5146HAL DOIback to text
26‌ inproceedingsV.Vincent Despré, C.Camille Lanuel‌, M.Marc Pouget and M.Monique Teillaud‌. ε-Net Algorithm Implementation on Hyperbolic Surfaces.‌European Symposium on Algorithms33rd Annual European Symposium‌ on Algorithms (ESA 2025)Warsaw, PolandSeptember 2025‌HAL DOI back to text

Doctoral dissertations and‌ habilitation theses

27 thesisC.Camille Lanuel.‌ Computing an -net of a hyperbolic surface.‌Université de LorraineNovember 2025HAL back to‌ text

Reports & preprints

28 reportM.Miriam‌ Backens, M.Magali Bardet, J.Jérémie‌ Bettinelli, M.Marie van den Bogaard,‌ S.Sylvie Boldo, M.Mathilde Bouvel,‌ P.Pierre Clairambault, M.Maxime Folschette,‌ L.Léo Gayral, X.Xavier Goaoc,‌ E.Eleonora Guerrini, T.Timothée Martinod,‌ É.Élodie Puybareau and M.Mathilde Vernet.‌ Code of Conduct of the GDR-IFM.GDR-IFM‌March 2026HAL
29 miscV.Vincent Despré‌, D.Dorian Perrot and M.Marc Pouget‌. Bowyer-Watson Algorithm for Delaunay Triangulation on Hyperbolic‌ Surfaces.February 2026HAL
30 miscX.‌Xavier Goaoc and A.Arnau Padrol. An‌ asymptotic rigidity property from the realizability of chirotope‌ extensions.May 2025HAL back to text‌
31 miscS.Sylvain Lazard and L.Leo‌ Valque. Removing self-intersections in 3D meshes while‌ preserving floating-point coordinates.January 2025HAL

11.3‌ Cited publications

32 inproceedingsD.Dominique Attali,‌ J.-D.Jean-Daniel Boissonnat and A.André Lieutier.‌ Complexity of the Delaunay triangulation of points on‌ surfaces: the smooth case.Proceedings of the‌ 19th Annual Symposium on Computational Geometry2003,‌ 201--210URL: http://dl.acm.org/citation.cfm?id=777823DOIback to text
33‌ bookF.Franz Aurenhammer, R.Rolf Klein‌ and D.-T.Der-Tsai Lee. Voronoi diagrams and Delaunay triangulations.World‌ Scientific2013, URL:‌ http://www.worldscientific.com/worldscibooks/10.1142/8685back to text‌‌
34 articleR.Rémi Bardenet, F.Frédéric‌ Lavancier, X.Xavier‌ Mary and A.Aurélien‌‌ Vasseur. On a few statistical applications of‌ determinantal point processes.‌ESAIM: Procs602017‌‌, 180-202URL: https://doi.org/10.1051/proc/201760180DOI back to text‌
35 articleM.Mikhail‌ Bogdanov, O.Olivier‌‌ Devillers and M.Monique Teillaud. Hyperbolic Delaunay‌ complexes and Voronoi diagrams‌ made practical.Journal‌‌ of Computational Geometry52014, 56--85HAL‌back to text back‌ to text
36 inproceedings‌‌M.Mikhail Bogdanov, M.Monique Teillaud and‌ G.Gert Vegter.‌ Delaunay triangulations on orientable‌‌ surfaces of low genus.Proceedings of the‌ 32nd International Symposium on‌ Computational Geometry2016,‌‌ 20:1--20:15HAL DOI back to text
37 inproceedings‌J.-D.Jean-Daniel Boissonnat,‌ O.Olivier Devillers and‌‌ S.Samuel Hornus. Incremental construction of the‌ Delaunay graph in medium‌ dimension.Proceedings of‌‌ the 25th Annual Symposium on Computational Geometry2009‌, 208--216HAL back‌ to text
38 article‌‌J.-D.Jean-Daniel Boissonnat, O.Olivier Devillers,‌ R.René Schott,‌ M.Monique Teillaud and‌‌ M.Mariette Yvinec. Applications of random sampling‌ to on-line algorithms in‌ computational geometry.Discrete‌‌ and Computational Geometry81992, 51--71HAL‌back to text
39‌ techreportY.Yacine Bouzidi‌‌, S.Sylvain Lazard, G.Guillaume Moroz‌, M.Marc Pouget‌, F.Fabrice Rouillier‌‌ and M.Michael Sagraloff. Improved algorithms for‌ solving bivariate systems via‌ Rational Univariate Representations.‌‌INRIAFebruary 2015HALback to text
40‌ articleY.Yacine Bouzidi‌, S.Sylvain Lazard‌‌, M.Marc Pouget and F.Fabrice Rouillier‌. Separating linear forms‌ and Rational Univariate Representations‌‌ of bivariate systems.Journal of Symbolic Computation‌68May 2015,‌ 84-119HAL DOI back‌‌ to text
41 phdthesisP.Pierre Calka.‌ Tessellations, convex hulls and‌ Boolean model: some properties‌‌ and connections.Université René Descartes - Paris‌ V2009HAL back‌ to text
42 inproceedings‌‌M.Manuel Caroli, P. M.Pedro M.‌ M. de Castro,‌ S.Sébastien Loriot,‌‌ O.Olivier Rouiller, M.Monique Teillaud and‌ C.Camille Wormser.‌ Robust and Efficient Delaunay‌‌ Triangulations of Points on or Close to a‌ Sphere.Proceedings of‌ the 9th International Symposium‌‌ on Experimental Algorithms6049Lecture Notes in Computer‌ Science2010, 462--473‌HAL back to text‌‌
43 incollectionM.Manuel Caroli and M.Monique‌ Teillaud. 3D Periodic‌ Triangulations.CGAL User‌‌ and Reference Manual3.5CGAL Editorial Board2009‌, URL: http://doc.cgal.org/latest/Manual/packages.html#PkgPeriodic3Triangulation3SummaryDOI‌back to text
44‌‌ inproceedingsM.Manuel Caroli and M.Monique Teillaud‌. Computing 3D Periodic‌ Triangulations.Proceedings of‌‌ the 17th European Symposium on Algorithms5757Lecture‌ Notes in Computer Science‌2009, 59--70back‌‌ to text
45 inproceedingsM.Manuel Caroli and‌ M.Monique Teillaud.‌ Delaunay Triangulations of Point‌‌ Sets in Closed Euclidean‌ $d$ -Manifolds.Proceedings of the 27th Annual‌ Symposium on Computational Geometry2011, 274--282HAL‌DOI back to text
46 incollectionB.Bernard‌ Chazelle and others. Application challenges to computational‌ geometry: CG impact task force report.Advances‌ in Discrete and Computational Geometry223Contemporary Mathematics‌ProvidenceAmerican Mathematical Society1999, 407--463back‌ to text
47 articleP.Pascal Chossat,‌ G.Grégory Faye and O.Olivier Faugeras.‌ Bifurcation of hyperbolic planforms.Journal of Nonlinear‌ Science212011, 465--498URL: http://link.springer.com/article/10.1007/s00332-010-9089-3DOI‌back to text back to text
48 inproceedings‌L. F.Lu\'is Felipe I. Cunha, I.‌Ignasi Sau, U.Uéverton Souza and M.‌Mario Valencia-Pabon. Computing Distances on Graph Associahedra‌ Is Fixed-Parameter Tractable.Leibniz International Proceedings in‌ Informatics (LIPIcs)334Leibniz International Proceedings in Informatics‌ (LIPIcs)Aarhus, DenmarkSchloss Dagstuhl -- Leibniz-Zentrum für‌ Informatik (LIPIcs)July 2025, 63:1-63:19HAL DOI‌back to text
49 inproceedingsV.Valentina Damerow‌ and C.Christian Sohler. Extreme points under‌ random noise.Proceedings of the 12th European‌ Symposium on Algorithms2004, 264--274URL: http://dx.doi.org/10.1007/978-3-540-30140-0_25‌DOI back to text
50 inproceedingsV.Vincent‌ Despré, C.Camille Lanuel and M.Monique‌ Teillaud. Computing an -net of a closed‌ hyperbolic surface.EuroCG'24 - 40th European Workshop‌ on Computational GeometryIoannina, GreeceMarch 2024HAL‌back to text
51 inproceedingsO.Olivier Devillers‌, M.Marc Glisse and X.Xavier Goaoc‌. Complexity analysis of random geometric structures made‌ simpler.Proceedings of the 29th Annual Symposium‌ on Computational GeometryJune 2013, 167-175HAL‌DOI back to text
52 inproceedingsO.Olivier‌ Devillers, M.Marc Glisse, X.Xavier‌ Goaoc and R.Rémy Thomasse. On the‌ smoothed complexity of convex hulls.Proceedings of‌ the 31st International Symposium on Computational GeometryLipics‌2015HAL DOI back to text
53 article‌O.Olivier Devillers. The Delaunay hierarchy.‌International Journal of Foundations of Computer Science13‌2002, 163-180HALback to text
54‌ articleL.Laurent Dupont, D.Daniel Lazard‌, S.Sylvain Lazard and S.Sylvain Petitjean‌. Near-Optimal Parameterization of the Intersection of Quadrics:‌ III. Parameterizing Singular Intersections.Journal of Symbolic‌ Computation4332008, 216--232HAL DOI‌back to text
55 articleL.Laurent Dupont‌, D.Daniel Lazard, S.Sylvain Lazard‌ and S.Sylvain Petitjean. Near-optimal parameterization of‌ the intersection of quadrics: I. The generic algorithm‌.Journal of Symbolic Computation4332008‌, 168--191HAL DOIback to text
56‌ articleL.Laurent Dupont, D.Daniel Lazard‌, S.Sylvain Lazard and S.Sylvain Petitjean‌. Near-optimal parameterization of the intersection of quadrics:‌ II. A classification of pencils.Journal of‌ Symbolic Computation4332008, 192--215HAL‌DOI back to text
57 articleA.Ana‌ Gargantini, A.Adrián Pastine, P.Pablo Torres and M.Mario‌ Valencia-Pabon. Spectral properties‌ of stellohedra.Procedia‌‌ Computer Science273XIII Latin American Algorithms, Graphs,‌ and Optimization Symposium (LAGOS‌ 2025)2025, 285-292‌‌URL: https://www.sciencedirect.com/science/article/pii/S1877050925036579DOI back to text
58 article‌M.Marc Glisse,‌ S.Sylvain Lazard,‌‌ J.Julien Michel and M.Marc Pouget.‌ Silhouette of a random‌ polytope.Journal of‌‌ Computational Geometry712016, 14HAL‌back to text
59‌ articleM.Michael Hemmer‌‌, L.Laurent Dupont, S.Sylvain Petitjean‌ and E.Elmar Schömer‌. A complete, exact‌‌ and efficient implementation for computing the edge-adjacency graph‌ of an arrangement of‌ quadrics.Journal of‌‌ Symbolic Computation4642011, 467-494HAL‌DOI back to text‌
60 inproceedingsJ.Johan‌‌ Hidding, R.Rien van de Weygaert,‌ G.Gert Vegter,‌ B. J.Bernard J.T.‌‌ Jones and M.Monique Teillaud. Video: the‌ sticky geometry of the‌ cosmic web.Proceedings‌‌ of the 28th Annual Symposium on Computational Geometry‌2012, 421--422back‌ to text back to‌‌ text
61 articleJ. B.J. B. Hough‌, M.M. Krishnapur‌, Y.Y. Peres‌‌ and B.B. Virág. Determinantal processes and‌ independence.Probab. Surv.‌32006, 206-229‌‌back to text
62 inproceedingsT.Takehiro Ito‌, N.Naonori Kakimura‌, N.Naoyuki Kamiyama‌‌, Y.Yusuke Kobayashi, S.-i.Shun-ichi Maezawa‌, Y.Yuta Nozaki‌ and Y.Yoshio Okamoto‌‌. Hardness of Finding Combinatorial Shortest Paths on‌ Graph Associahedra.50th‌ International Colloquium on Automata,‌‌ Languages, and Programming (ICALP 2023)261Leibniz International‌ Proceedings in Informatics (LIPIcs)‌Keywords: Graph associahedra, combinatorial‌‌ shortest path, NP-hardness, polymatroidsDagstuhl, GermanySchloss Dagstuhl‌ -- Leibniz-Zentrum für Informatik‌2023, 82:1--82:17URL:‌‌ https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.82DOI back to text
63 articleA.‌Alex Kulesza and B.‌Ben Taskar. Determinantal‌‌ Point Processes for Machine Learning.Foundations and‌ Trends® in Machine Learning‌52–32012,‌‌ 123-286URL: http://dx.doi.org/10.1561/2200000044DOIback to text
64‌ articleS.Sylvain Lazard‌, L.Lui sM.‌‌ Peñaranda and S.Sylvain Petitjean. Intersecting quadrics:‌ an efficient and exact‌ implementation.Computational Geometry:‌‌ Theory and Applications351-22006, 74--99‌HAL back to text‌
65 articleO.Odile‌‌ Macchi. The coincidence approach to stochastic point‌ processes.Advances in‌ Applied Probability71‌‌1975, 83–122DOIback to text
66‌ articleM.Marisa Mazón‌ and T.Tomás Recio‌‌. Voronoi diagrams on orbifolds.Computational Geometry:‌ Therory and Applications8‌1997, 219--230back‌‌ to text
67 miscA.Aymeric Pellé and‌ M.Monique Teillaud.‌ Periodic meshes for the‌‌ CGAL library.Research NoteLondres, United Kingdom‌2014HAL back to‌ text
68 articleA.‌‌Alfréd Rényi and R.Rolf Sulanke. Über‌ die konvexe Hülle von‌ $n$ zufällig gerwählten Punkten‌‌ I.Z. Wahrsch. Verw. Gebiete21963‌, 75--84URL: http://dx.doi.org/10.1007/BF00535300‌DOI back to text‌‌
69 articleA.Alfréd‌ Rényi and R.Rolf Sulanke. Über die‌ konvexe Hülle von $n$ zufällig gerwählten Punkten II‌.Z. Wahrsch. Verw. Gebiete31964,‌ 138--147URL: http://dx.doi.org/10.1007/BF00535973DOIback to text
70‌ inproceedingsG.Guodong Rong, M.Miao Jin‌ and X.Xiaohu Guo. Hyperbolic centroidal Voronoi‌ tessellation.Proceedings of the ACM Symposium on‌ Solid and Physical Modeling2010, 117--126URL:‌ http://dx.doi.org/10.1145/1839778.1839795DOI back to text
71 articleF.‌François Sausset, G.Gilles Tarjus and P.‌Pascal Viot. Tuning the fragility of a‌ glassforming liquid by curving space.Physical Review‌ Letters1012008, 155701(1)--155701(4)URL: http://dx.doi.org/10.1103/PhysRevLett.101.155701DOI‌back to text
72 articleM.Michael Schindler‌ and A. C.A. C. Maggs. Cavity‌ averages for hard spheres in the presence of‌ polydispersity and incomplete data.The European Physical‌ Journal E2015, 38--97URL: http://dx.doi.org/10.1103/PhysRevE.88.022315DOI‌back to text
73 articleD. A.Daniel‌ A. Spielman and S.-H.Shang-Hua Teng. Smoothed‌ analysis: why the simplex algorithm usually takes polynomial‌ time.Journal of the ACM513‌2004, 385--463URL: http://dx.doi.org/10.1145/990308.990310DOI back to‌ text
74 bookM.Monique Teillaud. Towards‌ dynamic randomized algorithms in computational geometry.758‌Lecture Notes Comput. Sci.Springer-Verlag1993, URL:‌ http://www.springer.com/gp/book/9783540575030DOI back to text
75 phdthesisL.‌Léo Valque. 3D Snap Rounding.Université‌ de Lorraine12 2024HAL back to text‌
76 inproceedingsR.Rien van de Weygaert,‌ G.Gert Vegter, H.Herbert Edelsbrunner,‌ B. J.Bernard J.T. Jones, P.Pratyush‌ Pranav, C.Changbom Park, W. A.‌Wojciech A. Hellwing, B.Bob Eldering,‌ N.Nico Kruithof, E.E.G.P. Bos,‌ J.Johan Hidding, J.Job Feldbrugge,‌ E.Eline ten Have, M.Matti van‌ Engelen, M.Manuel Caroli and M.Monique‌ Teillaud. Alpha, Betti and the megaparsec universe:‌ on the homology and topology of the cosmic‌ web. Transactions on Computational Science XIV 6970‌Lecture Notes in Computer ScienceSpringer-Verlag 2011,‌ 60--101URL: http://dx.doi.org/10.1007/978-3-642-25249-5_3DOIback to text back‌ to text
77 articleQ.Qingnan Zhou,‌ E.Eitan Grinspun, D.Denis Zorin and‌ A.Alec Jacobson. Mesh arrangements for solid‌ geometry.ACM Transactions on Graphics (TOG)35‌42016, 1--15URL: https://dl.acm.org/doi/abs/10.1145/2897824.2925901?preflayout=tabsback to‌ text
78 miscQ.Qingnan Zhou and A.‌Alec Jacobson. Thingi10K: A Dataset of 10,000‌ 3D-Printing Models.2016, URL: https://arxiv.org/abs/1605.04797back‌ to text

GAMBLE - 2025

GAMBLE - 2025

2025﻿﻿﻿‌Activity reportProject-TeamGAMBLE﻿‌​‌

Keywords

Computer Science​​﻿﻿ and Digital Science

Other Research Topics and﻿​﻿﻿ Application Domains

1 Team​​​‌ members, visitors, external collaborators﻿​﻿﻿

Research Scientists

Faculty Members

Post-Doctoral Fellow​‌﻿﻿

PhD Students

Interns and​​​‌ Apprentices

Administrative Assistants​​​‌

External​​​‌ Collaborators

Hirings and departures​​​‌

2﻿﻿﻿‌ Overall objectives

3 Research​​﻿﻿ program

3.1 Non-linear computational​​​‌ geometry

3.2﻿﻿﻿‌ Non-Euclidean computational geometry

3.3 Probability in computational﻿​﻿﻿ geometry

3.4 Discrete﻿﻿﻿‌ geometric structures

4 Application domains​​​‌

5﻿​​﻿ Highlights of the year​​​‌

6 Latest software﻿​​﻿ developments, platforms, open data​​​‌

6.1 Latest software developments﻿﻿﻿‌

6.1.1 CGAL Package: 2D﻿‌​‌ Triangulations on Hyperbolic Surfaces﻿​​﻿

6.1.2​​​‌ wdkroots

6.1.3​​﻿﻿ 3D SnapHeur

6.1.4 3D Snap​‌﻿﻿ Rounding

7 New​​﻿﻿ results

7.1 Non-Linear Computational​​​‌ Geometry

7.1.1 On Arrangements​‌﻿﻿ of Quadrics in Decomposing​​﻿﻿ the Parameter Space of​​​‌ 3D Digitized Rigid Motions﻿​﻿﻿

7.1.2 A﻿﻿﻿‌ Subquadratic Algorithm for Computing﻿‌​‌ the L1-distance﻿​​﻿ between Two Terrains

7.1.3 3D﻿‌​‌ snap rounding

7.2 Non-Euclidean Computational Geometry​‌﻿﻿

7.2.1 A Discrete​​​‌ Analog of Tutte's Barycentric﻿​﻿﻿ Embeddings on Surfaces

7.2.2 ϵ​​﻿﻿-Net Algorithm Implementation on​​​‌ Hyperbolic Surface

7.3 Discrete﻿​﻿﻿ Geometric structures

7.3.1 Hitting﻿﻿﻿‌ and Covering Affine Families﻿‌​‌ of Convex Polyhedra, with﻿​​﻿ Applications to Robust Optimization​​​‌

7.3.2 An asymptotic rigidity﻿‌​‌ property from the realizability﻿​​﻿ of chirotope extensions

7.3.3 Intersection patterns﻿﻿﻿‌ of set systems on﻿‌​‌ manifolds with slowly growing﻿​​﻿ homological shatter functions

7.3.4​‌﻿﻿ Computing shortest closed curves​​﻿﻿ on non-orientable surfaces

7.3.5 A canonical tree​​﻿﻿ decomposition for order types,​​​‌ and some applications

7.3.6 Computing Distances on​​﻿﻿ Graph Associahedra Is Fixed-Parameter​​​‌ Tractable

7.3.7﻿﻿﻿‌ Spectral properties of stellohedra﻿‌​‌

8 Bilateral﻿﻿﻿‌ contracts and grants with﻿‌​‌ industry

8.1 Bilateral contracts﻿​​﻿ with industry

8.1.1 Waterloo​​​‌ Maple Inc.

8.1.2 GeometryFactory

9 Partnerships and﻿‌​‌ cooperations

9.1 International initiatives​​​‌

9.1.1 Inria associate team﻿​﻿﻿ not involved in an​‌﻿﻿ IIL or an international​​﻿﻿ program

ConforLux - Computational​​​‌ Conformal Geometry

DIPPS -​‌﻿﻿ Discrete models for Intersection​​﻿﻿ Patterns and Point Sets​​​‌

9.2 International​​﻿﻿ research visitors

9.2.1 Visits​​​‌ of international scientists

Other﻿​﻿﻿ international visits to the​‌﻿﻿ team

Sergey Avvakumov

Jean Cardinal

Otfried Cheong

Dohyeon Lee

9.2.2 Visits to international​​﻿﻿ teams

Research stays abroad​​​‌

Niloufar Fuladi

Sarah Wajsbrot​‌﻿﻿

Marguerite﻿​​﻿ Bin

Mario Valencia-Pabon﻿‌​‌

9.3 National initiatives​​​‌

9.3.1 ANR PRC

ANR StratMesh

9.3.2 ANR JCJC﻿‌​‌

ANR Abysm

10 Dissemination

10.1﻿﻿﻿‌ Promoting scientific activities

Member﻿‌​‌ of the organizing committees﻿​​﻿

10.1.1 Scientific events:﻿﻿﻿‌ selection

Reviewer

10.1.2 Journal

Reviewer -​​​‌ reviewing activities

10.1.3​‌﻿﻿ Software Project

2025‌Activity reportProject-TeamGAMBLE‌‌

Computer Science and Digital Science

Other Research Topics and Application Domains

1 Team‌ members, visitors, external collaborators

Post-Doctoral Fellow‌

Interns and‌ Apprentices

Administrative Assistants‌

External‌ Collaborators

Hirings and departures‌

2‌ Overall objectives

3 Research program

3.1 Non-linear computational‌ geometry

3.2‌ Non-Euclidean computational geometry

3.3 Probability in computational geometry

3.4 Discrete‌ geometric structures

4 Application domains‌

5 Highlights of the year‌

6 Latest software developments, platforms, open data‌

6.1 Latest software developments‌

6.1.1 CGAL Package: 2D‌‌ Triangulations on Hyperbolic Surfaces

6.1.2‌ wdkroots

6.1.3 3D SnapHeur

6.1.4 3D Snap‌ Rounding

7 New results

7.1 Non-Linear Computational‌ Geometry

7.1.1 On Arrangements‌ of Quadrics in Decomposing the Parameter Space of‌ 3D Digitized Rigid Motions

7.1.2 A‌ Subquadratic Algorithm for Computing‌‌ the $L_{1}$ -distance between Two Terrains

7.1.3 3D‌‌ snap rounding

7.2 Non-Euclidean Computational Geometry‌

7.2.1 A Discrete‌ Analog of Tutte's Barycentric Embeddings on Surfaces

7.2.2 $ϵ$ -Net Algorithm Implementation on‌ Hyperbolic Surface

7.3 Discrete Geometric structures

7.3.1 Hitting‌ and Covering Affine Families‌‌ of Convex Polyhedra, with Applications to Robust Optimization‌

7.3.2 An asymptotic rigidity‌‌ property from the realizability of chirotope extensions

7.3.3 Intersection patterns‌ of set systems on‌‌ manifolds with slowly growing homological shatter functions

7.3.4‌ Computing shortest closed curves on non-orientable surfaces

7.3.5 A canonical tree decomposition for order types,‌ and some applications

7.3.6 Computing Distances on Graph Associahedra Is Fixed-Parameter‌ Tractable

7.3.7‌ Spectral properties of stellohedra‌‌

8 Bilateral‌ contracts and grants with‌‌ industry

8.1 Bilateral contracts with industry

8.1.1 Waterloo‌ Maple Inc.

9 Partnerships and‌‌ cooperations

9.1 International initiatives‌

9.1.1 Inria associate team not involved in an‌ IIL or an international program

ConforLux - Computational‌ Conformal Geometry

DIPPS -‌ Discrete models for Intersection Patterns and Point Sets‌

9.2 International research visitors

9.2.1 Visits‌ of international scientists

Other international visits to the‌ team

9.2.2 Visits to international teams

Research stays abroad‌

Sarah Wajsbrot‌

Marguerite Bin

Mario Valencia-Pabon‌‌

9.3 National initiatives‌

9.3.2 ANR JCJC‌‌

10.1‌ Promoting scientific activities

Member‌‌ of the organizing committees

10.1.1 Scientific events:‌ selection

Reviewer -‌ reviewing activities

10.1.3‌ Software Project

Member of the Editorial Boards.

10.1.4 Leadership within the scientific‌ community

10.1.5 Research administration

Local‌

National

10.2 Teaching - Supervision - Juries

10.2.1‌ Teaching Committees

10.2.3 Supervision

10.3‌‌ Popularization

10.3.2 Interventions

11‌ Scientific production

11.1 Major publications

11.2 Publications of the‌ year

International peer-reviewed conferences‌

Doctoral dissertations and‌ habilitation theses

Reports & preprints

11.3‌ Cited publications