6.1.1 dpp

• Name: Determinantal Point Process
• Keyword: Determinantal point processes
• Functional Description: This program allows to quickly generate a set of random points in the plane according to repulsive laws. The software is based on deterministic point processes, known for their repulsive properties. In particular, the Ginibre law generates with high probability a cloud of points in the disk without clustering.
• URL: https://gitlab.inria.fr/gmoro/point_process
• Publication: hal-02984323
• Contact: Guillaume Moroz

7.1.1 Clustering Complex Zeros of Triangular Systems of Polynomials

This work, published in the journal of Mathematics in Computer Science, gives the first algorithm for finding a set of natural $ϵ$-clusters of complex zeros of a regular triangular system of polynomials within a given polybox in ${ℂ}^n$, for any given $ϵ>0$. Our algorithm is based on a recent near-optimal algorithm of Becker et al (2016) for clustering the complex roots of a univariate polynomial where the coefficients are represented by number oracles. Our algorithm is based on recursive subdivision. It is local, numeric, certified and handles solutions with multiplicity. Our implementation is compared to well-known homotopy solvers on various triangular systems. Our solver always gives correct answers, is often faster than the homotopy solvers that often give correct answers, and sometimes faster than the ones that give sometimes correct results 17.

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

7.1.2 Isolating the singularities of the plane projection of a generic space curve

Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods 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 the projections of smooth curves in higher dimensions. This type of curves appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using transversality theory, and we also provide a semi-algorithm to check their validity 38.

7.2.1 Flipping Geometric Triangulations on Hyperbolic Surfaces

We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint 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 3.

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

7.2.2 Generalizing CGAL Periodic Delaunay Triangulations

Even though Delaunay originally introduced his famous triangulations in the case of infinite point sets with translational periodicity, a software that computes such triangulations in the general case is not yet available, to the best of our knowledge. Combining and generalizing previous work, we present a practical algorithm for computing such triangulations. The algorithm has been implemented and experiments show that its performance is as good as the one of the CGAL package, which is restricted to cubic periodicity 21.

In collaboration with Georg Osang (IST Austria) and Mael Rouxel-Labbé (Geometry Factory).

7.2.3 Delaunay triangulations of generalized Bolza surfaces

Let us consider a regular octagon in the Poincaré disk that is centered at the origin. The hyperbolic isometries identifying its opposite edges pairwise generate a group. The Bolza surface can be seen as the quotient of the hyperbolic plane under the action this group. We consider generalized Bolza surfaces $M_g$, where the octagon is replaced by the regular 4g-gon, leading to a genus $g$ surface. We propose an extension of Bowyer's algorithm to these surfaces. In particular, we compute the value of the systole of $M_g$; we also propose algorithms computing sets of points on $M_g$ whose Delaunay triangulation is a simplicial complex 34.

In collaboration with Matthijs Ebbens and Gert Vegter (Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence, University of Groningen).

7.2.4 Half-minimizers and Delaunay triangulations on closed hyperbolic surfaces

Given a finite point cloud $P$ in a Dirichlet fundamental domain $F$ with respect to a fundamental group $\Gamma$ of a closed hyperbolic surface $S$, we derive an explicit way to construct a set of copies of $F$ that accounts for all points incident to points of $P$ in the Delaunay triangulation of $\Gamma P$. We also compute precise bounds on the size of this set that only depend on the genus of $S$ and are thus independent of the hyperbolic metric under consideration. The results in this paper lay the foundations for a practical algorithm to compute Delaunay triangulations on an arbitrary hyperbolic surface, akin to existing implementations for periodic sets of points in Euclidean space 32.

7.2.5 Testing Balanced Splitting Cycles in Complete Triangulations

Let $T$ be a triangulation of an orientable surface $\Sigma$ of genus $g$. A cycle $C$ of $T$ is splitting if it cuts $\Sigma$ into two noncontractible parts ${\Sigma }_1$ and ${\Sigma }_2$ , with respective genus $0<g_1\le g_2$. The splitting cycle $C$ is called balanced if $g_1\ge g_2-1$. The complexity of computing a balanced splitting cycle in a given triangulation is open, but seems difficult even for complete triangulations. Our main result in this paper is to show that one can rule out in polynomial time the existence of a balanced splitting cycle when the triangulation is $ϵ$-far to have one. Implementing this algorithm, we show that large Ringel and Youngs triangulations (for instance on 22.363 vertices) have no balanced splitting cycle, the only limitation being the size of the input rather than the computation time. 23.

In collaboration with Michaël Rao and Stéphan Thomassé (LIP)

7.2.6 Enumerating tilings of triply-periodic minimal surfaces with rotational symmetries

We present a technique for the enumeration of all isotopically distinct ways of tiling, with disks, a hyperbolic surface of finite genus, possibly nonorientable and with punctures and boundary. This provides a generalization of the enumeration of Delaney-Dress combinatorial tiling theory on the basis of isotopic tiling theory. To accomplish this, we derive representations of the mapping class group of the orbifold associated to the symmetry group of the tiling under consideration as a set of algebraic operations on certain generators of the symmetry group. We derive explicit descriptions of certain subgroups of mapping class groups and of tilings as embedded graphs on orbifolds. We further use this explicit description to present an algorithm that we illustrate by producing an array of examples of isotopically distinct tilings of the hyperbolic plane with symmetries generated by rotations that are commensurate with the prominent Primitive, Diamond and Gyroid triply-periodic minimal surfaces, outlining how the approach yields an unambiguous enumeration. We also present the corresponding 3-periodic graphs on these surfaces 24.

In collaboration with Myfanwy Evans (University of Potsdam)

7.2.7 Isotopic tiling theory for hyperbolic surfaces

In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly non-orientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and un-ambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces 18.

In collaboration with Myfanwy Evans (University of Potsdam).

7.2.8 Towards a combinatorial algorithm for the enumeration of isotopy classes of tilings on hyperbolic surfaces

Based on the mathematical theory of isotopic tilings on hyperbolic surfaces and mapping class groups, we present the, to the best of our knowledge, first algorithms for the enumeration of isotopy classes of tilings by compact disks with a given symmetry group on hyperbolic surfaces, which is moreover combinatorial in nature. This enumeration is relevant for crystallography and material science. Using the theory of automatic groups, we give some results on the computational tractability of the presented algorithm. We also extend data structures for combinatorial classes of tilings to isotopy classes and give an implementation of the proposed algorithm for certain classes of tilings and illustrate the enumeration with examples 37.

7.2.9 Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons

We present a method to enumerate tile-transitive crystallographic tilings of the Euclidean and hyperbolic planes by unbounded ribbon tiles up to equivariant equivalence. The hyperbolic case is relevant to self-assembly of branched polymers. This is achieved by combining and extending known methods for enumerating crystallographic disk-like tilings. We obtain a natural way of describing all possible stabiliser subgroups of tile-transitive tilings using a topological viewpoint of the tile edges as a graph embedded in an orbifold, and a group theoretical one derived from the structure of fundamental domains for discrete groups of planar isometries 36.

In collaboration with Vanessa Robins (Australian National University).

7.3.1 Expected Complexity of Routing in Theta-6 and Half-Theta-6 Graphs

We study online routing algorithms on the $\Theta$6-graph and the half-$\Theta$6-graph (which is equivalent to a variant of the Delaunay triangulation). Given a source vertex s and a target vertex t in the $\Theta$6-graph (resp. half-$\Theta$6-graph), there exists a deterministic online routing algorithm that finds a path from s to t whose length is at most 2 st (resp. 2.89 st) which is optimal in the worst case [Bose et al., SIAM J. on Computing, 44(6)]. We propose alternative, slightly simpler routing algorithms that are optimal in the worst case and for which we provide an analysis of the average routing ratio for the $\Theta$6-graph and half-$\Theta$6-graph defined on a Poisson point process. For the $\Theta$6-graph, our online routing algorithm has an expected routing ratio of 1.161 (when s and t random) and a maximum expected routing ratio of 1.22 (maximum for fixed s and t where all other points are random), much better than the worst-case routing ratio of 2. For the half-$\Theta$6-graph, our memoryless online routing algorithm has an expected routing ratio of 1.43 and a maximum expected routing ratio of 1.58 (see Figure 3). Our online routing algorithm that uses a constant amount of additional memory has an expected routing ratio of 1.34 and a maximum expected routing ratio of 1.40. The additional memory is only used to remember the coordinates of the starting point of the route. Both of these algorithms have an expected routing ratio that is much better than their worst-case routing ratio of 2.89 13.

In collaboration with Prosenjit Bose (University Carleton) and Jean-Lou De Carufel (University of Ottawa)

7.3.2 Random polytopes and the wet part for arbitrary probability distributions

We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in ${ℝ}^d$ relates to the wet part of that measure. This extends classical results for the uniform distribution from a convex set [Bárány and Larman 1988]. The lower bound of Bárány and Larman continues to hold in the general setting, but the upper bound must be relaxed by a factor of $logn$. We show by an example that this is tight 11.

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)

7.3.3 Optimal transport between determinantal point processes and application to fast simulation

We analyze several optimal transportation problems between determinantal point processes. We show how to estimate some of the distances between distributions of DPP they induce. We then apply these results to evaluate the accuracy of a new and fast DPP simulation algorithm. We can now simulate in a reasonable amount of time more than ten thousand points 31 (see also Section 6).

In collaboration with Laurent Decreusefond (Laboratoire Traitement et Communication de l'Information)

7.4.1 Convex hulls of random order types

We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of rank 3):

• The number of extreme points in an $n$-point order type, chosen uniformly at random from all such order types, is on average $4+o\left(1\right)$. For labeled order types, this number has average $4-8/(n^2-n+2)$ and variance at most 3.
• The (labeled) order types read off a set of n points sampled independently from the uniform measure on a convex planar domain, smooth or polygonal, or from a Gaussian distribution are concentrated, i.e. such sampling typically encounters only a vanishingly small fraction of all order types of the given size.

Result (a) generalizes to arbitrary dimension d for labeled order types with the average number of extreme points $2d+o\left(1\right)$ and constant variance. We also discuss to what extent our methods generalize to the abstract setting of uniform acyclic oriented matroids. Moreover, our methods allow to show the following relative of the Erdős-Szekeres theorem: for any fixed k, as $n\to \infty$, a proportion $1-O(1/n)$ of the n-point simple order types contain a triangle enclosing a convex k-chain over an edge. For the unlabeled case in (a), we prove that for any antipodal, finite subset of the 2-dimensional sphere, the group of orientation preserving bijections is cyclic, dihedral or one of A4, S4 or A5 (and each case is possible). These are the finite subgroups of SO(3) and our proof follows the lines of their characterization by Felix Klein 6.

In collaboration with Emo Welzl (ETH Zürich)

7.4.2 Convexité combinatoire

This chapter (in French) offers an introduction to combinatorial convexity, its algorithmic applications and its extensions in topological combinatorics 28.

7.5.1 Variable-width contouring for additive manufacturing

In most layered additive manufacturing processes, a tool solidifies or deposits material while following pre-planned trajectories to form solid beads. Many interesting problems arise in this context, among which one concerns the planning of trajectories for filling a planar shape as densely as possible. This is the problem we tackle in the present paper. Recent works have shown that allowing the bead width to vary along the trajectories helps increase the filling density. We present a novel technique that, given a deposition width range, constructs a set of closed beads whose width varies within the prescribed range and fills the input shape. The technique outperforms the state of the art in important metrics: filling density (while still guaranteeing the absence of bead overlap) and smoothness of trajectories. We give a detailed geometric description of our algorithm, explore its behavior on example inputs and provide a statistical comparison with the state of the art. We show that it is possible to obtain high quality fabricated layers on commodity FDM printers 16.

In collaboration with Samuel Hornus, Jonàs Martinez, Sylvain Lefebvre (project-team MFX ), Marc Glisse (project-team DataShape ), and Tim Kuipers (Ultimaker).

7.5.2 Covering families of triangles

A cover for a family $ℱ$ of sets in the plane is a set into which every set in $ℱ$ can be isometrically moved. We are interested in the convex cover of smallest area for a given family of triangles. Park and Cheong  25 conjectured that any family of triangles of bounded diameter has a smallest convex cover that is itself a triangle. The conjecture is equivalent to the claim that for every convex set $𝒳$ there is a triangle $Z$ whose area is not larger than the area of $𝒳$, such that $Z$ covers the family of triangles contained in $𝒳$. We prove this claim for the case where a diameter of $𝒳$ lies on its boundary. We also give a complete characterization of the smallest convex cover for the family of triangles contained in a half-disk, and for the family of triangles contained in a square (see Figure 4). In both cases, this cover is a triangle 30.

In collaboration with Otfried Cheong (KAIST) and Marc Glisse (project-team DataShape ).

7.5.3 CovBundled Crossings Revisited

An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into bundles. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between two bundles, i.e., as a bundled crossing. We consider the problem of bundled crossing minimization: A graph is given and the goal is to find a bundled drawing with at most $k$ bundled crossings. We show that the problem is NP-hard when we require a simple drawing. Our main result is an FPT algorithm (in $k$) for simple circular layouts where vertices must be placed on a circle and edges must be drawn inside the circle. These results make use of the connection between bundled crossings and graph genus. We also consider bundling crossings in a given drawing, in particular for storyline visualizations 14.

In collaboration with Thomas van Dijk, Myroslav Kryven, Alexander Wolff (Universität Würzburg), Steven Chaplick (Maastricht and Würzburg universities), and Alexander Ravsky (Pidstryhach Institute for Applied Problems of Mechanics and Mathematics).

9.1.1 Inria Associate Team not involved in an Inria International Lab

9.1.2 Participation in other international programs

9.2.1 Visits of international scientists

Otfried Cheong visited Gamble for one week in March.

9.2.2 Visits to international teams

Monique Teillaud visited Gert Vegter's group, Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen (two weeks in February).

9.3.1 ANR PRC

10.1.1 Scientific events: organisation

10.1.2 Scientific events: selection

10.1.3 Journal

10.1.4 Software Project

10.1.5 Invited talks

• Monique Teillaud gave a keynote talk at the 36th European Workshop on Computational Geometry: Triangulations in CGAL - To non-Euclidean spaces and beyond! 26.
• Xavier Goaoc gave 3h of lectures at the École jeunes chercheurs en informatique mathématique 28.
• Besides these two invited talks, Benedikt Kolbe gave a talk at the workshop on invitation: Structure of Materials.

10.1.6 Leadership within the scientific community

10.1.7 Scientific expertise

Members of Gamble are occasionally reviewing proposals or applications for foreign research agencies (e.g., FWF, NWO, NSERC, ISF, etc.) or foreign universities. We are not giving more details here to preserve anonymity.

10.1.8 Research administration

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

10.2.1 Committees

• V. Despré: Head of the Engineer diploma speciality SIR, Systèmes d'Information et Réseaux, Polytech Nancy, Université de Lorraine.
• L. Dupont is the secretary of Commission Pédagogique Nationale Carrières Sociales / Information-Communication / Métiers du Multimédia et de l'Internet (2017-2022).
• L. Dupont represents the Commission Pédagogique Nationale Carrières Sociales / Information-Communication / Métiers du Multimédia et de l'Internet at the national working group on D.U.T/B.U.T reform
• L. Dupont: Co-creator and Head of the Bachelor diploma Licence Professionnelle Animateur, Facilitateur de Tiers-lieux Eco-Responsables, Université de Lorraine.
• L. Dupont: Co-creator of the Bachelor diploma Licence Professionnelle Fabrication additive : Conception, design et réalisation, Université de Lorraine.
• L.Dupont: Responsible of fablab "Charlylab" of I.U.T. Nancy-Charlemagne

10.2.2 Teaching

• Licence: Vincent Despré, Programmation orientée objet, 62h, L2, Polytech Nancy, France.
• Licence: Vincent Despré, Algorithmique, 108h, L3, Polytech Nancy, France.
• Master: Vincent Despré, Programmation réseau, 88h, M1, Polytech Nancy, France.
• Master: Vincent Despré, Architecture Java EE, 50h, M1, Polytech Nancy, France.
• Master: Olivier Devillers, Modèles d'environnements, planification de trajectoires, 18h, M2 AVR, Université de Lorraine (web).
• Licence: Charles Duménil, Algorithmique et programmation avancée, 10h, M2, FST, Université de Lorraine, France.
• Licence: Charles Duménil, Découverte de l'informatique, 104h, L1, 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, Operation research, 16 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 HETD, M1, École des Mines de Nancy Nancy, France.
• Master: Xavier Goaoc, machine learning, 12 HETD, M1, École des Mines de Nancy, France.
• Master: Xavier Goaoc, Introduction to blockchains, 42 HETD, M1, École des Mines de Nancy + Polytech Nancy, France.
• Licence: Galatée Hemery, Programmation, 64 HETD, L3, École des Mines de Nancy, France.
• Licence: Benedikt Kolbe, Programmation orientée objet, 22 HETD, L2, Polytech Nancy.
• Licence: George Krait, Python, 24h, L3, Polytech Nancy, Université de Lorraine, France.
• Licence: George Krait, Bases de données, 64h, L3, Polytech Nancy, Université de Lorraine, France.
• Master: Marc Pouget, Introduction to computational geometry, 10.5h, M2, École Nationale Supérieure de Géologie, France.

10.2.3 Supervision

• PhD: Sény Diatta, Topologie de courbes algébriques planes et projection de surfaces analytiques réelles, defended in January 2020, supervised by Daouda Niang Diatta, Marie-Françoise Roy and Guillaume Moroz 29.
• 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, abandoned Aug. 2020, 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.
• PhD in progress: Léo Valque, Rounding 3D meshes, started in Sept. 2020, supervised by Sylvain Lazard.

10.2.4 Juries

• M. Teillaud was a reviewer and a member of the PhD committee of Martin Wilhelm (Otto-von-Guericke Universität Magdeburg). She chaired the PhD committee of Simon Masson (Université de Lorraine).
• X. Goaoc was a reviewer and committee member of the habilitation thesis of Arnau Padrol (Sorbonne Université, Paris).

10.3.1 Education

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

10.3.2 Interventions

L. Dupont participated to "Day of Science", in Oct. 2020 at "Mines of Neuves-Maisons" : Virtual Reality presentation.

International journals

• 11 articleImreI. Barany, MatthieuM. Fradelizi, XavierX. Goaoc, AlfredoA. Hubard and GünterG. Rote. Random polytopes and the wet part for arbitrary probability distributionsAnnales Henri Lebesgue32020, 701-715
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• 12 articleJean-DanielJ.-D. Boissonnat, OlivierO. Devillers, KunalK. Dutta and MarcM. Glisse. Randomized incremental construction of Delaunay triangulations of nice point setsDiscrete and Computational Geometry642020, 33
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• 13 articleProsenjitP. Bose, Jean-LouJ.-L. De Carufel and OlivierO. Devillers. Expected Complexity of Routing in ${}_6$ and Half-${}_6$ Graphs'Journal of Computational Geometry1112020, 212 - 234
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• 14 article StevenS. Chaplick, Thomas CT. Van Dijk, MyroslavM. Kryven, Ji-wonJ.-w. Park, AlexanderA. Ravsky and AlexanderA. Wolff. Bundled Crossings Revisited Journal of Graph Algorithms and Applications June 2020
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• 15 article OlivierO. Devillers, SylvainS. Lazard and WilliamW. Lenhart. Rounding meshes in 3D Discrete and Computational Geometry April 2020
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• 16 article SamuelS. Hornus, TimT. Kuipers, OlivierO. Devillers, MoniqueM. Teillaud, JonàsJ. Martínez, MarcM. Glisse, SylvainS. Lazard and SylvainS. Lefebvre. Variable-width contouring for additive manufacturing ACM Transactions on Graphics 39 4 (Proc. SIGGRAPH) July 2020
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• 17 article RémiR. Imbach, MarcM. Pouget and CheeC. Yap. Clustering Complex Zeros of Triangular Systems of Polynomials Mathematics in Computer Science June 2020
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• 18 article BenediktB. Kolbe and MyfanwyM. Evans. Isotopic tiling theory for hyperbolic surfaces Geometriae Dedicata July 2020
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International peer-reviewed conferences

• 19 inproceedings VincentV. Despré, Jean-MarcJ.-M. Schlenker and MoniqueM. Teillaud. Flipping Geometric Triangulations on Hyperbolic Surfaces SoCG 2020 - 36th International Symposium on Computational Geometry Zurich, Switzerland 2020
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• 20 inproceedingsBest paperXavierX. Goaoc and EmoE. Welzl. Convex Hulls of Random Order TypesSoCG 2020 - 36th International Symposium on Computational Geometry16436th International Symposium on Computational Geometry (SoCG 2020)Zürich / Virtual, Switzerland2020, 49:1--49:15
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• 21 inproceedingsBest paperGeorgG. Osang, MaelM. Rouxel-Labbé and MoniqueM. Teillaud. Generalizing CGAL Periodic Delaunay TriangulationsALGO 2020 - 28th European Symposium on AlgorithmsPise / Virtual, Italyhttp://algo2020.di.unipi.it/ESA2020/September 2020, 75:1--75:17
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Conferences without proceedings

• 22 inproceedings ProsenjitP. Bose, Jean-LouJ.-L. De Carufel and OlivierO. Devillers. Expected Complexity of Routing in ${}_6$ and Half-${}_6$ Graphs' EuroCG 2020 - 36th European Workshop on Computational Geometry Würzburg, Germany March 2020
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• 23 inproceedings VincentV. Despré, MichaëlM. Rao and StéphanS. Thomassé. Testing Balanced Splitting Cycles in Complete Triangulations Canadian Conference on Computational Geometry (CCCG 2020) Saskatchewan/Online, Canada August 2020
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• 24 inproceedings BenediktB. Kolbe and MyfanwyM. Evans. Enumerating tilings of triply-periodic minimal surfaces with rotational symmetries EuroCG 2020- 36th European Workshop on Computational Geometry Würzburg, Germany 2020
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• 25 inproceedings Ji-wonJ.-w. Park and OtfriedO. Cheong. Smallest Universal Covers for Families of Triangles EuroCG 2020 - 36th European Workshop on Computational Geometry Würzburg, Germany http://www1.pub.informatik.uni-wuerzburg.de/eurocg2020/ March 2020
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• 26 inproceedings MoniqueM. Teillaud. Triangulations in CGAL - To non-Euclidean spaces and beyond! EuroCG 2020 - 36th European Workshop on Computational Geometry Würzburg, Germany March 2020
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Scientific book chapters

• 27 inbookDamienD. Chablat, GuillaumeG. Moroz, FabriceF. Rouillier and PhilippeP. Wenger. Using Maple to analyse parallel robotsMaple in Mathematics Education and ResearchMaple in Mathematics Education and ResearchFebruary 2020, 50-64
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• 28 inbook XavierX. Goaoc. Convexité combinatoire Informatique Mathématique : Une photographie en 2020 https://www.gdr-im.fr/im-photographie/ 2020
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Doctoral dissertations and habilitation theses

• 29 thesis SenyS. Diatta. Topology of real algebraic curves and projection of real analytic surfaces. Université Assane Seck de Ziguinchor (UASZ) January 2020
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Reports & preprints

• 30 reportOtfriedO. Cheong, OlivierO. Devillers, MarcM. Glisse and Ji-wonJ.-w. Park. Covering families of trianglesINRIA2020, 31
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• 31 misc LaurentL. Decreusefond and GuillaumeG. Moroz. Optimal transport between determinantal point processes and application to fast simulation October 2020
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• 32 misc VincentV. Despré, BenediktB. Kolbe and MoniqueM. Teillaud. Half-minimizers and Delaunay triangulations on closed hyperbolic surfaces December 2020
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• 33 misc OlivierO. Devillers, PhilippeP. Duchon, MarcM. Glisse and XavierX. Goaoc. On Order Types of Random Point Sets May 2020
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• 34 misc MatthijsM. Ebbens, IordanI. Iordanov, MoniqueM. Teillaud and GertG. Vegter. Delaunay triangulations of generalized Bolza surfaces 2020
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• 35 misc XavierX. Goaoc and EmoE. Welzl. Convex Hulls of Random Order Types March 2020
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• 36 misc BenediktB. Kolbe and VanessaV. Robins. Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons December 2020
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• 37 misc BenediktB. Kolbe. Towards a combinatorial algorithm for the enumeration of isotopy classes of tilings on hyperbolic surfaces December 2020
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• 38 misc GeorgeG. Krait, SylvainS. Lazard, GuillaumeG. Moroz and MarcM. Pouget. Isolating the singularities of the plane projection of a generic space curve May 2020
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• 39 misc GuillaumeG. Moroz. Fast real and complex root-finding methods for well-conditioned polynomials February 2021
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