Team VEGAS
Members
Overall Objectives
Scientific Foundations
Application Domains
Software
New Results
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years

[1]
C. Borcea, X. Goaoc, S. Lazard, S. Petitjean.
Common Tangents to Spheres in Im3 $\#8477 ^3$ , in: Discrete and Computational Geometry, 2006, vol. 35, no 2, p. 287-300.
[2]
H. Brönnimann, H. Everett, S. Lazard, F. Sottile, S. Whitesides.
Transversals to line segments in three-dimensional space, in: Discrete and Computational Geometry, 2005, vol. 34, no 3, p. 381 - 390
http://hal.inria.fr/inria-00000384/en/.
[3]
H. Brönnimann, O. Devillers, V. Dujmovic, H. Everett, M. Glisse, X. Goaoc, S. Lazard, H.-S. Na, S. Whitesides.
Lines and free line segments Tangent to Arbitrary Three-dimensional Convex Polyhedra, in: SIAM Journal on Computing, 2007, vol. 37, p. 522-551
http://hal.inria.fr/inria-00103916/en/.
[4]
J. Cheng, S. Lazard, L. Peñaranda, M. Pouget, F. Rouillier, E. P. Tsigaridas.
On the topology of planar algebraic curves, in: Proceedings of the 25th annual symposium on Computational geometry, Danemark Aarhus, J. Hershberger, E. Fogel (editors), ACM, 2009, p. 361–370
http://hal.inria.fr/inria-00425383/en/.
[5]
O. Cheong, X. Goaoc, A. Holmsen, S. Petitjean.
Hadwiger and Helly-type theorems for disjoint unit spheres, in: Discrete & Computational Geometry, 2008, vol. 39, p. 194-212
http://hal.inria.fr/inria-00103856/en/.
[6]
O. Devillers, V. Dujmovic, H. Everett, X. Goaoc, S. Lazard, H.-S. Na, S. Petitjean.
The expected number of 3D visibility events is linear, in: SIAM Journal on Computing, Jun 2003, vol. 32, no 6, p. 1586-1620.
[7]
L. Dupont, D. Lazard, S. Lazard, S. Petitjean.
Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm; II. A Classification of Pencils; III. Parameterizing Singular Intersections, in: Journal of Symbolic Computation, 2008, vol. 43, p. 168–191, 192–215, 216–232
http://hal.inria.fr/inria-00186089/en/, autres url : http://hal.inria.fr/inria-00186090/en/, http://hal.inria.fr/inria-00186091/en/.
[8]
H. Everett, D. Lazard, S. Lazard, M. Safey El Din.
The Voronoi diagram of three lines, in: Journal of Discrete and Computational Geometry, 2009, vol. 42, no 1, p. 94-130
http://hal.inria.fr/inria-00431518/en/.
[9]
M. Glisse, S. Lazard.
An Upper Bound on the Average Size of Silhouettes, in: Discrete & Computational Geometry, 2008, vol. 40, p. 241-257
http://hal.inria.fr/inria-00336571/en/.
[10]
S. Lazard, L. Peñaranda, S. Petitjean.
Intersecting Quadrics: An Efficient and Exact Implementation, in: Computational Geometry, Theory and Applications, 2006, vol. 35, no 1-2, p. 74–99
http://hal.inria.fr/inria-00000380/en/, (Preliminary version in Proc. of 20th Annual Symposium on Computational Geometry (SoCG'04), New-York).

Publications of the year

Doctoral Dissertations and Habilitation Theses

[11]
L. Zhang.
Squelette de visibilité en trois dimensions: implantation et analyse, McGill University, 08 2009
http://tel.archives-ouvertes.fr/tel-00431464/en/, Ph. D. Thesis.

Articles in International Peer-Reviewed Journal

[12]
E. W. Chambers, E. Colin De Verdière, J. Erickson, S. Lazard, F. Lazarus, S. Thite.
Homotopic Fréchet Distance Between Curves or, Walking Your Dog in the Woods in Polynomial Time, in: Computational Geometry: Theory and Applications, 2010, vol. 43, p. 295-311
http://hal.inria.fr/inria-00438463/en/.
[13]
J. Demouth, O. Devillers, H. Everett, M. Glisse, S. Lazard, R. Seidel.
On the Complexity of Umbra and Penumbra, in: Computational Geometry: Theory and Applications, 2009, vol. 42, no 8, p. 758–771
http://hal.inria.fr/inria-00431418/en/.
[14]
J. Demouth, O. Devillers, M. Glisse, X. Goaoc.
Helly-type theorems for approximate covering, in: Discrete and Computational Geometry, 2009, vol. 42, no 3, p. 379–398
http://hal.inria.fr/inria-00404171/en/.
[15]
H. Everett, D. Lazard, S. Lazard, M. Safey El Din.
The Voronoi diagram of three lines, in: Discrete and Computational Geometry, 2009, vol. 42, no 1, p. 94-130
http://hal.inria.fr/inria-00431518/en/.
[16]
H. Everett, S. Lazard, B. Lenhart, L. Zhang.
On the Degree of Standard Geometric Predicates for Line Transversals in 3D, in: Computational Geometry: Theory and Applications, 2009, vol. 42, no 5, p. 484-494
http://hal.inria.fr/inria-00431441/en/.
[17]
H. Everett, S. Lazard, G. Liotta, S. Wismath.
Universal Sets of n Points for One-bend Drawings of Planar Graphs with n Vertices, in: Discrete and Computational Geometry, 2009
http://hal.inria.fr/inria-00431769/en/.
[18]
X. Goaoc, J. Kratochvil, Y. Okamoto, C.-S. Shin, A. Spillner, A. Wolff.
Untangling a Planar Graph, in: Discrete and Computational Geometry, 2009-12, vol. 42, no 4, p. 542-569
http://hal.inria.fr/inria-00431408/en/.
[19]
S. Lazard.
Editorial of the 24th European Workshop on Computational Geometry, EuroCG'08, in: Computational Geometry: Theory and Applications, 2010, vol. 43, no 2.

International Peer-Reviewed Conference/Proceedings

[20]
J. Cheng, S. Lazard, L. Peñaranda, M. Pouget, F. Rouillier, E. P. Tsigaridas.
On the topology of planar algebraic curves, in: Proceedings of the 25th annual symposium on Computational geometry, Danemark Aarhus, J. Hershberger, E. Fogel (editors), ACM, 2009, p. 361–370
http://hal.inria.fr/inria-00425383/en/.
[21]
O. Cheong, X. Goaoc, A. Holmsen.
Lower Bounds for Pinning Lines by Balls (Extended Abstract), in: European Conference on Combinatorics, Graph Theory and Applications European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009), France Bordeaux, 2009-08, vol. 34, p. 567-571
http://hal.inria.fr/inria-00431437/en/.
[22]
S. Lazard, L. Peñaranda, E. P. Tsigaridas.
Univariate Algebraic Kernel and Application to Arrangements, in: International Symposium on Experimental Algorithms – SEA Experimental Algorithms, 8th International Symposium, SEA 2009, Allemagne Dortmund, Springer, 2009, vol. 5526/2009, p. 209-220
http://hal.inria.fr/inria-00431559/en/.
[23]
S. Petitjean.
Characterizing the intersection pattern of two conics: a Bezoutian-based approach, in: Joint Asian Symposium on Computer Mathematics/International Conference on Mathematical Aspects of Computer and Information Sciences, Japon Fukuoka, 2009-12-14
http://hal.inria.fr/inria-00431724/en/.

Workshops without Proceedings

[24]
J. Demouth, X. Goaoc.
Computing Direct Shadows Cast by Convex Polyhedra, in: European Workshop on Computational Geometry, Belgique Brussels, 2009
http://hal.inria.fr/inria-00431544/en/.
[25]
H. Everett, C. Gillot, D. Lazard, S. Lazard, M. Pouget.
The Voronoi diagram of three arbitrary lines in R3, in: 25th European Workshop on Computational Geometry - EuroCG'09, Belgique Bruxelles, 2009
http://hal.inria.fr/inria-00425378/en/.

Internal Reports

[26]
D. Attali, O. Devillers, X. Goaoc.
The Effect of Noise on the Number of Extreme Points, INRIA, 2009, no RR-7121
http://hal.inria.fr/inria-00438409/en/, Research Report.
[27]
O. Cheong, X. Goaoc, A. Holmsen.
Lower Bounds for Pinning Lines by Balls, INRIA, 2009
http://hal.inria.fr/inria-00395837/en/, RR-6961.
[28]
S. Lazard, L. Peñaranda, E. P. Tsigaridas.
Univariate Algebraic Kernel and Application to Arrangements, INRIA, 2009
http://hal.inria.fr/inria-00372234/en/, RR-6893.

Other Publications

[29]
B. Aronov, O. Cheong, X. Goaoc, G. Röte.
Lines Pinning Lines, 2009, Submitted to the 26th annual Symposium on Computational geometry (SoCG'10).
[30]
D. Attali, O. Devillers, X. Goaoc.
The Effect of Noise on the Number of Extreme Points, 2009, Submitted to the 26th annual Symposium on Computational geometry (SoCG'10).
[31]
J. Cheng, S. Lazard, L. Peñaranda, M. Pouget, F. Rouillier, E. P. Tsigaridas.
On the topology of planar algebraic curves, 2009, Submitted to Mathematics in computer science, special issue on Computational Geometry and Computer-Aided Geometric Design.
[32]
O. Cheong, X. Goaoc, C. Nicaud.
Set Systems and Families of Permutations with Small Traces, 2009, Manuscript.
[33]
O. Cheong, H. Everett, M. Glisse, J. Gudmundsson, S. Hornus, S. Lazard, M. Lee, H.-S. Na.
Farthest-Polygon Voronoi Diagrams, 2009, Submitted to Transactions on Algorithms.
[34]
L. Dupont, M. Hemmer, S. Petitjean, E. Schomer.
A Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics, 2009, Submitted to the Journal of Symbolic Computation.
[35]
M. Glisse, S. Lazard.
On the complexity of sets of free lines and line segments among balls in three dimensions, 2009, Submitted to the 26th annual Symposium on Computational geometry (SoCG'10).
[36]
X. Goaoc, H.-S. Kim, S. Lazard.
Bounded-Curvature Shortest Paths Through a Sequence of Points, 2009, Submitted to the 26th annual Symposium on Computational geometry (SoCG'10).
[37]
X. Goaoc, S. Koenig, S. Petitjean.
Pinning a Line by Smooth Convex Sets, 2009, Manuscript.

References in notes

[38]
GMP: the GNU MP Bignum Library
http://gmplib.org/, The Free Software Foundation.
[39]
LiDIA: a C++ Library for Computational Number Theory
http://www.informatik.tu-darmstadt.de/TI/LiDIA, Darmstadt University of Technology.
[40]
QI: a C++ package for parameterizing intersections of quadrics, 2005
http://www.loria.fr/equipes/vegas/qi, LORIA, INRIA Lorraine, VEGAS project.
[41]
H. Alt, M. Glisse, X. Goaoc.
On the worst-case complexity of the silhouette of a polytope, in: Proceedings of 15th Canadian Conference on Computational Geometry (CCCG'03), Aug 2003.
[42]
C. Borcea, X. Goaoc, S. Petitjean.
Line transversals to disjoint balls, in: Discrete and Computational Geometry, 2008, vol. 39, p. 158–173
http://hal.inria.fr/inria-00176198/en/.
[43]
D. Bremner, J. Lenchner, G. Liotta, C. Paul, M. Pouget, S. Stolpner, S. Wismath.
A Note on alpha-Drawable k-Trees, in: CCCG'08: Canadian Conference on Computational Geometry, Canada, 2008
http://hal-lirmm.ccsd.cnrs.fr/lirmm-00324589/en/.
[44]
H. Brönnimann, O. Devillers, S. Lazard, F. Sottile.
Lines tangent to four triangles in three-dimensional space, in: Discrete & Computational Geometry, 2007, vol. 37, p. 369-380
http://hal.inria.fr/inria-00000598/en/.
[45]
F. Cazals, M. Pouget.
Approximation of Ridges and Umbilics on Triangulated Surface Meshes, in: CGAL User and Reference Manual, CGAL Editorial Board (editor), CGAL Editorial Board, 2007
http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#Pkg:Ridges_3.
[46]
F. Cazals, M. Pouget.
Estimation of Local Differential Properties, in: CGAL User and Reference Manual, CGAL Editorial Board (editor), CGAL Editorial Board, 2007
http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/packages.html#Pkg:Jet_fitting_3.
[47]
O. Cheong, X. Goaoc, A. Holmsen, S. Petitjean.
Hadwiger and Helly-type theorems for disjoint unit spheres, in: Discrete & Computational Geometry, 2008, vol. 39, p. 194-212
http://hal.inria.fr/inria-00103856/en/.
[48]
O. Cheong, X. Goaoc, H.-S. Na.
Disjoint Unit Spheres Admit At Most Two Line Transversals, in: Proceedings of the 11th Annual European Symposium on Algorithms (ESA'03), Sept. 2003
http://hal.inria.fr/inria-00071729/fr/.
[49]
O. Cheong, X. Goaoc, H.-S. Na.
Geometric permutations of disjoint unit spheres, in: Computational Geometry: Theory and Applications, 2005, vol. 30, p. 253-270.
[50]
O. Cheong, A. Vigneron, J. Yon.
Reverse nearest neighbor queries in fixed dimension, 2009, arXiv:0905.4441.
[51]
J. Demouth, O. Devillers, M. Glisse, X. Goaoc.
Helly-type theorems for approximate covering, in: Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08, États-Unis d'Amérique Washington, ACM, 2008, p. 120–128
http://hal.inria.fr/inria-00331435/en/.
[52]
O. Devillers, V. Dujmovic, H. Everett, S. Hornus, S. Whitesides, S. Wismath.
Maintaining Visibility Information of Planar Point Sets with a Moving Viewpoint, in: International Journal of Computational Geometry & Applications, 2007, vol. 17, p. 297-304
http://hal.inria.fr/inria-00192927/en/.
[53]
O. Devillers, M. Glisse, S. Lazard.
Predicates for line transversals to lines and line segments in three-dimensional space, in: 24th Annual ACM Symposium Computational Geometry, États-Unis d'Amérique College Park, Maryland, M. Teillaud (editor), ACM, 2008, p. 174-181
http://hal.inria.fr/inria-00336256/en/.
[54]
L. Dupont, M. Hemmer, S. Petitjean, E. Schomer.
Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics, in: 15th Annual European Symposium on Algorithms - ESA 2007 Algorithms - ESA 2007 15th Annual European Symposium, Eilat, Israel, October 8-10, 2007. Proceedings Lecture Notes in Computer Science, Israël Eilat, Israel, October 8-10, 2007, Springer Berlin / Heidelberg, Yossi Azar, Tel-Aviv U. and Microsoft Research uy Even, Tel-Aviv U. Amos Fiat, Tel-Aviv U. (Chair) Seffi Naor, Technion and Microsoft Research, 2007, vol. 4698, p. 633-644
http://hal.inria.fr/inria-00165663/en/.
[55]
L. Dupont, D. Lazard, S. Lazard, S. Petitjean.
Near-Optimal Parameterization of the Intersection of Quadrics: I. The Generic Algorithm, in: Journal of Symbolic Computation, 2008, vol. 43, p. 168–191
http://hal.inria.fr/inria-00186089/en/.
[56]
L. Dupont, D. Lazard, S. Lazard, S. Petitjean.
Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils, in: Journal of Symbolic Computation, 2008, vol. 43, p. 192–215
http://hal.inria.fr/inria-00186090/en/.
[57]
L. Dupont, D. Lazard, S. Lazard, S. Petitjean.
Near-Optimal Parameterization of the Intersection of Quadrics: III. Parameterizing Singular Intersections, in: Journal of Symbolic Computation, 2008, vol. 43, p. 216–232
http://hal.inria.fr/inria-00186091/en/.
[58]
F. Durand.
Visibilité tridimensionnelle : étude analytique et applications, Université Joseph Fourier - Grenoble I, 1999, Ph. D. Thesis.
[59]
H. Everett, S. Lazard, S. Petitjean, L. Zhang.
On the Expected Size of the 2D Visibility Complex, in: International Journal of Computational Geometry & Applications, 2007, vol. 17, p. 361-381
http://hal.inria.fr/inria-00103926/en/.
[60]
M. Glisse, S. Lazard.
An Upper Bound on the Average Size of Silhouettes, in: Discrete & Computational Geometry, 2008, vol. 40, p. 241-257
http://hal.inria.fr/inria-00336571/en/.
[61]
X. Goaoc.
Some Discrete Properties of the Space of Line Transversals to Disjoint Balls, in: Non-linear Computational Geometry IMA Volume Series, I. Emiris, F. Sottile, T. Theobald (editors), Springer, 2008
http://hal.inria.fr/inria-00335946/en/.
[62]
G. Lauvaux.
La réalisation d'œuvres d'art par prototypage rapide avec le procédé de stratoconception, Université de Reims Champagne-Ardennes, France, LORIA, June 2005, Ph. D. Thesis.
[63]
S. Petitjean.
Invariant-based characterization of the relative position of two projective conics, in: Non-Linear Computational Geometry, I. Emiris, F. Sottile, T. Theobald (editors), Springer, 2008
http://hal.inria.fr/inria-00335968/en/.
[64]
M. Pocchiola, G. Vegter.
The visibility complex, in: International Journal of Computational Geometry and Applications, 1996, vol. 6, no 3, p. 1-30.
[65]
A. Requicha, H. Voelcker.
Solid modeling: a historical summary and contemporary assessment, in: IEEE Computer Graphics and Applications, 1982, vol. 2, no 1, p. 9-24.
[66]
L. Zhang, H. Everett, S. Lazard, C. Weibel, S. Whitesides.
On the Size of the 3D Visibility Skeleton: Experimental Results, in: Algorithms - ESA, Allemagne Karlsruhe, 2008, p. 805–816
http://hal.inria.fr/inria-00336502/en/.

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