Bibliography

Major publications by the team in recent years

• 1Y. Bouzidi, S. Lazard, M. Pouget, F. Rouillier.
  
  Separating linear forms and Rational Univariate Representations of bivariate systems, in: Journal of Symbolic Computation, 2015, pp. 84-119.
  
  https://hal.inria.fr/hal-00977671
• 2H. 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, n^o 2, pp. 522-551. [ DOI : 10.1137/S0097539705447116 ]
• 3J. Cheng, S. Lazard, L. Peñaranda, M. Pouget, F. Rouillier, E. Tsigaridas.
  
  On the topology of real algebraic plane curves, in: Mathematics in Computer Science, 2010, vol. 4, n^o 1, pp. 113-137. [ DOI : 10.1007/s11786-010-0044-3 ]
  
  https://hal.inria.fr/inria-00517175
• 4O. Devillers, M. Glisse, X. Goaoc.
  
  Complexity Analysis of Random Geometric Structures Made Simpler, in: 29th Annual Symposium on Computational Geometry, Rio, Brazil, June 2013, pp. 167-175. [ DOI : 10.1145/2462356.2462362 ]
  
  https://hal.inria.fr/hal-00833774
• 5L. 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, pp. 168–191, 192–215, 216–232.
  
  http://hal.inria.fr/inria-00186090/en/
• 6H. 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, n^o 1, pp. 94-130. [ DOI : 10.1007/s00454-009-9173-3 ]
  
  http://www.springerlink.com/content/f5601q6324664k2p/?p=6d7bb74bf9df40b0b7756b3a5153809f&pi=5
• 7M. Glisse, S. Lazard.
  
  An Upper Bound on the Average Size of Silhouettes, in: Discrete & Computational Geometry, 2008, vol. 40, n^o 2, pp. 241-257. [ DOI : 10.1007/s00454-008-9089-3 ]
• 8X. Goaoc, H.-S. Kim, S. Lazard.
  
  Bounded-Curvature Shortest Paths through a Sequence of Points using Convex Optimization, in: SIAM Journal on Computing, 2013, vol. 42, n^o 2, pp. 662-684. [ DOI : 10.1137/100816079 ]
  
  https://hal.inria.fr/hal-00927100
• 9M. Hemmer, L. Dupont, S. Petitjean, E. Schömer.
  
  A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics, in: Journal of Symbolic Computation, 2011, vol. 46, n^o 4, pp. 467-494. [ DOI : 10.1016/j.jsc.2010.11.002 ]
  
  https://hal.inria.fr/inria-00537592

Publications of the year

Articles in International Peer-Reviewed Journals

• 10D. Attali, O. Devillers, M. Glisse, S. Lazard.
  
  Recognizing Shrinkable Complexes Is NP-Complete, in: Journal of Computational Geometry, 2016, vol. 7, n^o 1, pp. 430–443. [ DOI : 10.20382/jocg.v7i1a18 ]
  
  https://hal.inria.fr/hal-01384396
• 11Y. Bouzidi, S. Lazard, G. Moroz, M. Pouget, F. Rouillier, M. Sagraloff.
  
  Solving bivariate systems using Rational Univariate Representations, in: Journal of Complexity, 2016, vol. 37, pp. 34–75. [ DOI : 10.1016/j.jco.2016.07.002 ]
  
  https://hal.inria.fr/hal-01342211
• 12N. Broutin, O. Devillers, R. Hemsley.
  
  Efficiently navigating a random Delaunay triangulation, in: Random Structures and Algorithms, 2016, vol. 49, n^o 1, pp. 95–136. [ DOI : 10.1002/rsa.20630 ]
  
  https://hal.inria.fr/hal-00940743
• 13M. Caroli, M. Teillaud.
  
  Delaunay triangulations of closed Euclidean d-orbifolds, in: Discrete and Computational Geometry, 2016, vol. 55, n^o 4, pp. 827–853. [ DOI : 10.1007/s00454-016-9782-6 ]
  
  https://hal.inria.fr/hal-01294409
• 14O. Devillers, M. Glisse, X. Goaoc, R. Thomasse.
  
  Smoothed complexity of convex hulls by witnesses and collectors, in: Journal of Computational Geometry, 2016, vol. 7, n^o 2, pp. 101-144. [ DOI : 10.20382/jocg.v7i2a6 ]
  
  https://hal.inria.fr/hal-01285120
• 15O. Devillers, R. Hemsley.
  
  The worst visibility walk in a random Delaunay triangulation is $O\left(\sqrt{n}\right)$, in: Journal of Computational Geometry, 2016, vol. 7, n^o 1, pp. 332-359. [ DOI : 10.20382/jocg.v7i1a16 ]
  
  https://hal.inria.fr/hal-01348831
• 16M. Glisse, S. Lazard, J. Michel, M. Pouget.
  
  Silhouette of a random polytope, in: Journal of Computational Geometry, 2016, vol. 7, n^o 1, 14 p.
  
  https://hal.inria.fr/hal-01289699
• 17R. Imbach, G. Moroz, M. Pouget.
  
  A certified numerical algorithm for the topology of resultant and discriminant curves, in: Journal of Symbolic Computation, 2016, vol. 80, Part 2, pp. 285–306. [ DOI : 10.1016/j.jsc.2016.03.011 ]
  
  https://hal.inria.fr/hal-01402194
• 18P. Kamousi, S. Lazard, A. Maheshwari, S. Wuhrer.
  
  Analysis of Farthest Point Sampling for Approximating Geodesics in a Graph, in: Computational Geometry, 2016, vol. 57, pp. 1-7. [ DOI : 10.1016/j.comgeo.2016.05.005 ]
  
  https://hal.inria.fr/hal-01297624
• 19G. Moroz, B. Aronov.
  
  Computing the Distance between Piecewise-Linear Bivariate Functions, in: ACM Transactions on Algorithms, February 2016, vol. 12, n^o 1, pp. 3:1-3:13.
  
  https://hal.archives-ouvertes.fr/hal-01112394

International Conferences with Proceedings

• 20M. Bogdanov, M. Teillaud, G. Vegter.
  
  Delaunay triangulations on orientable surfaces of low genus, in: International Symposium on Computational Geometry, Boston, United States, June 2016, pp. 20:1–20:15. [ DOI : 10.4230/LIPIcs.SoCG.2016.20 ]
  
  https://hal.inria.fr/hal-01276386
• 21D. Bremner, O. Devillers, M. Glisse, S. Lazard, G. Liotta, T. Mchedlidze, S. Whitesides, S. Wismath.
  
  Monotone Simultaneous Paths Embeddings in ${ℝ}^d$, in: 24th International Symposium on Graph Drawing & Network Visualization, Athens, Greece, Proceedings of 24th International Symposium on Graph Drawing & Network Visualization, Springer, September 2016, vol. 9801.
  
  https://hal.inria.fr/hal-01366148
• 22O. Devillers, M. Karavelas, M. Teillaud.
  
  Qualitative Symbolic Perturbation, in: SoCG 2016 - International Symposium on Computational Geometry, Boston, United States, June 2016, pp. 33:1-33:15. [ DOI : 10.4230/LIPIcs.SoCG.2016.33 ]
  
  https://hal.inria.fr/hal-01276444
• 23R. Jha, D. Chablat, F. Rouillier, G. Moroz.
  
  Influence of the trajectory planning on the accuracy of theorthoglide 5-axis, in: ASME International Design Engineering Technical Conference and the Computer and Information in Engineering Conference (IDETC/CIE), Charlotte, NC, United States, August 2016.
  
  https://hal.archives-ouvertes.fr/hal-01309190
• 24G. Moroz, É. Schost.
  
  A Fast Algorithm for Computing the Truncated Resultant, in: ISSAC '16, Waterloo, Canada, M. Rosenkranz (editor), Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ACM, July 2016, pp. 341-348. [ DOI : 10.1145/2930889.2930931 ]
  
  https://hal.archives-ouvertes.fr/hal-01366386
• 25K. Pluta, G. Moroz, Y. Kenmochi, P. Romon.
  
  Quadric arrangement in classifying rigid motions of a 3D digital image, in: The 18th International Workshop on Computer Algebra in Scientific Computing, Bucharest, Romania, Lecture Notes in Computer Science, Springer, June 2016, vol. volume 9890.
  
  https://hal.archives-ouvertes.fr/hal-01334257

Internal Reports

• 26N. Chenavier, O. Devillers.
  
  Stretch Factor of Long Paths in a planar Poisson-Delaunay Triangulation, Inria, July 2016, n^o RR-8935, 34 p.
  
  https://hal.inria.fr/hal-01346203
• 27O. Devillers, L. Noizet.
  
  Walking in a Planar Poisson-Delaunay Triangulation: Shortcuts in the Voronoi Path, Inria Nancy, August 2016, n^o RR-8946.
  
  https://hal.inria.fr/hal-01353585
• 28R. Imbach.
  
  A Subdivision Solver for Systems of Large Dense Polynomials, Inria Nancy, March 2016, n^o RT-0476, 13 p.
  
  https://hal.inria.fr/hal-01293526
• 29R. Imbach, P. Mathis, P. Schreck.
  
  A Robust and Efficient Method for Solving Point Distance Problems by Homotopy, Inria, July 2016, n^o RR-8705.
  
  https://hal.inria.fr/hal-01135230
• 30I. Iordanov, M. Teillaud.
  
  Implementing Delaunay triangulations of the Bolza surface, Inria Nancy, 2016, n^o RR-8994.
  
  https://hal.inria.fr/hal-01411415
• 31P. Machado Manhães De Castro, O. Devillers.
  
  Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation, Inria, August 2016, n^o RR-8947.
  
  https://hal.inria.fr/hal-01353735

References in notes

• 32QI: a C++ package for parameterizing intersections of quadrics, 2005, LORIA, Inria Lorraine, VEGAS project.
  
  http://www.loria.fr/equipes/vegas/qi