Publications

• The Hyperbolic Plane in E3
  V. Borrelli, R. Denis, F. Lazarus, M. Theillière, B. Thibert,
  preprint arxiv, March 2023.
  
• Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures
  J.-O. Lachaud, D. Coeurjolly, C. Labart, P. Romon, B. Thibert,
  Computer Graphics Forum (Proceedings of Symposium on Geometry Processing), July, 2023
  
• Entropy-regularized Wasserstein distributionally robust shape and topology optimization
  C. Dapogny, F. Iutzeler, A. Meda, B. Thibert,
  Structural and Multidisciplinary Optimization, vol. 66, art. 42, 2023.
  
• Strong c-concavity and stability in optimal transport
  A. Gallouët, Q. Mérigot, B. Thibert, preprint, July 2022.
  
• Metasurfaces and Optimal transport
  C.E. Gutiérrez, Q. Huang, Q. Mérigot, B. Thibert,
  SMAI Journal of Computational Mathematics, Volume 8, pp. 201-224, 2022.
  
• A damped Newton algorithm for Generated Jacobian equations
  A. Gallouët, Q. Mérigot, B. Thibert,
  Calculus of Variations and Partial Differential Equations (CVPDE) 61 (49), 2022.
  
• Corrected curvature measures
  J.-O. Lachaud, P. Romon, B. Thibert,
  Discrete and Computational Geometry (DCG),68:477–524, 2022.
  
• Interpolated corrected curvature measures for polygonal surfaces
  J.-O. Lachaud, P. Romon, B. Thibert, D. Coeurjolly,
  Computer Graphics Forum (Proceedings of Symposium on Geometry Processing), July 2020.
  
• Convergence of a Newton algorithm for semi-discrete optimal transport
  J. Kitagawa, Q. Mérigot, B. Thibert,
  Journal of the European Mathematical Society (JEMS), 21, 2603-2651, 2019.
  
• Light in Power: A General and Parameter-free Algorithm for Caustic Design
  J. Meyron, Q. Mérigot, B. Thibert,
  ACM Transactions on Graphics (TOG) Volume 37 Issue 6, No. 224, 2018.
  (Proceedings of Siggraph Asia 2018).
  
• An algorithm for optimal transport between a simplex soup and a point cloud
  Q. Mérigot, J. Meyron, B. Thibert,
  SIAM Journal on Imaging Sciences (SIIMS), 11(2), pp.1363-1389, 2018.
  
• An explicit isometric reduction of the unit sphere into an arbitrarily small ball
  E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert,
  Foundations of Computational Mathematics (FoCM), 18(4), 1015-1042, 2018.
  
• Distributable Consistent Multi-Object Matching
  N. Hu, Q. Huang, B. Thibert, L. Guibas,
  Computer Vision and Pattern Recognition (CVPR) 2018.
• Shape-Aware Spatio-Temporal Descriptors for Interaction Classification
  S. Pirk, O. Diamanti, B. Thibert, D. Xu, L. Guibas,
  IEEE International Conference on Image Processing (ICIP) 2017.
  
• Stable Region Correspondences Between Non-Isometric Shapes
  V. Ganapathi-Subramanian, B. Thibert, M. Ovsjanikov, L. Guibas,
  Computer Graphics Forum 28(5), 2016. (Proceedings of SGP 2016)
  
• Far-field reflector problem and intersection of paraboloids
  P. Machado Manhães de Castro, Q. Mérigot, B. Thibert,
  Numerische Mathematik, Vol 134, pages 389-411, 2016.
  (also in the Proc. of Symp. on Computational Geometry (SoCG), 2014).
• Properties of Gauss digitized shapes and digital surface integration,,
  J-O Lachaud, B. Thibert,
  Journal of Mathematical Imaging and Vision, Vol 54, No. 2, pp. 162-180, 2016.
  
• Robust Geometry Estimation using the Generalized Voronoi Covariance Measure,
  L. Cuel, J-O Lachaud, Q. Mérigot, B. Thibert
  SIAM Journal on Imaging Sciences (SIIMS), Vol. 8, No. 2. pp. 1293-1314, 2015.
  
• Far-field reflector problem under design constraints
  J. André, D. Attali, Q. Mérigot, B. Thibert,
  International Journal of Computational Geometry and Applications, Vol 25, No 2, pp 143-163, 2015
• Voronoi-based geometry estimator for 3D digital surfaces,
  L. Cuel, J-O Lachaud, B. Thibert,
  Proc. Symp. on Discrete Geometry for Computer Imagery, 2014.
• Isometric embeddings of the square flat torus in ambient space.
  V. Borrelli, S. Jabrane, F. Lazarus, B. Thibert
  Ensaios Matemáticos, 24:1-91, 2013
  
• The Nash-Kuiper process for curves
  V. Borrelli, S. Jabrane, F. Lazarus, B. Thibert
  Actes du séminaire de théorie spectrale et géométrie, 2011-2012.
  
• Flat tori in three-dimensional space : an implementation of convex integration.
  V. Borrelli, S. Jabrane, F. Lazarus, B. Thibert
  Proceedings of the National Academy of Sciences (PNAS), april 2012.
  For a detailed presentation, please click here.
• Folded paper Geometry from 2D Pattern and 3D Contour.
  D. Rohmer, M.-P. Cani, S. Hahmann, B. Thibert
  Eurographics 2011, short paper, Avril 2011.
• Stability of Curvature Measures.
  F. Chazal, D. Cohen-Steiner, A. Lieutier, B. Thibert
  Computer Graphics Forum 28(5), 2009, 1485-1496 (Proceedings of SGP 2009).
• Convergence of geodesics on triangulations.
  A. Lieutier, B. Thibert
  Computer Aided Geometric Design, Vol 26/ 4, 2009, pp 412-424.
• Simple Flexible Skinning based on Manifold Modeling.
  F. Hétroy, C. Gérot, L. Lu, B. Thibert
  In International Conference on Computer Graphics Theory and Applications, GRAPP 2009: 259–265.
• Geodesic as limit of geodesics on PL-surfaces.
  A. Lieutier, B. Thibert
  Symposium on Geometric Modeling and Processing (GMP) 2008: 178-190.
• Developable Surfaces from Arbitrary Sketched Boundaries.
  K.Rose, A. Sheffer, J. Wither, M.-P., B.Thibert
  Symposium Geometry Processing (SGP) 2007.
• Shape Smoothing using Double Offsets.
  F. Chazal, D. Cohen-Steiner, A. Lieutier, B. Thibert
  Symposium on Solid and Physical Modeling (SPM) 2007: 183-192.
• Efficient identification of critical residues based only on protein structure by network analysis.
  M.P. Cusack, B. Thibert, D.E. Bredesen, G. Del Rio
  2007, PLoS ONE 2(5): e421.
• Unfolding Of Surfaces.
  J.-M. Morvan, B. Thibert
  Discrete and Computational Geometry, 2006, vol 36/3, pp 393-418.
• Improving prediction of critical residues for protein function based on network and phylogeny analyses.
  B. Thibert, D. Bredesen, G. Del Rio
  BMC Bioinformatics 2005, 6:213.
• A direct method for modelling and unfolding developable surfaces and its application to the Ventura Basin (California).
  B. Thibert, J.-P. Gratier, J.-M. Morvan
  Journal of Structural Geology, 2005, Vol 27/2 pp 303-316.
• Approximation of the Normal Vector Field and the Area of a Smooth Surface.
  J.-M. Morvan, B. Thibert
  Discrete and Computational Geometry 2004, vol 32/3 pp 383-400.
• Smooth Surface And Triangular Mesh : Comparison Of The Area, The Normals And The Unfolding.
  J.-M. Morvan, B. Thibert
  Symposium on Solid Modelling And Applications (SMA) 2002: 147-158.
• On the approximation of a smooth surface with a triangulated mesh.
  J.-M. Morvan, B. Thibert
  Computational Geometry Theory And Application, 2002, vol 23/3 pp 337-352.

Dissertations, survey

• Optimal transport: discretization and algorithms
  Q. Mérigot, B. Thibert,
  In Handbook of Numerical Analysis, Vol 22, Geometric PDEs - Part 2, pp 134-212, 2021.
  
• Inference of curvature using tubular neighborhoods
  F. Chazal, D. Cohen-Steiner, A. Lieutier, Q. Mérigot, B. Thibert
  book chapter in Modern approaches to discrete curvature, Springer LNM, 2017.
• Effective calculations in nonlinear geometric problems
  Habilitation à diriger des recherches, Université Grenobles Alpes, June 29, 2015.
• Approximation géométrique d'une surface lisse. Applications en géologie structurale
  PhD thesis, Université Lyon 1, May 2003.

Popularization

• Miroirs, lentilles et équations de Monge-Ampère
  Q. Mérigot, B. Thibert, La Gazette des Mathématiciens, pages 6-21, N°166, Octobre 2020.
• Mirrors, lenses and Monge–Ampère equations
  Q. Mérigot, B. Thibert, EMS Magazine, No. 120 , July 2021.
  (English translation of the article at La Gazette des Mathématiciens)
• Quelques exemples et réflexions sur la place des images en mathématiques
  V. Borrelli, F. Lazarus, B. Thibert, Séminaires & congrès, 33, collection SMF, p335-347, 2019.
• La révolution des fractales lisses
  F. Lazarus, B. Thibert, revue Tangente, hors série 70 sur Les surfaces, avril 2019.
• Problèmes inverses en optique anidolique
  Q. Mérigot, B. Thibert, lettre de l'INSMI, février 2019.
• Les fractales lisses
  V. Borrelli, F. Lazarus, B. Thibert Pour La Science, N° 425, mars 2013.