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40 results on '"Vivodtzev, Fabien"'

1. Identifying Locally Turbulent Vortices within Instabilities

Author

Vivodtzev, Fabien, Nauleau, Florent, Braeunig, Jean-Philippe, and Tierny, Julien

Subjects
Physics - Fluid Dynamics, Computer Science - Computer Vision and Pattern Recognition, Computer Science - Graphics, Computer Science - Machine Learning
Abstract

This work presents an approach for the automatic detection of locally turbulent vortices within turbulent 2D flows such as instabilites. First, given a time step of the flow, methods from Topological Data Analysis (TDA) are leveraged to extract the geometry of the vortices. Specifically, the enstrophy of the flow is simplified by topological persistence, and the vortices are extracted by collecting the basins of the simplified enstrophy's Morse complex. Next, the local kinetic energy power spectrum is computed for each vortex. We introduce a set of indicators based on the kinetic energy power spectrum to estimate the correlation between the vortex's behavior and that of an idealized turbulent vortex. Our preliminary experiments show the relevance of these indicators for distinguishing vortices which are turbulent from those which have not yet reached a turbulent state and thus known as laminar., Comment: IEEE LDAV 2024 poster

Published
2024

2. Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study

Author

Nauleau, Florent, Vivodtzev, Fabien, Bridel-Bertomeu, Thibault, Beaugendre, Heloise, and Tierny, Julien

Subjects
Physics - Fluid Dynamics, Computer Science - Computational Geometry, Computer Science - Computer Vision and Pattern Recognition, Computer Science - Graphics, Computer Science - Machine Learning
Abstract

This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypotheses by two comparison measures: (i) a standard distance used in scientific imaging (the L2 norm) and (ii) an established topological distance between persistence diagrams (the L2-Wasserstein metric). Extensive experiments on the input ensemble demonstrate the superiority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.

Published
2022

3. Topological Representations for Data Analysis: Use Cases on Instabilities and Turbulences

Author

Vivodtzev Fabien, Nauleau Florent, Casner Alexis, and Tierny Julien

Subjects
Physics, QC1-999
Abstract

Understanding physical phenomena implied in the design of a system or in the guarantee of its performances require to run high fidelity simulation codes and to create experimental campaigns at different scales. Thanks to the use of advanced sensors or imaging capabilities in large facilities such as the Laser Mega Joule and the use of High Performance Computing, very large and complex dataset are generated. The analysis of such data is a real challenge due to the size and the complexity of the data. When dealing with chaotic phenomena, traditional analysis methods often try to average the answer. In this paper, we introduce the use of Topological Data Analysis (TDA) to improve the understanding of the results and avoid costly traditional analysis methods. The key concepts of TDA are presented such as the notion of critical points, persistence and different simplification representations. Then we illustrate the advantages of TDA on successful use cases on the analysis of hydrodynamic instabilities observed during Laser shooting or turbulences computed with a computational fluid dynamic simulation code.

Published
2024
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4. Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data

Author

Allemand-Giorgis, Léo, Bonneau, Georges-Pierre, Hahmann, Stefanie, Vivodtzev, Fabien, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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5. Automatic Feature-based Surface Mapping for Brain Cortices

Author

Vivodtzev, Fabien, Wiley, David F., Linsen, Lars, Jones, James, Amenta, Nina, Hamann, Bernd, and Joy, Ken

Abstract

We present a method that maps a complex surface geometry to an equally complicated, similar surface. One main objective of our effort is to develop technology for automatically transferring surface annotations from an atlas brain to a subject brain. While macroscopic regions of brain surfaces often correspond, the detailed surface geometry of corresponding areas can vary greatly. We have developed a method that simplifies a subject brain's surface forming an abstract yet spatially descriptive point cloud representation, which we can match to the abstract point cloud representation of the atlas brain using an approach that iteratively improves the correspondence of points. The generation of the point cloud from the original surface is based on surface smoothing, surface simplification, surface classification with respect to curvature estimates, and clustering of uniformly classified regions. Segment mapping is based on spatial partitioning, principal component analysis, rigid affine transformation, and warping based on the thin-plate spline (TPS) method. The result is a mapping between topological components of the input surfaces allowing for transfer of annotations.

Published
2006

6. Hierachical Isosurface Segmentation Based on Discrete Curvature

Author

Vivodtzev, Fabien, Linsen, Lars, Bonneau, Georges-Pierre, Hamann, Bernd, Joy, Ken, and Olshausen, B. A.

Abstract

A high-level approach to describe the characteristics of a surface is to segment it into regions of uniform curvature behavior and construct an abstract representation given by a (topology)graph. We propose a surface segmentation method based on discrete mean and Gaussian curvature estimates. The surfaces are obtained from three-dimensional imaging data sets by isosurface extraction after data presmoothing and postprocessing the isosurfaces by a surface-growing algorithm. We generate a hierarchical multiresolution representation of the isosurface. Segmentation and graph generation algorithms can be performed at various levels of detail. At a coarse level of detail, the algorithm detects the main feature of the surface. This low-resolution description is used to determine constraints for the segmentation and graph generation at the higher resolutions. We have applied our methods to MRI data sets of human brains. The hierarchical segmentation framework can be used for brain-mapping purposes.

Published
2003

8. Immersed boundaries in hypersonic flows with considerations about high-fidelity and massive parallelism

Author

Nauleau, Florent, Bridel-Bertomeu, Thibault, Beaugendre, Heloise, Vivodtzev, Fabien, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Bordeaux (Bordeaux INP), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
High Order Reconstruction, Hypersonics, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Large Eddy Simulation, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Immersed Boundary Method
Abstract

This paper inscribes itself in the ongoing doctoral work of the first author which aims at adapting the immersed boundary conditions (IBC) technique to three-dimensional (3D) large eddy simulations (LES) of viscous hypersonic flows around complex vehicles. The work relies on a pre-existing in-house IBC code, HYPERION (HYPERsonic vehicle design using Immersed bOuNdaries), originally developed in two dimensions (2D) as a proof of concept that it is possible to use IBC in the presence of strongly shocked flows [4]. As a first step towards the optimization of the 3D HYPERION, we discuss in this paper a novel MPI/Open MP hybrid rasterization algorithm allowing for the detection of immersed cells in record time even for very large problems. We then consider the least-square-based reconstruction algorithm from HYPERION [4]. It was shown in the original paper that the number of neighbors used in the reconstruction is directly related to the condition number of the least-square matrix and an optimum can be found when the condition number reaches an asymptote. In 3D configurations it is found that the number of neighbors has to be very high to ensure the proper conditioning of the least-square matrix. If the computation is distributed on several MPI processes (as is always the case in 3D for realistic return times), gathering the information from that many neighbors can cause obvious communication issues it amounts to covering large stencils with unrealistically large MPI halos. We therefore introduce an algorithm designed for a hybrid MPI/OpenMP environment based on migratable tasks and the consensus algorithm developed by [9] to remedy the former shortcoming. Finally, we discuss the premise of the implementation of LES capabilities in HYPERION. The last milestone of the main author's doctoral work is indeed to study the feasibility of embedding wall laws in the IBC modeling and reconstruction algorithm to try and counteract the low accuracy of the near-wall phenomena caused by the lack of body-fitted mesh.

Published
2022

10. Brain Mapping Using Topology Graphs Obtained by Surface Segmentation

Author

Vivodtzev, Fabien, Linsen, Lars, Hamann, Bernd, Joy, Kenneth I., Olshausen, Bruno A., Farin, Gerald, editor, Hege, Hans-Christian, editor, Hoffman, David, editor, Johnson, Christopher R., editor, Polthier, Konrad, editor, Rumpf, Martin, editor, Bonneau, Georges-Pierre, editor, Ertl, Thomas, editor, and Nielson, Gregory M., editor

Published
2006
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12. Topological Data Analysis for numerical method comparisons of 2D turbulent flows

Author

Nauleau, Florent, Bridel-Bertomeu, Thibault, Vivodtzev, Fabien, Beaugendre, Héloïse, Tierny, Julien, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Institut Polytechnique de Bordeaux (Bordeaux INP), Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Algorithmes, Programmes et Résolution (APR), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Beaugendre, Héloïse, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[INFO]Computer Science [cs], [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO] Computer Science [cs], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2021

18. Hiérarchisation et visualisation multirésolution de résultats issus de codes de simulation

Author

Vivodtzev, Fabien, Virtual environments for animation and image synthesis of natural objects (EVASION), Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble (GRAVIR - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Université Joseph-Fourier - Grenoble I, Georges-Pierre BONNEAU(Georges-Pierre.Bonneau@imag.fr), and Vivodtzev, Fabien

Subjects
topological criteria, critères topologiques, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Visualisation, computer graphics, volumetric simplification, multirésolution, simulation-visualization coupling, informatique graphique, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC], [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], couplage simulation-visualisation, simplification volumique, Visualization
Abstract

Numerical simulations generate large amounts of data that is far greater than the available resources on a workstation and it is unlikely that future developments of resource technology will be able to keep up with the growing demand. The finite element meshes supporting these simulations are normally composed of several millions of volumetric cells having embedded sub-structures of varying dimensions (surfaces and linear features) such as thin material-boundary layers. Postprocessing this large data in order to reduce the required amount of data needed to represent it allows a user to visualize and manipulate the data interactively on a single workstation. However, existing tools in scientific visualization do not allow or only partially reach the interactive exploration goals for this type of data (i.e., large number of cells, sub-structures, thin layers . . .). The dissertation presents two main steps for interactively rendering large data ; a postprocessing and visualization step. The postprocessing step uses an approach having hierarchical organization of data in order to construct a multiresolution representation allowing subsequent interactive visualization. This step is based on a mesh simplification algorithm that uses iterative edge collapses while preserving both mesh topology and the topology of all embedded sub-structures. The robust topological criteria introduced in this work are derived from theoretical notions in algebraic topology. The visualization step uses the multiresolution representation produced in the first step to speed up rendering time of the data. In a progressive, invertible and local way, the method adapts dynamically to the required resolution, specified by the user, and the hardware resources available. This dissertation illustrates the application of these techniques of hierarchical organization and visualization on data from various fields, particularly on data obtained from electromagnetic simulations by the CEA/CESTA., Les simulations numériques génèrent une quantité de résultats disproportionnée par rapport aux moyens d'exploitation, sans espoir d'atténuation à terme. Les maillages supportant ces simulations, sont composés de plusieurs dizaines de millions de cellules volumiques avec, plus spécifiquement, des sous-structures imbriquées de différentes dimensions (surfaciques et linéiques) et des couches minces de matériaux. En phase de post-traitement, un utilisateur devrait être capable de visualiser et de manipuler ces données, à temps interactif, sur sa propre machine d'exploitation. Cependant, les outils existants en visualisation scientifique ne permettent pas ou que partiellement d'atteindre les objectifs souhaités avec ce type de données (grand nombre de mailles, sous-structures, couches minces, . . .).Dans cette thèse, une approche par hiérarchisation des données est proposée afin de construire une représentation multirésolution autorisant la visualisation interactive d'une grande quantité d'information. L'étape de hiérarchisation est basée sur un algorithme de simplification de maillages, par contractions itératives d'arêtes, préservant à la fois la topologie du maillage et celle de toutes les sous-structures imbriquées. Les critères topologiques robustes introduits dans ces travaux, s'appuient sur des notions théoriques en topologie algébrique. L'étape de visualisation utilise la représentation multirésolution pour accélérer l'affichage des résultats. De façon progressive, inversible et locale, l'utilisateur modifie dynamiquement la résolution selon ses besoins et les ressources matérielles dont il dispose.Cette thèse illustre la mise en oeuvre de ces techniques de hiérarchisation et de visualisation dans de nombreux domaines d'applications notamment dans le cadre d'exploitation de résultats issus de simulations en électromagnétismedu CEA/CESTA.

Published
2005

22. Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows An Experimental Study

Author

Nauleau, Florent, Vivodtzev, Fabien, Bridel-Bertomeu, Thibault, Beaugendre, Heloise, Tierny, Julien, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Bordeaux (Bordeaux INP), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), European Project: 863464,TORI, Centre d'études scientifiques et techniques d'Aquitaine (CESTA), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Algorithmes, Programmes et Résolution (APR), LIP6, and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], Computational Geometry (cs.CG), FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-DB]Computer Science [cs]/Databases [cs.DB], Computer Vision and Pattern Recognition (cs.CV), Fluid Dynamics (physics.flu-dyn), Computer Science - Computer Vision and Pattern Recognition, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], FOS: Physical sciences, Physics - Fluid Dynamics, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Graphics (cs.GR), Machine Learning (cs.LG), Computer Science - Graphics, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Computer Science - Computational Geometry, [INFO.INFO-MS]Computer Science [cs]/Mathematical Software [cs.MS]
Abstract

International audience; This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypotheses by two comparison measures: (i) a standard distance used in scientific imaging (the $L_2$ norm) and (ii) an established topological distance between persistence diagrams (the $L_2$-Wasserstein metric). Extensive experiments on the input ensemble demonstrate the superiority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an application-approved benchmark for the evaluation and design of further topological distances.

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23. Slycat Ensemble Analysis of Electrical Circuit Simulations

Author

Crossno, Patricia J., Shead, Timothy M., Sielicki, Milosz A., Hunt, Warren L., Martin, Shawn, Hsieh, Ming-Yu, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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24. Realization of Regular Maps of Large Genus

Author

Razafindrazaka, Faniry, Polthier, Konrad, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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25. Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

Author

Anthony, Eleanor, Grant, Sheridan, Gritzmann, Peter, Rojas, J. Maurice, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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26. Exercises in High-Dimensional Sampling: Maximal Poisson-Disk Sampling and k-d Darts

Author

Ebeida, Mohamed S., Mitchell, Scott A., Patney, Anjul, Davidson, Andrew A., Tzeng, Stanley, Awad, Muhammad A., Mahmoud, Ahmed H., Owens, John D., Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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27. Computing Accurate Morse-Smale Complexes from Gradient Vector Fields

Author

Gyulassy, Attila, Bhatia, Harsh, Bremer, Peer-Timo, Pascucci, Valerio, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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29. A Comparison of Pareto Sets and Jacobi Sets

Author

Huettenberger, Lars, Garth, Christoph, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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30. 3D Symmetric Tensor Fields: What We Know and Where To Go Next

Author

Zhang, Eugene, Zhang, Yue, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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31. Lyapunov Time for 2D Lagrangian Visualization

Author

Sadlo, Filip, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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32. Deformations Preserving Gauss Curvature

Author

Berres, Anne, Hagen, Hans, Hahmann, Stefanie, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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33. In-Situ Visualization in Computational Fluid Dynamics Using Open-Source tools: Integration of Catalyst into Code_Saturne

Author

Ribés, Alejandro, Lorendeau, Benjamin, Jomier, Julien, Fournier, Yvan, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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34. Shape Analysis and Description Using Real Functions

Author

Biasotti, Silvia, Cerri, Andrea, Spagnuolo, Michela, Falcidieno, Bianca, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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35. Optimal General Simplification of Scalar Fields on Surfaces

Author

Tierny, Julien, Günther, David, Pascucci, Valerio, Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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36. Sublinear Algorithms for Extreme-Scale Data Analysis

Author

Seshadhri, C., Pinar, Ali, Thompson, David, Bennett, Janine C., Farin, Gerald, Series editor, Hege, Hans-Christian, Series editor, Hoffman, David, Series editor, Johnson, Christopher R., Series editor, Polthier, Konrad, Series editor, Rumpf, Martin, Series editor, Bennett, Janine, editor, Vivodtzev, Fabien, editor, and Pascucci, Valerio, editor

Published
2015
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39. Deformations Preserving Gauß Curvature

Author

Anne Berres, Stefanie Hahmann, Hans Hagen, Department of Computer Science [Kaiserslautern], Technische Universität Kaiserslautern (TU Kaiserslautern), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio, European Project: 291184,EC:FP7:ERC,ERC-2011-ADG_20110209,EXPRESSIVE(2012), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
Surface (mathematics), Mean curvature flow, Mean curvature, Minimal surface, 010102 general mathematics, deformation, 020207 software engineering, Geometry, 02 engineering and technology, Curvature, 01 natural sciences, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], symbols.namesake, total curvature, 0202 electrical engineering, electronic engineering, information engineering, Gaussian curvature, symbols, Constant-mean-curvature surface, Total curvature, gauss curvature, 0101 mathematics, Mathematics, topologie
Abstract

(Proceedings of LHMTS 2013); International audience; In industrial surface generation, it is important to consider surfaces with minimal areas for two main reasons: these surfaces require less material than non-minimal surfaces, and they are cheaper to manufacture. Based on a prototype, a so-called masterpiece, the final product is created using small deformations to adapt a surface to the desired shape. We present a linear deformation technique preserving the total curvature of the masterpiece. In particular, we derive sufficient conditions for these linear deformations to be total curvature preserving when applied to the masterpiece. It is useful to preserve total curvature of a surface in order to minimise the amount of material needed, and to minimise bending energy.

Published
2014

40. Piecewise polynomial monotonic interpolation of 2D gridded data

Author

Léo Allemand-Giorgis, Georges-Pierre Bonneau, Stefanie Hahmann, Fabien Vivodtzev, Models and Algorithms for Visualization and Rendering (MAVERICK), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments (IMAGINE), Centre d'études scientifiques et techniques d'Aquitaine (CESTA), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio, Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Mathematical analysis, Monotone cubic interpolation, Monotonic function, 010103 numerical & computational mathematics, 01 natural sciences, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Interpolation, 010101 applied mathematics, Maxima and minima, Monotone Surfaces, Monotone polygon, Saddle point, Piecewise, Partial derivative, 0101 mathematics, Mathematics, Visualization
Abstract

International audience; A method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C$^1$-continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C$^1$ surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm.

Published
2014

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