Topology Preserving Simplification of 2D Non-Manifold Meshes with Embedded Structures

International audienceMesh simplification has received tremendous attention over the past years. Most of the previous works deal with a proper choice of error measures to guide the simplification. Preserving the topological characteristics of the mesh and possibly of data attached to the mesh is a more recent topic, the present paper is about.We introduce a new topology preserving simplification algorithm for triangular meshes, possibly non-manifold, with embedded polylines. In this context embedded means that the edges of the polylines are also edges of the mesh. The paper introduces a robust test to detect if the collapse of an edge in the mesh modifies either the topology of the mesh or the topology of the embedded polylines. This validity test is derived using combinatorial topology results. More precisely we define a so-called extended complex from the input mesh and the embedded polylines. We show that if an edge collapse of the mesh preserves the topology of this extended complex, then it also preserves both the topology of the mesh and the embedded polylines. Our validity test can be used for any 2-complex mesh, including non-manifold triangular meshes. It can be combined with any previously introduced error measure. Implementation of this validity test is described. We demonstrate the power and versatility of our method with scientific data sets from neuroscience, geology and CAD/CAM models from mechanical engineering

Piecewise polynomial monotonic interpolation of 2D gridded data

International audienceA 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

Topological Data Analysis for numerical method comparisons of 2D turbulent flows

International audienc

Hiérarchisation et visualisation multirésolution de résultats issus de codes de simulation

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

Hiérarchisation et visualisation multirésolution de résultats issus de codes de simulation

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 électromagnétisme du CEA/CESTA.GRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

Topological and statistical methods for complex data: tackling large-scale, high-dimensional, and multivariate data spaces

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data.   The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends.   Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets

Immersed boundaries in hypersonic flows with considerations about high-order for LES simulations

International audienc

Immersed boundaries in hypersonic flows with considerations about high-order for LES simulations

International audienc

Topological Analysis of High Velocity Turbulent Flow

International audienceIn order to guarantee the performances of complex systems, the CEA is driving large numerical simulations in various fields such as thermomechanics, electromagnetism and aerodynamics. Due to the size of the problems and the use of High Performance Computing approaches, large and complex datasets need to be explored to understand the physical phenomena. This paper focuses on the exploration of a compressible turbulent 2D flow, to better understand the flight behavior of an object. Topological data analysis (TDA) is used to improve understanding and avoid costly traditional methods such as 3D modal decomposition algorithms or highly technical hydrody-namic stability codes. The attention is put on the large eddies shed behind a cylinder hit by a crossflow. Thanks to TDA the tracking of the eddies, the identification of their origin and the evolution of their amplitude with the downstream distance are facilitated