Couplage ossature-peau pour l'animation interactive d'objets déformables

National audienceLa déformation interactive et temps-réel d'objets dans un espace tridimensionnel est un sujet largement étudié dans le domaine de l'animation du fait de ses nombreuses applications, notamment dans les jeux vidéos et la chirurgie assistée par ordinateur. Les contraintes soulevées par le problème sont tout d'abord de travailler sur un modèle de déformations physiquement réalistes aux yeux de l'observateur et précises du point de vue mécanique. Lié à la dynamique ainsi qu'à sa représentation géométrique, l'aspect visuel de l'objet - images affichées sur l'écran - doit lui aussi satisfaire l'utilisateur, c'est-à-dire de minimiser les artefacts visuels induits par la discrétisation des informations au sein de l'ordinateur, autant que faire se peut. La dernière des contraintes est temporelle; en effet, dans les domaines de la réalité virtuelle et de la synthèse d'images, les applications doivent être adaptées aux fréquences optiques et haptiques imposées par l'Homme, elles doivent rendre transparente l'utilisation de l'outil informatique pour immerger l'utilisateur dans un monde virtuel. L'aspect géométrique dans le cadre de l'animation d'objet déformables a été peu développé, dans ce rapport, nous nous pencherons particulièrement sur la résolution de ce problème en proposant une solution de modélisation multi-résolution adaptative d'objets déformables

A Vortex Method for Bi-phasic Fluids Interacting with Rigid Bodies

We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating bi-phase flow, such as liquid and gas, with a good level of realism. Vortex particles are localized at the interfaces between the two fluids and within the regions of high turbulence. We gain local precision and efficiency from the stable advection permitted by the vorticity formulation. Moreover, our numerical method straightforwardly solves the two-way coupling problem between the fluids and animated rigid solids. This new approach is validated through numerical comparisons with reference experiments from the computational fluid community. We also show that the visually appealing results obtained in the CG community can be reproduced with increased efficiency and an easier implementation

A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies

International audienceWe present a vortex method for the simulation of the interaction of an incompressible flow with rigid bodies. The method is based on a penalization technique where the system is considered as a single flow, subject to the Navier-Stokes equation with a penalization term that enforces continuity at the solid-fluid interface and rigid motion inside the solid. Level set functions are used to capture interfaces, compute rigid motions inside the solid bodies and model collisions between bodies. A vortex in cell algorithm is built on this method. Numerical comparisons with existing 3D methods on problems of sedimentation and collision of spheres are provided to illustrate the capabilities of the method

Calcul d'interaction fluide-structure par méthode vortex et application à la synthèse d'images

Fluid simulation is a classical problem in numerical analysis and scientific computing. Nowadays it holds a significant place in the computer graphics domain. Those kind of applications are eager of efficient and reliable techniques. My works focus on the development of Lagrangian-Eulerian hybrid methods in a vortex formulation which give good precision and know efficient computation algorithms. Those methods are flexible enough to allow to compute multi-phasic flows as well as fluid-structure interactions. Interfaces between various phases (fluids or solids) are captured by a level set function. I propose a novel method that offers to easily integrate interactions with rigid solids (thanks to a a penalization technique) and deal with collisions. The numerical resultats computed are compared to test cases from the litterature and I offer examples of realistic 3D animations for computer graphics.La simulation de fluides est un problème classique en analyse numérique et en calcul scientifique. Elle prend aujourd'hui une place importante dans le domaine de la synthèse d'images. Ces domaines d'application sont demandeurs de techniques fiables et rapides. Mes travaux concernent le développement de méthodes hybrides Lagrangiennes-Euleriennes en formulation tourbillon, possédant de bonnes propriétés de précision et de rapidité de calcul. Elles sont suffisamment flexibles pour permettre le calcul d'écoulements multi-phasiques et d'interactions fluide-structure. Les interfaces entre les différents milieux sont capturées par une fonction level set. Je propose une nouvelle méthode permettant d'intégrer aisément les interactions avec des solides rigides - par une technique de pénalisation - ainsi que le traitement des collisions. Les résultats obtenus sont validés sur des cas tests, et je propose des exemples d'animations réalistes pour la synthèse d'images

Couplage ossature-peau pour l'animation interactive d'objets déformables

National audienceLa déformation interactive et temps-réel d'objets dans un espace tridimensionnel est un sujet largement étudié dans le domaine de l'animation du fait de ses nombreuses applications, notamment dans les jeux vidéos et la chirurgie assistée par ordinateur. Les contraintes soulevées par le problème sont tout d'abord de travailler sur un modèle de déformations physiquement réalistes aux yeux de l'observateur et précises du point de vue mécanique. Lié à la dynamique ainsi qu'à sa représentation géométrique, l'aspect visuel de l'objet - images affichées sur l'écran - doit lui aussi satisfaire l'utilisateur, c'est-à-dire de minimiser les artefacts visuels induits par la discrétisation des informations au sein de l'ordinateur, autant que faire se peut. La dernière des contraintes est temporelle; en effet, dans les domaines de la réalité virtuelle et de la synthèse d'images, les applications doivent être adaptées aux fréquences optiques et haptiques imposées par l'Homme, elles doivent rendre transparente l'utilisation de l'outil informatique pour immerger l'utilisateur dans un monde virtuel. L'aspect géométrique dans le cadre de l'animation d'objet déformables a été peu développé, dans ce rapport, nous nous pencherons particulièrement sur la résolution de ce problème en proposant une solution de modélisation multi-résolution adaptative d'objets déformables

Calcul d'interaction fluide-structure par méthode vortex et application à la synthèse d'images

Fluid simulation is a classical problem in numerical analysis and scientific computing. Nowadays it holds a significant place in the computer graphics domain. Those kind of applications are eager of efficient and reliable techniques. My works focus on the development of Lagrangian-Eulerian hybrid methods in a vortex formulation which give good precision and know efficient computation algorithms. Those methods are flexible enough to allow to compute multi-phasic flows as well as fluid-structure interactions. Interfaces between various phases (fluids or solids) are captured by a level set function. I propose a novel method that offers to easily integrate interactions with rigid solids (thanks to a a penalization technique) and deal with collisions. The numerical resultats computed are compared to test cases from the litterature and I offer examples of realistic 3D animations for computer graphics.La simulation de fluides est un problème classique en analyse numérique et en calcul scientifique. Elle prend aujourd'hui une place importante dans le domaine de la synthèse d'images. Ces domaines d'application sont demandeurs de techniques fiables et rapides. Mes travaux concernent le développement de méthodes hybrides Lagrangiennes-Euleriennes en formulation tourbillon, possédant de bonnes propriétés de précision et de rapidité de calcul. Elles sont suffisamment flexibles pour permettre le calcul d'écoulements multi-phasiques et d'interactions fluide-structure. Les interfaces entre les différents milieux sont capturées par une fonction level set. Je propose une nouvelle méthode permettant d'intégrer aisément les interactions avec des solides rigides - par une technique de pénalisation - ainsi que le traitement des collisions. Les résultats obtenus sont validés sur des cas tests, et je propose des exemples d'animations réalistes pour la synthèse d'images

A generalized high-order momentum preserving (HOMP) method in the one-fluid model for incompressible two phase flows with high density ratio

Numerical methods for the simulation of two-phase flows based on the common one-fluid model suffer from important transfer of momentum between the two-phases when the density ratio becomes important, such as with common air and water. This problem has been addressed from various numerical frameworks. It principally arises from the hypothesis that the momentum equation can be simplified by subtracting the continuity equation to it. While this approach is correct in a continuous point of view, it however brings numerical errors at the discrete level, from both spatial and temporal points of view, errors that can highly deteriorate the fluids dynamic. Moreover, we have found this problem to be more and more present as the grid is refined. To correct this problem, we propose a High-Order Momentum Preserving (HOMP) method that is, additionally, independent on the interface representation (may it be level set, volume of fluid, etc.). Furthermore, HOMP can be easily implemented in an existing finite volume code. We show that this method permits to efficiently suppress dreadful momentum transfers at the interface on demonstrating examples. We also present how it enhances the quality of two-phase flows computation through the simulation of the dynamic of a breaking wave and the impact of a droplet in a liquid pool. Highlights • A consistent spatial and temporal numerical strategy is used for moment preservation. • A generic formulation makes it suitable for various interface methods in 2D and 3D. • The method drastically reduces spurious momentum transfers across the interface. • Stable and accurate incompressible two phase flows complex simulations are performed. • High-order WENO 5, 3 with RK 2 scheme is employed even with thin interface thickness

A framework for pencil-of-points structurefrom-motion

Abstract. Our goal is to match contour lines between images and to recover structure and motion from those. The main difficulty is that pairs of lines from two images do not induce direct geometric constraint on camera motion. Previous work uses geometric attributes — orientation, length, etc. — for single or groups of lines. Our approach is based on using Pencilof-Points (points on line) or pops for short. There are many advantages to using pops for structure-from-motion. The most important one is that, contrarily to pairs of lines, pairs of pops may constrain camera motion. We give a complete theoretical and practical framework for automatic structurefrom-motion using pops — detection, matching, robust motion estimation, triangulation and bundle adjustment. For wide baseline matching, it has been shown that cross-correlation scores computed on neighbouring patches to the lines gives reliable results, given 2D homographic transformations to compensate for the pose of the patches. When cameras are known, this transformation has a 1-dimensional ambiguity. We show that when cameras are unknown, using pops lead to a 3-dimensional ambiguity, from which it is still possible to reliably compute cross-correlation. We propose linear and non-linear algorithms for estimating the fundamental matrix and for the multiple-view triangulation of pops. Experimental results are provided for simulated and real data.

Geometrical level set reinitialization using closest points method and kink detection for thin filaments, topology changes and two-phase flows

We introduce a robust and high order strategy to perform the reinitialization in a level set framework. The reinitialization by closest-points (RCP) method is based on geometric considerations. It relies on a gradient descent to find the closest points at the interface in order to solve the eikonal equation and thus reinitializing the level set field. Furthermore, a new algorithm, also based on a similar geometric approach, is introduced to detect precisely all the ill-defined points of the level set. These points, also referred to as kinks, can mislead the gradient descent and more widely impact the accuracy of level set methods. This algorithm coupled with the precise computation of the closest points of the interface, permits the novel method to be robust and accurate even when performing the reinitialization every time step after solving the advection equation. Furthermore, they both require very few given parameters with the advantage of being based on a geometrical approach and independent of the application. The proposed method was tested on various benchmarks, and demonstrated equivalent or even better results compared to solving the Hamilton-Jacobi equation

Journal of Computational Physics

We introduce a robust and high order strategy to perform the reinitialization in a level set framework. The reinitialization by closest points (RCP) method is based on geometric considerations. It relies on a gradient descent to find the closest points at the interface in order to solve the Eikonal equation and thus reinitializing the level set field. Furthermore, a new algorithm, also based on a similar geometric approach, is introduced to detect precisely all the ill-defined points of the level set. These points, also referred to as kinks, can mislead the gradient descent and more widely impact the accuracy of level set methods. This algorithm, coupled with the precise computation of the closest points of the interface, permits the novel method to be robust and accurate when performing the reinitialization every time step after solving the advection equation. Furthermore, they both require very few given parameters with the advantage of being based on a geometrical approach and independent of the application. The proposed method was tested on various benchmarks, and demonstrated equivalent or even better results compared to solving the Hamilton-Jacobi equation