Section: New Results
Efficiently animating virtual clay is a challenge, since neither optimisations proposed for solids (and based on a constant topology) nor for fluids (since there is a moving limit surface) are directly applicable. In 2004, we proposed the first real-time model for this material based on a layered approach. Three sub-models respectively handling large-scale deformations, local matter displacements, and surface tension, cooperate over time for providing the desired behaviour. Our model handles an arbitrary number of tools that simultaneously interact with the clay. This makes it usable for direct hand manipulation, which is the last step in Guillaume Dewaele's thesis, defended on december the 7th, 2005  : the user's hand motion is video captured and used to control a virtual hand, serving as a multiple tool for editing the clay.
Adaptive deformation fields
The aim of this research is to develop novel methods for the represention and physical simulation of variations in highly deformable mesh structures for real-time animation (e.g. from the simulation of cloth to virtual surgery) through a level of detail (lod) topological approach. The research currently concentrates on the use of two primary hierarchical data structures, these being the octree and quadtree, for managing the changing multiresolution detail as well as the physical property details of mesh structures such as the likes of cloth during simulation (see Figure 13 ).
One of the primary ideas of this research is to be able to effectively use either data structure not only as a possible multiresolution paradigm for on the fly lod mesh generation during animation but also to integrate such data structures directly within the manipulation and management of the physical properties of the mesh as well. For example, collision detection could also simultaneously be handled directly through the same data structure which manages the current local mesh resolution, thus negating the neccessity of a secondary data structure for such a task.
Highly colliding deformable bodies
We address the question of simulating highly deformable objects in real-time, such as human tissues or cloth. The main problem is to detect and handle multiple (self-)collisions within the bodies. We have developed a new approach for collision detection, based on a pool of "active pairs" of geometric primitives. These pairs are randomly chosen, and they iteratively converge to a local distance minimum or to a pair of colliding elements. Managing the size of the pool allows us to tune the computation time devoted to collision detection. Temporal coherence is obtained by reusing the interesting pairs from one step to another. We have participated to several state-of-the-art reports  ,  .
This year we have focused on the robustness of collision handling in case of highly stiff objects, and come up with a new formulation of the dynamics of stiff elastic bodies. This new approach is based on an equation system which gathers the implicit integration equation and the contact constraints modeled using Lagrange multipliers. The contact constraints take into account the etablised contacts as well as the anticipated collisions computed using continuous collision detection. The contact constraints are actually modeled as inequalities and the problem can be formulated as a generic quadratic programing (QP) problem. We are currently investigating solutions of this QP to meet real-time constraints.
Robust finite elements for deformable solids
We continue a collaboration on surgical simulation with laboratory TIMC through a co-advised Ph.D. thesis. The purpose is to develop new models of finite elements for the interactive physically-based animation of human tissue. A new model of tetrahedron-based finite elements has been proposed  (see fig. 14 ) and compared with other approches  (see fig. 15 ). Its main feature is to remain physically plausible even when large displacements and large deformations occur (see fig. 14 ), while being almost as computationally efficient as a linear finite elements method.
Realistically predicting the shape of hair requires an accurate mechanical model that takes into account the mechanical properties of inextensible, naturally curled hair strands. In the framework of our collaboration with the industrial partner L'Oréal 7.1 , we developped a new physically-based method for predicting natural hairstyles in the presence of gravity and collisions  . The method is based upon a mechanically accurate model for static elastic rods (Kirchhoff model), which accounts for the natural curliness of hair, as well as for hair ellipticity. The equilibrium shape is computed in a stable and easy way by energy minimization. This yields various typical hair configurations that can be observed in the real world, such as ringlets (see Figure 16 ). The method can generate different hair types with very few input parameters and be used to perform virtual hairdressing operations such as wetting, cutting and drying hair. We are currently working on its extension to the dynamic animation of hair in motion.
Efficient high resolution smoke simulation based on vortex filaments
The approach consists in considering fluids in vorticity domain and representing vorticity as 1D filaments (linked particles). This is motivated by the fact that in numerous situations, non-zero vorticity in fluids concentrates in compact features which tend to be curves (e.g. smoke ring, tornado...). This allows for a huge compression of data and calculations. Moreover, these "vortical objects" are directly related to visual features (atomic mushroom, billowing...), which is very interesting in the scope of letting an artist tuning and controling a fluid. The Eulerian aspect yieds high precision on locations and avoids numerical dissipation. Associated to the fact that the background fluid between features has zero-vorticity, it allows as to simulate an open environment in which only curves associated whith turbulent features are stored. Finally, considering 1D-particles (curves) permits a correct account for vortex streching. Since it is very compact (it corresponds to a vectorial description on the current state of the fluid!), it allows efficient calculation and convenient manipulation in a modeler (much like ordinary keyframing and interpolation of geometric curves. Indeed, it is even feasable to store the entire vectorial animation for cheap). This work illustrated in figure 17 has led to a publication at I3D  .