Stable Constrained Dynamics

International audienceWe present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers

Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail

International audienceWe present a new framework for artist driven level of detail in solid simulations. Simulated objects are simultaneously embedded in several, separately designed deformation models with their own independent degrees of freedom. The models are ordered to apply their deformations hierarchically, and we enforce the uniqueness of the dynamics solutions using a novel kinetic filtering operator designed to ensure that each child only adds detail motion to its parent without introducing redundancies. This new approach allows artists to easily add fine-scale details without introducing unnecessary degrees-of-freedom to the simulation or resorting to complex geometric operations like anisotropic volume meshing. We illustrate the utility of our approach with several detail enriched simulation examples

Animating Shapes at Arbitrary Resolution with Non-Uniform Stiffness

International audienceWe present a new method for physically animating deformable shapes using finite element models (FEM). Contrary to commonly used methods based on tetrahedra, our finite elements are the bounding voxels of a given shape at arbitrary resolution. This alleviates the complexities and limitations of tetrahedral volume meshing and results in regular, well-conditionned meshes. We show how to build the voxels and how to set the masses and stiffnesses in order to model the physical properties as accurately as possible at any given resolution. Additionally, we extend a fast and robust tetrahedron-FEM approach to the case of hexahedral elements. This permits simulation of arbitrarily complex shapes at interactive rates in a manner that takes into account the distribution of material within the elements

Efficient, Physically Plausible Finite Elements

International audienceThis paper discusses FEM-based simulations of soft bodies in terms of speed and robustness. To be physically plausible, three fundamental laws must be respected: rotational invariance, Newton's law and Euler's law. We show that precomputed strain-displacement matrices generate nonphysical torques which can lead to visual artifacts. We then derive the fastest FEM-based method meeting our criteria of plausibility and robustness and discuss their limitations

6D Frictional Contact for Rigid Bodies

International audienceWe present a new approach to modeling contact between rigid objects that augments an individual Coulomb friction point-contact model with rolling and spinning friction constraints. Starting from the intersection volume, we compute a contact normal from the volume gradient. We compute a contact position from the first moment of the intersection volume, and approximate the extent of the contact patch from the second moment of the intersection volume. By incorporating knowledge of the contact patch into a point contact Coulomb friction formulation, we produce a 6D constraint that provides appropriate limits on torques to accommodate displacement of the center of pressure within the contact patch, while also providing a rotational torque due to dry friction to resist spinning. A collection of examples demonstrate the power and benefits of this simple formulation

Seamless Adaptivity of Elastic Models

International audienceA new adaptive model for viscoelastic solids is presented. Unlike previous approaches, it allows seamless transitions, and simplifications in deformed states. The deformation field is generated by a set of physically animated frames. Starting from a fine set of frames and mechanical energy integration points, the model can be coarsened by attaching frames to others, and merging integration points. Since frames can be attached in arbitrary relative positions, simplifications can occur seamlessly in deformed states, without returning to the original shape, which can be recovered later after refinement. We propose a new class of velocity-based simplification criterion based on relative velocities. Integration points can be merged to reduce the computation time even more, and we show how to maintain constant elastic forces through the levels of detail. This meshless adaptivity allows significant improvements of computation time

Biomechanical Morphing for Personalized Fitting of Scoliotic Torso Skeleton Models

The use of patient-specific biomechanical models offers many opportunities in the treatment of adolescent idiopathic scoliosis, such as the design of personalized braces. The first step in the development of these patient-specific models is to fit the geometry of the torso skeleton to the patient’s anatomy. However, existing methods rely on high-quality imaging data. The exposure to radiation of these methods limits their applicability for regular monitoring of patients. We present a method to fit personalized models of the torso skeleton that takes as input biplanar low-dose radiographs. The method morphs a template to fit annotated points on visible portions of the spine, and it relies on a default biomechanical model of the torso for regularization and robust fitting of hardly visible parts of the torso skeleton, such as the rib cage. The proposed method provides an accurate and robust solution to obtain personalized models of the torso skeleton, which can be adopted as part of regular management of scoliosis patients. We have evaluated the method on ten young patients who participated in our study. We have analyzed and compared clinical metrics on the spine and the full torso skeleton, and we have found that the accuracy of the method is at least comparable to other methods that require more demanding imaging methods, while it offers superior robustness to artifacts such as interpenetration of ribs. Normal-dose X-rays were available for one of the patients, and for the other nine we acquired low-dose X-rays, allowing us to validate that the accuracy of the method persisted under less invasive imaging modalities

Preserving Topology and Elasticity for Embedded Deformable Models

International audienceIn this paper we introduce a new approach for the embedding of linear elastic deformable models. Our technique results in significant improvements in the efficient physically based simulation of highly detailed objects. First, our embedding takes into account topological details, that is, disconnected parts that fall into the same coarse element are simulated independently. Second, we account for the varying material properties by computing stiffness and interpolation functions for coarse elements which accurately approximate the behaviour of the embedded material. Finally, we also take into account empty space in the coarse embeddings, which provides a better simulation of the boundary. The result is a straightforward approach to simulating complex deformable models with the ease and speed associated with a coarse regular embedding, and with a quality of detail that would only be possible at much finer resolution

Détection en temps réel d'auto-collisions sur des objets hautement déformables

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Modèle déformable par éléments finis - Elasticité linéaire et grands déplacements

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