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International audience; We introduce a selected set of protocols inspired from the Soft Matter Physics community in order to validate Computer Graphics simulators of slender elastic structures possibly subject to dry frictional contact. Although these simulators were primarily intended for feature film animation and visual effects, they are more and more used as virtual design tools for predicting the shape and deformation of real objects; hence the need for a careful, quantitative validation. Our tests, experimentally verified, are designed to evaluate carefully the predictability of these simulators on various aspects, such as bending elasticity, bend-twist coupling, and frictional contact. We have passed a number of popular codes of Computer Graphics through our benchmarks by defining a rigorous, consistent, and as fair as possible methodology. Our results show that while some popular simulators for plates/shells and frictional contact fail even on the simplest scenarios, more recent ones, as well as well-known codes for rods, generally perform well and sometimes even better than some reference commercial tools of Mechanical Engineering. To make our validation protocols easily applicable to any simulator, we provide an extensive description of our methodology, and we shall distribute all the necessary model data to be compared against.

Measuring contact friction in soft-bodies usually requires a specialised physics bench and a tedious acquisition protocol. This makes the prospect of a purely non-invasive, video-based measurement technique particularly attractive. Previous works have shown that such a video-based estimation is feasible for material parameters using deep learning, but this has never been applied to the friction estimation problem which results in even more subtle visual variations. Because acquiring a large dataset for this problem is impractical, generating it from simulation is the obvious alternative. However, this requires the use of a frictional contact simulator whose results are not only visually plausible, but physically-correct enough to match observations made at the macroscopic scale. In this paper, which is an extended version of our former work A. H. Rasheed, V. Romero, F. Bertails-Descoubes, S. Wuhrer, J.-S. Franco, and A Lazarus, "Learning to measure the static friction coefficient in cloth contact," in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit., 2020, pp. 9909-9918, we propose to our knowledge the first non-invasive measurement network and adjoining synthetic training dataset for estimating cloth friction at contact, for both cloth-hard body and cloth-cloth contacts. To this end we build a protocol for validating and calibrating a state-of-the-art frictional contact simulator, in order to produce a reliable dataset. We furthermore show that without our careful calibration procedure, the training fails to provide accurate estimation results on real data. We present extensive results on a large acquired test set of several hundred real video sequences of cloth in friction, which validates the proposed protocol and its accuracy.

International audience; Measuring friction coefficients between cloth and an external body is a longstanding issue in mechanical engineering , never yet addressed with a pure vision-based system. The latter offers the prospect of simpler, less invasive friction measurement protocols compared to traditional ones, and can vastly benefit from recent deep learning advances. Such a novel measurement strategy however proves challenging , as no large labelled dataset for cloth contact exists, and creating one would require thousands of physics work-bench measurements with broad coverage of cloth-material pairs. Using synthetic data instead is only possible assuming the availability of a soft-body mechanical simulator with true-to-life friction physics accuracy, yet to be verified. We propose a first vision-based measurement network for friction between cloth and a substrate, using a simple and repeatable video acquisition protocol. We train our network on purely synthetic data generated by a state-of-the-art fric-tional contact simulator, which we carefully calibrate and validate against real experiments under controlled conditions. We show promising results on a large set of contact pairs between real cloth samples and various kinds of sub-strates, with 93.6% of all measurements predicted within 0.1 range of standard physics bench measurements.

International audience; We propose a robust and efficient numerical model to compute stable equilibrium configurations of clamped elastic ribbons featuring arbitrarily curved natural shapes. Our spatial discretization scheme relies on elements characterized by a linear normal curvature and a quadratic geodesic torsion with respect to arc length. Such a high-order discretization allows for a great diversity of kine-matic representations, while guaranteeing the surface of the ribbon to remain perfectly inextensible. Stable equilibria are calculated by minimizing the sum of the gravitational and elastic energies of the ribbon, under a developability constraint. Our algorithm compares favorably to standard shooting and collocation methods, as well as to experiments. It furthermore shows significant differences in behavior compared to numerical models for thin elastic rods, while yielding a substantial speed-up compared to a more general thin elastic shell simula-tor. These results confirm the benefit of designing a special numerical model dedicated to ribbons..

International audience; Projective dynamics was introduced a few years ago as a fast method to yield an approximate yet stable solution to the dynamics of nodal systems subject to stiff internal forces. Previous attempts to include contact forces in that framework considered adding a quadratic penalty energy to the global system, which however broke the simple-constant matrix-structure of the global linear equation, while failing to treat contact in an implicit manner. In this paper we propose a simple yet effective method to integrate in a unified and semi-implicit way contact as well as dry frictional forces into the nested architecture of Projective dynamics. Assuming that contacts apply to nodes only, the key is to split the global matrix into a diagonal and a positive matrix, and use this splitting in the local step so as to make a good prediction of frictional contact forces at next iteration. Each frictional contact force is refined independently in the local step, while the original efficient structure of the global step is left unchanged. We apply our algorithm to cloth simulation and show that contact and dry friction can be captured at a reasonable precision within a few iterations only, hence one order of magnitude faster compared to global implicit contact solvers of the literature.

International audience; Understanding the flow of granular materials is of utmost importance for numerous industrial applications including the manufacturing, storing and transportation of grain assemblies (such as cement, pills, or corn), as well as for natural risk assessing considerations. Discrete Element Modeling (DEM) methods, which explicitly represent grain-grain interactions, allow for highly-tunable and precise simulations, but they suffer from a prohibitive computational cost when attempting to reproduce large scale scenarios. Continuum models have been recently investigated to overcome such scalability issues, but their numerical simulation still poses many challenges. In this work we propose a novel numerical framework for the continuous simulation of dilatable materials with pressure-dependent (Coulomb) yield stress. Relying upon convex optimization tools, we show that such a macroscopic, nonsmooth rheology can be interpreted as the exact analogous of the solid frictional contact problem at the heart of DEM methods, extended to the tensorial space. Combined with a carefully chosen finite-element discretization, this new framework allows us to avoid regularizing the continuum rheology while benefiting from the efficiency of nonsmooth optimization solvers, mainly leveraged by DEM methods so far. Our numerical results successfully compare to analytic solutions on model problems, and we retrieve qualitative flow features commonly observed in reported experiments of the literature.

We propose an inverse strategy for modeling thin elastic shells physically, just from the observation of their geometry. Our algorithm takes as input an arbitrary target mesh, and interprets this configuration automatically as a stable equilibrium of a shell simulator under gravity and frictional contact constraints with a given external object. Unknowns are the natural shape of the shell (i.e., its shape without external forces) and the frictional contact forces at play, while the material properties (mass density, stiffness, friction coefficients) can be freely chosen by the user. Such an inverse problem formulates as an ill-posed nonlinear system subject to conical constraints. To select and compute a plausible solution, our inverse solver proceeds in two steps. In a first step, contacts are reduced to frictionless bilateral constraints and a natural shape is retrieved using the adjoint method. The second step uses this result as an initial guess and adjusts each bilateral force so that it projects onto the admissible Coulomb friction cone, while preserving global equilibrium. To better guide minimization towards the target, these two steps are applied iteratively using a degressive regularization of the shell energy. We validate our approach on simulated examples with reference material parameters, and show that our method still converges well for material parameters lying within a reasonable range around the reference, and even in the case of arbitrary meshes that are not issued from a simulation. We finally demonstrate practical inversion results on complex shell geometries freely modeled by an artist or automatically captured from real objects, such as posed garments or soft accessories.

International audience; Cloth dynamics plays an important role in the visual appearance of moving characters. Properly accounting for contact and friction is of utmost importance to avoid cloth-body and cloth-cloth penetration and to capture typical folding and stick-slip behavior due to dry friction. We present here the first method able to account for cloth contact with exact Coulomb friction, treating both cloth self-contacts and contacts occurring between the cloth and an underlying character. Our key contribution is to observe that for a nodal system like cloth, the frictional contact problem may be formulated based on velocities as primary variables, without having to compute the costly Delassus operator. Then, by reversing the roles classically played by the velocities and the contact impulses, conical complementarity solvers of the literature can be adapted to solve for compatible velocities at nodes. To handle the full complexity of cloth dynamics scenarios, we have extended this base algorithm in two ways: first, towards the accurate treatment of frictional contact at any location of the cloth, through an adaptive node refinement strategy; second, towards the handling of multiple constraints at each node, through the duplication of constrained nodes and the adding of pin constraints between duplicata. Our method allows us to handle the complex cloth-cloth and cloth-body interactions in full-size garments with an unprecedented level of realism compared to former methods, while maintaining reasonable computational timings.

International audience; Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modeling of thin flexible structures such as DNA, hair, or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

Skinning was initially devised for computing the skin of a character deformed through a skeleton; but it is now also commonly used for deforming tight garments at a very cheap cost. However, unlike skin which may easily compress and stretch, tight cloth strongly resists compression: inside bending regions such as the interior of an elbow, cloth does not shrink but instead buckles, causing interesting folds and wrinkles which are completely missed by skinning methods. Our goal is to extend traditional skinning in order to capture such folding patterns automatically, without sacrificing efficiency. The key of our model is to replace the usual skinning formula — derived from, e.g., Linear Blend Skinning or Dual Quaternions — with a complementarity constraint, making an automatic switch between, on the one hand, classical skinning in zones prone to stretching, and on the other hand, a quasi-isometric scheme in zones prone to compression. Moreover, our method provides some useful handles to the user for directing the type of folds created, such as the fold density or the overall shape of a given fold. Our results show that our method can generate similar complexity of folds compared to full cloth simulation, while retaining interactivity of skinning approaches and offering intuitive user control.

Thin elastic filaments in real world such as vine tendrils, hair ringlets or curled ribbons often depict a very smooth, curved shape that low-order rod models --- e.g., segment-based rods --- fail to reproduce accurately and compactly. In this paper, we push forward the investigation of high-order models for thin, inextensible elastic rods by building the dynamics of a G 2 -continuous piecewise 3D clothoid: a smooth space curve with piecewise affine curvature. With the aim of precisely integrating the rod kinematic problem, for which no closed-form solution exists, we introduce a dedicated integration scheme based on power series expansions. It turns out that our algorithm reaches machine precision orders of magnitude faster compared to classical numerical integrators. This property, nicely preserved under simple algebraic and differential operations, allows us to compute all spatial terms of the rod kinematics and dynamics in both an efficient and accurate way. Combined with a semi-implicit time-stepping scheme, our method leads to the efficient and robust simulation of arbitrary curly filaments that exhibit rich, visually pleasing configurations and motion. Our approach was successfully applied to generate various scenarios such as the unwinding of a curled ribbon as well as the aesthetic animation of spiral-like hair or the fascinating growth of twining plants.

Curves are widely used in computer science to describe real-life objects such as slender deformable structures. Using only 3 parameters per element, piecewise helices offer an interesting and compact way of representing digital curves. In this paper, we present a robust and fast algorithm to approximate Bezier curves with G1 piecewise helices. Our approximation algorithm takes a Bezier spline as input along with an integer N and returns a piecewise helix with N elements that closely approximates the input curve. The key idea of our method is to take N+1 evenly distributed points along the curve, together with their tangents, and interpolate these tangents with helices by slightly relaxing the points. Building on previous work, we generalize the proof for Ghosh?s co-helicity condition, which serves us to guarantee the correctness of our algorithm in the general case. Finally, we demonstrate both the efficiency and robustness of our method by successfully applying it to various datasets of increasing complexity, ranging from synthetic curves created by an artist to automatic image-based reconstructions of real data such as hair, heart muscular fibers or magnetic field lines of a star. Highlights? We propose a novel algorithm to fit G1 piecewise helices to spatial curves. ? Our method is based on points relaxation and tangents interpolation. ? We show that our method is fast, precise and scalable to complex input datasets.

International audience; This work deals with the existence and uniqueness of the acceleration and contact forces for Lagrangian systems subject to bilateral and/or unilateral constraints with or without sliding Coulomb’s friction. Sliding friction is known to yield singularities in the system, such as Painlevé’s paradox. Our work aims at providing sufficient conditions on the parameters of the system so that singularities are avoided (i.e., the contact problem is at least solvable). To this end, the frictional problem is treated as a perturbation of the frictionless case. We provide explicit criteria, in the form of calculable upper bounds on the friction coefficients, under which the frictional contact problem is guaranteed to remain well-posed. Complementarity problems, variational inequalities, quadratic programs and inclusions in normal cones are central tools.

International audience; We present a new continuum-based method for the realistic simulation of large-scale free-flowing granular materials. We derive a compact model for the rheology of the material, which accounts for the exact nonsmooth Drucker-Prager yield criterion combined with a varying volume fraction. Thanks to a semi-implicit time-stepping scheme and a careful spatial discretization of our rheology built upon the Material-Point Method, we are able to preserve at each time step the exact coupling between normal and tangential stresses, in a stable way. This contrasts with previous approaches which either regularize or linearize the yield criterion for implicit integration, leading to unrealistic behaviors or visible grid artifacts. Remarkably, our discrete problem turns out to be very similar to the discrete contact problem classically encountered in multibody dynamics, which allows us to leverage robust and efficient nons-mooth solvers from the literature. We validate our method by successfully capturing typical macroscopic features of some classical experiments, such as the discharge of a silo or the collapse of a granular column. Finally, we show that our method can be easily extended to accommodate more complex scenarios including two-way rigid body coupling as well as anisotropic materials.

In this talk I will give an overview of our work on the simulation of fibers and entangled materials, such as hair, with a specific interest for virtual prototyping and computer graphics applications. I will first introduce a family of high-order, reduced models for discretizing Kirchhoff’s equations for thin elastic rods in a both faithful and robust way. Such models are particularly well-suited for simulating inextensible fibers subject to bending and twisting, and featuring an arbitrary curly resting geometry. Then I will show how such models can be coupled to frictional contact using the nonsmooth contact dynamics framework, and I will present a hybrid iterative solver suitable for robustly handling thousands packed fibers at reasonable frame rates. Finally, I will give some insights into the inverse modeling of fibers, consisting in taking an arbitrary curve geometry as input and inferring corresponding geometric and physical parameters of the simulator such that the input geometry corresponds to a stable configuration at equilibrium.

Piecewise clothoids are 2D curves with continuous, piecewise linear curvature. Due to their smoothness properties, they have been extensively used in road design and robot path planning, as well as for the compact representation of hand-drawn curves. In this paper we present the Super-Clothoid model, a new mechanical model that for the first time allows for the computing of the dynamics of an elastic, inextensible piecewise clothoid. We first show that the kinematics of this model can be computed analytically depending on the Fresnel integrals, and precisely evaluated when required. Secondly, the discrete dynamics, naturally emerging from the Lagrange equations of motion, can be robustly and efficiently computed by performing and storing formal computations as far as possible, recoursing to numerical evaluation only when assembling the linear system to be solved at each time step. As a result, simulations turn out to be both interactive and stable, even for large displacements of the rod. Finally, we demonstrate the versatility of our model by handling various boundary conditions for the rod as well as complex external constraints such as frictional contact, and show that our model is perfectly adapted to inverse statics. Compared to lower-order models, the super-clothoid appears as a more natural and aesthetic primitive for bridging the gap between 2D geometric design and physics-based deformation. © 2012 Wiley Periodicals, Inc.

International audience; Dry friction between hair fibers plays a major role in the collective hair dynamic behavior as it accounts for typical nonsmooth features such as stick-slip instabilities. However, due the challenges posed by the modeling of nonsmooth friction, previous mechanical models for hair either neglect friction or use an approximate smooth friction model, thus losing important visual features. In this paper we present a new generic robust solver for capturing Coulomb friction in large assemblies of tightly packed fibers such as hair. Our method is based on an iterative algorithm where each single contact problem is efficiently and robustly solved by introducing a hybrid strategy that combines a new zero-finding formulation of (exact) Coulomb friction together with an analytical solver as a fail-safe. Our global solver turns out to be very robust and highly scalable as it can handle up to a few thousand densely packed fibers subject to tens of thousands frictional contacts at a reasonable computational cost. It can be conveniently combined to any fiber model with various rest shapes, from smooth to curly. Our results, visually validated against real hair motions, depict typical hair collective effects and greatly enhance the realism of standard hair simulators.

International audience; Realistic hair modeling is a fundamental part of creating virtual humans in computer graphics. This paper surveys the state of the art in the major topics of hair modeling: hairstyling, hair simulation, and hair rendering. Because of the difficult, often unsolved, problems that arise in all these areas, a broad diversity of approaches are used, each with strengths that make it appropriate for particular applications. We discuss each of these major topics in turn, presenting the unique challenges facing each area and describing solutions that have been presented over the years to handle these complex issues. Finally, we outline some of the remaining computational challenges in hair modeling.

International audience; Cloth dynamics plays an important role in the visual appearance of moving characters. Properly accounting for frictional contact is of utmost importance to avoid cloth-body penetration and to capture folding behavior due to dry friction. We present here the first method able to account for contact with exact Coulomb friction between a cloth and the underlying character. Our key contribution is to formulate and solve the frictional contact problem merely on velocity variables, by leveraging some tools of convex analysis. Our method is both fast and robust, allowing us to simulate full-size garments with more realistic body-cloth interactions compared to former methods, while maintaining similar computational timings.

International audience; In the latest years, considerable progress has been achieved for accurately acquiring the geometry of human hair, thus largely improving the realism of virtual characters. In parallel, rich physics-based simulators have been successfully designed to capture the intricate dynamics of hair due to contact and friction. However, at the moment there exists no consistent pipeline for converting a given hair geometry into a realistic physics-based hair model. Current approaches simply initialize the hair simulator with the input geometry in the absence of external forces. This results in an undesired sagging effect when the dynamic simulation is started, which basically ruins all the efforts put into the accurate design and/or capture of the input hairstyle. In this paper we propose the first method which consistently and robustly accounts for surrounding forces --- gravity and frictional contacts, including hair self-contacts --- when converting a geometric hairstyle into a physics-based hair model. Taking an arbitrary hair geometry as input together with a corresponding body mesh, we interpret the hair shape as a static equilibrium configuration of a hair simulator, in the presence of gravity as well as hair-body and hair-hair frictional contacts. Assuming that hair parameters are homogeneous and lie in a plausible range of physical values, we show that this large underdetermined inverse problem can be formulated as a well-posed constrained optimization problem, which can be solved robustly and efficiently by leveraging the frictional contact solver of the direct hair simulator. Our method was successfully applied to the animation of various hair geometries, ranging from synthetic hairstyles manually designed by an artist to the most recent human hair data automatically reconstructed from capture.

1D deformable structures, often called strands, are ubiquitous in the real world. They range from plants (grass, lianas, stalks) to creatures organs (hair, tail, tentacles) and manufactured objects (cables, ropes). The realistic modeling and animation of such objects is essential for representing convincing virtual environments. Most often, the design pipeline is split in two distinct parts: the geometry creation process itself, namely geometric design, followed by the computation of motion, namely animation. For the sake of flexibility and control, the geometric design generally relies on a pure geometric process that allows the user to interactively edit curve primitives such as splines. In contrast, the animation of strands is often considered as a passive and complex phenomenon that can be realistically captured using physics-based simulation.

International audience; We focus on the challenging problem of simulating thin elastic rods in contact, in the presence of friction. Most previous approaches in computer graphics rely on a linear complementarity formulation for handling contact in a stable way, and approximate Coulombs's friction law for making the problem tractable. In contrast, following the seminal work by Alart and Curnier in contact mechanics, we simultaneously model contact and exact Coulomb friction as a zero finding problem of a nonsmooth function. A semi-implicit time-stepping scheme is then employed to discretize the dynamics of rods constrained by frictional contact: this leads to a set of linear equations subject to an equality constraint involving a non-differentiable function. To solve this one-step problem we introduce a simple and practical nonsmooth Newton algorithm, which proves to be reasonably efficient and robust for systems that are not over-constrained. We show that our method is able to finely capture the subtle effects that occur when thin elastic rods with various geometries enter into contact, such as stick-slip instabilities in free configurations, entangling curls, resting contacts in braid-like structures, or the formation of tight knots under large constraints. Our method can be viewed as a first step towards the accurate modeling of dynamic fibrous materials.

International audience; Thin elastic rods such as cables, phone coils, tree branches, or hair, are common objects in the real world but computing their dynamics accurately remains challenging. The recent Super-Helix model, based on the discrete equations of Kirchhoff for a piecewise helical rod, is one of the most promising models for simulating non-stretchable rods that can bend and twist. However, this model suffers from a complexity at least quadratic in the number of discrete elements, which, in the context of interactive applications, makes it limited to a few number of degrees of freedom - or equivalently to a low number of variations in curvature along the mean curve. This paper proposes a new, recursive scheme for the dynamics of a Super-Helix, inspired by the popular algorithm of Featherstone for serial multibody chains. Similarly to Featherstone's algorithm, we exploit the recursive kinematics of a Super-Helix to propagate elements inertias from the free end to the clamped end of the rod, while the dynamics is solved within a second pass traversing the rod in the reverse way. Besides the gain in linear complexity, which allows us to simulate a rod of complex shape much faster than the original approach, our algorithm makes it straightforward to simulate tree-like structures of Super-Helices, which turns out to be particularly useful for animating trees and plants realistically, under large displacements.

The last five years have seen a profusion of innovative solutions to one of the most challenging tasks in character synthesis: hair simulation. This class covers both recent and novel research ideas in hair animation and rendering, and presents time tested industrial practices that resulted in spectacular imagery.The course is aimed at an intermediate level and addresses the special-effects developers and technical directors who are looking for innovation as well as proven methodologies in hair simulation. The audience will get a good grasp of the state of the art in hair simulation and will have plenty of working solutions that they can readily implement in their production pipelines. The course will also be a bootcamp for aspiring computer graphics researchers interested in physically based modeling in computer graphics.The class addresses the special-effects developers and technical directors who are looking for innovation as well as proven methodologies in hair simulation. The audience will get a good grasp of the state of the art in hair simulation and will have plenty of working solutions that they can readily implement in their production pipelines. The class will also be a boot-camp for aspiring computer graphics researchers interested in physically based modeling.The class covers two crucial tasks in hair simulation: animation and rendering. For hair animation, we first discuss recent successful models for simulating the dynamics of individual hair strands, before presenting viable solutions for complex hair-hair and hair-body interactions. For rendering, we address issues related to shading models, multiple scattering, and volumetric shadows. We finally demonstrate how hair simulation techniques are nowadays developed and applied in the feature films industry to produce outstanding visual effects.

Award: Best Course Notes for a New Course.; International audience; The last six years has seen a renaissance in hair modeling, rendering and animation. This course covers the gamut of hair simulation problems and present working solutions, from recent and novel research ideas to time tested industrial practices that resulted in spectacular imagery. The course is aimed at an intermediate level and addresses the special-effects developers and technical directors who are looking for innovation as well as proven methodologies in hair simulation. The audience will get a good grasp of the state of the art in hair simulation and will have plenty of working solutions that they can readily implement in their production pipelines. The course will also be a bootcamp for aspiring computer graphics researchers interested in physically based modeling in computer graphics. The course reviews all the three main tasks in hair simulation: hairstyling, hair animation and hair rendering. First, the nature of human hair will be shortly discussed, to point out why modeling this material has been such a challenge for Computer Graphics. The basics for coping with the hair complexity oin terms of the number of strands will be given. Subsequently, the latest methodologies pertaining to each of the tasks will be covered. For hair dynamics, we will cover an elaborate as well as viable stiffness dynamics model of an individual hair strand. We will present two novel models for complex hair-hair, hair-body and hair-air interactions. For rendering, we discuss issues related to shading models, multiple scattering, and volumetric shadows. We also present the recent advances in programmable graphics hardware in the context of hair rendering. Advanced techniques in production quality hair rendering, self shadowing and lighting models for short and long hair will also be presented.

International audience; This paper explores a sketch-based interface for quickly yet accurately creating visually realistic hair for virtual characters. Recently, physically-based models have proved successful for generating a wide variety of hair types, but they do not provide a straightforward method for designing target hairstyles. The contribution of this paper is to propose a user-friendly method for controlling such a physically-based model, requiring no specific knowledge of mechanics or hair styling: the user sketches example hair strands over a side view of the character's head, or alternatively annotates a picture of real hair viewed from the side serving as a reference. We show how the sketch can be used to infer the geometric and mechanical properties of the hair strands, to adjust the shape of the scalp, and to generate an adequate hair volume. Our method is validated on a wide variety of hair styles, from straight to curly and short to long hair.

International audience; Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new variational approach which allows robust and accurate solution on relatively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling between fluid and arbitrary solid simulations that always gives a well-posed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the framework with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.

Simulating human hair is recognized as one of the most difficult tasks in computer animation. In this paper, we show that the Kirchhoff equations for dynamic, inextensible elastic rods can be used for accurately predicting hair motion. These equations fully account for the nonlinear behavior of hair strands with respect to bending and twisting. We introduce a novel deformable model for solving them: each strand is represented by aSuper-Helix, i.e., a piecewise helical rod which is animated using the principles of Lagrangian mechanics. This results in a realistic and stable simulation, allowing large time steps. Our second contribution is an in-depth validation of the Super-Helix model, carried out through a series of experiments based on the comparison of real and simulated hair motions. We show that our model efficiently handles a wide range of hair types with a high level of realism.

National audience; This paper presents 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. As our results show, the method can generate different hair types with a very few input parameters, and perform virtual hairdressing operations such as wetting, cutting and drying hair.; Nous présentons une nouvelle approche physique permettant de simuler la forme d'une chevelure naturelle à partir des propriétés physiques, structurelles et ethniques caractérisant les cheveux d'une personne. Notre méthode se base sur le modèle mécanique de Kirchhoff pour les tiges élastiques, afin de prendre précisément en compte la frisure naturelle d'un cheveu, ainsi que la géométrie elliptique de sa section. La forme à l'équilibre d'un cheveu est calculée de manière stable et efficace par la minimisation de son énergie potentielle. Cette technique, étendue à l'échelle de la mèche, nous permet de générer diverses configurations typiques telles que les boucles anglaises. La méthode permet de prédire la forme au naturel d'une chevelure, quel que soit le type ethnique d'origine, et offre à l'utilisateur la possibilité de réaliser virtuellement des opérations de coiffure classiques telles le mouillage, la coupe et le séchage.

Preprint for an article submitted with Journal of Fluid Mechanics latex template, In this paper, transient granular flows are examined both numerically and experimentally. Simulations are performed using the 3D nonsmooth numerical granular model introduced in Daviet & Bertails-Descoubes (2016), which represents the granular medium as an inelastic and dilatable continuum subject to the Drucker-Prager yield criterion in the dense regime. One feature of this numerical model is to resolve such a nonsmooth rheology without any regularisation, by leveraging tools from nonsmooth optimisation. We show that this nonsmooth simulator, which relies on a constant friction coefficient, is able to reproduce with high fidelity various experimental granular collapses over inclined erodible beds, provided the friction coefficient is set to the avalanche angle - and not to the stop angle, as generally done. Our results, obtained for two different granular materials and for bed inclinations ranging from 0° to 20°, suggest that a simple constant friction rheology choice remains reasonable for capturing a large variety of granular collapses up to aspect ratios in the order of 10. We further investigate the precise role of the frictional walls by performing experimental and simulated collapses with various channel widths. We find out that, unlike some assumptions formerly made in the literature, the channel width has lower influence on the granular flow. Finally, we extend the constant coefficient model with an hysteretic model, thereby improving the predictions of the early-stage dynamics of the collapse. This illustrates the potential effects of such phenomenology on transient flows, paving the way to more elaborate analysis.

This thesis deals with the direct simulation and inverse design of garments in the presence of frictional contact.The shape of draped garments results from the slenderness of the fabric, which can be represented in mechanics by a thin elastic plate or shell, and from its interaction with the body through dry friction. This interaction, necessary to reproduce the threshold friction occuring in such contacts, is described by a non smooth law, which, in general, makes its integration complex. In a first contribution, we modify the so-called Projective Dynamics algorithm to incorporate this dry frictional contact law in a simple way. Projective Dynamics is a popular method in Computer Graphics that quickly simulates deformable objects such as plates with moderate accuracy, yet without including frictional contact. The rationale of this algorithm is to solve the integration of the dynamics by successively calculating estimates of the shape of the object at the next timestep. We take up the same idea to incorporate a procedure for estimating the frictional contact law that robustly captures the threshold phenomenon. In addition it is interesting to note that simulators developed in Computer Graphics, originally targeted at visual animation, have become increasingly accurate over the years. They are now being used in more "critical" applications such as architecture, robotics or medicine, which are more demanding in terms of accuracy. In collaboration with mechanicists and experimental physicists, we introduce into the Computer Graphics community protocols to verify the correctness of simulators, and we present in this manuscript our contributions related to plate and shell simulators. Finally, in a last part, we focus on garment inverse design. The interest of this process is twofold. Firstly, for simulations, solving the inverse problem provides a "force-free" and possibly curved version of the input (called the rest or natural shape), whether it comes from a 3D design or a 3D capture, that allows to start the simulation with the input as the initial deformed shape. To this end, we propose an algorithm for the inverse design of clothes represented by thin shells that also accounts for dry frictional contact. Within our framework, the input shape is considered to be a mechanical equilibrium subject to gravity and contact forces. Then our algorithm computes a rest shape such that this input shape can be simulated without any sagging. Secondly, it is also appealing to use these rest shapes for a real life application to manufacture the designed garments without sagging. However, the traditional cloth fabrication process is based on patterns, that is sets of flat panels sewn together. In this regard, we present in our more prospective part our results on the adaptation of the previous algorithm to include geometric constraints, namely surface developability, in order to get flattenable rest shapes.; Cette thèse porte sur la simulation directe et la conception inverse de vêtements en présence de contact frottant. La forme de vêtements portés résulte en effet à la fois de la minceur du tissu, représentable en mécanique par une plaque ou une coque mince et élastique, et de son interaction avec le corps à travers un phénomène de contact frottant solide. Cette interaction, nécessaire pour reproduire le frottement à seuil typique des interactions entre solides, est décrite par une loi non régulière, ce qui rend son intégration généralement complexe. Dans une première contribution, nous modifions l'algorithme Projective Dynamics afin d'y introduire simplement cette loi de contact frottant. Projective Dynamics est une méthode populaire en Informatique Graphique qui simule rapidement avec une précision modérée des objets déformables tels que les plaques, mais sans inclure de contact frottant. L'idée principale de cet algorithme est de résoudre l'intégration de la dynamique en calculant successivement des estimations de la forme de l'objet au pas de temps suivant. Nous reprenons la même idée afin d'y incorporer une procédure d'estimation de la loi de contact frottant qui parvient de manière robuste à capturer le phénomène de seuil.Par ailleurs, il est intéressant de noter que les simulateurs développés en Informatique Graphique, dédiés à l'origine à l'animation, sont devenus de plus en plus précis au fil des ans. Ils sont maintenant sollicités dans des applications plus "critiques" telles que l'architecture, la robotique ou la médecine plus exigeantes en terme de justesse. Dans une collaboration avec des mécaniciens et des physiciens expérimentateurs, nous introduisons de nouveaux protocoles de validation des simulateurs graphiques et nous présentons dans ce manuscrit nos contributions relatives aux simulateurs de plaques et de coques.Enfin, dans une dernière partie, nous nous intéressons à la conception inverse de vêtements. L'intérêt de ce procédé est double. En premier lieu, pour des simulations, résoudre le problème inverse fournit une version "sans force" et possiblement courbée de l'entrée (dite naturelle ou au repos), que celle-ci provienne d'un modèle 3D ou d'une capture 3D, qui permet d'initier la simulation avec la forme de l'entrée en tant que forme déformée initiale. En ce sens, nous proposons un algorithme pour la conception inverse de coques en présence de contact frottant. Dans notre cadre, la forme donnée en entrée est considérée comme un équilibre mécanique soumis à la gravité et aux forces de contact. Notre algorithme calcule ensuite une forme au repos telle que l'entrée puisse être simulée sans qu'elle ne s'affaisse. En second lieu, il est aussi tentant de vouloir utiliser ces formes naturelles pour une application concrète afin de confectionner lesdits vêtements sans qu'ils ne s'affaissent. Cependant, le processus classique de fabrication de vêtements est basé sur l'usage de patrons, c'est-à-dire d'ensembles de panneaux plats à coudre ensemble. Nous présentons donc dans une partie finale plus prospective nos résultats sur l'adaptation de notre algorithme précédent afin d'y incorporer des contraintes géométriques, en l'occurrence la développabilité des surfaces, afin d'obtenir des formes au repos aplatissables.

Inverse problems arise in various physical domains and solving them from real-world visual observations poses a significant challenge due to the high dimensional nature of the data. Furthermore gathering enough observations that a data driven model can accurately capture the complete distribution of a physical phenomenon is often intractable. In this work we use deep learning to solve inverse problems by applying two basic principles. Deep learning models can be trained using synthetic data generated from physics based simulations. And the employed simulator itself needs to be verified for physical accuracy thus allowing the model to learn the exact physical phenomenon that is desired.To validate the simulator, we introduce rich and compact physical protocols, originally proposed in soft matter physics literature to measure physical parameters. These protocols can be easily replicated in a simulator to test the physical correctness of the model, and the validity of the simulator.We solve the inverse measurement problem of estimating contact friction in soft-bodies which otherwise requires a specialized physics bench and entails tedious acquisition protocols. This makes the prospect of a purely non-invasive, video-based measurement technique particularly attractive. Previous works have shown that such a video-based estimation is feasible for material parameters using deep learning, but this has never been applied to the friction estimation problem which results in even more subtle visual variations. Since acquiring a large dataset for this problem is impractical, we generate it using a frictional contact simulator. As the simulator has been calibrated and verified using controlled experiments, the results are not only visually plausible, but physically-correct enough to match observations made at the macroscopic scale. We propose to our knowledge the first non-invasive measurement network and adjoining synthetic training dataset for estimating cloth friction at contact, for both cloth-hard body and cloth-cloth contacts. We also acquire an extensive dataset of real world experiments for testing. Both the training and test datasets have been made freely available to the community.We also utilize the same protocol for solving the inverse measurement problem of estimating the deformed curvature of a suspended Kirchhoff rod. In order to do such estimation on physical rods, we utilize a deep learning model to visually predict a curvature field from a suspended rod. As creating a dataset from physical rods (even if synthetically constructed), that faithfully covers a representative manifold of deformed curvatures is intractable, we rely on generating such a dataset from a verified simulator. Our work shows a promising way forward for utilizing deep learning models as part of an inversion measurement pipeline.; Des problèmes inverses surviennent dans divers domaines physiques et les résoudre à partir d'observations visuelles du monde réel pose un défi important en raison de la nature hautement dimensionnelle des données. De plus, rassembler suffisamment d'observations pour qu'un modèle basé sur les données puisse capturer avec précision la distribution complète d'un phénomène physique est souvent insoluble. Dans ce travail, nous utilisons l'apprentissage profond pour résoudre des problèmes inverses en appliquant deux principes de base. Les modèles d'apprentissage profond peuvent être entraînés à l'aide de données synthétiques générées à partir de simulations basées sur la physique. Et la précision physique du simulateur employé, lui-même, doit être vérifiée, permettant ainsi au modèle d'apprendre le phénomène physique exact souhaité.Afin de valider le simulateur, nous introduisons des protocoles physiques riches et compacts, proposés à l'origine dans la littérature de physique de la matière molle pour mesurer des paramètres physiques. Ces protocoles peuvent être facilement répliqués dans un simulateur pour tester l'exactitude physique du modèle et la validité du simulateur.Nous résolvons le problème de mesure inverse de l'estimation du frottement de contact dans les corps mous qui nécessite sinon un banc de physique spécialisé et un protocole d'acquisition fastidieux. Cela rend la perspective d'une technique de mesure purement non invasive basée sur la vidéo particulièrement attrayante. Des travaux antérieurs ont montré qu'une telle estimation basée sur la vidéo est réalisable pour les paramètres de matériaux en utilisant l'apprentissage profond, mais cela n'a jamais été appliqué au problème d'estimation de la friction qui entraîne des variations visuelles encore plus subtiles. Étant donné qu'il n'est pas pratique d'acquérir un grand ensemble de données pour ce problème, nous le générons à l'aide d'un simulateur de contact frictionnel. Comme le simulateur a été calibré et vérifié à l'aide d'expériences contrôlées, les résultats sont non seulement visuellement plausibles, mais suffisamment corrects physiquement pour correspondre aux observations faites à l'échelle macroscopique. Nous proposons à notre connaissance le premier réseau de mesure non invasif et un jeu de données d'entraînement synthétique adjacent pour estimer le frottement du tissu au contact, à la fois pour les contacts tissu-corps dur et tissu-tissu. Nous acquérons également un vaste ensemble de données d'expériences du monde réel pour les tests. Les ensembles de données de formation et de test ont été mis gratuitement à la disposition de la communauté.Nous utilisons également le même protocole pour résoudre le problème de mesure inverse de l'estimation de la courbure déformée d'une tige de Kirchhoff suspendue. Afin de faire une telle estimation sur des tiges physiques, nous utilisons un modèle d'apprentissage profond pour prédire visuellement un champ de courbure à partir d'une tige suspendue. Comme la création d'un ensemble de données à partir de tiges physiques (même si elles sont synthétiquement construites), qui couvre fidèlement une variété représentative de courbures déformées est insoluble, nous comptons sur la génération d'un tel ensemble de données à partir d'un simulateur vérifié. Notre travail montre une voie prometteuse pour l'utilisation de modèles d'apprentissage profond dans le cadre d'un pipeline de mesure d'inversion.

Ribbons are a thin structure intermediate between rods and shells. They are used to model a wide range of real objects at various scales. For example, at the nanoscopic scale we find proteins or DNA molecules that can be represented by ribbons. At the mesoscopic scale we find strips of fabric or paper. And at the macroscopic scale, ribbons are becoming popular in architecture, for example to build deployable structures. While many numerical models have been developed in the last decades for rods and plates, very few are specific to ribbons. In this thesis, we propose a robust and efficient numerical model to calculate the stable equilibrium states of a naturally flat or curved ribbon. Our contribution can be divided into three parts.First, the establishment of the numerical model relies on the analytic description of van der Heijden and Audoly. The spatial discretization is based on elements with linear normal curvature and quadratic geodesic torsion in the curvilinear abscissa, which allows a great richness of kinematic representations while guaranteeing the perfect inextensibility of the ribbon. The stable equilibria are calculated by minimizing the gravitational and elastic energies of the ribbon according to the Sadowsky or Wunderlich formulation, under developability constraints. The ribbon can be clamped at one or both of its extremities. Also, the contact is managed between the ribbon and one or more planes.In a second contribution, we compare our ribbon model to the super-clothoid rod model and the Naghdi shell model. Being more general, the shell model gives the same equilibria as our model. However, being non-specific, the shell model takes several minutes a given equilibrium, compared to the few seconds needed for our model. We thus validate the latter, while showing its effectiveness. However, the rod model with a flat cross-section does not reach the same equilibria, showing the usefulness of a ribbon model.Finally, we carry out a series of experiments, in particular the calculation of a heavy Moebius ribbon placed on a table, Benoît Roman's experiment consisting in constraining a ribbon between two plates, and a lateral buckling experiment. This finally leads us to discuss the limits of our reduced model, both in terms of the continuous equations on which it is based, and their discretization., Les rubans constituent une structure mince intermédiaire entre les tiges et les coques. Ils servent à modéliser une large gamme d'objets réels à diverses échelles. Par exemple, à l'échelle nanoscopique on retrouve les protéines ou molécules d'ADN qui peuvent être représentées par des rubans. À l'échelle mésoscopique on retrouve les bandes de tissu ou de papier. Et à l'échelle macroscopique les rubans deviennent populaires en architecture, servant par exemple à réaliser des structures déployables. Si de nombreux modèles numériques ont été développés ces dernières décennies pour les tiges et les plaques, il en existe en revanche très peu qui soient spécifiques aux rubans. Dans cette thèse, nous proposons un modèle numérique robuste et efficace pour calculer les états d'équilibre stables d'un ruban naturellement plat ou courbé. Notre contribution se décompose en trois axes.Premièrement, l'établissement du modèle numérique s'appuie sur la description analytique de van der Heijden et Audoly. La discrétisation spatiale se base sur des éléments à courbure normale linéaire et torsion géodésique quadratique en l'abscisse curviligne, qui permettent une grande richesse de représentation cinématique tout en garantissant l'inextensibilité parfaite du ruban. Les équilibres stables sont calculés par minimisation des énergies de gravité et d'élasticité du ruban selon la formulation de Sadowsky ou de Wunderlich, sous contrainte de développabilité. Le ruban peut être encastré par une ou deux de ses extrémités. Aussi, le contact est géré entre le ruban et un ou plusieurs plans.Dans une seconde contribution, nous comparons notre modèle de ruban au modèle de tige des super-clothoïdes et au modèle de coques de Naghdi. Étant plus général, le modèle de coque donne les mêmes équilibres que ceux de notre modèle. Cependant, étant non spécifique, le modèle de coque prend plusieurs minutes pour converger vers l'équilibre, à comparer aux quelques secondes nécessaires à notre modèle. On valide ainsi ce dernier, tout en montrant son efficacité. De son côté, le modèle de tige avec une section plate ne parvient pas aux même résultats, montrant l'utilité d'un modèle de rubans.Enfin nous menons une série d'expériences, en particulier le calcul d'un ruban de Moebius pesant que l'on pose sur une table, l'expérience de Benoît Roman consistant à écraser un ruban entre deux plaques et une expérience de déversement latéral. Cela nous conduit finalement à discuter les limites de notre modèle réduit, tant au niveau des équations continues dont il s'inspire, que de leur discrétisation.