Fast Cloth Simulation with Implicit Contact and Exact Coulomb Friction

International audienceCloth 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

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this problem class. Recent numerical methods for nonsmooth dynamical systems subject to unilateral contact and friction illustrate the topicality of this development.Comment: Preprint of Book Chapte

Inverse Elastic Cloth Design with Contact and Friction

Physically based cloth modeling is classically achieved through a trial and error process. The rest (undeformed) configuration of the cloth, often represented as a 2D pattern assembly, is edited geometrically and adjusted iteratively depending on the feedback provided by a static cloth simulator, which predicts the deformed 3D shape under gravity and contacts. Matching a reference 3D shape while keeping the time of the modeling process reasonable is thus difficult , unless the user possesses advanced skills in real cloth tailoring. In contrast, in this paper we investigate a new, inverse strategy for modeling realistic cloth intuitively. Our goal is to take as input a target (deformed) 3D shape, and to interpret this configuration automatically as a stable equilibrium of a cloth simulator, by retrieving the unknown rest shape. In the presence of gravity and frictional contact, such an inverse problem formulates as an ill-posed nonlinear system subject to nonsmooth constraints. To select and compute a plausible solution, we design an iterative two-step solving process. In a first step, contacts are reduced to frictionless bilateral constraints, and starting from an as-flat-as possible pose, a unique rest pose is retrieved using the adjoint method on a regularized energy. The second step modifies this rest pose so as to project bilateral forces onto the admissible Coulomb friction cone, for each contact. We show that our method converges well in most cases towards a plausible rest configuration, and demonstrate practical inversion results on various cloth geometries modeled by an artist

A multi-scale model for coupling strands with shear-dependent liquid

We propose a framework for simulating the complex dynamics of strands interacting with compressible, shear-dependent liquids, such as oil paint, mud, cream, melted chocolate, and pasta sauce. Our framework contains three main components: the strands modeled as discrete rods, the bulk liquid represented as a continuum (material point method), and a reduced-dimensional flow of liquid on the surface of the strands with detailed elastoviscoplastic behavior. These three components are tightly coupled together. To enable discrete strands interacting with continuum-based liquid, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. We also develop an extended constraint-based collision handling method that supports cohesion between strands. Furthermore, we present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We explore a series of challenging scenarios, involving splashing, shaking, and agitating the liquid which causes the strands to stick together and become entangled.This work was supported in part by the National Science Foundation under Grant Nos.: 1717178, 1319483, CAREER-1453101, the Natu- ral Sciences and Engineering Research Council of Canada under Grant No. RGPIN-04360-2014, SoftBank Group, Pixar, Adobe, and SideFX

Super Space Clothoids

Special Issue: SIGGRAPH 2013 ConferenceInternational audienceThin 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 G2-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

Multi-Scale Models to Simulate Interactions between Liquid and Thin Structures

In this dissertation, we introduce a framework for simulating the dynamics between liquid and thin structures, including the effects of buoyancy, drag, capillary cohesion, dripping, and diffusion. After introducing related works, Part I begins with a discussion on the interactions between Newtonian fluid and fabrics. In this discussion, we treat both the fluid and the fabrics as continuum media; thus, the physical model is built from mixture theory. In Part II, we discuss the interactions between Newtonian fluid and hairs. To have more detailed dynamics, we no longer treat the hairs as continuum media. Instead, we treat them as discrete Kirchhoff rods. To deal with the thin layer of liquid that clings to the hairs, we augment each hair strand with a height field representation, through which we introduce a new reduced-dimensional flow model to solve the motion of liquid along the longitudinal direction of each hair. In addition, we develop a faithful model for the hairs' cohesion induced by surface tension, where a penalty force is applied to simulate the collision and cohesion between hairs. To enable the discrete strands interact with continuum-based, shear-dependent liquid, in Part III, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. Accordingly, we extend the reduced-dimensional flow model to simulate liquid with elastoviscoplastic behavior. Furthermore, we use a constraint-based model to replace the penalty-force model to handle contact, which enables an accurate simulation of the frictional and adhesive effects between wet strands. We also present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We demonstrate a wide range of effects, including the challenging animation scenarios involving splashing, wringing, and colliding of wet clothes, as well as flipping of hair, animals shaking, spinning roller brushes from car washes being dunked in water, and intricate hair coalescence effects. For complex liquids, we explore a series of challenging scenarios, including strands interacting with oil paint, mud, cream, melted chocolate, and pasta sauce