Category: Rods

Menglei Chai, Changxi Zheng, Kun Zhou

Realistic hair animation is a crucial component in depicting virtual characters in interactive applications. While much progress has been made in high-quality hair simulation, the overwhelming computation cost hinders similar fidelity in realtime simulations. To bridge this gap, we propose a data-driven solution. Building upon precomputed simulation data, our approach constructs a reduced model to optimally represent hair motion characteristics with a small number of guide hairs and the corresponding interpolation relationships. At runtime, utilizing such a reduced model, we only simulate guide hairs that capture the general hair motion and interpolate all rest strands. We further propose a hair correction method that corrects the resulting hair motion with a position-based model to resolve hair collisions and thus captures motion details. Our hair simulation method enables a simulation of a full head of hairs with over 150K strands in realtime. We demonstrate the efficacy and robustness of our method with various hairstyles and driven motions (e.g., head movement and wind force), and compared against full simulation results that does not appear in the training data.

A Reduced Model for Interactive Hairs

Alexandre Derouet-Jourdan, Florence Bertails-Descoubes, Gilles Daviet, Joelle Thollot

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 and robust 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 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 robustly and efficiently solved 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 reconstructed from capture.

Inverse Dynamic Hair Modeling with Frictional Contact

Matthias Mueller, Tae-Young Kim, Nuttapong Chentanez

In this short paper we focus on the fast simulation of hair and fur on animated characters. While it is common in films to simulate single hair strands on virtual humans and on furry animals, those features are either not present on characters in computer games or modeled with simplified textured meshes. The main difficulty of simulating hair in real time applications is the sheer number of hair strands and the fact that each hair is inextensible. Keeping thousands of deformable objects from being stretched is computationally expensive. In this paper, we present a robust method for simulating hair and fur that guarantees inextensiblity with a single iteration per frame. For an iteration count this low, existing methods either become unstable or introduce a substantial amount of stretching. Our method is geometric in nature and able to simulate thousands of inextensible hair strands in real time.

Fast Simulation of Inextensible Hair and Fur

Hayley Iben, Mark Meyer, Lena Petrovic, Olivier Soares, John Anderson, Andrew Witkin

We present a novel method for stably simulating stylized curly hair that addresses artistic needs and performance demands, both found in the production of feature films. To satisfy the artistic requirement of maintaining the curl’s helical shape during motion, we propose a hair model based upon an extensible elastic rod. We introduce a novel method for stably computing a frame along the hair curve, essential for stable simulation of curly hair. Our hair model introduces a novel spring for controlling the bending of the curl and another for maintaining the helical shape during extension. We also address performance concerns often associated with handling hair-hair contact interactions by efficiently parallelizing the simulation. To do so, we present a novel algorithm for pruning both hair-hair contact pairs and hair particles. Our method is in use on a full length feature film and has proven to be robust and stable over a wide range of animated motion and on a variety of hair styles, from straight to wavy to curly.

Artistic Simulation of Curly Hair

Florence Bertails-Descoubes

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.

Super-Clothoids

A significant challenge in applications of computer animation is the simulation of ropes, cables, and other highly constrained strand-like physical curves. Such scenarios occur frequently, for instance, when a strand wraps around rigid bodies or passes through narrow sheaths. Purely Lagrangian methods designed for less constrained applications such as hair simulation suffer from difficulties in these important cases. To overcome this, we introduce a new framework that combines Lagrangian and Eulerian approaches. The two key contributions are the reduced node, whose degrees of freedom precisely match the constraint, and the Eulerian node, which allows constraint handling that is independent of the initial discretization of the strand. The resulting system generates robust, efficient, and accurate simulations of massively constrained systems of rigid bodies and strands.

Large-Scale Dynamic Simulation of Highly Constrained Strands

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 discretizethe 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.

A Nonsmooth Newton Solver for Capturing Exact Coulomb Friction in Fiber Assemblies