Physics-Based Animation

Hongyi Xu, Jernej Barbič

To date, material modeling in physically based computer animation has largely focused on mass and stiffness material properties. However, deformation dynamics is largely affected also by the damping properties. In this paper, we propose an interactive design method for nonlinear isotropic and anisotropic damping of complex three-dimensional solids simulated using the Finite Element Method (FEM). We first give a damping design method and interface whereby the user can set the damping properties so that motion aligned with each of a few chosen example deformations is damped by an independently prescribed amount, whereas the rest of the deformation space follows standard Rayleigh damping, or any viscous damping. Next, we demonstrate how to design nonlinear damping that depends on the magnitude of the deformation along each example deformation, by editing a single spline curve for each example deformation. Our user interface enables an art-directed and intuitive approach to controlling damping in solid simulations. We mathematically prove that our nonlinear anisotropic damping generalizes the frequency-dependent Caughey damping model, when starting from the Rayleigh damping. Finally, we give an inverse design method whereby the damping curve parameters can be inferred automatically from high-level user input, such as the amount of amplitude loss in one oscillation cycle along each of the chosen example deformations. To minimize numerical damping for implicit integration, we introduce an accurate and stable implicit integrator, which removes spurious high-frequency oscillations while only introducing a minimal amount of numerical damping. Our damping can generate effects not possible with previous methods, such as controllable nonlinear decaying envelopes whereby large deformations are damped faster or slower than small deformations, and damping anisotropic effects. We also fit our damping to videos of real-world objects undergoing large deformations, capturing their nonlinear and anisotropic damping dynamics.

Example-Based Damping Design

Kiwon Um, Xiangyu Hu, Nils Thuerey

This paper proposes a novel framework to evaluate fluid simulation methods based on crowd-sourced user studies in order to robustly gather large numbers of opinions. The key idea for a robust and reliable evaluation is to use a reference video from a carefully selected real-world setup in the user study. By conducting a series of controlled user studies and comparing their evaluation results, we observe various factors that affect the perceptual evaluation. Our data show that the availability of a reference video makes the evaluation consistent. We introduce this approach for computing scores of simulation methods as visual accuracy metric. As an application of the proposed framework, a variety of popular simulation methods are evaluated.

Perceptual Evaluation of Liquid Simulation Methods

A. Pradhana Tampubolon, T. Gast, G. Klar, C. Fu, J. Teran, C. Jiang, K. Museth

We present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use a two-grid Material Point Method to discretize the governing equations. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop an improved return mapping for sand plasticity that prevents volume gain artifacts in the traditional Drucker-Prager model.

Multi-species simulation of porous sand and water mixtures

Dan Koschier, Jan Bender, Nils Thuerey

In this paper we present a robust remeshing-free cutting algorithm on the basis of the eXtended Finite Element Method (XFEM) and fully implicit time integration. One of the most crucial points of the XFEM is that integrals over discontinuous polynomials have to be computed on subdomains of the polyhedral elements. Most existing approaches construct a cut-aligned auxiliary mesh for integration. In contrast, we propose a cutting algorithm that includes the construction of specialized quadrature rules for each dissected element without the requirement to explicitly represent the arising subdomains. Moreover, we solve the problem of ill-conditioned or even numerically singular solver matrices during time integration using a novel algorithm that constrains non-contributing degrees of freedom (DOFs) and introduce a preconditioner that efficiently reuses the constructed quadrature weights.

Our method is particularly suitable for fine structural cutting as it decouples the added number of DOFs from the cut’s geometry and correctly preserves geometry and physical properties by accurate integration. Due to the implicit time integration these fine features can still be simulated robustly using large time steps. As opposed to this, the vast majority of existing approaches either use remeshing or element duplication. Remeshing based methods are able to correctly preserve physical quantities but strongly couple cut geometry and mesh resolution leading to an unnecessary large number of additional DOFs. Element duplication based approaches keep the number of additional DOFs small but fail at correct conservation of mass and stiffness properties. We verify consistency and robustness of our approach on simple and reproducible academic examples while stability and applicability are demonstrated in large scenarios with complex and fine structural cutting.

Robust eXtended Finite Elements for Complex Cutting of Deformables

Yeara Kozlov, Derek Bradley, Moritz Bächer, Thabo Beeler, Markus Gross

Oftentimes facial animation is created separately from overall body motion. Since convincing facial animation is challenging enough in itself, artists tend to create and edit the face motion in isolation. Or if the face animation is derived from motion capture, this is typically performed in a mo-cap booth while sitting relatively still. In either case, recombining the isolated face animation with body and head motion is non-trivial and often results in an uncanny result if the body dynamics are not properly reflected on the face (e.g. the bouncing of facial tissue when running). We tackle this problem by introducing a simple and intuitive system that allows to add physics to facial blendshape animation. Unlike previous methods that try to add physics to face rigs, our method preserves the original facial animation as closely as possible. To this end, we present a novel simulation framework that uses the original animation as per-frame rest-poses without adding spurious forces. As a result, in the absence of any external forces or rigid head motion, the facial performance will exactly match the artist-created blendshape animation. In addition, we propose the concept of blendmaterials to give artists an intuitive means to account for changing material properties due to muscle activation. This system allows to automatically combine facial animation and head motion such that they are consistent while preserving the original animation as closely as possible. The system is easy to use and readily integrates with existing animation pipelines.

Enriching Facial Blendshape Rigs with Physical Simulation

Liwen Hu, Derek Bradley, Hao Li, Thabo Beeler

Physical simulation has long been the approach of choice for generating realistic hair animations in CG. A constant drawback of simulation, however, is the necessity to manually set the physical parameters of the simulation model in order to get the desired dynamic behavior. To alleviate this, researchers have begun to explore methods for reconstructing hair from the real world and even to estimate the corresponding simulation parameters through the process of inversion. So far, however, these methods have had limited applicability, because dynamic hair capture can only be played back without the ability to edit, and solving for simulation parameters can only be accomplished for static hairstyles, ignoring the dynamic behavior. We present the first method for capturing dynamic hair and automatically determining the physical properties for simulating the observed hairstyle in motion. Since our dynamic inversion is agnostic to the simulation model, the proposed method applies to virtually any hair simulation technique, which we demonstrate using two state-of-the-art hair simulation models. The output of our method is a fully simulation-ready hairstyle, consisting of both the static hair geometry as well as its physical properties. The hairstyle can be easily edited by adding additional external forces, changing the head motion, or re-simulating in completely different environments, all while remaining faithful to the captured hairstyle.

Simulation-Ready Hair Capture

Marek Dvorožňák, Pierre Bénard, Pascal Barla, Oliver Wang, Daniel Sýkora

We present a novel approach to facilitate the creation of stylized 2D rigid body animations. Our approach can handle multiple rigid objects following complex physically-simulated trajectories with collisions, while retaining a unique artistic style directly specified by the user. Starting with an existing target animation (e.g., produced by a physical simulation engine) an artist interactively draws over a sparse set of frames, and the desired appearance and motion stylization is automatically propagated to the rest of the sequence. The stylization process may also be performed in an off-line batch process from a small set of drawn sequences. To achieve these goals, we combine parametric deformation synthesis that generalizes and reuses hand-drawn exemplars, with non-parametric techniques that enhance the hand-drawn appearance of the synthesized sequence. We demonstrate the potential of our method on various complex rigid body animations which are created with an expressive hand-drawn look using notably less manual interventions as compared to traditional techniques.

Example-Based Expressive Animation of 2D Rigid Bodies

Mridul Aanjaneya, Ming Gao, Haixiang Liu, Christopher Batty and Eftychios Sifakis

We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree’s simulation variables to reflect the structure and connectivity of a power diagram, which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancements to adaptive level set advection, velocity extrapolation, and the fast marching method for redistancing. Our overall framework gracefully accommodates the task of dynamically adapting the octree topology during simulation. We demonstrate end-to-end simulations of complex adaptive flows in irregularly shaped domains, with tens of millions of degrees of freedom.

Power Diagrams and Sparse Paged Grids for High Resolution Adaptive Liquids

Egor Larionov, Christopher Batty, Robert Bridson

We propose a novel unsteady Stokes solver for coupled viscous and pressure forces in grid-based liquid animation which yields greater accuracy and visual realism than previously achieved. Modern fluid simulators treat viscosity and pressure in separate solver stages, which reduces accuracy and yields incorrect free surface behavior. Our proposed implicit variational formulation of the Stokes problem leads to a symmetric positive definite linear system that gives properly coupled forces, provides unconditional stability, and treats difficult boundary conditions naturally through simple volume weights. Surface tension and moving solid boundaries are also easily incorporated. Qualitatively, we show that our method recovers the characteristic rope coiling instability of viscous liquids and preserves fine surface details, while previous grid-based schemes do not. Quantitatively, we demonstrate that our method is convergent through grid refinement studies on analytical problems in two dimensions. We conclude by offering practical guidelines for choosing an appropriate viscous solver, based on the scenario to be animated and the computational costs of different methods.

Variational Stokes: A Unified Pressure-Viscosity Solver for Accurate Viscous Liquids

Yun (Raymond) Fei, Henrique Teles Maia, Christopher Batty, Changxi Zheng, Eitan Grinspun

The diverse interactions between hair and liquid are complex and span multiple length scales, yet are central to the appearance of humans and animals in many situations. We therefore propose a novel multi-component simulation framework that treats many of the key physical mechanisms governing the dynamics of wet hair. The foundations of our approach are a discrete rod model for hair and a particle-in-cell model for fluids. To treat the thin layer of liquid that clings to the hair, we augment each hair strand with a height field representation. Our contribution is to develop the necessary physical and numerical models to evolve this new system and the interactions among its components. We develop a new reduced-dimensional liquid model to solve the motion of the liquid along the length of each hair, while accounting for its moving reference frame and influence on the hair dynamics. We derive a faithful model for surface tension-induced cohesion effects between adjacent hairs, based on the geometry of the liquid bridges that connect them. We adopt an empirically-validated drag model to treat the effects of coarse-scale interactions between hair and surrounding fluid, and propose new volume-conserving dripping and absorption strategies to transfer liquid between the reduced and particle-in-cell liquid representations. The synthesis of these techniques yields an effective wet hair simulator, which we use to animate hair flipping, an animal shaking itself dry, a spinning car wash roller brush dunked in liquid, and intricate hair coalescence effects, among several additional scenarios.

A Multi-Scale Model for Simulating Liquid-Hair Interactions