A Divergence-free Mixture Model for Multiphase Fluids

We present a novel divergence free mixture model for multiphase flows and the related fluid-solid coupling. The new mixture model is built upon a volume-weighted mixture velocity so that the divergence free condition is satisfied for miscible and immiscible multiphase fluids. The proposed mixture velocity can be solved efficiently by adapted single phase incompressible solvers, allowing for larger time steps and smaller volume deviations. Besides, the drift velocity formulation is corrected to ensure mass conservation during the simulation. The new approach increases the accuracy of multiphase fluid simulation by several orders. The capability of the new divergence-free mixture model is demonstrated by simulating different multiphase flow phenomena including mixing and unmixing of multiple fluids, fluid-solid coupling involving deformable solids and granular materials.     

Mixing Yarns and Triangles in Cloth Simulation

This paper presents a method to combine triangle and yarn models in cloth simulation, and hence leverage their best features. The majority of a garment uses a triangle-based model, which reduces the overall computational and memory cost. Key areas of the garment use a yarn-based model, which elicits rich effects such as structural nonlinearity and plasticity. To combine both models in a seamless and robust manner, we solve two major technical challenges. We propose an enriched kinematic representation that augments triangle-based deformations with yarn-level details. Naïve enrichment suffers from kinematic redundancy, but we devise an optimal kinematic filter that allows a smooth transition between triangle and yarn models. We also introduce a preconditioner that resolves the poor conditioning produced by the extremely different inertia of triangle and yarn nodes. This preconditioner deals effectively with rank deficiency introduced by the kinematic filter. We demonstrate that mixed yarns and triangles succeed to efficiently capture rich effects in garment fit and drape.     

Effective time step restrictions for explicit MPM simulation

Time steps for explicit MPM simulation in computer graphics are often selected by trial and error due to the challenges in automatically selecting stable time step sizes. Our time integration scheme uses time step restrictions that take into account forces, collisions, and even grid-to-particle transfers calculated near the end of the time step. We propose a novel set of time step restrictions that allow a time step to be selected that is stable, efficient to compute, and not too far from optimal. We derive the general solution for the sound speed in nonlinear isotropic hyperelastic materials, which we use to enforce the classical CFL time step restriction. We identify a single-particle instability in explicit MPM integration and propose a corresponding time step restriction in the fluid case. We also propose a reflection-based boundary condition for domain walls that supports separation and accurate Coulomb friction while preventing particles from penetrating the domain walls.     

Local Bases for Model-reduced Smoke Simulations

We present a flexible model reduction method for simulating incompressible fluids. We derive a novel vector field basis composed of localized basis flows which have simple analytic forms and can be tiled on regular lattices, avoiding the use of complicated data structures or neighborhood queries. Local basis flow interactions can be precomputed and reused to simulate fluid dynamics on any simulation domain without additional overhead. We introduce heuristic simulation dynamics tailored to our basis and derived from a projection of the Navier-Stokes equations to produce physically plausible motion, exposing intuitive parameters to control energy distribution across scales. Our basis can adapt to curved simulation boundaries, can be coupled with dynamic obstacles, and offers simple adjustable trade-offs between speed and visual resolution.     

Semi-analytical Solid Boundary Conditions for Free Surface Flows

The treatment of solid boundary conditions remains one of the most challenging parts in the SPH method. We present a semi-analytical approach to handle complex solid boundaries of arbitrary shape. Instead of calculating a renormalizing factor for the particle near the boundary, we propose to calculate the volume integral inside the solid boundary under the local spherical frame of a particle. By converting the volume integral into a surface integral, a computer aided design (CAD) mesh file representing the boundary can be naturally integrated for particle simulations. To accelerate the search for a particle's neighboring triangles, a uniform grid is applied to store indices of intersecting triangles. The new semi-analytical solid boundary handling approach is integrated into a position-based method [MM13] as well as a projection-based [HWW*20] to demonstrate its effectiveness in handling complex boundaries. Experiments show that our method is able to achieve comparable results with those simulated using ghost particles. In addition, since our method requires no boundary particles for deforming surfaces, our method is flexible enough to handle complex solid boundaries, including sharp corners and shells.     

Simulation of Arbitrarily-shaped Magnetic Objects

We propose a novel method for simulating rigid magnets in a stable way. It is based on analytic solutions of the magnetic vector potential and flux density, which make the magnetic forces and torques calculated using them seldom diverge. Therefore, our magnet simulations remain stable even though magnets are in close proximity or penetrate each other. Thanks to the stability, our method can simulate magnets of any shapes. Another strength of our method is that the time complexities for computing the magnetic forces and torques are significantly reduced, compared to the previous methods. Our method is easily integrated with classic rigid-body simulators. The experiment results presented in this paper prove the stability and efficiency of our method.     

Efficient 2D Simulation on Moving 3D Surfaces

We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle-based fluid simulation) in three-dimensional space, we add a second simulation on this base animation. In general, we solve a partial differential equation (PDE) on a level set surface obtained from the animated input surface. The properties of the input surface are transferred to a sparse volume data structure that is then used for the simulation. We introduce one-way coupling strategies from input properties to our simulation and we add conservation of mass and momentum to existing methods that solve a PDE in a narrow-band using the Closest Point Method. In this way, we efficiently compute high-resolution 2D simulations on coarse input surfaces. Our approach helps visual effects creators easily integrate a workflow to simulate material flow on evolving surfaces into their existing production pipeline.     

Particle-based Liquid Control using Animation Templates

It is notoriously difficult for artists to control liquids while generating plausible animations. We introduce a new liquid control tool that allows users to load, transform, and apply precomputed liquid simulation templates in a scene in order to control a particle-based simulation. Each template instance generates control forces that drive the global simulated liquid to locally reproduce the templated liquid behavior. Our system is augmented with a variable proportion of temporary particles to help efficiently reproduce the templated liquid density, with fewer requirements on the surrounding environment. The resulting control strategy adds only a small computational overhead, leading to quick visual feedback for resolutions allowing interactive simulation. We demonstrate the robustness and ease of use of our method on various examples in 2D and 3D.     

A Bending Model for Nodal Discretizations of Yarn-Level Cloth

To deploy yarn-level cloth simulations in production environments, it is paramount to design very efficient implementations, which mitigate the cost of the extremely high resolution. To this end, nodal discretizations aligned with the regularity of the fabric structure provide an optimal setting for efficient GPU implementations. However, nodal discretizations complicate the design of robust and controllable bending. In this paper, we address this challenge, and propose a model of bending that is both robust and controllable, and employs only nodal degrees of freedom. We extract information of yarn and fabric orientation implicitly from the nodal degrees of freedom, with no need to augment the model explicitly. But most importantly, and unlike previous formulations that use implicit orientations, the computation of bending forces bears no overhead with respect to other nodal forces such as stretch. This is possible by tracking optimal orientations efficiently. We demonstrate the impact of our bending model in examples with controllable anisotropy, as well as ironing, wrinkling, and plasticity.     

Higher-Order Time Integration for Deformable Solids

Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first-order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second-order methods, their use is not widespread. Many of these well-known methods have significant drawbacks such as severe numerical damping or scene-dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first-order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge-Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher-order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor-corrector approach that leads to consistent behavior with higher-order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.     

Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions

In this paper, we propose and evaluate fast, scalable approaches for solving the linear complementarity problems (LCP) arising from the fluid pressure equations with separating solid boundary conditions. Specifically, we present a policy iteration method, a penalty method, and a modified multigrid method, and demonstrate that each is able to properly handle the desired boundary conditions. Moreover, we compare our proposed methods against existing approaches and show that our solvers are more efficient and exhibit better scaling behavior; that is, the number of iterations required for convergence is essentially independent of grid resolution, and thus they are faster at larger grid resolutions. For example, on a 256³ grid our multigrid method was 30 times faster than the prior multigrid method in the literature.     

Modeling and Estimation of Nonlinear Skin Mechanics for Animated Avatars

Data-driven models of human avatars have shown very accurate representations of static poses with soft-tissue deformations. However they are not yet capable of precisely representing very nonlinear deformations and highly dynamic effects. Nonlinear skin mechanics are essential for a realistic depiction of animated avatars interacting with the environment, but controlling physics-only solutions often results in a very complex parameterization task. In this work, we propose a hybrid model in which the soft-tissue deformation of animated avatars is built as a combination of a data-driven statistical model, which kinematically drives the animation, an FEM mechanical simulation. Our key contribution is the definition of deformation mechanics in a reference pose space by inverse skinning of the statistical model. This way, we retain as much as possible of the accurate static data-driven deformation and use a custom anisotropic nonlinear material to accurately represent skin dynamics. Model parameters including the heterogeneous distribution of skin thickness and material properties are automatically optimized from 4D captures of humans showing soft-tissue deformations.     

Simulation of Dendritic Painting

We present a new system for interactive dendritic painting. Dendritic painting is characterized by the unique and intricate branching patterns that grow from the interaction of inks, solvents and medium. Painting sessions thus become very dynamic and experimental. To achieve a compelling simulation of this painting technique we introduce a new Reaction-Diffusion model with carefully designed terms to allow natural interactions in a painting context. We include additional user control not possible in the real world to guide and constrain the growth of the patterns in expressive ways. Our multi-field model is able to capture and simulate all these complex phenomena efficiently in real time, expanding the tools available to the digital artist, while producing compelling animations for motion graphics.     

Asynchronous Eulerian Liquid Simulation

We present a novel method for simulating liquid with asynchronous time steps on Eulerian grids. Previous approaches focus on Smoothed Particle Hydrodynamics (SPH), Material Point Method (MPM) or tetrahedral Finite Element Method (FEM) but the method for simulating liquid purely on Eulerian grids have not yet been investigated. We address several challenges specifically arising from the Eulerian asynchronous time integrator such as regional pressure solve, asynchronous advection, interpolation, regional volume preservation, and dedicated segregation of the simulation domain according to the liquid velocity. We demonstrate our method on top of staggered grids combined with the level set method and the semi-Lagrangian scheme. We run several examples and show that our method considerably outperforms the global adaptive time step method with respect to the computational runtime on scenes where a large variance of velocity is present.     

Cosserat Rod with rh-Adaptive Discretization

Rod-like one-dimensional elastic objects often exhibit complex behaviors which pose great challenges to the discretization method for pursuing a faithful simulation. By only moving a small portion of material points, the Eulerian-on-Lagrangian (EoL) method already shows great adaptivity to handle sharp contact, but it is still far from enough to reproduce rich and complex geometry details arising in simulations. In this paper, we extend the discrete configuration space by unifying all Lagrangian and EoL nodes in representation for even more adaptivity with every sample being assigned with a dynamic material coordinate. However, this great extension will immediately bring in much more redundancy in the dynamic system. Therefore, we propose additional energy to control the spatial distribution of all material points, seeking to equally space them with respect to a curvature-based density field as a monitor. This flexible approach can effectively constrain the motion of material points to resolve numerical degeneracy, while simultaneously enables them to notably slide inside the parametric domain to account for the shape parameterization. Besides, to accurately respond to sharp contact, our method can also insert or remove nodes online and adjust the energy stiffness to suppress possible jittering artifacts that could be excited in a stiff system. As a result of this hybrid rh-adaption, our proposed method is capable of reproducing many realistic rod dynamics, such as excessive bending, twisting and knotting while only using a limited number of elements.     

Monocular Human Pose and Shape Reconstruction using Part Differentiable Rendering

Superior human pose and shape reconstruction from monocular images depends on removing the ambiguities caused by occlusions and shape variance. Recent works succeed in regression-based methods which estimate parametric models directly through a deep neural network supervised by 3D ground truth. However, 3D ground truth is neither in abundance nor can efficiently be obtained. In this paper, we introduce body part segmentation as critical supervision. Part segmentation not only indicates the shape of each body part but helps to infer the occlusions among parts as well. To improve the reconstruction with part segmentation, we propose a part-level differentiable renderer that enables part-based models to be supervised by part segmentation in neural networks or optimization loops. We also introduce a general parametric model engaged in the rendering pipeline as an intermediate representation between skeletons and detailed shapes, which consists of primitive geometries for better interpretability. The proposed approach combines parameter regression, body model optimization, and detailed model registration altogether. Experimental results demonstrate that the proposed method achieves balanced evaluation on pose and shape, and outperforms the state-of-the-art approaches on Human3.6M, UP-3D and LSP datasets.     

Ray-aligned Occupancy Map Array for Fast Approximate Ray Tracing

We present a new software ray tracing solution that efficiently computes visibilities in dynamic scenes. We first introduce a novel scene representation: ray-aligned occupancy map array (ROMA) that is generated by rasterizing the dynamic scene once per frame. Our key contribution is a fast and low-divergence tracing method computing visibilities in constant time, without constructing and traversing the traditional intersection acceleration data structures such as BVH. To further improve accuracy and alleviate aliasing, we use a spatiotemporal scheme to stochastically distribute the candidate ray samples. We demonstrate the practicality of our method by integrating it into a modern real-time renderer and showing better performance compared to existing techniques based on distance fields (DFs). Our method is free of the typical artifacts caused by incomplete scene information, and is about 2.5×–10× faster than generating and tracing DFs at the same resolution and equal storage.     

Online Avatar Motion Adaptation to Morphologically-similar Spaces

In avatar-mediated telepresence systems, a similar environment is assumed for involved spaces, so that the avatar in a remote space can imitate the user's motion with proper semantic intention performed in a local space. For example, touching on the desk by the user should be reproduced by the avatar in the remote space to correctly convey the intended meaning. It is unlikely, however, that the two involved physical spaces are exactly the same in terms of the size of the room or the locations of the placed objects. Therefore, a naive mapping of the user's joint motion to the avatar will not create the semantically correct motion of the avatar in relation to the remote environment. Existing studies have addressed the problem of retargeting human motions to an avatar for telepresence applications. Few studies, however, have focused on retargeting continuous full-body motions such as locomotion and object interaction motions in a unified manner. In this paper, we propose a novel motion adaptation method that allows to generate the full-body motions of a human-like avatar on-the-fly in the remote space. The proposed method handles locomotion and object interaction motions as well as smooth transitions between them according to given user actions under the condition of a bijective environment mapping between morphologically-similar spaces. Our experiments show the effectiveness of the proposed method in generating plausible and semantically correct full-body motions of an avatar in room-scale space.     

A Bayesian Inference Framework for Procedural Material Parameter Estimation

Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from photographs, presenting a unified view of the problem in a Bayesian framework. In addition to computing point estimates of the parameters by optimization, our framework uses a Markov Chain Monte Carlo approach to sample the space of plausible material parameters, providing a collection of plausible matches that a user can choose from, and efficiently handling both discrete and continuous model parameters. To demonstrate the effectiveness of our framework, we fit procedural models of a range of materials—wall plaster, leather, wood, anisotropic brushed metals and layered metallic paints—to both synthetic and real target images.