An Advection-Reflection Solver for Detail-Preserving Fluid Simulation

Jonas Zehnder, Rahul Narain, Bernhard Thomaszewski

Advection-projection methods for fluid animation are widely appreciated for their stability and efficiency. However, the projection step dissipates energy from the system, leading to artificial viscosity and suppression of small-scale details. We propose an alternative approach for detail-preserving fluid animation that is surprisingly simple and effective. We replace the energy-dissipating projection operator applied at the end of a simulation step by an energy-preserving reflection operator applied at mid-step.We show that doing so leads to two orders of magnitude reduction in energy loss, which in turn yields vastly improved detail-preservation. We evaluate our reflection solver on a set of 2D and 3D numerical experiments and show that it compares favorably to state-of-the-art methods. Finally, our method integrates seamlessly with existing projection-advection solvers and requires very little additional implementation.

An Advection-Reflection Solver for Detail-Preserving Fluid Simulation

Projective Skinning

Martin Komaritzan, Mario Botsch

We present a novel approach for physics-based character skinning. While maintaining real-time performance it overcomes the well-known artifacts of commonly used geometric skinning approaches, it enables dynamic effects, and it resolves local self-collisions. Our method is based on a two-layer model consisting of rigid bones and an elastic soft tissue layer. This volumetric model is easily and efficiently computed from an input surface mesh of the character and its underlying skeleton. In particular, our method neither requires skinning weights, which are often expensive to compute or tedious to hand-tune, nor a complex volumetric tessellation, which fails for many real-world input meshes due to self-intersections.

Projective Skinning

Interactive Two-Way Shape Design of Elastic Bodies

Rajaditya Mukherjee, Longhua Wu, Huamin Wang
We present a novel system for interactive elastic shape design in both forward and inverse fashions. Using this system, the user can choose to edit the rest shape or the quasistatic shape of an elastic solid, and obtain the other shape that matches under the quasistatic equilibrium condition at the same time. The development of this system is based on the discovery that inverse quasistatic simulation can be immediately solved by Newton’s method with a direct solver. To implement our simulator, we propose a Jacobian matrix evaluation scheme for the inverse elastic problem and we present step length and matrix evaluation techniques that improve the simulation performance. While our simulator is efficient, it is still not fast enough for the system to generate the result in real time. Our solution is a shape initialization method using the recent projective dynamics technique. Shape initialization not only works as a fast preview function during the user editing process, but also speeds up the convergence of quasistatic or inverse quasistatic simulation afterwards. The use of a heterogeneous algorithm structure allows the system to further reduce its preview cost, by utilizing the power of both the CPU and the GPU. Our experiment demonstrates that the whole system is fast, robust, and convenient for the designer to use in both forward and inverse elastic shape design. It can handle a variet of nonlinear elastic material models, and its runtime performance has space for more improvement.

Learning Nonlinear Soft-Tissue Dynamics for Interactive Avatars

Dan Casas, Miguel Otaduy

We present a novel method to enrich existing vertex-based human body models by adding soft-tissue dynamics. Our model learns to predict per-vertex 3D offsets, referred to as dynamic blendshapes, that reproduce nonlinear mesh deformation effects as a function of pose information. This enables the synthesis of realistic 3D mesh animations, including soft-tissue effects, using just skeletal motion. At the core of our method there is a neural network regressor trained on high-quality 4D scans from which we extract pose, shape and soft-tissue information. Our regressor uses a novel nonlinear subspace, which we build using an autoencoder, to efficiently compact soft-tissue dynamics information. Once trained, our method can be plugged to existing vertex-based skinning methods with little computational overhead (<10ms), enabling real-time nonlinear dynamics. We qualitatively and quantitatively evaluate our method, and show compelling animations with soft-tissue effects, created using publicly available motion capture datasets

Learning Nonlinear Soft-Tissue Dynamics for Interactive Avatars

Comparison of Mixed Linear Complementarity Problem Solvers for Multibody Simulations with Contact

Andreas Enzenhofer, Sheldon Andrews, Marek Teichmann, Jozsef Kövecses

The trade-off between accuracy and computational performance is one of the central conflicts in real-time multibody simulations, much of which can be attributed to the method used to solve the constrained multibody equations. This paper examines four mixed linear complementarity problem (MLCP) algorithms when they are applied to physical problems involving frictional contact. We consider several different, and challenging, test cases such as grasping, stability of static models, closed loops, and long chains of bodies. The solver parameters are tuned for these simulations and the results are evaluated in terms of numerical accuracy and computational performance. The objective of this paper is to determine the accuracy properties of each solver, find the appropriate method for a defined task, and thus draw conclusions regarding the applicability of each method

Comparison of Mixed Linear Complementarity Problem Solvers for Multibody Simulations with Contact

A Material Point Method for Thin Shells with Frictional Contact

Qi Guo, Xuchen Han, Chuyuan Fu, Theodore Gast, Rasmus Tamstorf, Joseph Teran

We present a novel method for simulation of thin shells with frictional contact using a combination of the Material Point Method (MPM) and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. Furthermore we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials.

A Material Point Method for Thin Shells with Frictional Contact

Fluid Directed Rigid Body Control Using Deep Reinforcement Learning

Yunsheng Tian, Pingchuan Ma, Zherong Pan, Bo Ren, and Dinesh Manocha

We present a learning-based method to control a coupled 2D system involving both fluid and rigid bodies. Our approach is used to modify the fluid/rigid simulator’s behavior by applying control forces only at the simulation domain boundaries. The rest of the domain, corresponding to the interior, is governed by the Navier-Stokes equation for fluids and Newton-Euler’s equation for the rigid bodies. We represent our controller using a general neural-net, which is trained using deep reinforcement learning. Our formulation decomposes a control task into two stages: a precomputation training stage and an online generation stage. We utilize various fluid properties, e.g., the liquid’s velocity field or the smoke’s density field, to enhance the controller’s performance. We set up our evaluation benchmark by letting controller drive fluid jets move on the domain boundary and allowing them to shoot fluids towards a rigid body to accomplish a set of challenging 2D tasks such as keeping a rigid body balanced, playing a two-player ping-pong game, and driving a rigid body to sequentially hit specified points on the wall. In practice, our approach can generate physically plausible animations.

Fluid Directed Rigid Body Control Using Deep Reinforcement Learning

Eulerian-on-Lagrangian Cloth Simulation

Nicholas J. Weidner, Kyle Piddington, David I. W. Levin, Shinjiro Sueda

We resolve the long-standing problem of simulating the contact-mediated interaction of cloth and sharp geometric features by introducing an Eulerian-on-Lagrangian (EOL) approach to cloth simulation. Unlike traditional Lagrangian approaches to cloth simulation, our EOL approach permits bending exactly at and sliding over sharp edges, avoiding parasitic locking caused by over-constraining contact constraints. Wherever the cloth is in contact with sharp features, we insert EOL vertices into the cloth, while the rest of the cloth is simulated in the standard Lagrangian fashion. Our algorithm manifests as new equations of motion for EOL vertices, a contact-conforming remesher, and a set of simple constraint assignment rules, all of which can be incorporated into existing state-of-the-art cloth simulators to enable smooth, inequality-constrained contact between cloth and objects in the world.

Eulerian-on-Lagrangian Cloth Simulation

Tetrahedral Meshing in the Wild

Yixin Hu, Qingnan Zhou, Xifeng Gao, Alec Jacobson, Denis Zorin, Daniele Panozzo

We propose a novel tetrahedral meshing technique that is unconditionally robust, requires no user interaction, and can directly convert a triangle soup into an analysis-ready volumetric mesh. The approach is based on several core principles: (1) initial mesh construction based on a fully robust, yet efficient, filtered exact computation (2) explicit (automatic or user-defined) tolerancing of the mesh relative to the surface input (3) iterative mesh improvement with guarantees, at every step, of the output validity. The quality of the resulting mesh is a direct function of the target mesh size and allowed tolerance: increasing allowed deviation from the initial mesh and decreasing the target edge length both lead to higher mesh quality. Our approach enables black-box analysis, i.e., it allows to automatically solve partial differential equations on geometrical models available in the wild, offering a robustness and reliability comparable to, e.g., image processing algorithms, opening the door to automatic, large scale processing of real-world geometric data.

Tetrahedral Meshing in the Wild

A Multi-Scale Model for Simulating Liquid-Fabric Interactions

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

We propose a method for simulating the complex dynamics of partially and fully saturated woven and knit fabrics interacting with liquid, including the effects of buoyancy, nonlinear drag, pore (capillary) pressure, dripping, and convection-diffusion. Our model evolves the velocity fields of both the liquid and solid relying on mixture theory, as well as tracking a scalar saturation variable that affects the pore pressure forces in the fluid. We consider the porous microstructure implied by the fibers composing individual threads, and use it to derive homogenized drag and pore pressure models that faithfully reflect the anisotropy of fabrics. In addition to the bulk liquid and fabric motion, we derive a quasi-static flow model that accounts for liquid spreading within the fabric itself. Our implementation significantly extends standard numerical cloth and fluid models to support the diverse behaviors of wet fabric, and includes a numerical method tailored to cope with the challenging nonlinearities of the problem. We explore a range of fabric-water interactions to validate our model, including challenging animation scenarios involving splashing, wringing, and collisions with obstacles, along with qualitative comparisons against simple physical experiments.

A Multi-Scale Model for Simulating Liquid-Fabric Interactions