Physics-Based Animation

Lei Lan, Guanqun Ma, Yin Yang, Changxi Zheng, Minchen Li, Chenfanfu Jiang

We present a GPU algorithm for deformable simulation. Our method offers good computational efficiency and penetration-free guarantee at the same time, which are not common with existing techniques. The main idea is an algorithmic integration of projective dynamics (PD) and incremental potential contact (IPC). PD is a position-based simulation framework, favored for its robust convergence and convenient implementation. We show that PD can be employed to handle the variational optimization with the interior point method e.g., IPC. While conceptually straightforward, this requires a dedicated rework over the collision resolution and the iteration modality to avoid incorrect collision projection with improved numerical convergence. IPC exploits a barrier-based formulation, which yields an infinitely large penalty when the constraint is on the verge of being violated. This mechanism guarantees intersection-free trajectories of deformable bodies during the simulation, as long as they are apart at the rest configuration. On the downside, IPC brings a large amount of nonlinearity to the system, making PD slower to converge. To mitigate this issue, we propose a novel GPU algorithm named A-Jacobi for faster linear solve at the global step of PD. A-Jacobi is based on Jacobi iteration, but it better harvests the computation capacity on modern GPUs by lumping several Jacobi steps into a single iteration. In addition, we also re-design the CCD root finding procedure by using a new minimum-gradient Newton algorithm. Those saved time budgets allow more iterations to accommodate stiff IPC barriers so that the result is both realistic and collision-free. Putting together, our algorithm simulates complicated models of both solids and shells on the GPU at an interactive rate or even in real time.

Penetration-free Projective Dynamics on the GPU

Ziyin Qu, Minchen Li, Fernando de Goes, Chenfanfu Jiang

This paper introduces a new weighting scheme for particle-grid transfers that generates hybrid Lagrangian/Eulerian fluid simulations with uniform particle distributions and precise volume control. At its core, our approach reformulates the construction of Power Particles [de Goes et al . 2015] by computing volume-constrained density kernels. We employ these optimized kernels as particle domains within the Generalized Interpolation Material Point method (GIMP) in order to incorporate Power Particles into the Particle-In-Cell framework, hence the name the Power Particle-In-Cell method. We address the construction of volume-constrained density kernels as a regularized optimal transportation problem and describe an iterative solver based on localized Gaussian convolutions that leads to a significant performance speedup compared to [de Goes et al . 2015]. We also present novel extensions for handling free surfaces and solid obstacles that bypass the need for cell clipping and ghost particles. We demonstrate the advantages of our transfer weights by improving hybrid schemes for fluid simulation such as the Fluid Implicit Particle (FLIP) method and the Affine Particle-In-Cell (APIC) method with volume preservation and robustness to varying particle-per-cell ratio, while retaining low numerical dissipation, conserving linear and angular momenta, and avoiding particle reseeding or post-process relaxations.

The Power Particle-In-Cell Method

Xuan Li, Minchen Li, Chenfanfu Jiang

In this paper, we propose Energetically Consistent Inelasticity (ECI), a new formulation for modeling and discretizing finite strain elastoplasticity/viscoelasticity in a way that is compatible with optimization-based time integrators. We provide an in-depth analysis for allowing plasticity to be implicitly integrated through an augmented strain energy density function. We develop ECI on the associative von-Mises J2 plasticity, the non-associative Drucker-Prager plasticity, and the finite strain viscoelasticity. We demonstrate the resulting scheme on both the Finite Element Method (FEM) and the Material Point Method (MPM). Combined with a custom Newton-type optimization integration scheme, our method enables simulating stiff and large-deformation inelastic dynamics of metal, sand, snow, and foam with larger time steps, improved stability, higher efficiency, and better accuracy than existing approaches.

Energetically Consistent Inelasticity for Optimization Time Integration

Yunuo Chen*, Minchen Li* (equal contributions), Lei Lan, Hao Su, Yin Yang, Chenfanfu Jiang

We present a simulation framework for multibody dynamics via a universal variational integration. Our method naturally supports mixed rigid-deformables and mixed codimensional geometries, while providing guaranteed numerical convergence and accurate resolution of contact, friction, and a wide range of articulation constraints. We unify (1) the treatment of simulation degrees of freedom for rigid and soft bodies by formulating them both in terms of Lagrangian nodal displacements, (2) the handling of general linear equality joint constraints through an efficient change-of-variable strategy, (3) the enforcement of nonlinear articulation constraints based on novel distance potential energies, (4) the resolution of frictional contact between mixed dimensions and bodies with a variational Incremental Potential Contact formulation, and (5) the modeling of generalized restitution through semi-implicit Rayleigh damping. We conduct extensive unit tests and benchmark studies to demonstrate the efficacy of our method.

A Unified Newton Barrier Method for Multibody Dynamics

Jiong Chen, Mathieu Desbrun

The fundamental solutions (Green’s functions) of linear elasticity for an infinite and isotropic media are ubiquitous in interactive graphics applications that cannot afford the computational costs of volumetric meshing and finite-element simulation. For instance, the recent work of de Goes and James [2017] leveraged these Green’s functions to formulate sculpting tools capturing in real-time broad and physically-plausible deformations more intuitively and realistically than traditional editing brushes. In this paper, we extend this family of Green’s functions by exploiting the anisotropic behavior of general linear elastic materials, where the relationship between stress and strain in the material depends on its orientation. While this more general framework prevents the existence of analytical expressions for its fundamental solutions, we show that a finite sum of spherical harmonics can be used to decompose a Green’s function, which can be further factorized into directional, radial, and material-dependent terms. From such a decoupling, we show how to numerically derive sculpting brushes to generate anisotropic deformation and finely control their falloff profiles in real-time.

Go Green: General Regularized Green’s Functions for Elasticity

Yadi Cao, Yunuo Chen, Minchen Li, Yin Yang, Xinxin Zhang, Mridul Aanjaneya, Chenfanfu Jiang

This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.

An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids

Yitong Deng, Mengdi Wang, Xiangxin Kong, Shiying Xiong, Zangyueyang Xian, Bo Zhu

We present the Moving Eulerian-Lagrangian Particles (MELP), a novel mesh-free method for simulating incompressible fluid on thin films and foams. Employing a bi-layer particle structure, MELP jointly simulates detailed, vigorous flow and large surface deformation at high stability and efficiency. In addition, we design multi-MELP: a mechanism that facilitates the physically-based interaction between multiple MELP systems, to simulate bubble clusters and foams with non-manifold topological evolution. We showcase the efficacy of our method with a broad range of challenging thin film phenomena, including the Rayleigh-Taylor instability across double-bubbles, foam fragmentation with rim surface tension, recovery of the Plateau borders, Newton black films, as well as cyclones on bubble clusters.

A Moving Eulerian-Lagrangian Particle Method for Thin Film and Foam Simulation

Mohammad Sina Nabizadeh, Stephanie Wang, Ravi Ramamoorthi, Albert Chern

The animation of delicate vortical structures of gas and liquids has been of great interest in computer graphics. However, common velocity-based fluid solvers can damp the vortical flow, while vorticity-based fluid solvers suffer from performance drawbacks. We propose a new velocity-based fluid solver derived from a reformulated Euler equation using covectors. Our method generates rich vortex dynamics by an advection process that respects the Kelvin circulation theorem. The numerical algorithm requires only a small local adjustment to existing advection-projection methods and can easily leverage recent advances therein. The resulting solver emulates a vortex method without the expensive conversion between vortical variables and velocities. We demonstrate that our method preserves vorticity in both vortex filament dynamics and turbulent flows significantly better than previous methods, while also improving preservation of energy.

Covector Fluids

Cristian Romero, Dan Casas, Maurizio M. Chiaramonte, Miguel A. Otaduy

We propose a novel method to machine-learn highly detailed, nonlinear contact deformations for real-time dynamic simulation. We depart from previous deformation-learning strategies, and model contact deformations in a contact-centric manner. This strategy shows excellent generalization with respect to the object’s configuration space, and it allows for simple and accurate learning. We complement the contact-centric learning strategy with two additional key ingredients: learning a continuous vector field of contact deformations, instead of a discrete approximation; and sparsifying the mapping between the contact configuration and contact deformations. These two ingredients further contribute to the accuracy, efficiency, and generalization of the method. We integrate our learning-based contact deformation model with subspace dynamics, showing real-time dynamic simulations with fine contact deformation detail.

Contact-Centric Deformation Learning

Wojtek Pałubicki, Miłosz Makowski, Weronika Gajda, Torsten Hädrich, Dominik L. Michels, Sören Pirk

One of the greatest challenges to mankind is understanding the underlying principles of climate change. Over the last years, the role of forests in climate change has received increased attention. This is due to the observation that not only the atmosphere has a principal impact on vegetation growth but also that vegetation is contributing to local variations of weather resulting in diverse microclimates. The interconnection of plant ecosystems and weather is described and studied as ecoclimates. In this work we take steps towards simulating ecoclimates by modeling the feedback loops between vegetation, soil, and atmosphere. In contrast to existing methods that only describe the climate at a global scale, our model aims at simulating local variations of climate. Specifically, we model tree growth interactively in response to gradients of water, temperature and light. As a result, we are able to capture a range of ecoclimate phenomena that have not been modeled before, including geomorphic controls, forest edge effects, the Foehn effect and spatial vegetation patterning. To validate the plausibility of our method we conduct a comparative analysis to studies from ecology and climatology. Consequently, our method advances the state-of-the-art of generating highly realistic outdoor landscapes of vegetation.

Ecoclimates: Climate-Response Modeling of Vegetation