Physics-Based Animation

Xingyu Ni, Bo Zhu, Bin Wang, Baoquan Chen

We present a versatile numerical approach to simulating various magnetic phenomena using a level-set method. At the heart of our method lies a novel two-way coupling mechanism between a magnetic field and a magnetizable mechanical system, which is based on the interfacial Helmholtz force drawn from the Minkowski form of the Maxwell stress tensor. We show that a magnetic-mechanical coupling system can be solved as an interfacial problem, both theoretically and computationally. In particular, we employ a Poisson equation with a jump condition across the interface to model the mechanical-to-magnetic interaction and a Helmholtz force on the free surface to model the magnetic-to-mechanical effects. Our computational framework can be easily integrated into a standard Euler fluid solver, enabling both simulation and visualization of a complex magnetic field and its interaction with immersed magnetizable objects in a large domain. We demonstrate the efficacy of our method through an array of magnetic substance simulations that exhibit rich geometric and dynamic characteristics, encompassing ferrofluid, rigid magnetic body, deformable magnetic body, and multi-phase couplings.

A Level-Set Method for Magnetic Substance Simulation

Hui Wang, Yongxu Jin, Anqi Luo, Xubo Yang, Bo Zhu

We propose a new Eulerian-Lagrangian approach to simulate the various surface tension phenomena characterized by volume, thin sheets, thin filaments, and points using Moving-Least-Squares (MLS) particles. At the center of our approach is a meshless Lagrangian description of the different types of codimensional geometries and their transitions using an MLS approximation. In particular, we differentiate the codimension-1 and codimension-2 geometries on Lagrangian MLS particles to precisely describe the evolution of thin sheets and filaments, and we discretize the codimension-0 operators on a background Cartesian grid for efficient volumetric processing. Physical forces including surface tension and pressure across different codimensions are coupled in a monolithic manner by solving one single linear system to evolve the surface-tension driven Navier-Stokes system in a complex non-manifold space. The codimensional transitions are handled explicitly by tracking a codimension number stored on each particle, which replaces the tedious meshing operators in a conventional mesh-based approach. Using the proposed framework, we simulate a broad array of visually appealing surface tension phenomena, including the fluid chain, bell, polygon, catenoid, and dripping, to demonstrate the efficacy of our approach in capturing the complex fluid characteristics with mixed codimensions, in a robust, versatile, and connectivity-free manner.

Codimensional Surface Tension Flow using Moving-Least-Squares Particles

Christoph Gissler, Andreas Henne, Stefan Band, Andreas Peer, Matthias Teschner

Snow is a complex material. It resists elastic normal and shear deformations, while some deformations are plastic. Snow can deform and break. It can be significantly compressed and gets harder under compression. Existingsnow solvers produce impressive results. E.g., hybrid Lagrangian/Euleriantechniques have been used to capture all material properties of snow. The auxiliary grid, however, makes it challenging to handle small volumes. In particular, snow fall and accumulation on surfaces have not been demonstrated with these solvers yet. Existing particle-based snow solvers, on the other hand, can naturally handle small snow volumes. However, existing solutions consider simplified material properties. In particular, shear deformation and the hardening effect are typically omitted. We present a novel Lagrangian snow approach based on Smoothed Particle Hydrodynamics (SPH). Snow is modeled as an elastoplastic continuous material that captures all above-mentioned effects. The compression of snow is handled by a novel compressible pressure solver, where the typically employed state equation is replaced by an implicit formulation. Acceleration due to shear stress is computed using a second implicit formulation. The linear solvers of the two implicit formulations for accelerations due to shear and normal stress are realized with matrix-free implementations. Using implicit formulations and solving them with matrix-free solvers al-lows to couple the snow to other phases and is beneficial to the stability and the time step size, i.e., performance of the approach. Solid boundaries are represented with particles and a novel implicit formulation is used to handle friction at solid boundaries. We show that our approach can simulate accumulation, deformation, breaking, compression and hardening of snow. Furthermore, we demonstrate two-way coupling with rigid bodies, interaction with incompressible and highly viscous fluids and phase change from fluid to snow.

An Implicit Compressible SPH Solver for Snow Simulation

Tomas Skrivan, Andreas Soderstrom, John Johansson, Christoph Sprenger, Ken Museth, Chris Wojtan

We propose a method to enhance the visual detail of a water surface simula-tion. Our method works as a post-processing step which takes a simulationas input and increases its apparent resolution by simulating many detailedLagrangian water waves on top of it. We extend linear water wave theoryto work in non-planar domains which deform over time, and we discretizethe theory using Lagrangian wave packets attached to spline curves. Themethod is numerically stable and trivially parallelizable, and it produceshigh frequency ripples with dispersive wave-like behaviors customized tothe underlying fluid simulation.

Wave Curves: Simulating Lagrangian water waves on dynamically deforming surfaces

Weizhen Huang, Julian Iseringhausen, Tom Kneiphof, Ziyin Qu, Chenfanfu Jiang, Matthias B. Hullin

Soap bubbles are widely appreciated for their fragile nature and their colorful appearance. The natural sciences and, in extension, computer graphics, have comprehensively studied the mechanical behavior of films and foams, as well as the optical properties of thin liquid layers. In this paper, we focus on the dynamics of material flow within the soap film, which results in fascinating, extremely detailed patterns. This flow is characterized by a complex coupling between surfactant concentration and Marangoni surface tension. We propose a novel chemomechanical simulation framework rooted in lubrication theory, which makes use of a custom semi-Lagrangian advection solver to enable the simulation of soap film dynamics on spherical bubbles both in free flow as well as under body forces such as gravity or external air flow. By comparing our simulated outcomes to videos of real-world soap bubbles recorded in a studio environment, we show that our framework, for the first time, closely recreates a wide range of dynamic effects that are also observed in experiment.

Chemomechanical Simulation of Soap Film Flow on Spherical Bubbles

Yixin Hu, Teseo Schneider, Bolun Wang, Denis Zorin, Daniele Panozzo

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to construct and optimize the output mesh, interleaving triangle insertion and mesh optimization. Our approach makes it possible to maintain a valid floating-point tetrahedral mesh at all algorithmic stages, eliminating the need for costly constructions with rational numbers used by TetWild, while maintaining full robustness and similar output quality. This allows us to improve on TetWild in two ways. First, our algorithm is significantly faster, with running time comparable to less robust Delaunay-based tetrahedralization algorithms. Second, our algorithm is guaranteed to produce a valid tetrahedral mesh with floating-point vertex coordinates, while TetWild produces a valid mesh with rational coordinates which is not guaranteed to be valid after floating-point conversion. As a trade-off, our algorithm no longer guarantees that all input triangles are present in the output mesh, but in practice, as confirmed by our tests on the Thingi10k dataset, the algorithm always succeeds in inserting all input triangles.

Fast Tetrahedral Meshing in the Wild

Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, Danny M. Kaufman

Contacts weave through every aspect of our physical world, from daily household chores to acts of nature. Modeling and predictive computation of these phenomena for solid mechanics is important to every discipline concerned with the motion of mechanical systems, including engineering and animation. Nevertheless, efficiently time-stepping accurate and consistent simulations of real-world contacting elastica remains an outstanding computational challenge. To model the complex interaction of deforming solids in contact we propose Incremental Potential Contact (IPC) – a new model and algorithm for variationally solving implicitly time-stepped nonlinear elastodynamics. IPC maintains an intersection- and inversion-free trajectory regardless of material parameters, time step sizes, impact velocities, severity of deformation, or boundary conditions enforced. Constructed with a custom nonlinear solver, IPC enables efficient resolution of time-stepping problems with separate, user-exposed accuracy tolerances that allow independent specification of the physical accuracy of the dynamics and the geometric accuracy of surface-to-surface conformation. This enables users to decouple, as needed per application, desired accuracies for a simulation’s dynamics and geometry. The resulting time stepper solves contact problems that are intersection-free (and thus robust), inversion-free, efficient (at speeds comparable to or faster than available methods that lack both convergence and feasibility), and accurate (solved to user-specified accuracies). To our knowledge, this is the first implicit time-stepping method, across both the engineering and graphics literature that can consistently enforce these guarantees as we vary simulation parameters. In an extensive comparison of available simulation methods, research libraries and commercial codes we confirm that available engineering and computer graphics methods, while each succeeding admirably in custom-tuned regimes, often fail with instabilities, egregious constraint violations and/or inaccurate and implausible solutions, as we vary input materials, contact numbers and time step. We also exercise IPC across a wide range of existing and new benchmark tests and demonstrate its accurate solution over a broad sweep of reasonable time-step sizes and beyond (up to h=2s) across challenging large-deformation, large-contact stress-test scenarios with meshes composed of up to 2.3M tetrahedra and processing up to 498K contacts per time step. For applications requiring high-accuracy we demonstrate tight convergence on all measures. While, for applications requiring lower accuracies, e.g. animation, we confirm IPC can ensure feasibility and plausibility even when specified tolerances are lowered for efficiency.

Incremental Potential Contact: Intersection- and Inversion-free, Large-Deformation Dynamic

Marc ten Bosch

I present a formulation for Rigid Body Dynamics that is independent of the dimension of the space. I describe the state and equations of motion of rigid bodies using geometric algebra. Using collision detection algorithms extended to nD I resolve collisions and contact between bodies. My implementation is 4D, but the techniques described here apply to any number of dimensions. I display these four-dimensional rigid bodies by taking a three-dimensional slice through them. I allow the user to manipulate these bodies in real-time.

N-Dimensional Rigid Body Dynamics

Mickael Ly, Jean Jouve, Laurence Boissieux, Florence Bertails-Descoubes

Projective dynamics was introduced a few years ago as a fast method to yield an approximate yet stable solution to the dynamics of nodal systems subject to stiff internal forces. Previous attempts to include contact forces in that framework considered adding a quadratic penalty energy to the global system, which however broke the simple, constant matrix, structure of the global linear equation, while failing to treat contact in an implicit manner. In this paper, we propose a simple yet effective method to integrate in a unified and semi-implicit way contact as well as dry frictional forces into the nested architecture of Projective dynamics. Assuming that contacts apply to nodes only, the key is to split the global matrix into a diagonal and a positive matrix, and use this splitting in the local step so as to make a good prediction of frictional contact forces at next iteration. Each frictional contact force is refined independently in the local step, while the original efficient structure of the global step is left unchanged. We apply our algorithm to cloth simulation and show that contact and dry friction can be captured at a reasonable precision within a few iterations only, hence one order of magnitude faster compared to global implicit contact solvers of the literature.

Projective Dynamics with Dry Frictional Contact

Kazem Cheshmi, Danny M. Kaufman, Shoaib Kamil, Maryam Mehri Dehnavi

Quadratic programs (QP), minimizations of quadratic objectives subject to linear inequality and equality constraints, are at the heart of algorithms across scientific domains. Applications include fundamental tasks in geometry processing, simulation, engineering, animation, and finance where the accurate, reliable, efficient, and scalable solution of QP problems is critical. However, available QP algorithms generally provide either accuracy or scalability – but not both. Some algorithms reliably solve QP problems to high accuracy but work only for smaller-scale QP problems due to their reliance on dense matrix methods. Alternately, many other QP solvers scale well via sparse, efficient algorithms but cannot reliably deliver solutions requested accuracies. Towards addressing the need for accurateandefficientQP solvers at scale, we develop NASOQ, a new, full-space QP algorithm that provides accurate, efficient, and scalable solutions for QP problems. To enable NASOQ we construct a new row modification method and fast implementation of LDL factorization for indefinite systems. Together they enable efficient updates and accurate solutions of the iteratively modified KKT systems required for accurate QP solves. While QP methods have been previously tested on large synthetic benchmarks, to test and compare NASOQ’ssuitability for real-world applications we collect here a new benchmark set comprising a wide range of graphics-related QPs across physical simulation, animation, and geometry processing tasks. We combine these problems with numerous pre-existing stress-test QP benchmarks to form, to our knowledge, the largest-scale test set of application-based QP problems currently available. Building off of our base NASOQ solver we then develop and test two NASOQ variants against best, state-of-the-art available QP libraries –both commercial and open-source. Our two NASOQ-based methods each solve respectively 98.8% and 99.5% of problems across a range of requested accuracies from 10^−3 to 10^−9 with average speedups ranging from 1.7× to 24.8× over the fastest competing methods.

NASOQ: Numerically Accurate Sparsity-Oriented QP Solver