Physics-Based Animation

Dan Koschier, Jan Bender, Barbara Solenthaler, Matthias Teschner

Throughout the past decades, the graphics community has spent major resources on the research and development of physics simulators on the mission to computer-generate behaviors achieving outstanding visual effects or to make the virtual world indistinguishable from reality. The variety and impact of recent research based on Smoothed Particle Hydrodynamics (SPH) demonstrates the concept’s importance as one of the most versatile tools for the simulation of fluids and solids. With this survey, we offer an overview of the developments and still-active research on physics simulation methodologies based on SPH that has not been addressed in previous SPH surveys. Following an introduction about typical SPH discretization techniques, we provide an overview over the most used incompressibility solvers and present novel insights regarding their relation and conditional equivalence. The survey further covers recent advances in implicit and particle-based boundary handling and sampling techniques. While SPH is best known in the context of fluid simulation we discuss modern concepts to augment the range of simulatable physical characteristics including turbulence, highly viscous matter, deformable solids, as well as rigid body contact handling. Besides the purely numerical approaches, simulation techniques aided by machine learning are on the rise. Thus, the survey discusses recent data-driven approaches and the impact of differentiable solvers on artist control. Finally, we provide context for discussion by outlining existing problems and opportunities to open up new research directions.

A Survey on SPH Methods in Computer Graphics

Qiang Chen, Tingsong Lu, Yang Tong, Guoliang Luo, Xiaogang Jin, Zhigang Deng

As one of ubiquitous insects on the earth, butterflies are also widely-known
for inspiring thrill resonance with their elegant and peculiar flights. However, realistically modeling and simulating butterfly flights, in particular, for real-time graphics and animation applications, remains an under-explored problem. In this paper we propose an efficient and practical model to simulate butterfly flights. Specifically, we first model a butterfly with parametric maneuvering functions, including wing-abdomen interaction. Then, we simulate dynamic maneuvering control of the butterfly through our force-based model that includes both the aerodynamics force and the vortex force. Through many simulation experiments and comparisons, we demonstrate that our method can efficiently simulate realistic butterfly flight motions in various real-world settings.

A Practical Model for Realistic Butterfly Flight Simulation

Teseo Schneider, Yixin Hu, Xifeng Gao, Jeremie Dumas, Denis Zorin, Daniele Panozzo

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs.
The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance.

A Large-Scale Comparison of Tetrahedral and Hexahedral Elements for Solving Elliptic PDEs with the Finite Element Method

Bolun Wang, Zachary Ferguson, Xin Jiang, Marco Attene, Daniele Panozzo, Teseo Schneider

We introduce the first exact root parity counter for continuous collision detection (CCD). That is, our algorithm computes the parity (even or odd) of the number of roots of the cubic polynomial arising from a CCD query. We note that the parity is unable to differentiate between zero (no collisions) and the rare case of two roots (collisions). Our method does not have numerical parameters to tune, has a performance comparable to efficient approximate algorithms, and is exact. We test our approach on a large collection of synthetic tests and real simulations, and we demonstrate that it can be easily integrated into existing simulators.

Fast and Exact Root Parity for Continuous Collision Detection

Qisi Wang, Yutian Tao, Eric Brandt, Court Cutting, Eftychios Sifakis

We present a method for the efficient processing of contact and collision in volumetric elastic models simulated using the Projective Dynamics paradigm. Our approach enables interactive simulation of tetrahedral meshes with more than half a million elements, provided that the model satisfies two fundamental properties: the region of the model’s surface that is susceptible to collision events needs to be known in advance, and the simulation degrees of freedom associated with that surface region should be limited to a small fraction (e.g. 5\%) of the total simulation nodes. Despite this conscious delineation of scope, our hypotheses hold true for common animation subjects, such as simulated models of the human face and parts of the body. In such scenarios, a partial Cholesky factorization can abstract away the behavior of the collision-safe subset of the face into the Schur Complement matrix with respect to the collision-prone region. We demonstrate how fast and accurate updates of penalty-based collision terms can be incorporated into this representation, and solved with high efficiency on the GPU. We also demonstrate the opportunity to iterate a partial update of the element rotations, akin to a selective application of the local step, specifically on the smaller collision-prone region without explicitly paying the cost associated with the rest of the simulation mesh. We demonstrate efficient and robust interactive simulation in detailed models from animation and medical applications

Optimized Processing of Localized Collisions in Projective Dynamics

Haozhe Su, Tao Xue, Chengguizi Han, Mridul Aanjaneya

We present an arbitrary updated Lagrangian Material Point Method (A-ULMPM) to alleviate issues, such as the cell-crossing instability and numerical fracture, that plague state of the art Eulerian formulations of MPM, while still allowing for large deformations that arise in fluid simulations. Our proposed framework spans MPM discretizations from total Lagrangian formulations to Eulerian formulations. We design an easy-to-implement physics-based criterion that allows A-ULMPM to update the reference configuration adaptively for measuring physical states including stress, strain, interpolation kernels and their derivatives. For better efficiency and conservation of angular momentum, we further integrate the APIC[Jiang et al. 2015] and MLS-MPM[Hu et al. 2018] formulations in A-ULMPM by augmenting the accuracy of velocity rasterization using both the local velocity and its first-order derivatives. Our theoretical derivations use a nodal discretized Lagrangian, instead of the weak form discretization in MLS-MPM[Hu et al. 2018], and naturally lead to a “modified” MLS-MPM in A-ULMPM, which can recover MLS-MPM using a completely Eulerian formulation. A-ULMPM does not require significant changes to traditional Eulerian formulations of MPM, and is computationally more efficient since it only updates interpolation kernels and their derivatives when large topology changes occur. We present end-to-end 3D simulations of stretching and twisting hyperelastic solids, splashing liquids, and multi-material interactions with large deformations to demonstrate the efficacy of our novel A-ULMPM framework.

A-ULMPM: An Arbitrary Updated Lagrangian Material Point Method for Efficient Simulation of Solids and Fluids

• A-ULMPM: An Arbitrary Updated Lagrangian Material Point Method for Efficient Simulation of Solids and Fluids
• Coupling 3D Liquid with Simulation with 2D Wave Propagation for Large Scale Water Surface Animation using the Equivalent Sources Method
• Fast and Exact Root Parity for Continuous Collision Detection
• Mesh-Based Network for Quasi-Static Cloth Deformation
• Optimized Processing of Localized Collisions in Projective Dynamics

Mianlun Zheng, Yi Zhou, Duygu Ceylan, Jernej Barbič

Fast and light-weight methods for animating 3D characters are desirable in various applications such as computer games. We present a learning-based approach to enhance skinning-based animations of 3D characters with vivid secondary motion effects. We design a neural network that encodes each local patch of a character simulation mesh where the edges implicitly encode the internal forces between the neighboring vertices. The network emulates the ordinary differential equations of the character dynamics, predicting new vertex positions from the current accelerations, velocities and positions. Being a local method, our network is independent of the mesh topology and generalizes to arbitrarily shaped 3D character meshes at test time. We further represent per-vertex constraints and material properties such as stiffness, enabling us to easily adjust the dynamics in different parts of the mesh. We evaluate our method on various character meshes and complex motion sequences. Our method can be over 30 times more efficient than ground-truth physically based simulation, and outperforms alternative solutions that provide fast approximations.

A Deep Emulator for Secondary Motion of 3D Characters

Jing Li, Tiantian Liu, Ladislav Kavan

We propose a fast and robust solver to simulate continuum-based deformable models with constraints, in particular, rigid-body and joint constraints useful for soft articulated characters. Our method embeds the degrees of freedom of both articulated rigid bodies and deformable bodies in one unified constrained optimization problem, thus coupling the deformable and rigid bodies. Inspired by Projective Dynamics which is a fast numerical solver to simulate deformable objects, we also propose a novel local/global solver that takes full advantage of the pre-factorized system matrices to accelerate the solve of our constrained optimization problem. Therefore, our method can efficiently simulate character models, with rigid-body parts (bones) being correctly coupled with deformable parts (flesh). Our method is stable because backward Euler time integration is applied to both rigid and deformable degrees of freedom. Our unified optimization problem is rigorously derived from constrained Newtonian mechanics. When simulating only articulated rigid bodies as a special case, our method converges to the state-of-the-art rigid body simulators.

Soft Articulated Characters in Projective Dynamics

Happy new year 2022, Physics-Based Animation readers! Aside from the usual papers that appear here, I also maintain a page for tutorial resources and courses: http://www.physicsbasedanimation.com/resources-courses/ Since there have been quite a few nice new ones produced over the last 3-4 years, I thought I would highlight them with this post (including Matthias Mueller-Fischer’s YouTube series, that I just added this morning):

Bargteil & Shinar SIGGRAPH Course: An Introduction to Physics-Based Animation (2018) [Video from SIGGRAPH 2019]

Fratarcangeli et al. SIGGRAPH Asia Course: Parallel Iterative Solvers for Real-Time Elastic Deformations (2018)

Koschier et al. Eurographics Tutorial: Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids (2019)

Kim & Eberle’s Dynamic Deformables: Implementation and Production Practicalities (2020)

David I.W. Levin’s Physics-Based Animation YouTube series (2020)

Andrews & Erleben’s Contact and Friction Simulation for Computer Graphics (2021)

Matthias Mueller-Fischer’s Ten Minute Physics YouTube series (2021)