Physics-Based Animation

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)

Bo Ren, Ben Xu, Chenfeng Li

Porous materials are common in daily life. They include granular material (e.g. sand) that behaves like liquid flow when mixed with fluid and foam material (e.g. sponge) that deforms like solid when interacting with liquid. The underlying physics is further complicated when multiple fluids interact with porous materials involving coupling between rigid and fluid bodies, which may follow different physics models such as the Darcy’s law and the multiple-fluid Navier-Stokes equations. We propose a unified particle framework for the simulation of multiple-fluid flows and porous materials. A novel virtual phase concept is introduced to avoid explicit particle state tracking and runtime particle deletion/insertion. Our unified model is flexible and stable to cope with multiple fluid interacting with porous materials, and it can ensure consistent mass and momentum transport over the whole simulation space.

Unified particle system for multiple-fluid flow and porous material

Yue Chang, Shusen Liu, Xiaowei He, Sheng Li, Guoping Wang

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.

Semi-analytical Solid Boundary Conditions for Free Surface Flows

Chengguizi Han*, Tao Xue*, Mridul Aanjaneya

We propose a Lagrangian particle-based formulation for simulating deformation, fracture, and diffusion in thin membrane-like structures, such as aluminium foil, rubbery films, and seaweed flakes. We integrate our model with diffusion processes and derive a unified framework for simulating deformation-diffusion coupled phenomena, which is applied to provide realistic heterogeneity induced by the diffusion process to fracture patterns. To the best of our knowledge, our work is the first to simulate the complex fracture patterns of single-layered membranes in computer graphics and introduce heterogeneity induced by the diffusion process, which generates more geometrically rich fracture patterns. Our end-to-end 3D simulations show that our deformation-diffusion coupling framework captures detailed fracture growth patterns in thin membranes due to both in-plane and out-of-plane motions, producing realistically wrinkled slit edges, and heterogeneity introduced due to diffusion.

A Lagrangian Particle-based Formulation for Coupled Simulation of Fracture and Diffusion in Thin Membranes

Tetsuya Takahashi, Christopher Batty

We propose FrictionalMonolith, a monolithic pressure-friction-contact solver for more accurately, robustly, and efficiently simulating two-way interactions of rigid bodies with continuum granular materials or inviscid liquids. By carefully formulating the components of such systems within a single unified minimization problem, our solver can simultaneously handle unilateral incompressibility and implicit integration of friction for the interior of the continuum, frictional contact resolution among the rigid bodies, and mutual force exchanges between the continuum and rigid bodies. Our monolithic approach eliminates various problematic artifacts in existing weakly coupled approaches, including loss of volume in the continuum material, artificial drift and slip of the continuum at solid boundaries, interpenetrations of rigid bodies, and simulation instabilities. To efficiently handle this challenging monolithic minimization problem, we present a customized solver for the resulting quadratically constrained quadratic program that combines elements of staggered projections, augmented Lagrangian methods, inexact projected Newton, and active-set methods. We demonstrate the critical importance of a unified treatment and the effectiveness of our proposed solver in a range of practical scenarios.

FrictionalMonolith: A Monolithic Optimization-based Approach for Granular Flow with Contact-Aware Rigid-Body Coupling

Qiaodong Cui, Timothy Langlois, Pradeep Sen, and T. Kim

We introduce a fast, expressive method for simulating fluids over radial domains, including discs, spheres, cylinders, ellipses, spheroids, and tori. We do this by generalizing the spectral approach of Laplacian Eigenfunctions, resulting in what we call spiral-spectral fluid simulations. Starting with a set of divergence-free analytical bases for polar and spherical coordinates, we show that their singularities can be removed by introducing a set of carefully selected enrichment functions. Orthogonality is established at minimal cost, viscosity is supported analytically, and we specifically design basis functions that support scalable FFT-based reconstructions. Additionally, we present an efficient way of computing all the necessary advection tensors. Our approach applies to both three-dimensional flows as well as their surface-based, codimensional variants. We establish the completeness of our basis representation, and compare against a variety of existing solvers.

Spiral-Spectral Fluid Simulation