Physics-Based Animation

Li Huang, Fan Yang, Chendi Wei, Yuju (Edwin) Chen, Chun Yuan, Ming Gao

This paper introduces a hair simulator optimized for real-time applications, including console and cloud gaming, avatar live-streaming, and metaverse environments. We view the collisions between strands as a mechanism to preserve the overall volume of the hair and adopt explicit Material Point Method (MPM) to resolve the strand-strand collision. For simulating single-strand behavior, a semi-implicit Discrete Elastic Rods (DER) model is used. We build upon a highly efficient GPU MPM framework recently presented by Fei et al. [2021b] and propose several schemes to largely improve the performance of building and solving the semi-implicit DER systems on GPU. We demonstrate the efficiency of our pipeline by a few practical scenes that achieve up to 260 frames-per-second (FPS) with more than two thousand simulated strands on Nvidia GeForce RTX 3080.

Towards Realtime: A Hybrid Physics-based Method for Hair Animation on GPU

Paul Zhang, Zoë Marschner, Justin Solomon, Rasmus Tamstorf

Sum-of-Squares Programming (SOSP) has recently been introduced to graphics as a unified way to address a large set of difficult problems involving higher order primitives. Unfortunately, a challenging aspect of this approach is the computational cost—especially for problems involving multiple geometries like collision detection. In this paper, we present techniques to reduce the cost of SOSP significantly. We use these improvements to speed up difficult problems like collision detection between Bézier triangles by as much as 300×. In addition, motivated by hair bundle simulation, we present SOSP based collision detection on the tapered cubic cylinder. We also present an algebraic formulation of rigid body motion enabling SOSP based collision detection for curved geometries and trajectories simultaneously. While these new formulations are complex, our speedups make them feasible. These advances improve the applicability of SOSP based collision detection and enable the continued progress of higher-order geometry processing.

Sum-of-Squares Collision Detection for Curved Shapes and Paths

Alexandre Mercier-Aubin, Paul G. Kry

We present a method to improve the computation time of thin shell simulations by using adaptive rigidification to reduce the number of degrees of freedom. Our method uses a discretization independent metric for bending rates, and we derive a membrane strain rate to curvature rate equivalence that permits the use of a common threshold. To improve accuracy, we enhance the elastification oracle by considering both membrane and bending deformation to determine when to rigidify or elastify. Furthermore, we explore different approaches that are compatible with the previous work on adaptive rigidifcation and enhance the accuracy of the elastification on new contacts without increasing the computational overhead. Additionally, we propose a scaling approach that reduces the conditioning issues that arise from mixing rigid and elastic bodies in the same model.

Adaptive Rigidification of Discrete Shell

Tetsuya Takahashi, Christopher Batty

Efficiently solving large-scale box-constrained convex quadratic programs (QPs) is an important computational challenge in physical simulation. We propose a new multilevel preconditioning scheme based on the active-set method and combine it with modified proportioning with reduced gradient projections (MPRGP) to efficiently solve such QPs arising from pressure Poisson equations with non-negative pressure constraints in fluid animation. Our method employs a purely algebraic multigrid method to ensure the solvability of the coarser level systems and to merge only algebraically-connected components, thereby avoiding performance degradation of the preconditioner. We present a filtering scheme to efficiently apply our multilevel preconditioning only to unconstrained subsystems of the pressure Poisson system while reusing the hierarchy constructed per simulation step. We demonstrate the effectiveness of our method over previous approaches in various examples.

A Multilevel Active-Set Preconditioner for Box-Constrained Pressure Poisson Solvers

Haozhe Su, Xuan Li, Tao Xue, Chenfanfu Jiang, Mridul Aanjaneya

We present a generalized constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating material behaviors that involve plasticity, including elastoplasticity and viscoplasticity. We show how our generalized Kirchhoff stress tensor can be coupled together into a generalized constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. We present several side-by-side comparisons with physics simulations for specific constitutive models to show that our generalized model produces visually similar results. More notably, our formulation allows for inverse learning of unknown material properties directly from data using differentiable physics simulations. We present several 3D simulations to highlight the robustness of our method, even with multiple different materials. To the best of our knowledge, our approach is the first to recover the knowledge of unknown material properties without making explicit assumptions about the data.

A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable Physics

Fabian Löschner, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Andreas Longva, Jan Bender

We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material’s strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions. For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points. In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.

Micropolar Elasticity in Physically-Based Animation

Lukas Westhofen, Stefan Rhys Jeske, Jan Bender

A well-known issue with the widely used Smoothed Particle Hydrodynamics (SPH) method is the neighborhood deficiency. Near the surface, the SPH interpolant fails to accurately capture the underlying fields due to a lack of neighboring particles. These errors may introduce ghost forces or other visual artifacts into the simulation. In this work we investigate three different popular methods to correct the first-order spatial derivative SPH operators up to linear accuracy, namely the Kernel Gradient Correction (KGC), Moving Least Squares (MLS) and Reproducing Kernel Particle Method (RKPM). We provide a thorough, theoretical comparison in which we remark strong resemblance between the aforementioned methods. We support this by an analysis using synthetic test scenarios. Additionally, we apply the correction methods in simulations with boundary handling, viscosity, surface tension, vorticity and elastic solids to showcase the reduction or elimination of common numerical artifacts like ghost forces. Lastly, we show that incorporating the correction algorithms in a state-of-the-art SPH solver only incurs a negligible reduction in computational performance.

A comparison of linear consistent correction methods for first-order SPH derivatives

Tuur Stuyck, Hsiao-yu Chen

We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with respect to a goal function simultaneously leveraging a performant simulation model. The method is efficient, thus enabling differentiable simulations of high resolution geometries and degrees of freedom (DoFs). Collisions are naturally included in the framework. Our differentiable model allows a user to easily add additional optimization variables. Every control variable gradient requires the computation of only a few partial derivatives which can be computed using automatic differentiation code. We demonstrate the efficacy of the method with examples such as elastic material parameter estimation, initial value optimization, optimizing for underlying body shape and pose by only observing the clothing, and optimizing a time-varying external force sequence to match sparse keyframe shapes at specific times. Our approach demonstrates excellent efficiency and we demonstrate this on high resolution meshes with optimizations involving over 26 million degrees of freedom. Making an existing solver differentiable requires only a few modifications and the model is compatible with both modern CPU and GPU multi-core hardware.

DiffXPBD : Differentiable Position-Based Simulation of Compliant Constraint Dynamics

Yuhan Wu, Nobuyuki Umetani

Skinning transformations allow digital characters to be animated with minimal user inputs. Physics simulations can improve the detailed dynamic movement of the animated character; however, such details are typically added in the post-processing stage after the overall animation is specified. We propose a novel interactive framework that unifies skinning transformations and kinematic simulations using position-based dynamics (PBD). Our framework allows an arbitrarily skinned character to be partially manipulated by the user, and a kinematic physics solver automatically complements the behavior of the entire character. We achieve this by introducing new steps in the PBD algorithm, (i) lightweight optimization to identify the skinning transformations, which is similar to inverse kinematics, and (ii) a position-based constraint to restrict the PBD solver in the complementary subspace of the skinning deformation. Our method combines the best of the two methods: the controllability and shape preservation of the skinning transformation and the efficiency, simplicity, and unconditional stability of the PBD solver. Our interface allows novices to create vibrant animations without the need for tedious editing.

Two-Way Coupling of Skinning Transformations and Position Based Dynamics

Jonathan Panuelos, Ryan Goldade, Eitan Grinspun, David Levin, Christopher Batty

Standard liquid simulators apply operator splitting to independently solve for pressure and viscous stresses, a decoupling that induces incorrect free surface boundary conditions. Such methods are unable to simulate fluid phenomena reliant on the balance of pressure and viscous stresses, such as the liquid rope coil instability exhibited by honey. By contrast, unsteady Stokes solvers retain coupling between pressure and viscosity, thus resolving these phenomena, albeit using a much larger and thus more computationally expensive linear system compared to the decoupled approach. To accelerate solving the unsteady Stokes problem, we propose a reduced fluid model wherein interior regions are represented with incompressible polynomial vector fields. Sets of standard grid cells are consolidated into super-cells, each of which are modelled using a quadratic field of 26 degrees of freedom. We demonstrate that the reduced field must necessarily be at least quadratic, with the affine model being unable to correctly capture viscous forces. We reproduce the liquid rope coiling instability, as well as other simulated examples, to show that our reduced model is able to reproduce the same fluid phenomena at a smaller computational cost. Futhermore, we performed a crowdsourced user survey to verify that our method produces imperceptible differences compared to the full unsteady Stokes method.

PolyStokes: A Polynomial Model Reduction Method for Viscous Fluid Simulation