Physics-Based Animation

Ningxiao Tao, Liangwang Ruan , Yitong Deng, Bo Zhu, Bin Wang, Baoquan Chen

This paper introduces a novel physically-based vortex fluid model for films, aimed at accurately simulating cascading vortical structures on deforming thin films. Central to our approach is a novel mechanism decomposing the film’s tangential velocity into circulation and dilatation components. These components are then evolved using a hybrid particle-mesh method, enabling the effective reconstruction of three-dimensional tangential velocities and seamlessly integrating surfactant and thickness dynamics into a unified framework. By coupling with its normal component and surface-tension model, our method is particularly adept at depicting complex interactions between in-plane vortices and out-of-plane physical phenomena, such as gravity, surfactant dynamics, and solid boundary, leading to highly realistic simulations of complex thin-film dynamics, achieving an unprecedented level of vortical details and physical realism.

A Vortex Particle-on-Mesh Method for Soap Film Simulation

Zhongtian Zheng, Tongtong Wang, Qijia Feng, Zherong Pan, Xifeng Gao, Kui Wu

Simulating high-resolution cloth poses computational challenges in real-time applications. In the gaming industry, the proxy mesh technique offers an alternative, simulating a simplified low-resolution cloth geometry, proxy mesh. This proxy mesh’s dynamics drive the detailed high-resolution geometry, visual mesh, through Linear Blended Skinning (LBS). However, generating a suitable proxy mesh with appropriate skinning weights from a given visual mesh is non-trivial, often requiring skilled artists several days for fine-tuning. This paper presents an automatic pipeline to convert an ill-conditioned high-resolution visual mesh into a single-layer low-poly proxy mesh. Given that the input visual mesh may not be simulation-ready, our approach then simulates the proxy mesh based on specific use scenarios and optimizes the skinning weights, relying on differential skinning with several well-designed loss functions to ensure the skinned visual mesh appears plausible in the final simulation. We have tested our method on various challenging cloth models, demonstrating its robustness and effectiveness.

Proxy Asset Generation for Cloth Simulation in Games

Jerry Hsu, Tongtong Wang, Zherong Pan, Xifeng Gao, Cem Yuksel, Kui Wu

Strand-based hair simulations have recently become increasingly popular for a range of real-time applications. However, accurately simulating the full number of hair strands remains challenging. A commonly employed technique involves simulating a subset of guide hairs to capture the overall behavior of the hairstyle. Details are then enriched by interpolation using linear skinning. Hair interpolation enables fast real-time simulations but frequently leads to various artifacts during runtime. As the skinning weights are often pre-computed, substantial variations between the initial and deformed shapes of the hair can cause severe deviations in fine hair geometry. Straight hairs may become kinked, and curly hairs may become zigzags. This work introduces a novel physical-driven hair interpolation scheme that utilizes existing simulated guide hair data. Instead of directly operating on positions, we interpolate the internal forces from the guide hairs before efficiently reconstructing the rendered hairs based on their material model. We formulate our problem as a constraint satisfaction problem for which we present an efficient solution. Further practical considerations are addressed using regularization terms that regulate penetration avoidance and drift correction. We have tested various hairstyles to illustrate that our approach can generate visually plausible rendered hairs with only a few guide hairs and minimal computational overhead, amounting to only about 20% of conventional linear hair interpolation. This efficiency underscores the practical viability of our method for real-time applications.

Real-time Physically Guided Hair Interpolation

Jiawang Yu, Zhendong Wang

Creating super-resolution cloth animations, which refine coarse cloth meshes with fine wrinkle details, faces challenges in preserving spatial consistency and temporal coherence across frames. In this paper, we introduce a general framework to address these issues, leveraging two core modules. The first module interleaves a simulator and a corrector. The simulator handles cloth dynamics, while the corrector rectifies differences in low-frequency features across various resolutions. This interleaving ensures prompt correction of spatial errors from the coarse simulation, effectively preventing their temporal propagation. The second module performs mesh-based super-resolution for detailed wrinkle enhancements. We decompose garment meshes into overlapping patches for adaptability to various styles and geometric continuity. Our method achieves an 8× improvement in resolution for cloth animations. We showcase the effectiveness of our method through diverse animation examples, including simple cloth pieces and intricate garments.

Super-Resolution Cloth Animation with Spatial and Temporal Coherence

Xudong Feng, Huamin Wang, Yin Yang, Weiwei Xu

Real-world fabrics, composed of threads and yarns, often display complex stress-strain relationships, making their homogenization a challenging task for fast simulation by continuum-based models. Consequently, existing homogenized yarn-level models frequently struggle with numerical stability without line search at large time steps, forcing a trade-off between model accuracy and stability. In this paper, we propose a neural-assisted homogenized constitutive model for simulating yarn-level cloth. Unlike analytic models, a neural model is advantageous in adapting to complex dynamic behaviors, and its inherent smoothness naturally mitigates stability issues. We also introduce a sector-based warm-start strategy to accelerate the data collection process in homogenization. This model is trained using collected strain energy datasets and its accuracy is validated through both qualitative and quantitative experiments. Thanks to our model’s stability, our simulator can now achieve two-orders-of-magnitude speedups with large time steps compared to previous models.

Neural-Assisted Homogenization of Yarn-Level Cloth

Jean Jouve, Victor Romero, Rahul Narain, Laurence Boissieux, Theodore Kim, Florence Bertails-Descoubes

Feathers exhibit a highly anisotropic behaviour, governed by their complex hierarchical microstructure composed of individual hairs (barbs) clamped onto a spine (rachis) and attached to each other through tiny hooks (barbules). Previous methods in computer graph- ics have approximated feathers as strips of cloth, thus failing to cap- ture the particular macroscopic nonlinear behaviour of the feather surface (vane). To investigate the anisotropic properties of a feather vane, we design precise measurement protocols on real feather samples. Our experimental results suggest a linear strain-stress relationship of the feather membrane with orientation-dependent coefficients, as well as an extreme ratio of stiffnesses in the barb and barbule direction, of the order of 10 4 . From these findings we build a simple continuum model for the feather vane, where the vane is represented as a three-parameter anisotropic elastic shell. However, implementing the model numerically reveals severe lock- ing and ill-conditioning issues, due to the extreme stiffness ratio between the barb and the barbule directions. To resolve these is- sues, we align the mesh along the barb directions and replace the stiffest modes with an inextensibility constraint. We extensively validate our membrane model against real-world laboratory mea- surements, by using an intermediary microscale model that allows us to limit the number of required lab experiments. Finally, we enrich our membrane model with anisotropic bending, and show its practicality in graphics-like scenarios like a full feather and a larger-scale bird. Code and data for this paper are available at https://gitlab.inria.fr/elan-public-code/feather-shell/.

Modelling a feather as a strongly anisotropic elastic shell

Raphaël Charrondière, Sébastien Neukirch, Florence Bertails-Descoubes

Thin elastic ribbons represent a class of intermediary objects lying in-between thin elastic plates and thin elastic rods. Although the two latter families of thin structures have received much interest from the Computer Graphics community over the last decades, ribbons have seldom been considered and modelled numerically so far, in spite of a growing number of applications in Computer Design. In this paper, starting from the reduced developable ribbon models recently popularised in Soft Matter Physics, we propose a both accurate and efficient algorithm for computing the statics of a thin elastic ribbon. Inspired by the super-clothoid model for thin elastic rods, our method relies on compact ribbon elements whose normal curvature varies linearly with respect to arc length s, while their geodesic torsion is quadratic in s. In contrast however, for the sake of efficiency our algorithm avoids building a fully reduced kinematic chain and instead treats each element independently, gluing them only at the final solving stage through well-chosen bilateral constraints. Thanks to this mixed variational strategy, which yields a banded Hessian, our algorithm recovers the linear complexity of low-order models while preserving the quadratic convergence of curvature-based models. As a result, our approach is scalable to a large number of elements, and suitable for various boundary conditions and unilateral contact constraints, making it possible to handle challenging scenarios such as confined buckling experiments or Möbius bands with contact. Remarkably, our mixed algorithm proves an order of magnitude faster compared to Discrete Element Ribbon models of the literature while achieving, in a few seconds only, high accuracy levels that remain out of reach for such low-order models. Additionally, our numerical model can incorporate various ribbon energies, including the Ribext model for quasi-developable ribbons recently introduced in Physics, which allows to transition smoothly between a rectangular Kirchhoff rod and a (developable) Sadowsky ribbon. Our numerical scheme is carefully validated against demanding experiments of the Physics literature, which demonstrates its accuracy, efficiency, robustness, and versatility. Our MERCI code is publicly available at https://gitlab.inria.fr/elan-public-code/merci for the sake of reproducibility and future benchmarking.

Merci: Mixed curvature-based elements for computing equilibria of thin elastic ribbons

Zhiqi Li, Barnabás Börcsök, Duowen Chen, Yutong Sun, Bo Zhu, Greg Turk,

This paper introduces a novel Lagrangian fluid solver based on covector flow maps. We aim to address the challenges of establishing a robust flow-map solver for incompressible fluids under complex boundary conditions. Our key idea is to use particle trajectories to establish precise flow maps and tailor path integrals of physical quantities along these trajectories to reformulate the Poisson problem during the projection step. We devise a decoupling mechanism based on path-integral identities from flow-map theory. This mechanism integrates long-range flow maps for the main fluid body into a short-range projection framework, ensuring a robust treatment of free boundaries. We show that our method can effectively transform a long-range projection problem with integral boundaries into a Poisson problem with standard boundary conditions — specifically, zero Dirichlet on the free surface and zero Neumann on solid boundaries. This transformation significantly enhances robustness and accuracy, extending the applicability of flow-map methods to complex free-surface problems.

Lagrangian Covector Fluid with Free Surface

Honglin Chen, Hsueh-Ti Derek Liu, David I.W. Levin, Changxi Zheng, Alec Jacobson

Volume-preserving hyperelastic materials are widely used to model near-incompressible materials such as rubber and soft tissues. However, the numerical simulation of volume-preserving hyperelastic materials is notoriously challenging within this regime due to the non-convexity of the energy function. In this work, we identify the pitfalls of the popular eigenvalue clamping strategy for projecting Hessian matrices to positive semi-definiteness during Newton’s method. We introduce a novel eigenvalue filtering strategy for projected Newton’s method to stabilize the optimization of Neo-Hookean energy and other volume-preserving variants under high Poisson’s ratio (near 0.5) and large initial volume change. Our method only requires a single line of code change in the existing projected Newton framework, while achieving significant improvement in both stability and convergence speed. We demonstrate the effectiveness and efficiency of our eigenvalue projection scheme on a variety of challenging examples and over different deformations on a large dataset.

Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton

Junwei Zhou, Duowen Chen, Molin Deng, Yitong Deng, Yuchen Sun, Sinan Wang, Shiying Xiong, Bo Zhu

We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation naturally embodies a perfect flow map. Centered on this concept, we have developed an Eulerian-Lagrangian framework comprising four essential components: Lagrangian particles for a natural and precise representation of bidirectional flow maps; a dual-scale map representation to accommodate the mapping of various flow quantities; a particle-to-grid interpolation scheme for accurate quantity transfer from particles to grid nodes; and a hybrid impulse-based solver to enforce incompressibility on the grid. The efficacy of PFM has been demonstrated through various simulation scenarios, highlighting the evolution of complex vortical structures and the details of turbulent flows. Notably, compared to NFM, PFM reduces computing time by up to 49 times and memory consumption by up to 41%, while enhancing vorticity preservation as evidenced in various tests like
leapfrog, vortex tube, and turbulent flow.

Eulerian-Lagrangian Fluid Simulation on Particle Flow Maps