Physics-Based Animation

Tomoyo Kikuchi, Takashi Kanai

We present a unified, primitive-first framework with DCD for collision response in physics-based simulations. Previous methods do not provide sufficient solutions on a framework that resolves edge-triangle and edge-edge collisions when handling self-collisions and inter-object collisions in a unified manner. We define a scalar function and its gradient, representing the distance between two triangles and the movement direction for collision response, respectively. The resulting method offers an effective solution for collisions with minor computational overhead and robustness for any type of deformable object, such as solids or cloth. The algorithm is conceptually simple and easy to implement. When using PBD/XPBD, it is straightforward to incorporate our method into a collision constraint.

A Unified Discrete Collision Framework for Triangle Primitives

Yuhan Wu, Nobuyuki Umetani

We propose BlendSim, a novel framework for editable simulation, and its lightweight storage using spacetime optimization. Traditional spacetime control methods suffer from a high computational complexity, which limits their use in interactive animation. The proposed approach effectively reduces the dimensionality of the problem by representing the motion trajectories of each vertex using continuous parametric Bézier splines with variable keyframe times. Because this mesh animation representation is continuous and fully differentiable, it can be optimized such that it follows the laws of physics under various constraints. The proposed method also integrates constraints, such as collisions and cyclic motion, making it suitable for real-world applications where seamless looping and physical interactions are required. Leveraging projective dynamics, we further enhance the computational efficiency by decoupling the optimization into local parallelizable and global quadratic steps, enabling a fast and stable simulation.

BlendSim: Simulation on Parametric Blendshapes using Spacetime Projective Dynamics

Xiaowei He, Shusen Liu, Yuzhong Guo, Jian Shi, Ying Qiao

In simulating fluids using position-based dynamics, the accuracy and robustness depend on numerous numerical parameters, including the time step size, iteration count, and particle size, among others. This complexity can lead to unpredictable control of simulation behaviors. In this paper, we first reformulate the problem of enforcing fluid compressibility/incompressibility into an nonlinear optimization problem, and then introduce a semi-implicit successive substitution method (SISSM) to solve the nonlinear optimization problem by adjusting particle positions in parallel. In contrast to calculating an intermediate variable, such as pressure, to enforce fluid incompressibility within the position-based dynamics (PBD) framework, the proposed semi- implicit approach eliminates the necessity of such calculations. Instead, it directly employs successive substitution of particle positions to correct density errors. This method exhibits reduced dependency to numerical parameters, such as particle size and time step variations, and improves consistency and stability in simulating fluids that range from highly compressible to nearly incompressible. We validates the effectiveness of applying a variety of different techniques in accelerating the convergence rate.

A Semi-Implicit SPH Method for Compressible and Incompressible
Flows with Improved Convergence

Joel Wretborn, Alexey Stomakhin, Christopher Batty

We introduce a novel unified mixture-based method for simulating underwater bubbles across a range of bubble scales. Our approach represents bubbles as a set of Lagrangian particles that are coupled with the surrounding Eulerian water volume. When bubble particles are sparsely distributed, each particle, typically smaller than the liquid grid voxel size, corresponds to an individual spherical bubble. As the sub-grid particles increase in local density our model smoothly aggregates them, ultimately forming connected, fully aerated volumetric regions that are properly resolved by the Eulerian grid. We complement our scheme with a continuous surface tension model, defined via the gradient of the bubbles’ local volume fractions, which works seamlessly across this scale transition. Our unified representation allows us to capture a wide range of effects across different scales—from tiny dispersed sub-grid air pockets to fully Eulerian two-phase interfacial flows.

A unified multi-scale method for simulating immersed bubbles

Yuchen Sun, Linglai Chen, Weiyuan Zeng, Tao Du, Shiying Xiong, Bo Zhu

This paper introduces a two-phase interfacial fluid model based on the impulse variable to capture complex vorticity-interface interactions. Our key idea is to leverage bidirectional flow map theory to enhance the transport accuracy of both vorticity and interfaces simultaneously and address their coupling within a unified Eulerian framework. At the heart of our framework is an impulse ghost fluid method to solve the two-phase incompressible fluid characterized by its interfacial dynamics. To deal with the history-dependent jump of gauge variables across a dynamic interface, we develop a novel path integral formula empowered by spatiotemporal buffers to convert the history-dependent jump condition into a geometry-dependent jump condition when projecting impulse to velocity. We demonstrate the efficacy of our approach in simulating and visualizing several interface-vorticity interaction problems with cross-phase vortical evolution, including interfacial whirlpool, vortex ring reflection, and leapfrogging bubble rings.

An Impulse Ghost Fluid Method for Simulating Two-Phase Flows

• A Unified Multi-scale Method for Simulating Immersed Bubbles
• A Semi-Implicit SPH Method for Compressible and Incompressible Flows with Improved Convergence
• A Hybrid Lagrangian-Eulerian Formulation of Thin-shell Fracture
• Rest Shape Optimization for Sag-Free Discrete Elastic Rods
• BlendSim: Simulation on Parametric Blendshapes using Spacetime Projective Dynamics
• A Unified Discrete Collision Framework for Triangle Primitives
• Cloth Animation with Time-dependent Persistent Wrinkles
• Corotational Hinge-based Thin Plates/Shells
• Eigenvalue Blending for Projected Newton

Tetsuya Takahashi, Christopher Batty

We propose a new rest shape optimization framework to achieve sag-free simulations of discrete elastic rods. To optimize rest shape parameters, we formulate a minimization problem based on the kinetic energy with a regularizer while imposing box constraints on these parameters to ensure the system’s stability. Our method solves the resulting constrained minimization problem via the Gauss-Newton algorithm augmented with penalty methods. We demonstrate that the optimized rest shape parameters enable discrete elastic rods to achieve static equilibrium for a wide range of strand geometries and material parameters.

Rest Shape Optimization for Sag-Free Discrete Elastic Rods

L. Fan, Floyd M. Chitalu, Taku Komura

The hybrid Lagrangian/Eulerian formulation of continuum shells is highly effective for producing challenging simulations of thin materials like cloth with bending resistance and frictional contact. However, existing formulations are restricted to materials that do not undergo tearing nor fracture due to the difficulties associated with incorporating strong discontinuities of field quantities like velocity via basis enrichment while maintaining C^1 continuity or H^2 regularity. We propose an extension of this formulation to simulate dynamic tearing and fracturing of thin-shells using Kirchhoff-Love continuum theory. Damage, which manifests as cracks or tears, is propagated by tracking the evolution of a time-dependent phase-field in the co-dimensional manifold, where a moving least-squares (MLS) approximation then captures the strong discontinuities of interpolated field quantities near the crack. Our approach is capable of simulating challenging scenarios of this tearing and fracture, all-the-while harnessing the existing benefits of the hybrid Lagrangian/Eulerian formulation to expand the domain of possible effects. The method is also amenable to user-guided control, which serves to influence the propagation of cracks or tears such that they follow prescribed paths during simulation.

A Hybrid Lagrangian–Eulerian Formulation of Thin-Shell Fracture

Meng Zhang, Jun Li

Achieving efficient, high-fidelity, high-resolution garment simulation is challenging due to its computational demands. Conversely, low-resolution garment simulation is more accessible and ideal for low-budget devices like smartphones. In this paper, we introduce a lightweight, learning-based method for garment dynamic super-resolution, designed to efficiently enhance high-resolution, high-frequency details in low-resolution garment simulations. Starting with low-resolution garment simulation and underlying body motion, we utilize a mesh-graph-net to compute super-resolution features based on coarse garment dynamics and garment-body interactions. These features are then used by a hyper-net to construct an implicit function of detailed wrinkle residuals for each coarse mesh triangle. Considering the influence of coarse garment shapes on detailed wrinkle performance, we correct the coarse garment shape and predict detailed wrinkle residuals using these implicit functions. Finally, we generate detailed high-resolution garment geometry by applying the detailed wrinkle residuals to the corrected coarse garment. Our method enables roll-out prediction by iteratively using its predictions as input for subsequent frames, producing fine-grained wrinkle details to enhance the low-resolution simulation. Despite training on a small dataset, our network robustly generalizes to different body shapes, motions, and garment types not present in the training data. We demonstrate significant improvements over state-of-the-art alternatives, particularly in enhancing the quality of high-frequency, fine-grained wrinkle details.

Neural Garment Dynamic Super-Resolution

Huancheng Lin, Floyd M. Chitalu, Taku Komura

Anisotropic hyperelastic distortion energies are used to solve many problems in fields like computer graphics and engineering with applications in shape analysis, deformation, design, mesh parameterization, biomechanics and more. However, formulating a robust anisotropic energy that is low-order and yet sufficiently non-linear remains a challenging problem for achieving the convergence promised by Newton-type methods in numerical optimization. In this paper, we propose a novel analytic formulation of an anisotropic energy that is smooth everywhere, low-order, rotationally-invariant and at-least twice differentiable. At its core, our approach utilizes implicit rotation factorizations with invariants of the Cauchy-Green tensor that arises from the deformation gradient. The versatility and generality of our analysis is demonstrated through a variety of examples, where we also show that the constitutive law suggested by the anisotropic version of the well-known As-Rigid-As-Possible energy is the foundational parametric description of both passive and active elastic materials. The generality of our approach means that we can systematically derive the force and force-Jacobian expressions for use in implicit and quasistatic numerical optimization schemes, and we can also use our analysis to rewrite, simplify and speedup several existing anisotropic and isotropic distortion energies with guaranteed inversion-safety.

Analytic rotation-invariant modelling of anisotropic finite elements