Physics-Based Animation

Chen Zhao, Tamar Shinar, Craig Schroeder

Recently, Zhao et al . [2024] proposed a new method for constructing signed distance functions from fluid simulation particles. This method was able to achieve superior surface smoothness, noise reduction, and temporal coherence compared with previous methods. One of the main limitations of the method was its relatively slow construction times, even though it utilized both the CPU and GPU. In this paper, we consider two modifications to this scheme that make the algorithm easier to optimize without introducing any perceptible changes in reconstruction quality, as illustrated in Figure 1. With these improvements, a surface can be reconstructed from a single fluid simulation with 2M particles in 2.21 seconds, compared with 72.3 seconds for the original method, resulting in a single-frame reconstruction speedup of about 33×, making the surface reconstruction fast enough for use within a simulation framework. When reconstructing surface for multiple simulation frames together, we achieve a speedup of about 5× compared with the original. The optimized implementation will be released with the publication.

Fast Reconstruction of Implicit Surfaces Using Convolutional Neural Networks

Yue Chang, Mengfei Liu, Zhecheng Wang, Peter Yichen Chen, Eitan Grinspun

Cutting thin-walled deformable structures is common in daily life, but poses significant challenges for simulation due to the introduced spatial discontinuities. Traditional methods rely on mesh-based domain representations, which require frequent remeshing and refinement to accurately capture evolving discontinuities. These challenges are further compounded in reduced-space simulations, where the basis functions are inherently geometry- and mesh-dependent, making it difficult or even impossible for the basis to represent the diverse family of discontinuities introduced by cuts. Recent advances in representing basis functions with neural fields offer a promising alternative, leveraging their discretization-agnostic nature to represent deformations across varying geometries. However, the inherent continuity of neural fields is an obstruction to generalization, particularly if discontinuities are encoded in neural network weights. We present Wind Lifter, a novel neural representation designed to ac-
curately model complex cuts in thin-walled deformable structures. Our approach constructs neural fields that reproduce discontinuities precisely at specified locations, without “baking in” the position of the cut line. To achieve this, we augment the input coordinates of the neural field with the generalized winding number of any given cut line, effectively lifting the input from two to three dimensions. Lifting allows the network to focus on the easier problem of learning a 3D everywhere-continuous volumetric field, while a corresponding restriction operator enables the final output field to precisely resolve strict discontinuities. Crucially, our approach does not embed the discontinuity in the neural network’s weights, opening avenues to generalization of cut placement. Our method achieves real-time simulation speeds and supports dynamic updates to cut line geometry during the simulation. Moreover, the explicit representation of discontinuities makes our neural field intuitive to control and edit, offering a significant advantage over traditional neural fields, where discontinuities are embedded within the network’s weights, and enabling new applications that rely on general cut placement.

Lifting the Winding Number: Precise Discontinuities in Neural Fields for Physics Simulation

Xingyu Ni, Jingrui Xing, Xingqiao Li, Bin Wang, Baoquan Chen

Accurately reconstructing continuous flow fields from sparse or indirect measurements remains an open challenge, as existing techniques often suffer from oversmoothing artifacts, reliance on heterogeneous architectures, and the computational burden of enforcing physics-informed losses in implicit neural representations (INRs). In this paper, we introduce a novel flow field reconstruction framework based on divergence-free kernels (DFKs), which inherently enforce incompressibility while capturing fine structures without relying on hierarchical or heterogeneous representations. Through qualitative analysis and quantitative ablation studies, we identify the matrix-valued radial basis functions derived from Wendland’s polynomial (DFKs-Wen4) as the optimal form of analytically divergence-free approximation for velocity fields, owing to their favorable numerical properties, including compact support, positive definiteness, and second-order differentiability. Experiments across various reconstruction tasks, spanning data compression, inpainting, super-resolution, and time-continuous flow inference, have demonstrated that DFKs-Wen4 outperform INRs and other divergence-free representations in both reconstruction accuracy and computational efficiency, while requiring the fewest trainable parameters.

Representing Flow Fields with Divergence-Free Kernels for Reconstruction

Joël Pelletier-Guénette, Alexandre Mercier-Aubin, Sheldon Andrews

We introduce an efficient solution to the problem of continuous collision detection (CCD) between triangle geometry and signed distance fields (SDFs). We formulate the triangle-SDF collision problem as a novel spatio-temporal local optimization that solves for the first time of impact between a triangle and an SDF isosurface. Our method offers improved robustness over point sampling methods, and outperforms recent triangle-SDF discrete collision detection (DCD) algorithms. Furthermore, a novel method for adaptively refining the potential collision points on large triangles is proposed for robust triangle-SDF collision detection with coarse meshes. This enables the use of reduced geometry for efficient simulations. We demonstrate the benefits of our approach by comparing to state-of-the-art algorithms for triangle-SDF collision detection, and showcase its effectiveness through simulations involving complex collision scenarios.

Real-Time Triangle-SDF Continuous Collision Detection

Melissa Katz, Paul G. Kry, Sheldon Andrews

We extend the concept of traditional rigging, which links polygonal meshes to an underlying skeleton for 3D characters, to the creation of physics-based wheeled vehicle models directly from surface geometry. Unlike character rigging, physics-based rigging involves assigning joints and collision proxies to animate the surface geometry. We present an automated pipeline that transforms a polygon soup into a physics-based, multi-wheeled vehicle model. The pipeline begins by using text-driven 2D image segmentation to identify vehicle components, which are then mapped onto the 3D mesh. A rough estimate of collision geometries and joint parameters is then used to initialize a rigid body simulation of the vehicle. Then, a numerical optimization refines these parameters in order to produce more realistic vehicle behaviour. The final result is a functioning physics-based vehicle for real-time simulations, which is demonstrated across a variety of vehicles, including cars, tricycles, lunar rovers, and even a semi-truck with 10 wheels.

Rig My Ride: Automatic Rigging of Physics-based Vehicles for Games

Jiayi Eris Zhang, Doug L. James, Danny M. Kaufman

The recently developed Progressive Dynamics framework [Zhang et al. 2024] addresses the long-standing challenge in enabling rapid iterative design for high-fidelity cloth and shell animation. In this work, we identify fundamental limitations of the original method in terms of stability and temporal continuity. For robust progressive dynamics simulation we seek methods that provide: (1) stability across all levels of detail (LOD) and timesteps, (2) temporally continuous animations without jumps or jittering, and (3) user-controlled balancing between geometric consistency and enrichment at each timestep, thereby making it a practical previewing tool with high-quality results at the finest level to be used as the final output. We propose a general framework, Progressive Dynamics++, for constructing a family of progressive dynamics integration methods that advance physical simulation states forward in both time and spatial resolution, which includes Zhang et al. [2024]’s method as one member. We analyze necessary stability conditions for Progressive Dynamics integrators and introduce a novel, stable method that significantly improves temporal continuity, supported by a new quantitative measure. Additionally, we present a quantitative analysis of the trade-off between geometric consistency and enrichment, along with strategies for balancing between these aspects in transitions across resolution and time.

Progressive Dynamics++: A Framework for Stable, Continuous, and Consistent Animation Across Resolution and Time

Federico Sichetti, Enrico Puppo, Zizhou Huang, Marco Attene, Denis Zorin, Daniele Panozzo

Many problems in computer graphics can be formulated as finding the
global minimum of a function subject to a set of non-linear constraints
(Minimize), or finding all solutions of a system of non-linear constraints
(Solve). We introduce MiSo, a domain-specific language and compiler for
generating efficient C++ code for low-dimensional Minimize and Solve
problems, that uses interval methods to guarantee conservative results while
using floating point arithmetic. We demonstrate that MiSo-generated code
shows competitive performance compared to hand-optimized codes for
several computer graphics problems, including high-order collision detection
with non-linear trajectories, surface-surface intersection, and geometrical
validity checks for finite element simulation.

MiSo: A DSL for Robust and Efficient SOLVE and MINIMIZE Problems

Siyuan Chen, Yixin Chen, Jonathan Panuelos, Otman Benchekroun, Yue Chang, Eitan Grinspun, Zhecheng Wang

We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of both spatial reduced order models (ROMs) as well as spectral decompositions. By optimizing for the operator that evolves a system state from one timestep to the next, rather than the system state itself, we gain both the compressive power of spatial ROMs as well as the intuitive physical dynamics of spectral methods. The latter property is of particular interest in graphics applications, where user control of fluid phenomena is of high demand. We demonstrate this in various applications including spatial and temporal modulation tools and fluid upscaling with added turbulence. We adapt DMD for graphics applications by reducing computational overhead, incorporating user-defined force inputs, and optimizing memory usage with randomized SVD. The integration of OptDMD and DMD with Control (DMDc) facilitates noise-robust reconstruction and real-time user interaction. We demonstrate the technique’s robustness across diverse simulation scenarios, including artistic editing, time-reversal, and super-resolution. Through experimental validation on challenging scenarios, such as colliding vortex rings and boundary-interacting plumes, our method also exhibits superior performance and fidelity with significantly fewer basis functions compared to existing spatial ROMs. Leveraging the inherent linearity of the DMD formulation, we demonstrate a range of diverse applications. This work establishes another avenue for developing real-time, high-quality fluid simulations, enriching the space of fluid simulation techniques in interactive graphics and animation.

Fast Subspace Fluid Simulation With A Temporally-Aware Basis

Guirec Maloisel, Ruben Grandia, Christian Schumacher, Espen Knoop, Moritz Bächer

We present a constrained Rigid Body Dynamics (RBD) that guarantees satisfaction of kinematic constraints, enabling direct simulation of complex mechanical systems with arbitrary kinematic structures. We present a constrained Rigid Body Dynamics (RBD) that guarantees satisfaction of kinematic constraints, enabling direct simulation of complex mechanical systems with arbitrary kinematic structures. To ensure constraint satisfaction, we use an implicit integration scheme. For this purpose, we derive compatible dynamic equations expressed through the quaternion time derivative, adopting an additive approach to quaternion updates instead of a multiplicative one, while enforcing quaternion unit-length as a constraint. We support all joints between rigid bodies that restrict subsets of the three translational or three rotational degrees of freedom, including position- and force-based actuation. Their constraints are formulated such that Lagrange multipliers are interpretable as joint forces and torques. We discuss a unified solution strategy for systems with redundant constraints, overactuation, and passive degrees of freedom, by eliminating redundant constraints and navigating the subspaces spanned by multipliers. As our method uses a standard additive update, we can interface with unconditionally-stable implicit integrators. Moreover, the simulation can readily be made differentiable as we show with examples.

A Versatile Quaternion-based Constrained Rigid Body Dynamics