Physics-Based Animation

Rasmus Gabelgaard Nielsen, Kenny Erleben

We present a fast, robust method for continuous collision detection (CCD) directly between pairs of complex signed distance fields (SDFs). By casting CCD as an alternating spatio-temporal optimization and driving a small set of smartly sampled surface points along SDF tangent spaces, our approach avoids dense sampling or triangle meshes entirely. The result is real-time SDF-SDF time-of-impact queries—often within 1 ms on a single CPU core—even for highly detailed, non-convex geometry undergoing fast spinning motion. This is, to our knowledge, the first practical CCD method operating directly on SDF pairs.

Alternating Spatial-Temporal Optimization for Continuous Collision Detection of Signed Distance Fields

Juan Sebastian Montes Maestre, Ladislav Kavan, Edmond Boyer, Ryan Goldade, Stelian Coros, Bernhard Thomaszewski

Facial skin dynamics are inherently challenging to simulate due to a combination of geometric, material, and anatomical complexities. Human skin is a nonlinear layered material with spatially heterogeneous attachments to the underlying tissues. During contact events, localized compression and shear induce mechanical instabilities, leading to fine-scale wrinkling patterns governed by a delicate interplay of geometry, boundary conditions, and through-the-thickness stresses. We present a finite element framework to simulate contact-induced wrinkling of facial skin. We model skin as a viscoelastic material with time-dependent relaxation that governs the rate, persistence, and damping of wrinkle formation. We employ high-order prismatic solid-shell elements to resolve through-thickness stresses and high-frequency deformation modes. Central to our approach, we introduce a continuum-based formulation of skin ligaments to model heterogeneous skin attachments and provide anatomically inspired mobility constraints. These skin ligaments control the formation and appearance of facial wrinkles by modulating their amplitude, wavelength, and spatial distribution. We evaluate our method on a set of synthetic examples and compare simulations with real-world footage. These results demonstrate that our skin model produces temporally coherent and visually realistic wrinkle patterns during transient contact.

Physics-Based Simulation of Contact-Induced Facial Wrinkling

Xuan Tang, Kemeng Huang, Gilbert Bernstein, Minchen Li, Tzumao Li

Incremental Potential Contact (IPC) has emerged as a robust and unifying formulation for contact-rich physical simulation by casting elasticity and collision handling as a single energy minimization problem. Achieving high performance, however, typically requires heavily specialized implementations that hard-code assumptions about energies, primitive types, and parameterizations, creating a major barrier to extensibility. Adding new energies or alternative parameterizations often requires re-deriving first and second-order derivatives, and implementing new assembly logic for the global Hessian and gradient. This challenge is further exacerbated by collision energies, where the same energy definition is often applied to mixed parameterizations, which can lead to a combinatorial explosion of parameterization-specific derivative and assembly cases. In this paper we introduce YASPS, a framework for physical simulation that resolves this limitation by making structural relationships explicit in a differentiable representation. YASPS introduces two relational operators, JOIN and UNION, which encode connectivity and heterogeneous parameterizations directly in the symbolic computation graph. Using symbolic differentiation over these operators, YASPS automatically derives local derivatives, and determines the induced sparsity and block structure of global gradients and Hessians from the same description while avoiding any code explosion induced by mixed-parameterizations. Targeting IPC workloads, YASPS compiles the resulting symbolic graphs into GPU kernels for local energy evaluation, derivative computation, and block-sparse matrix assembly, and solves the resulting Newton systems using a GPU-based iterative solver. This approach achieves performance competitive with state-of-the-art IPC implementations while enabling new energies and parameterizations to be added through localized symbolic definitions, without hand-written derivative or assembly code.

YASPS: A Symbolic Framework for Extensible, High-Performance IPC Simulation

Doug L. James, Ethan James

We present Mixwell, a family of sharp 2D fluid brushes and GPU-accelerated analytical methods for progressive, resolution-independent physics-based mixing. Derived from idealized potential flow around a cylindrical tine, Mixwell includes a cusped, Kelvinlet-style regularized velocity brush that parsimoniously captures cylinder-fluid interactions. Building on Maxwell’s 1869 drift formulation, we develop GPU-friendly evaluation strategies for particle drift in both infinite and finite strokes. For image-based workflows, we introduce cylindrical Reverse-Drift Functions (RDFs), displacement fields that encode tine insertion, motion, and removal. Like signed distance fields in geometric modeling, RDFs compose naturally and can be chained in shaders to model complex operations while avoiding intermediate texture blur. We also propose a periodicity-exploiting composition scheme for complex RDF patterns. All Mixwell operations are evaluated independently per sample, enabling truly progressive mixing and rendering without global solves, grids, or intermediate texture resampling. We demonstrate real-time GLSL and HLSL implementations and production integrations in Houdini (OpenCL, OSL), enabling progressive, arbitrary-resolution mixing and rendering with negligible numerical dissipation.

Mixwell: Sharp 2D Fluid Brushes for Progressive Physics-Based Mixing

Bastian Abt, David Stotko, Nils Wandel, Reinhard Klein

Simulating inviscid, incompressible fluids on non-simply-connected curved surfaces requires careful treatment of the flow’s local and global behavior. While recent theoretical advancements have established the critical dynamics of the harmonic component in such flows, practical applications remain computationally restricted by a lack of spatial and temporal adaptivity. Furthermore, simulations on poor-quality meshes often lead to numerical instability and a failure to preserve the flow’s underlying harmonic component when using naive interpolation methods. In this paper, we introduce Adaptive Fluid Cohomology, a framework that integrates dynamic spatial and temporal refinement into the simulation of the Euler equations. We leverage a posteriori error estimation to adjust spatial resolution on the fly, alongside a standard Dormand-Prince 5(4) time-stepping scheme for temporal accuracy. To ensure stability during mesh mutations, we develop a novel method that robustly transfers the harmonic basis during remeshing. While our experimental evaluation focuses on 2D surface flows, the underlying theoretical formulation is presented to capture the 3D setting as well. Our evaluation demonstrates that this adaptive approach accurately recreates the dynamics of high-resolution simulations while reducing the memory footprint by up to $86\mathrm{\%}86\backslash ,\backslash \%$86% and maintaining numerical stability even on poor-quality triangulations where static methods fail.

Adaptive Fluid Cohomology on Surfaces

Yixin Chen, David I.W. Levin, Timothy R. Langlois

We present a physics-based fluid control method utilizing localized spacetime windows, extending force-based fluid control to substantially larger simulation scales. In many practical editing scenarios, user-specified objectives affect only a small region of an otherwise satisfactory simulation, resulting in optimal control force distributions that are highly sparse in both space and time. However, existing optimization-based fluid control methods typically solve for control forces over the entire spacetime domain, leading to unnecessarily high computational cost and poor scalability. Motivated by this observation, we restrict optimization to localized spacetime regions surrounding the edit of interest, significantly reducing the dimensionality of the control problem. Within this framework, control forces are parameterized on a coarse “floating” background grid, decoupling control degrees of freedom from simulation resolution and promoting smooth, physically plausible forces. We further analyze spacetime-window selection as a joint spatial-temporal problem. While the full problem can be formulated as a 2D search over spatial and temporal window extents, practical workflows can often leverage user-specified spatial regions and lightweight temporal-window selection strategies to reduce search cost. Our method enables a range of intuitive editing tasks, where sparse user inputs can induce coherent motion in surrounding fluid structures. We demonstrate the effectiveness and efficiency of our method with various 2D and 3D particle-based free-surface simulation examples.

Fluid Control with Localized Spacetime Windows

Hongcheng Song, Ye Fan, Uri M. Ascher, Dinesh K. Pai

Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone-constrained linear response and a scalar non-associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non-associated coupling explicitly, and an inner solve for a strongly convex cone-constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid-body benchmarks with stick-slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.

A Splitting Architecture for Exact Reduced Coulomb Friction

Bernhard Braun, Rene Winchenbach, Jan Bender, Nils Thuerey

We present ST-FLIP, a spatiotemporal extension of the Fluid-Implicit Particle (FLIP) method for incompressible free-surface and two-phase liquid simulation. ST-FLIP enables time steps up to an order of magnitude larger than those typically used in CFL-constrained solvers, while preserving detailed flow structures and visual fidelity. It addresses a common failure mode of large time steps in hybrid particle–grid liquid solvers: temporal under-sampling of particle motion produces aliasing-driven free-surface artifacts after projection. Our key idea is to interpret particles as samples in four-dimensional space-time: in addition to standard spatial jittering, we randomize particle positions along the time axis as well and perform particle-to-grid deposition using a separable 4D kernel. This yields a Monte Carlo estimator of per-step time-slab-integrated particle quantities. Although particles are treated as samples in 4D space-time, our approach works as a lightweight plug-in by collapsing to slab‑integrated 3D grid fields for projection. Building on recent particle‑based phase‑field work, we reuse the particle-to-grid weight accumulators as a conceptual space–time phase field, providing variable‑coefficient projection weights and eliminating the need for per‑step surface reconstruction. The method can be easily integrated into existing FLIP/PIC or APIC solvers with negligible additional computational cost per time step. The effectiveness of our approach is demonstrated through a series of comparisons with state-of-the-art solvers, yielding several-fold speedups for multi-billion-particle simulations at high effective 3D resolutions on a single workstation.

Spatiotemporal FLIP for Fast Free-Surface and Two-Phase Simulation With Very Large Time Steps

Shixun Huang, Siyuan Chen, Yue Chang, Zhecheng Wang, Peter Yichen Chen

Cyclic animation is widely used in computer graphics and interactive content. It supports seamless playback in games, VR, and interactive simulation, where short clips must repeat smoothly over long durations. Achieving physically plausible cyclic synthesis from an input sequence is challenging because the endpoint states of the observed sequence rarely match exactly, and the governing equations of the underlying system are often unavailable.
We therefore propose an equation-free framework that identifies a Koopman surrogate from the observed trajectory and computes a cyclic trajectory by applying a Fourier-parameterized, time-varying control force under a hard temporal periodicity constraint. The resulting formulation reduces cyclic synthesis to a linearly constrained quadratic program that can be solved efficiently through a structured KKT system. Our method is applicable to a diverse range of examples, including N-body systems, cloth, deformable objects, shallow water, etc.

Closing Trajectories: Equation-Free Cyclic Animation via Koopman Surrogates

Rupesh Kumar, Sabhya Khurana, Rahul Narain

We present a technique for simulating detailed cloth dynamics on coarse meshes at interactive rates, by coupling the base mesh simulation with dynamic wrinkles in a physically consistent manner. Building on the wrinkle parameterization introduced by Chen et al. 2021, we introduce a dynamics model for a cloth sheet represented as a superposition of a base surface and a wrinkle distribution parameterized by spatially varying amplitude and frequency. Our model incorporates two-way coupling of the base surface and the wrinkle parameters, allowing the base deformation to drive emergence of wrinkles and permitting compression of the base surface in turn. To deform the mesh using the computed wrinkle parameters, we also introduce a simple phase reconstruction strategy that produces dynamically evolving, temporally coherent wrinkles on the simulated mesh.

Dynamic Wrinkling on Coarsely-Meshed Cloth