Physics-Based Animation

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

Kangrui Zhang, Ruihong Cen, Siyan Zhu, Ruoyan Chen, Bo Ren

We present DIQ-MPM, a novel monolithic two-way coupling framework for simulating interactions between solids modeled with the total Lagrangian formulation and Eulerian incompressible fluids using the Material Point Method (MPM). Our approach combines an implicit TLMPM formulation with a mixed velocity-pressure scheme to robustly simulate compressible solids undergoing large deformations, while eliminating numerical fractures. To enable strong fluid–solid coupling without relying on overlapping grids, we introduce a Dual Interface Quadrature (DIQ) mechanism that maps fluid-solid interface information consistently between the current and reference configurations. This allows us to construct a unified sparse pressure-only system via Schur complement, leading to efficient and stable coupling. We also integrate a particle-based contact force model to resolve solid-solid and solid-boundary contacts within implicit TLMPM. Experimental results demonstrate that our method stably captures free-slip coupling, large deformation phenomena, and complex interactions between compressible solids and incompressible fluids.

DIQ-MPM: Dual Interface Quadrature MPM for Simulating Large Deformation and Fluid-Solid Coupling

Gilles Daviet

We present a family of mixed Material Point Methods well suited to CFL-rate simulation of stiff elastoviscoplastic materials, up to the incompressible limit. Our work builds on the mixed discretization from Daviet and Bertails-Descoubes [2016a] and extends it to handle finite-strain viscoelasticity and more general flow rules, allowing the simulation of a much wider range of materials. Our implicit integration scheme yields a well-posed, symmetric optimization problem with compact stencils, together with an efficient GPU solver. We demonstrate our method on a variety of examples ranging from granular materials and snow to elastic solids, including two-way coupling with rigid-body solvers.

Mixed Material Point Methods for Stiff Elastoplasticity

Li Liao, Pengfei Shen, Yifan Peng

Eigenanalysis of partial differential operators is central to reduced-order physical simulation, but neural shape-space eigenanalysis has largely been limited to natural Neumann boundary conditions. This prevents direct control over supports, openings, heat-exchange boundaries, and other boundary effects that change the underlying operator. We extend neural eigenanalysis for Laplace-type operators to Dirichlet, Robin, and mixed boundary conditions. Boundary placement and Robin coefficients are treated as model inputs, giving a joint shape-boundary space where eigenfunctions and spectra vary continuously with both geometry and boundary configuration. The resulting boundary-aware bases support resonance tuning, reduced-order elastic simulation with changing supports, and transient heat analysis under controllable boundary exchange.

Boundary-aware Neural Model Reduction for PDEs

Lorenzo Diazzi, Jiacheng Dai, Daniele Panozzo, Marco Attene

We present an algorithm that produces high quality tetrahedral meshes conforming with input polyhedra. Our meshing algorithm is based on Ruppert’s Delaunay refinement where convergence is guaranteed thanks to a novel chamfering approach that removes all acute angles from the input. On such a modified input Delaunay refinement produces a Delaunay tetrahedrization where all the faces have bounded angles. The input portions that were removed by the chamfering are re-inserted in this tetrahedrization to achieve exact conformance at the cost of a small number of bad-shaped tetrahedra near the formerly acute input angles. Numerical robustness is guaranteed along all the phases thanks to a clever use of modern indirect geometric predicates and the definition of a new type of implicit point to represent Steiner vertices on the input faces. In practice, our prototype implementation produces meshes having a quality comparable to the state-of-the-art tetgen software: while tetgen fails on 37% of the 3942 valid models in the Thingi10k dataset, our method succeeds on all of them.

Surface chamfering for robust tetrahedral meshing

Aleksei Kalinov, Mickaël Ly, Christian Hafner, Chris Wojtan

The appearance of simulated natural phenomena heavily depends on the way surfaces are textured. However, applying texture maps to dynamic deformable surfaces presents a significant challenge, due to ever-shifting differences in length scales involved. When these surfaces move and advect the texture along with them, their final appearance degrades as deformed regions dramatically distort their texture map. Modifications to the texture directly at the pixel level in response to the deformation may introduce ghosting artifacts and look unnatural. In the real world, the appearance of surface details on a deforming material changes through the interplay of physical processes such as rupturing, exposure of internal structure, or wrinkling. Motivated by these behaviors, in this work we explore how physical principles can guide the texturing methods based on the measure of surface deformation. We present two novel wave-based procedural texturing algorithms which reproduce common physical properties like advection and self-similarity, enabling the plausible animation of deforming objects with extreme texture map distortions. Our algorithms are fully procedural, require no actual physics simulation, and store no state or history of deformation besides the input UV map, making them highly parallelizable on the GPU and efficient enough for real-time applications. We show the versatility of the method by animating physical phenomena with extreme deformations such as flowing lava, stretching putty and outpouring sludge.

Physics-inspired procedural texturing of extremely deformable surfaces

Xuwen Chen, Junyu Wang, Cheng Yu, Xingyu Ni, Meng Zhang, Bin Wang, Mengyu Chu, Baoquan Chen

Continuous Collision Detection is essential in simulation and modeling for accurately identifying object collisions. While robust CCD techniques have matured for triangle meshes, ensuring floating-point robustness for parametric surfaces remains an open challenge due to their representational complexity and heightened algorithmic sensitivity. In this paper, we present the first floating-point-robust CCD framework for parametric surfaces. Built on the Time-Dependent Inclusion-Based Method (TDIBM), our approach introduces a novel error decomposition strategy that separates coefficient and arithmetic errors, enabling structured analysis and safety guarantees. To rigorously benchmark robustness, we develop a rational arithmetic-based dataset by inverting the CCD process — we generate exact ground-truth datasets from prescribed collision outcomes. Our construction captures both typical scenarios and near-degenerate cases. We evaluate several CCD algorithms using this benchmark to provide an in-depth analysis. Together, our method and dataset establish a comprehensive foundation for analyzing, benchmarking, and improving floating-point robustness in parametric surface CCD. Code and dataset will be published upon acceptance.

Floating-Point Robustness in Parametric Surface Continuous Collision Detection: From Algorithm to Benchmarking

Behrooz Zarebavani, Ahmed H. Mahmoud, Ana Dodik, Changcheng Yuan, Serban D. Porumbescu, John D. Owens, Maryam Mehri Dehnavi, Justin Solomon

We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than enforcing strict balance and separator optimality, the algorithm deliberately relaxes these design decisions to favor fast partitioning and efficient elimination-tree construction. Our method decomposes permutation into patch-level local orderings and a compact quotient-graph ordering of separators, preserving the essential structure required by sparse Cholesky factorization while avoiding its most expensive components. We integrate our algorithm into vendor-maintained sparse Cholesky solvers on both CPUs and GPUs. Across a range of graphics applications, including single factorizations and repeated factorizations, our method reduces permutation time and improves the sparse Cholesky solve performance by up to 6.27x. Our code is available at this https URL.

Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers