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.

We consider the problem of adding dynamic rain effects to in-the-wild scenes in a physically-correct manner. Recent advances in scene modeling have made significant progress, with NeRF and Gaussian Splatting techniques emerging as powerful tools for reconstructing complex scenes. However, while effective for novel view synthesis, these methods typically struggle with challenging scene editing tasks, such as physics-based rain simulation. In contrast, traditional physics-based simulations can generate realistic rain effects, such as raindrops and splashes, but they often rely on skilled artists to carefully set up high-fidelity scenes. This process lacks flexibility and scalability, limiting its applicability to broader, open-world environments. In this work, we introduce RainyGS, a novel approach that leverages the strengths of both physics-based modeling and Gaussian Splatting to generate photorealistic, dynamic rain effects in open-world scenes with physical accuracy. At the core of our method is the integration of physically-based raindrop and shallow water simulation techniques within the fast Gaussian Splatting rendering framework, enabling realistic and efficient simulations of raindrop behavior, splashes, and reflections. Our method supports synthesizing rain effects at over 30 fps, offering users flexible control over rain intensity—from light drizzles to heavy downpours. We demonstrate that RainyGS performs effectively for both real-world outdoor scenes and large-scale driving scenarios, delivering more photorealistic and physically-accurate rain effects compared to state-of-the-art methods. Project page can be found at https://pku-vcl-geometry.github.io/RainyGS/.

We investigate how to enhance the physical fidelity of video generation models by leveraging synthetic videos derived from computer graphics pipelines. These rendered videos respect real-world physics, such as maintaining 3D consistency, and serve as a valuable resource that can potentially improve video generation models. To harness this potential, we propose a solution that curates and integrates synthetic data while introducing a method to transfer its physical realism to the model, significantly reducing unwanted artifacts. Through experiments on three representative tasks emphasizing physical consistency, we demonstrate its efficacy in enhancing physical fidelity. While our model still lacks a deep understanding of physics, our work offers one of the first empirical demonstrations that synthetic video enhances physical fidelity in video synthesis. Website: https://kevinz8866.github.io/simulation/

Abstract We present FlowCapX , a physics‐enhanced framework for flow reconstruction from sparse video inputs, addressing the challenge of jointly optimizing complex physical constraints and sparse observational data over long time horizons. Existing methods often struggle to capture turbulent motion while maintaining physical consistency, limiting reconstruction quality and downstream tasks. Focusing on velocity inference, our approach introduces a hybrid framework that strategically separates representation and supervision across spatial scales. At the coarse level, we resolve sparse‐view ambiguities via a novel optimization strategy that aligns long‐term observation with physics‐grounded velocity fields. By emphasizing vorticity‐based physical constraints, our method enhances physical fidelity and improves optimization stability. At the fine level, we prioritize observational fidelity to preserve critical turbulent structures. Extensive experiments demonstrate state‐of‐the‐art velocity reconstruction, enabling velocity‐aware downstream tasks, e.g., accurate flow analysis, scene augmentation with tracer visualization and re‐simulation. Our implementation is released at ://github.com/taoningxiao/FlowCapX.git .

The simulation of sand-water mixtures requires capturing the stochastic behavior of individual sand particles within a uniform, continuous fluid medium. However, most existing approaches, which only treat sand particles as markers within fluid solvers, fail to account for both the forces acting on individual sand particles and the collective feedback of the particle assemblies on the fluid. This prevents faithful reproduction of characteristic phenomena including transport, deposition, and clogging. Building upon kinetic ensemble averaging technique, we propose a physically consistent coupling strategy and introduce a novel Granule-In-Cell (GIC) method for modeling such sand-water interactions. We employ the Discrete Element Method (DEM) to capture fine-scale granule dynamics and the Particle-In-Cell (PIC) method for continuous spatial representation and density projection. To bridge these two frameworks, we treat granules as macroscopic transport flow rather than solid boundaries within the fluid domain. This bidirectional coupling allows our model to incorporate a range of interphase forces using different discretization schemes, resulting in more realistic simulations that strictly adhere to the mass conservation law. Experimental results demonstrate the effectiveness of our method in simulating complex sand-water interactions, uniquely capturing intricate physical phenomena and ensuring exact volume preservation compared to existing approaches.

Continuous collision detection (CCD) between parametric surfaces is typically formulated as a five-dimensional constrained optimization problem. In the field of CAD and computer graphics, common approaches to solving this problem rely on linearization or sampling strategies. Alternatively, inclusion-based techniques detect collisions by employing 5D inclusion functions, which are typically designed to represent the swept volumes of parametric surfaces over a given time span, and narrowing down the earliest collision moment through subdivision in both spatial and temporal dimensions. However, when high detection accuracy is required, all these approaches significantly increases computational consumption due to the high-dimensional searching space. In this work, we develop a new time-dependent inclusion-based CCD framework that eliminates the need for temporal subdivision and can speedup conventional methods by a factor ranging from 36 to 138. To achieve this, we propose a novel time-dependent inclusion function that provides a continuous representation of a moving surface, along with a corresponding intersection detection algorithm that quickly identifies the time intervals when collisions are likely to occur. We validate our method across various primitive types, demonstrate its efficacy within the simulation pipeline and show that it significantly improves CCD efficiency while maintaining accuracy.

This paper introduces a novel Induce-on-Boundary (IoB) solver designed to address the magnetostatic governing equations of ferrofluids. The IoB solver is based on a single-layer potential and utilizes only the surface point cloud of the object, offering a lightweight, fast, and accurate solution for calculating magnetic fields. Compared to existing methods, it eliminates the need for complex linear system solvers and maintains minimal computational complexities. Moreover, it can be seamlessly integrated into conventional fluid simulators without compromising boundary conditions. Through extensive theoretical analysis and experiments, we validate both the convergence and scalability of the IoB solver, achieving state-of-the-art performance. Additionally, a straightforward coupling approach is proposed and executed to showcase the solver's effectiveness when integrated into a grid-based fluid simulation pipeline, allowing for realistic simulations of representative ferrofluid instabilities.

research-article Share on GARM-LS: A Gradient-Augmented Reference-Map Method for Level-Set Fluid Simulation Authors: Xingqiao Li School of IST & National Key Lab. of AGI, Peking University, China School of IST & National Key Lab. of AGI, Peking University, China 0000-0002-8131-6140View Profile , Xingyu Ni School of CS & National Key Lab. of AGI, Peking University, China School of CS & National Key Lab. of AGI, Peking University, China 0000-0003-1127-2848View Profile , Bo Zhu Georgia Institute of Technology, United States of America and Dartmouth College, United States of America Georgia Institute of Technology, United States of America and Dartmouth College, United States of America 0000-0002-1392-0928View Profile , Bin Wang Beijing Institute for General Artificial Intelligence, China Beijing Institute for General Artificial Intelligence, China 0000-0001-9496-772XView Profile , Baoquan Chen School of IST & National Key Lab. of AGI, Peking University, China School of IST & National Key Lab. of AGI, Peking University, China 0000-0003-4702-036XView Profile Authors Info & Claims ACM Transactions on GraphicsVolume 42Issue 6Article No.: 192pp 1–20https://doi.org/10.1145/3618377Published:05 December 2023Publication History 1citation71DownloadsMetricsTotal Citations1Total Downloads71Last 12 Months71Last 6 weeks23 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Magnetoelastic thin shells exhibit great potential in realizing versatile functionalities through a broad range of combination of material stiffness, remnant magnetization intensity, and external magnetic stimuli. In this paper, we propose a novel computational method for forward simulation and inverse design of magnetoelastic thin shells. Our system consists of two key components of forward simulation and backward optimization. On the simulation side, we have developed a new continuum mechanics model based on the Kirchhoff-Love thin-shell model to characterize the behaviors of a megnetolelastic thin shell under external magnetic stimuli. Based on this model, we proposed an implicit numerical simulator facilitated by the magnetic energy Hessian to treat the elastic and magnetic stresses within a unified framework, which is versatile to incorporation with other thin shell models. On the optimization side, we have devised a new differentiable simulation framework equipped with an efficient adjoint formula to accommodate various PDE-constraint, inverse design problems of magnetoelastic thin-shell structures, in both static and dynamic settings. It also encompasses applications of magnetoelastic soft robots, functional Origami, artworks, and meta-material designs. We demonstrate the efficacy of our framework by designing and simulating a broad array of magnetoelastic thin-shell objects that manifest complicated interactions between magnetic fields, materials, and control policies.

We propose a novel numerical scheme to simulate interactions between a magnetic field and nonlinearly magnetized objects immersed in it. Under our nonlinear magnetization framework, the strength of magnetic forces is effectively saturated to produce stable simulations without requiring any parameter tuning. The mathematical model of our approach is based upon Langevin's nonlinear theory of paramagnetism, which bridges microscopic structures and macroscopic equations after a statistical derivation. We devise a hybrid Eulerian-Lagrangian numerical approach to simulating this strongly nonlinear process by leveraging the discrete material points to transfer both material properties and the number density of magnetic micro-particles in the simulation domain. The magnetic equations can then be built and solved efficiently on a background Cartesian grid, followed by a finite difference method to incorporate magnetic forces. The multi-scale coupling can be processed naturally by employing the established particle-grid interpolation schemes in a conventional MLS-MPM framework. We demonstrate the efficacy of our approach with a host of simulation examples governed by magnetic-mechanical coupling effects, ranging from magnetic deformable bodies to magnetic viscous fluids with nonlinear elastic constitutive laws.

We present a versatile numerical approach to simulating various magnetic phenomena using a level-set method. At the heart of our method lies a novel two-way coupling mechanism between a magnetic field and a magnetizable mechanical system, which is based on the interfacial Helmholtz force drawn from the Minkowski form of the Maxwell stress tensor. We show that a magnetic-mechanical coupling system can be solved as an interfacial problem, both theoretically and computationally. In particular, we employ a Poisson equation with a jump condition across the interface to model the mechanical-to-magnetic interaction and a Helmholtz force on the free surface to model the magnetic-to-mechanical effects. Our computational framework can be easily integrated into a standard Euler fluid solver, enabling both simulation and visualization of a complex magnetic field and its interaction with immersed magnetizable objects in a large domain. We demonstrate the efficacy of our method through an array of magnetic substance simulations that exhibit rich geometric and dynamic characteristics, encompassing ferrofluid, rigid magnetic body, deformable magnetic body, and multi-phase couplings.