Abstract We present an efficient and scalable method for the inverse shape design problem of elastic objects, with broad applicability to diverse materials and interactive editing. The core idea is to decouple material nonlinearity from geometry optimization by introducing the Cauchy stress tensor as an auxiliary variable. We design a three‐stage scheme that iteratively optimizes the stress tensors and the rest shape, with each stage being well‐posed and efficiently‐solvable. To address the lack of a theoretical convergence guarantee arising from the decoupled energy formulation, we incorporate a relaxation method that ensures robust stability in practice. As a result, our method achieves a 3 × speedup over the state‐of‐the‐art asymptotic method [Jia21] on a model with 40k vertices and 112k elements (Fig. 2), and exhibits near‐linear scalability to large systems (Fig. 8). We demonstrate applications including rest shape design for various materials (ranging from standard models to complex spline‐based materials [XSZB15]), interactive material and force editing, and elastic object reconstruction from images.

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.

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.

We propose MiNNIE, a simple yet comprehensive framework for real-time simulation of nonlinear near-incompressible elastics. To avoid the common volumetric locking issues at high Poisson's ratios of linear finite element methods (FEM), we build MiNNIE upon a mixed FEM framework and further incorporate a pressure stabilization term to ensure excellent convergence of multigrid solvers. Our pressure stabilization strategy injects bounded influence on nodal displacement which can be eliminated using a quasiNewton method. MiNNIE has a specially tailored GPU multigrid solver including a modified skinning-space interpolation scheme, a novel vertex Vanka smoother, and an efficient dense solver using Schur complement. MiNNIE supports various elastic material models and simulates them in real-time, supporting a full range of Poisson's ratios up to 0.5 while handling large deformations, element inversions, and self-collisions at the same time.

This paper introduces a novel physically-based vortex fluid model for films, aimed at accurately simulating cascading vortical structures on deforming thin films. Central to our approach is a novel mechanism decomposing the film's tangential velocity into circulation and dilatation components. These components are then evolved using a hybrid particle-mesh method, enabling the effective reconstruction of three-dimensional tangential velocities and seamlessly integrating surfactant and thickness dynamics into a unified framework. By coupling with its normal component and surface-tension model, our method is particularly adept at depicting complex interactions between in-plane vortices and out-of-plane physical phenomena, such as gravity, surfactant dynamics, and solid boundary, leading to highly realistic simulations of complex thin-film dynamics, achieving an unprecedented level of vortical details and physical realism.

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.

This paper presents a novel approach to simulating surface tension flow within a position-based dynamics (PBD) framework. We enhance the conventional PBD fluid method in terms of its surface representation and constraint enforcement to furnish support for the simulation of interfacial phenomena driven by strong surface tension and contact dynamics. The key component of our framework is an on-the-fly local meshing algorithm to build the local geometry around each surface particle. Based on this local mesh structure, we devise novel surface constraints that can be integrated seamlessly into a PBD framework to model strong surface tension effects. We demonstrate the efficacy of our approach by simulating a multitude of surface tension flow examples exhibiting intricate interfacial dynamics of films and drops, which were all infeasible for a traditional PBD method.

We propose a novel three-way coupling method to model the contact interaction between solid and fluid driven by strong surface tension. At the heart of our physical model is a thin liquid membrane that simultaneously couples to both the liquid volume and the rigid objects, facilitating accurate momentum transfer, collision processing, and surface tension calculation. This model is implemented numerically under a hybrid Eulerian-Lagrangian framework where the membrane is modelled as a simplicial mesh and the liquid volume is simulated on a background Cartesian grid. We devise a monolithic solver to solve the interactions among the three systems of liquid, solid, and membrane. We demonstrate the efficacy of our method through an array of rigid-fluid contact simulations dominated by strong surface tension, which enables the faithful modeling of a host of new surface-tension-dominant phenomena including: objects with higher density than water that remains afloat; 'Cheerios effect' where floating objects attract one another; and surface tension weakening effect caused by surface-active constituents.

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.

Designing a camera motion controller that has the capacity to move a virtual camera automatically in relation with contents of a 3D animation, in a cinematographic and principled way, is a complex and challenging task. Many cinematographic rules exist, yet practice shows there are significant stylistic variations in how these can be applied. In this paper, we propose an example-driven camera controller which can extract camera behaviors from an example film clip and re-apply the extracted behaviors to a 3D animation, through learning from a collection of camera motions. Our first technical contribution is the design of a low-dimensional cinematic feature space that captures the essence of a film's cinematic characteristics (camera angle and distance, screen composition and character configurations) and which is coupled with a neural network to automatically extract these cinematic characteristics from real film clips. Our second technical contribution is the design of a cascaded deep-learning architecture trained to (i) recognize a variety of camera motion behaviors from the extracted cinematic features, and (ii) predict the future motion of a virtual camera given a character 3D animation. We propose to rely on a Mixture of Experts (MoE) gating+prediction mechanism to ensure that distinct camera behaviors can be learned while ensuring generalization. We demonstrate the features of our approach through experiments that highlight (i) the quality of our cinematic feature extractor (ii) the capacity to learn a range of behaviors through the gating mechanism, and (iii) the ability to generate a variety of camera motions by applying different behaviors extracted from film clips. Such an example-driven approach offers a high level of controllability which opens new possibilities toward a deeper understanding of cinematographic style and enhanced possibilities in exploiting real film data in virtual environments.

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.