We introduce an implicit representation of continuous, bijective, orientation-preserving maps between genus zero surfaces with or without boundary. The distortion of these maps can easily be minimized by optimizing the Ginzburg-Landau functional—a ubiquitous model in physics and differential geometry—leading to a simple algorithm for computing bijective correspondences using only standard tools of the tangent vector field toolbox. The method avoids combinatorial mesh modifications and does not require barrier functions to enforce bijectivity making it more robust to noise and simpler to implement. Moreover, the algorithm does not assume a bijective initialization and can untangle non-bijective correspondences generated by computationally cheaper methods such as functional maps. It supports the use of both landmark points and landmark curves to guide the correspondence. The key idea is that a bijection between surfaces defines a two-dimensional mapping surface sitting inside the four-dimensional product space of the two inputs, and this mapping surface can be stored implicitly as the zero set of a complex section—essentially a complex function defined on the product space. Now the distortion of the map can be optimized by minimizing the area of this mapping surface, which amounts to minimizing the Ginzburg-Landau functional of the complex section. We demonstrate the practical benefits of our method by comparing to state-of-the-art correspondence algorithms and show that our implicit representation offers improved stability and naturally supports constraints that are difficult to enforce with explicit map representations.
论文检索
输入标题、作者或关键词，从 4,294 篇学术成果中精准定位
Collaborative human-object interaction shows dynamic and complex movements that require mutual anticipation and continuous adjustment between participants and the shared object. Understanding and modeling such collaborative multi-human object interaction (MHOI) scenarios requires high-quality data acquisition as a foundational step, however, this is a challenging task due to the inherent complexity of MHOI scenarios where human-human and human-object interactions occur simultaneously. Such complexity leads to noisy MHOI captures characterized by several artifacts: contact misalignment between hands and objects, motion jitter and temporal inconsistencies in the captured sequences, and missing or incomplete finger-level articulation details. To address these challenges, we present MOCHI (MOtion Enhancement of Collaborative Human-object Interactions), a two-stage framework for enhancing noisy MHOI data. Our approach first generates physically plausible hand grasps through optimization from noisy body input, producing grasps that are both physically plausible and semantically consistent with the body pose, where these optimized grasps are extended into complete hand-object interaction sequences. Consequently, the full-body motion for all participants are refined through a diffusion-based noise optimization framework that uses single-person motion priors. During the optimization process, we introduce optimization objectives to encode human-object and human-human interaction information within these single-person priors. Experimental results demonstrate the effectiveness of our pipeline across diverse MHOI data, either acquired by existing capture methods or synthesized by generative models. We further show robustness of our system across varying numbers of participants and types of interactions, and demonstrate various applications including keyframe-based MHOI creation and data augmentation through varying object geometries.
We present a data-driven approach for physics-based, muscle-driven dexterous control that enables musculoskeletal hands to perform precise piano playing for novel pieces of music outside the reference dataset. Our approach combines high-frequency muscle-level control with low-frequency latent-space coordination in a hierarchical architecture. At the low level, general single-hand policies are trained via reinforcement learning to generate dynamic muscle-tendon activations while tracking trajectories from a large reference motion dataset. The resulting tracking policies are then distilled into variational autoencoder (VAE) models, yielding smooth and structured latent spaces that abstract away low-level muscle dynamics. For the high level, we train piece-specific policies to operate in this latent space, coordinating bimanual motions based on specific goals, denoted by note events extracted from given musical scores, to synthesize performances beyond the reference data. High-level control is formulated as a decentralized multiagent reinforcement learning problem combined with adversarial learning for motion imitation. In addition, we present an enhanced musculoskeletal hand model that supports fine control of fingers for accurate low-level motion tracking and diverse high-level motion synthesis. We evaluate the control pipeline of our approach on a diverse piano repertoire spanning multiple musical styles and technical demands. Results demonstrate that our approach can synthesize coordinated bimanual motions with accurate key presses, and achieve the state-of-the-art performance of piano playing in physics-based dexterous control, while generalizing to sheet music that is not presented in the reference dataset. We also show that our musculoskeletal hand model demonstrates superior biomechanical stability and tracking precision compared to the existing model, and validate that our musculoskeletal hand model and muscle-driven controller can generate physiologically plausible activation patterns that align with human electromyography (EMG) recordings when subjects perform multiple tasks.
To enable large-scale reuse of real-world 3D assets-where garments and characters rarely share skeletons, templates, or dense correspondences-we present a fully automated virtual try-on system that dresses complex, multi-layer garments onto diverse, arbitrarily posed humanoids. Our key idea is to use SMPL as an intermediate proxy and decompose clothing-to-body transfer into two correspondence tasks with distinct challenges: (1) clothing-to-SMPL (partial-to-complete alignment) and (2) body-to-SMPL (large pose/shape variation and stylization). We address clothing-to-SMPL using a geometry-driven correspondence model, and introduce a diffusion-based body-to-SMPL correspondence approach that leverages multi-view consistent appearance features together with a pretrained 2D foundation model. Using these correspondences, we register SMPL/SMPL+D (Displacement) to the garment and target body and then perform simulator-driven fitting by transferring the garment along a smooth SMPL→SMPL+D transition, producing physically plausible draping on the target. Our system handles complex garment topology (including non-manifold meshes) and generalizes to a wide range of humanoid characters (e.g., humans, robots, cartoons, and creatures) while remaining computationally practical. Upon draping, our system also supports fast customization of clothing size. We show that our system can produce high-quality 3D clothing fittings without any human labor, even when 2D clothing sewing patterns are not available. Our project page is: https://cao-cong0.github.io/LUIVITON-Learned-Universal-Interoperable-VIrtual-Try-ON/.
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.
We introduce MPM Lite, a hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard Material Point Method (MPM) practices suffer from a performance bottleneck where expensive implicit solves are proportional to particle-per-cell (PPC) counts due to the the choices of particle-based quadrature and wide-stencil kernels. By contrast, MPM Lite treats particles primarily as carriers of kinematic state and material history. Conceptualizing the background Cartesian grid as a voxel hexahedral mesh, we resample particle states onto fixed-location quadrature points using efficient, compact linear kernels. This architectural shift allows force assembly and the entire time-integration process to proceed without accessing particles, thus making the solver's complexity independent of the particle count. At the core of our method is a novel stress transfer and stretch reconstruction strategy. To avoid non-physical averaging of deformation gradients, we resample the extensive Kirchhoff stress and derive a rotation-free deformation reference solution, which naturally supports an optimization-based incremental potential formulation. Consequently, MPM Lite can be implemented as modular resampling units coupled with an FEM-style integration module, enabling the direct use of off-the-shelf nonlinear solvers, preconditioners, and unambiguous boundary conditions. We demonstrate through extensive experiments that MPM Lite preserves the robustness and versatility of traditional MPM across diverse materials while delivering significant speedups in implicit settings while simultaneously improving explicit ones. Project page: https://mpmlite.github.io.
To enable the design and manufacturing of optimized composite structures using fabric plies, we propose a field-driven optimization framework that jointly optimizes structural topology and manufacturable layers. A central challenge in this setting is the modeling and optimization of partial fabric layers with near-uniform thickness, which we formulate as a semi-continuous periodic scalar field parameterized by a continuous implicit neural vector field. Within this concurrent structure-layer optimization framework, we further derive a formulation of inter-layer anisotropic mechanical behavior that enables effective modeling of mechanical property transitions induced by partial-layer boundaries, together with additional objectives for manufacturability and field regularization. We validate the effectiveness of our approach through both numerical simulations and physical experiments, demonstrating that the optimized fabric-reinforced laminated composites achieve up to 43.8% higher stiffness compared to counterparts fabricated using planar fabric plies.
Constant mean curvature surfaces are æsthetically appealing geometric objects with applications in physics, differential geometry, and architecture. We present a straightforward discretization of constant mean curvature surfaces based on the classical observation that their Gauß maps are harmonic. Our construction is elementary—requiring only discrete Dirichlet energy minimization and a Poisson solve—yet it exactly mirrors this aspect of the smooth theory. A discrete analog of conjugation produces discrete constant Gauß curvature surfaces. Their unit offsets are discrete CMC surfaces with a conformal parameterization. Additionally, we introduce a novel Möbius-invariant discretization of the Dirichlet energy for sphere-valued maps on dual meshes that is derived from the discrete Willmore energy. It is more robust than standard formulations based on inverse cotangent weights. Our approach to the construction of constant mean curvature surfaces provides direct control over tangent planes along a boundary, if present, and naturally handles closed and periodic examples. We demonstrate the approach on a range of free-boundary, symmetric, and periodic CMC surfaces.
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.
Many non-photorealistic rendering (NPR) styles, such as feature lines and hatching, are defined by image-space structure inherited from hand-drawn media. While recent path-space formulations like the stylized rendering equation (SRE) enable stylization to interact naturally with light transport, they provide no mechanism for enforcing image-space consistency. We present a conceptual framework for lifting image-space stylizations into path-space in a principled, SRE-compatible manner. Our key observation is that image-space consistency can be achieved by establishing geometrically-driven mappings from image-space to path-space. We demonstrate this through two complementary stylizations: feature lines and tone. For feature line rendering, we introduce a conditional lifting based on partial path-space variation, where a geometric path parametrization is combined with parallel transport to preserve image-space structure under distribution effects. This enables a curvature-aware, stochastic, geometry-driven formulation of line detection that generalizes prior ray-based methods. For tone-based styles, such as hatching and halftone, we propose a canonical lifting anchored to a material-independent mapping, motivated by stationary-phase arguments from wave optics. Its locally invertible approximation enables evaluation of image-space tone fields at arbitrary path vertices while preserving image-space structure under complex light transport. Both methods are implemented as ordinary style functions under the SRE and work with existing estimation and sampling strategies; demonstrating how image-space structure can be preserved within path-space rendering, enabling a broader class of expressive, physically-grounded NPR styles.
To enable differentiation with respect to object geometries, boundary path integrals—central to physics-based differentiable rendering—must be estimated numerically. Although their mathematical formulation is well established, designing efficient and robust numerical estimators remains challenging. Most state-of-the-art boundary sampling methods rely on primary-sample-space guiding, which tends to break down on finely tessellated geometries; reparameterization-based alternatives, meanwhile, often incur high variance and/or significant computational overhead. In this paper, we introduce a simple, robust, and consistent solution to this problem. At the core of our approach is a novel formulation of the boundary integral based on kernel-density estimation. Much like photon mapping, we slightly expand the measure-zero domain of integration with a kernel, sidestepping the need to sample directly on a delta-function region in path space. To our knowledge, this is the first such application of kernel-density methods for boundary integral evaluation. We validate our method by comparing its derivative estimates against finite differences (FD), and further demonstrate its practical utility by benchmarking against several state-of-the-art baselines in synthetic inverse-rendering scenarios.
Differentiable path tracing offers a principled route to recovering physical material and lighting parameters, but the combination of high variance and poor numerical conditioning often makes it too brittle to use in practice. This is especially the case when lighting is altogether unknown, or when the scene contains complex light transport effects. Prior work recently showed that the variance reduction provided by a radiance cache can alleviate these challenges. We revisit the combination of inverse rendering and radiance caching with a twist, by introducing a spatial blending field that locally interpolates between the cache and standard unbiased estimators. Recursive application of this idea yields a rich design space of evaluation strategies and inter-estimator consistency losses; we map this space and identify effective components. A surprising property of the resulting algorithm is that it can accurately recover material parameters even when the lighting is not uniquely identifiable from the observations. Our experiments demonstrate significant improvements in speed and robustness over prior work, making a strong case for including radiance caching as a standard component of future physically based inverse rendering systems.
Providing haptic feedback in virtual reality (VR) remains challenging, with active haptic systems often being bulky and expensive, while passive haptics typically require pre-fabricated objects or extensive real-world setup. We present ProXeek, an LLM-based multi-agent system that opportunistically leverages real-world objects as haptic proxies for VR experiences. During VR development, the designers could annotate the virtual interactables with emphasized haptic characteristics using our node-based editing interface. On the user side, end users capture environmental snapshots via commodity VR headset, and the system employs LLM-based multimodal reasoning and multi-objective optimization to match virtual objects with viable physical proxies. Our technical evaluation demonstrates that ProXeek effectively identifies viable proxies, confirming the effectiveness of the algorithmic constraint design in our matching pipeline. Our user study further reveals that the ProXeek-selected physical objects could deliver significantly higher haptic fidelity and enhance presence compared to 3D-printed replicas and visual-only interaction.
Mixed Reality (MR) headsets promise a future of immersive telepresence where virtual humans blend indistinguishably into their real or virtual surroundings. Achieving this vision requires a method capable of capturing a user's motion, estimating their appearance under novel lighting, and understanding the surrounding environment - all from the constrained viewpoint of a head-mounted display (HMD). Existing approaches treat these as isolated problems: they either focus on driving avatars with baked-in lighting or rely on complex studio setups for relighting. In this paper, we present EgoRelight, a holistic framework for egocentric telepresence that simultaneously captures full-body human performance, synthesizes photorealistic and relightable appearance, and estimates high dynamic range (HDR) environment maps from a single HMD. First, to ensure accurate motion and surface reconstruction, we propose an egocentric perception module that leverages stereo down-facing cameras to extract dense depth maps, which serve as robust geometric control signals to drive a mesh-based avatar. Second, we introduce a novel neural appearance model that learns to synthesize view-dependent specular and view-independent diffuse shading separately. By employing a specialized ray-sampling strategy, our model generalizes to unseen illumination without relying on restrictive analytical BRDF priors. Third, we enable seamless avatar integration into the physical world via a test-time inverse rendering process, which recovers an HDR environment map by matching the pre-trained avatar's appearance to the live egocentric camera observations. We demonstrate the efficiency of our system through a social telepresence application, where remote users are coherently relit according to their local physical environment. Extensive experiments show that our individual components and the integrated system significantly outperform the best combinations of state-of-the-art baselines in both geometric accuracy and rendering as well as relighting fidelity. Further details can be found on our project page1.
End-to-end (e2e) latency in head-mounted displays (HMD) is the time delay between a physical change in the world (e.g., a user's head movement) and the moment the display updates to reflect that change. Tracking, rendering, and other computation in real systems invariably introduce some amount of e2e latency to all HMDs. In modern devices this latency is usually in the range of 12-60 milliseconds which is partially addressed through pose prediction and late stage reprojection which means that perceptual studies and user experience evaluations cannot explore latencies below these values. Here, we introduce a video passthrough HMD, called Camsicle, which is capable of 2-millisecond e2e latency and, additionally, uses a catadioptric design to achieve perspective-correct passthrough without reprojection. This platform enables naturalistic user studies to interrogate the impacts of latency on user experience, preference, and performance. Across two user studies and 57 participants we find that 2 and 14.3 millisecond latencies are preferred over 23 and 29 milliseconds when attempting to catch a ball. Additionally, we compare individual latency preferences in this naturalistic ball-catching task to psychophysical thresholds for latency detection in a reference-grade system with zero latency to investigate how psychophysical thresholds may relate to subjective evaluations in naturalistic scenarios.
Lattice metamaterials enable lightweight, multifunctional structures, yet homogenization-based evaluation of their effective properties remains computationally expensive. Neural surrogates offer speed but often lack the accuracy and stability required for engineering-grade simulations. We introduce GMT, a Geometric Multigrid Transformer - a neural solver with high numerical fidelity for fast and reliable lattice homogenization. GMT achieves architectural alignment with Geometric Multigrid (GMG) by restructuring Point Transformer V3 to operate across sparse GMG hierarchies, capturing long-range dependencies and cross-level interactions essential for multigrid convergence. To enforce physical consistency, GMT incorporates physics-aware positional encoding for strict enforcement of periodicity and predicts both the finest-level solution and multi-level residual corrections. These predictions deliver a spectrally-aligned initialization, enabling end-to-end training under physics-informed and solver-aware losses and requiring only a single GMG V-cycle refinement to reach convergence. This fusion of neural prediction and numerical rigor achieves relative residual errors of 10-5 with a 160× speedup over state-of-the-art GPU-based solvers at equivalent accuracy - particularly at high resolutions (e.g., 5123), where traditional methods become most costly. We validate GMT across mechanical and thermal domains, demonstrate robust generalization to unseen geometries and non-periodic settings, and showcase scalability to high resolutions - enabling real-time design iteration, multi-scale simulations, high-throughput material discovery, and inverse design.
We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; (ii) particles live in physical space, so the flow's terminal velocity has physical meaning and can encode geometric attributes (e.g., surface normals). OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state-of-the-art with 5× fewer steps and reaches airplane EMD comparable to DiT-3D with 26× fewer parameters and 5× fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.
We propose a unified, few-step generative modeling framework based on cumulative flow maps for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and cumulative parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction instantiation. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.
Capturing cloth motion with high fidelity is challenging due to fine-scale wrinkles, large deformation, and frequent self-occlusion. We present a 4D (spatio-temporal) cloth capture system that achieves 1 mm spatial resolution using only 16 RGB cameras. Our approach uses a two-level marker pattern: sparse, colored L-shaped markers provide robust detection and orientation, while dense noise patterns within each marker enable both marker identification and precise keypoint localization. By unwarping detected markers to a canonical frame, we factor out perspective distortion and most of cloth deformation, allowing the localizer to achieve sub-pixel accuracy. The localized keypoints are triangulated across views to form an incomplete point cloud. A physics-based optimization then deforms a template mesh to match the captured geometry while maintaining penetration-free constraints and physical plausibility for occluded regions. Our method produces temporally coherent sequences that faithfully capture fine wrinkles and folds even during complex motions with self-contact.
While yarn-level garments offer rich dynamic details and compelling visual realism compared to triangle-based models, their wide adoption is hindered by the immense computational cost due to the presence of a large number of degrees of freedom (DOFs). This paper proposes a novel simulation framework designed to enhance the performance and stability for numerical simulation of nonlinear, non-convex, and high-resolution knitwear. Our method generalizes the Douglas-Rachford Splitting (DRS) scheme to resolve the non-convex coupling between stretching, shearing, bending, twisting, and contacting at each yarn thread. A key contribution is a nested decomposition strategy that decouples the non-convex variational energy into independent and convex sub-problems. Such convexification improves solver robustness and removes the necessity for frequent line searches. We provide a theoretically grounded strategy for metric selection for each sub-problem, derived from an analysis of the convergence guarantee of DRS. Consequently, our method achieves close-to-optimal convergence along the nonlinear iterations rather than relying on ad-hoc parameter tuning. The paper also clarifies a formal connection between our generalized DRS and the ADMM (Alternating Direction Method of Multipliers) framework, extending the applicability of our analysis to a broader set of constrained dynamics problems. Experimental results demonstrate that our method robustly handles complex knitwear simulation scenes with superior efficiency, stability, and physical fidelity compared to existing methods. With a matrix-free GPU parallelization, our method allows an interactive simulation rate of knitwear of multi-million DOFs.