We present a new method for simplifying the topology of a 3D shape. Unlike existing methods that either remove all topological features or offer indirect control over the target topology, our method aims at exactly preserving the user-prescribed numbers of topological features of each type (e.g., components, handles, and voids), while making minimal geometric changes. Guided by persistent homology, our method removes features with low persistence by performing either cutting or filling. This is achieved by an algorithm for computing candidate cuts and fills that remove only low-persistence features, an efficient algorithm for selecting an optimal subset of candidates by computing a weighted independent set, and an iterative framework that alternates between candidate computation and selection. Our method is shown to be highly successful in achieving the prescribed topology on a large test suite involving many complex 3D shapes and target topologies.
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The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features—for instance, by aligning the MAT boundary with the locus of rolling ball centers within fillet regions. However, computing such an ideal MAT remains a significant challenge, particularly when the input is a discrete triangle mesh. In this paper, we follow the established technical pipeline of initializing the MAT via a 3D Voronoi diagram of surface samples and subsequently simplifying the Voronoi structure through a QEM-like scheme. Our key insight is to explicitly track the correspondence between MAT vertices and surface regions throughout the progressive simplification process, ensuring that the resulting MAT triangles accurately reflect the intrinsic symmetries between surface patches. We translate these geometric requirements into a suite of priority control strategies that govern the sequencing of edge collapses. Through extensive evaluation against state-of-the-art MAT algorithms, we validate the strong performance of our approach regarding runtime efficiency, structural alignment, boundary regularity, triangle quality, and robustness to noise. Our resulting MATs remain highly expressive for both articulated shapes and CAD models, even under extreme simplification—effectively capturing the global structure of complex geometries with only a few hundred vertices. Finally, we showcase the utility of our approach through two potential applications: capturing the locus of rolling ball centers within fillet regions, a structural capability not previously demonstrated in the existing literature, and surface extraction from unsigned distance fields, where the medial axis of the є-isosurface naturally yields a clean single-layer result. Source code is available at https://github.com/sssomeone/structural-mat.
Self-intersections are widespread in surface meshes and invalidate downstream simulation, fabrication, and learning pipelines. Existing approaches typically treat self-intersections as local collision events, but embeddedness (i.e., lack of self-intersections) is a global geometric property that cannot be enforced through local reasoning alone. We introduce an energy-based framework that enforces surface embeddedness simultaneously at the shape and mesh levels, based on the insight that successful untangling requires accounting for both global shape-level interactions and local mesh-level interactions. A shape-level energy captures global entanglement independent of discretization, while a mesh-level penalty regularizes local discrete interactions. Together, these energies enable reliable removal of self-intersections without changing mesh connectivity and apply to a broad class of geometries, including surfaces with boundary, non-manifold configurations, immersion failures, and multi-object scenes. Compared to prior state-of-the-art methods, our approach resolves self-intersections across challenging datasets, enabling reliable downstream processing of surface meshes.
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.
Recent advances in generative models have democratized the creation of high-quality static 3D assets, yet animating these meshes remains a labor-intensive bottleneck. Traditional pipelines fracture this process into sequential stages—rigging, skinning, and motion synthesis—ignoring the inherent coupling between morphological structure and motor function. To bridge this gap, we introduce ACT, a unified generative framework that reformulates rigging and animation not as independent tasks, but as complementary views of a single hyper-kinematic process. Our key insight is to model the joint distribution of skeletal topology and temporal motion within a shared latent space. ACT utilizes a Vision Language Model (VLM) to extract semantic topological priors from arbitrary meshes, which then condition a Diffusion Transformer (DiT) backbone. By treating static rest poses and dynamic trajectories as a unified sequence, our model employs a task-aware masking strategy to flexibly perform zero-shot rigging, text-guided motion generation, and motion completion within a single end-to-end architecture. Furthermore, a geometry-guided decoder ensures that surface deformations are tightly coupled with the generated kinematics. Extensive experiments demonstrate that ACT generalizes robustly to diverse, non-humanoid characters without retraining. By replacing brittle cascaded pipelines with a holistic prior, our method enables novel applications such as semantic-driven topology editing and generative in-betweening, offering a versatile and efficient solution for automating 3D character animation.
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.
We introduce Soft Anisotropic Diagrams (SAD), an explicit and differentiable image representation parameterized by a set of adaptive sites in the image plane. In SAD, each site specifies an anisotropic metric and an additively weighted distance score, and we compute pixel colors as a softmax blend over a small per-pixel top-K subset of sites. We induce a soft anisotropic additively weighted Voronoi partition (i.e., an Apollonius diagram) with learnable persite temperatures, preserving informative gradients while allowing clear, content-aligned boundaries and explicit ownership. Such a formulation enables efficient rendering by maintaining a per-query top-K map that approximates nearest neighbors under the same shading score, allowing GPU-friendly, fixed-size local computation. We update this list using our top-K propagation scheme inspired by jump flooding, augmented with stochastic injection to provide probabilistic global coverage. Training follows a GPU-first pipeline with gradient-weighted initialization, Adam optimization, and adaptive budget control through densification and pruning. Across standard benchmarks, SAD consistently outperforms Image-GS and Instant-NGP at matched bitrate. On Kodak, SAD reaches 46.0 dB PSNR with 2.2 s encoding time (vs. 28s for Image-GS), and delivers 4–19× end-to-end training speedups over state-of-the-art baselines. We demonstrate the effectiveness of SAD by showcasing the seamless integration with differentiable pipelines for forward and inverse problems, efficiency of fast random access, and compact storage. You can find the code here: https://luckyiyi.github.io/SAD.
While the human eye can perceive an impressive twenty stops of dynamic range, smartphone camera sensors remain limited to about twelve stops despite decades of research. A variety of high dynamic range (HDR) image capture and processing techniques have been proposed, and, in practice, they can extend the dynamic range by 3–5 stops for handheld photography. This paper proposes an approach that robustly captures dynamic range using a handheld smartphone camera and lightweight networks suitable for running on mobile devices. Our method operates indirectly on linear raw pixels in bracketed exposures. Every pixel in the final HDR image is a convex combination of input pixels in the neighborhood, adjusted for exposure, and thus avoids hallucination artifacts typical of recent deep image synthesis networks. We validate our system on both synthetic imagery and unseen real bracketed images — we confirm zero-shot generalization of the method to smartphone camera captures. Our iterative inference architecture is capable of processing an arbitrary number of bracketed input photos, and we show examples from capture stacks containing 3–9 images. Our training process relies only on synthetic captures yet generalizes to unseen real photos from several cameras. Moreover, we show that this training scheme improves other SOTA methods over their pretrained counterparts. Project page: https://lucky-hdr.github.io/.
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/.
Fungal wood decay is a complex biophysical phenomenon that involves the degradation of a variety of structural wood components, ranging from lignin and carbohydrates to defensive chemical agents. All these substrates serve as varying resources with different material properties that determine the rate of fungal propagation and the structural integrity and color of decaying wood. We propose a novel approach to simulate the dynamic interactions between the biological and mechanical components of wood decay, including fungal colonization, chemical defense, and moisture-driven fracture. We propose a novel volumetric representation of trees that includes grain-aligned mesh generation, internal moisture dynamics, and tissue-specific health states. Furthermore, we model the anisotropic diffusion, consumption, and resulting material failure caused by white and brown rot fungi. This allows simulating and rendering 3D volumetric decaying trees that realistically capture key aspects of the process, such as the progression of cuboid fracture patterns, the hollowing of trunks, and the effects of environmental moisture on structural stability.
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 present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable dynamics and predicts future states through efficient matrix evaluations instead of sequential time integration. This yields log-linear scaling in the number of time steps and allows large portions of the trajectory to be skipped while retaining accuracy. The resulting temporal efficiency is especially advantageous for optimization tasks such as control and initial-state estimation, where the objective often depends largely on the final configuration. To broaden the scope of Koopman-based reduced-order models in graphics, we introduce a discretization-agnostic extension that learns shared dynamic behavior across multiple shapes and mesh resolutions. Prior DMD-based approaches have been restricted to a single shape and discretization, which limits their usefulness for tasks involving geometry variation. Our formulation generalizes across both shape and discretization, which enables fast shape optimization that was previously impractical for DMD models. This expanded capability highlights the potential of Koopman operator learning as a practical tool for efficient deformable simulation and design.
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.
We present a family of mixed Material Point Methods well suited for the CFL-rate simulation of stiff elastoviscoplastic materials, up to the incompressible limit. Our work builds upon the mixed discretization from Daviet and Bertails-Descoubes [2016a] and extends it to handle finite-strain vis-coelasticity and more general flow rules, allowing the simulation of a much wider range of materials. Our implicit integration scheme leads to a well-posed, symmetric optimization problem with compact stencils for which we propose 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.
We extend Progressive Dynamics [Zhang et al. 2024, 2025] from cloth and shells to volumetric finite elements, enabling an efficient level-of-detail (LOD) animation-design pipeline with predictive coarse-resolution previews for rapid iteration toward a final high-resolution volumetric elastodynamics animation. To achieve this, we introduce VelPro Splitter, a principled and substantially improved VelPro-type integrator [Zhang et al. 2025] that splits the current-level velocity and recombines its high-resolution component with prolonged coarse-level velocity. The resulting VelPro Splitter is general and applies to both shell and volumetric discretizations. This splitting strategy better generates the high-frequency dynamic details that motivate highresolution elastodynamics animation, going beyond the previously mostly geometric enrichment due to prolonged coarse-level velocity, while maintaining cross-level consistency in bulk deformation across LOD results. As a result, it largely decouples finest-level enrichment quality from the number of LOD levels, addressing a practical limitation of VelPro at small timestep sizes where many levels are required to obtain sufficient enrichment. To make this volumetric setting practical for Progressive Dynamics, we add two supporting contributions. First, we construct volumetric hierarchies and introduce a simple and effective topology-aware boundary-binding method that enables reliable prolongation between overlapping, but not-necessarily-conforming, meshes using a barycentric-like linear interpolant. Second, instead of applying the subspace approach of Zhang et al. [2024] for reducing coarse model locking, we show that a lightweight, resolution-based stiffness rescaling via a simple Young's-modulus adjustment [Chen et al. 2017] is both effective and well-suited for progressive volumetric simulation. Together, these contributions jointly realize Volumetric Progressive Dynamics. We demonstrate its high-fidelity LOD matching for volumetric elastodynamics across 1D, 2D, and 3D scenarios with high speeds, large deformations, and frictional contact.
Cages are fundamental structures in computer graphics, serving as versatile proxies for a wide range of applications. A high-quality cage must balance two competing objectives: minimizing the face count to ensure simplicity, and maximizing tightness to maintain high geometric fidelity to the input mesh. In this paper, we propose PR-Cage, a nested optimization framework for automated cage generation. For the outer control layer, we introduce a thickness parameter τ that defines a feasibility region; the evolving cage is guided by the τ-offset surface. We observe that an optimal balance between simplicity and tightness is achievable by progressively relaxing the parameter τ via a staircase schedule. For the inner iterations, we extend the traditional Quadric Error Metric (QEM) framework by incorporating rigorous linear inequality constraints to suppress triangle degeneration and prevent normal flips. Our algorithm relies exclusively on the atomic operations of edge collapses and edge flips, resulting in high computational efficiency and robustness. Comparative experiments on public datasets demonstrate that PR-Cage consistently outperforms existing methods, achieving extreme simplification while maintaining high adherence to the underlying geometry; see the teaser figure. Due to these favorable properties, we demonstrate the utility of our method in several downstream applications, such as contact simulation and deformation, where PR-Cage exhibits significant advantages in both quality and performance.
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.
We present a computational framework for numerical homogenization of origami materials—thin sheets structured with periodic crease patterns that, once folded, exhibit diverse and often unusual mechanical properties. Whereas the in-plane stiffness of conventional sheet materials is typically orders of magnitude larger than their resistance to bending, origami-based folding introduces geometric structure that can drastically reshape both bending and stretching behavior. However, predicting how a particular crease pattern gives rise to effective macroscopic properties remains challenging due to the complex coupling of crease geometry, folding kinematics, and surface deformations. In this work, we introduce a computational framework that integrates simulation-based folding and numerical homogenization to explore the relationship between crease pattern and effective material behavior. To describe the macromechanical response of origami materials, we employ a quadratic energy model based on Classical Laminate Theory, together with a simplified treatment of crease plasticity. Our unified representation accommodates both straight- and curved-crease designs, revealing a rich space of origami materials with diverse behavior. In particular, we examine how pattern symmetry governs material symmetries, demonstrating examples that span the full spectrum from perfectly isotropic to highly anisotropic membrane and bending responses. Our framework further enables controlled exploration of parameter variations, illustrating how geometric features such as crease curvature shape macroscopic mechanical behavior. We showcase the potential of this approach through a broad set of examples, ranging from canonical straight-crease patterns such as Miura-ori to complex curved-crease tessellations. While a quantitative analysis is left for future work, we validate our homogenized descriptions against native-scale simulations and qualitatively compare deformation behaviors with real-world prototypes.
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.