Meshes

Mid-surface abstraction is an important preprocessing step for finite element analysis of thin-walled CAD models, and face pairing is its central subproblem. Existing face-pairing methods rely on handcrafted geometric criteria whose thresholds are hard to tune when a model has multiple local wall thicknesses; their groupings depend on threshold settings and processing order, so the same model can yield inconsistent results. We present MidSurfNet, a learning-based face-pairing method that couples a learned face-pair scorer with a deterministic face-group composition. The scorer evaluates every unordered face pair with two separately learned evidence streams: a geometry stream combining continuous pairing criteria with a conditional shape correction, and an attributed-topology stream over the B-Rep face-adjacency graph. A pair-conditioned gate fuses the two streams, and independent per-pair decisions retain opposing-face support relations at one operating threshold selected once on validation data, replacing rather than adding to the per-model thresholds of rule-based pipelines. Under a connected-and-bipartite condition, the composition stage organizes the retained relations into variable-cardinality m-to-n face groups, each independent of processing order for a fixed support graph and unique up to its two side labels. We also construct the MidSurf dataset, a benchmark of 1,575 manually annotated CAD models. On the test set, MidSurfNet attains a pair-level F1-Score of 87.32%, 23.22 percentage points above the strongest rule-based baseline, and an end-to-end Completion Rate of 75.42%, including 61.90% on the multi-wall-thickness category the evaluated rule-based implementations do not support. We demonstrate practical utility by generating mid-surfaces from the composed face groups through an industrial mid-surface API and running finite element analyses on the resulting shell models.

Hierarchical 3D Scene Graphs (3DSG) have emerged as an actionable and scalable representation for long-term autonomy incorporating metric, semantic, and topological information in the scene. However, the question of geometric representation of objects in 3DSG has been overlooked as most methods use simplified geometric models such as partial point clouds or 3D bounding boxes. In this work, we introduce a hierarchical object representation that can be leveraged for high-fidelity object-level reconstruction, object-based robust re-localization or map alignment, and efficient and analytical collision checking for safe robot navigation planning in dense and cluttered environments. The representation is structurally organized into four distinct layers, progressively abstracting the scene from raw sensor data to dense 3D meshes to analytical primitives such as superquadrics, which provide a sparse and analytical representation for object geometry. We develop a pipeline that builds the hierarchical object representation from RGB-D image stream captured by a robot, and demonstrate its working in real-world open-set object scenes in both indoor and outdoor environments. Extensive experiments across diverse datasets including HOPE, ReplicaCAD, Kimera-Multi, and NUS Campus Dataset collected using Unitree B2 Robot validate our pipeline in both indoor and outdoor environments. We show that our superquadric-based map alignment method outperforms the current state-of-the-art object based map alignment method ROMAN. Our code can be found at https://github.com/perceptica-robotics/Hickory.

We present SHELLS (Semantic Head Estimation via Layered Local Sampling), an efficient feed-forward framework for 3D head reconstruction in dense semantic correspondence from multi-view images. Existing methods typically refine vertices independently via localized feature volumes. This approach couples memory-intensive feature sampling to mesh resolution, which limits scalability for dense topologies (> 10k vertices) and introduces surface noise. In contrast, SHELLS decouples feature extraction from mesh resolution via a hierarchical sampling strategy. We extract multi-view features using a DINOv2 backbone with LoRA adaptation, projectively sample a sparse global feature cloud, and predict an intermediate coarse mesh. This coarse prior guides the construction of layered, surface-aware sampling shells that serve as a discrete search space for the final reconstruction. SHELLS maintains surface consistency while using 88% less inference GPU memory (2.4GB vs. 20GB) than volumetric baselines. It reduces median registration error by 21% to 29% with a 3.5x inference speedup (0.08s vs. 0.29s) for 18k-vertex meshes. Notably, our model is trained exclusively on synthetic data yet generalizes effectively to real-world captures, eliminating the need for the costly, pre-registered multi-view datasets common in prior work.

Texturing 3D meshes plays a vital role in determining the visual realism of digital objects and scenes. Although recent generative 3D approaches based on Neural Radiance Fields and Gaussian Splatting can produce textured assets directly, polygonal meshes remain the core representation across modeling, animation, visual effects, and gaming pipelines. Neural 3D mesh texturing therefore continues to be an essential and active area of research. In this survey, we present a comprehensive review of recent advances in neural 3D mesh texturing, covering methods for texture synthesis, transfer, and completion. We first summarize key foundations in mesh geometry, texture mapping, differentiable rendering, and neural generative models, and then organize the literature into a unified taxonomy spanning early GAN-based methods to modern diffusion-based pipelines. We further analyze common architectures and supervision strategies, review datasets and evaluation protocols, and discuss emerging applications, practical/commercial systems, and open challenges. Together, these insights provide a structured perspective on the current landscape and help guide future developments in learning-based 3D mesh texturing.

Compositional implicit surface representations model scenes as collections of objects, each encoded by a Signed Distance Field (SDF). A fundamental limitation of this approach is that multiple SDFs can produce geometries that interpenetrate, violating physical plausibility. Existing mitigation strategies rely on soft penalty terms that reduce but do not eliminate intersections, and require careful loss weighting. To truly prevent interpenetration, we propose a hard constraint on vector-valued SDFs and introduce S2MDF, a lightweight plug-and-play module that enforces the constraint on any object-compositional SDF representation without architectural modifications. It introduces negligible computational overhead and is compatible with linearly-interpolated standard meshing algorithms such as Marching Cubes. It can be applied during training or as a post-processing step. Experiments on multiple state-of-the-art compositional methods show that S2MDF reduces intersections to numerical precision while preserving reconstruction quality, outperforming existing mitigation strategies.

We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to obtain due to challenges in scanning and triangulating complex shapes, or by neural fields that require per-shape optimization. We propose to adopt a Reproducing Kernel Particle Method (RKPM) representation, which enables the construction of reduced-order skinning weights by solving a generalized eigensystem on the Hessian matrix of the elastic energy. We demonstrate that this formulation not only leads to a 40x training speedup compared with the per-shape optimization of neural fields, but also achieves lower simulation error when evaluated against the converged results of finite element method. We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats, as well as the application of our method in the downstream task of robot simulation.

Interactive 3D assets used in games and simulation are typically decomposed into specific semantic parts to support animation, physics, and scripted behaviors, yet most generative 3D models produce either monolithic meshes or arbitrary part decompositions that cannot be aligned with application-specific requirements. We present CubePart, a generative framework for open-vocabulary, part-controllable 3D mesh generation that exposes part structure as an explicit inference-time control signal. Given a global text prompt and a user-defined parts schema expressed as an open-ended list of part names, our method generates a set of meshes - one per schema element - that assemble into a coherent object while respecting the specified semantic structure. To enable this capability, we introduce a scalable data pipeline to construct a large open-vocabulary, part-labeled 3D dataset, along with a two-stage generative architecture that separates global shape synthesis from part-level decoding. We demonstrate that the resulting assets can be directly integrated into game engines and driven by animation and behavior scripts without manual post-processing. Project Page: https://cubepart.github.io/

Current video-to-4D methods struggle with complex topology changes, transparent materials, thin structures, and inner surfaces. We present Helix4D, a dynamic mesh generation framework by inheriting the expressive representation of Trellis2, adapting it from image-to-3D to video-conditioned 4D generation. Our design arises from two key questions: (a) how to enable Trellis2's frame-local attention to share information across frames while preserving its pretrained quality on rare cases such as transparent objects and inner surfaces, and (b) how to inject temporal information into a purely 3D positional encoding without breaking pretrained capabilities. We address (a) with a sliding-window cross-frame attention and anchor on the first frame. The first frame is generated by the base Trellis2 model and injected into our model, letting it inherit Trellis2's quality in rare cases through cross-frame attention. We address (b) with a 4D temporal encoding that repurposes redundant low-frequency spatial RoPE bands for time, extending the encoding from 3D with no additional parameters. Extensive experiments show the effectiveness of Helix4D for high-quality dynamic mesh generation on ActionBench and our own challenging complex dynamics set.

We present CrossLift, a technique for computing cross fields on meshes guided by visual features in images. We leverage powerful text-to-image priors that are capable of synthesizing images of feature-aligned quad meshes in 2D. We extract this signal as explicit per-pixel directions in the 2D images, which we then back-project to the mesh surface. We aggregate these candidate surface directions by performing two smooth interpolations on the mesh surface (first within each view and second across multiple views). We propose custom confidence-based weights for the candidate directions in each interpolation that allow us to resolve conflicts between candidates on the same face and smoothly interpolate our field to occluded faces. Our method is modular and can be used with many different 2D visual priors. We show additional applications to texture-aligned quad meshing as well as interactive cross-field design using coarse, user-drawn lines as signal. We demonstrate the effectiveness of CrossLift on a diverse set of both organic and mechanical shapes and produce quad meshes that exhibit superior semantic alignment as compared to existing methods. Project page at: https://crosslift.github.io/

Advancements in 3D curve skeletonization are accelerating progress across a wide range of applications. However, developing robust skeletonization algorithms that capture intricate object details remains challenging. Skeletonization via Local Separators (LS) offers an efficient graph-based approach but suffers from representation inaccuracies due to its discrete nature. To address this, we introduce CSCD, a novel framework for Curve Skeletonization in the Continuous Domain, generalizing LS to manifolds. Specifically, we present two realizations: CSCD-M for meshes and CSCD-PC for point clouds. CSCD-M leverages the intrinsic triangulation of a mesh for resilience to noise and improved topological preservation, while CSCD-PC employs tufted Laplacians for enhanced robustness. To our knowledge, CSCD-M is the first intrinsic method for curve skeletonization. Our results show CSCD-M matches LS performance across diverse meshes and outperforms LS (TOG'21) on benchmarks like Thingi10k dataset. CSCD-PC qualitatively outperforms CoverageAxis++ (Eurographics'24) and EPCS (CAG'23). Finally, we demonstrate the efficacy of CSCD in a few downstream tasks: object classification, shape segmentation, identifying handles, tunnels, and constrictions in objects. Project Website: https://cscd-skel.pages.dev

While 3D generation is progressing rapidly, recent work has often focused on obtaining high-resolution assets, leaving user experience and deployability as afterthoughts. We present AssetGen, a 3D generator that focuses instead on these two aspects. Given one reference image, in 30 seconds it produces a high-quality mesh with baked normals, a color texture, and a controlled polygon budget suitable for real-time rendering, including mobile use cases. The AssetGen Flash variant further reduces latency to 14 seconds for interactive and agentic creation loops. Our model generates the object geometry with a coarse-to-refine VecSet framework, which implements mesh simplification, cleaning, and normal baking on the GPU, and a fast parallel UV unwrapping. It then generates textures in a multi-view fashion, followed by backprojection and 3D inpainting. Model distillation, kernel optimization, and pipeline parallelization are co-designed to accelerate the system end-to-end. We introduce numerous automated and blind human evaluations and demonstrate competitive visual quality against leading commercial solutions in 30 seconds and preview-quality results in less than 15 seconds. The final result is a system that supports AI-assisted, deployable 3D content creation in interactive workflows.

Graph Network Simulators (GNSs) have emerged as powerful surrogates for complex physics-based simulation, offering inherent differentiability and orders-of-magnitude speedups over traditional solvers. However, GNSs typically assume access to the underlying material parameters, such as stiffness or viscosity, severely limiting their utility in realistic experimental settings. While recent meta-learning approaches address the parameter dependency by inferring properties from mesh trajectories, reconstructing a mesh from an observed scene is challenging. In this work, we introduce Point Cloud Encoding for Accurate Context Handling (PEACH), a novel framework that applies in-context learning on point clouds to adapt a learned simulator to unseen physical properties during inference. Our approach relies on a novel spatio-temporal point cloud sequence encoder, as well as two forms of auxiliary supervision to help improve simulation fidelity. We demonstrate that PEACH is capable of accurate zero-shot sim-to-real transfer on a challenging, dynamic scene. Experiments on simulation scenes show that PEACH even outperforms mesh-based baselines on prediction accuracy, while being much more practical for real-world deployment.

4D mesh generation has recently emerged as a powerful paradigm for recovering dynamic 3D structure from videos, but existing methods remain slow, computationally expensive, and difficult to scale to longer sequences. We introduce a training-free approach that accelerates 4D mesh generation while improving temporal correspondence quality. Our key observation is that temporal correspondences emerge inside a 4D backbone long before its generated meshes become visually accurate. We exploit this with a general framework we call Spatio-Temporal Attention Chain which propagates information across space and time. Starting from vertices on an anchor mesh, the chain maps vertices to latent tokens. It then follows temporal correspondences in latent space, and recovers frame-specific vertices through latent-to-vertex attention. This design avoids expensive explicit matching while preserving anchor mesh details and thereby improving dynamic mesh geometry and temporal consistency. Compared to state-of-the-art, our method generates a 4D mesh in 9 seconds, achieving a $13\times$ speedup while producing higher-quality results. Moreover, our approach scales to videos up to $16\times$ longer without degrading mesh quality. Beyond generation, the improved correspondences enable competitive zero-shot performance on two downstream tasks: 2D object tracking and 4D tracking. We further show that our framework enables reliable camera estimation, a capability not supported by prior 4D mesh generation methods.

This paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts the flow matching (FM) paradigm to a mesh-based, triangulation-agnostic setting. Theoretically, it proposes a specific noise distribution which is triangulation agnostic, to be used inside the FM model's denoising process. While noise distributions are usually trivial to devise for, e.g., images, devising a triangulation-agnostic distribution proves to be a much more difficult task. We formulate a mathematical definition of triangulation agnosticism of distributions, via their spectrum. We then show that a discretization of a specific Gaussian random field called a Matérn process holds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to the triangulation-agnostic setting by using a state-of-the-art approach for learning signals on meshes in the gradient domain -- PoissonNet -- as the denoiser. We conduct experiments on elaborate tasks such as sampling elastic rest states, and generating poses of humanoids. Our method is shown to be capable of producing highly realistic results for meshes of over one million triangles, significantly exceeding the state-of-the-art in quality and diversity.

Hexahedral meshes are widely used in simulation pipelines, yet automatic generation remains challenging for complex CAD geometries. Polycube-based hexahedral meshing is a representative approach due to its regular, parameterization-friendly structure, but existing polycube construction methods often rely on intricate surface segmentation and local heuristics, which can produce artifacts or fail on difficult shapes. In this paper, we propose an end-to-end framework for polycube generation based on conditional diffusion models. Given an input geometry represented as a point cloud, our method directly produces a corresponding polycube point cloud, eliminating the need for explicit surface segmentation or predefined polycube templates. At the core of our approach is a dual-latent conditional diffusion architecture that confines computationally expensive self-attention operations to a fixed-capacity, low-dimensional latent space. This design effectively decouples computational complexity from the resolution of both the input geometry and the output polycube, thereby avoiding the quadratic cost typical of point cloud self-attention mechanisms while supporting flexible input and output resolutions. To obtain a hexahedral mesh, the generated polycube is aligned to the input shape via rigid and non-rigid point cloud registration to establish surface correspondence, followed by a polycube-to-hex pipeline. We additionally create and release a paired dataset of CAD meshes and their corresponding polycube meshes, together with the core implementation of our model. Experiments show that PolycubeNet generalizes to complex CAD models with arbitrary genus and produces high-quality polycube structures within seconds, improving robustness and efficiency over prior learning-based approaches.

The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing either pure triangular meshes or pure quadrilateral meshes with isotropic densities. In this paper, we present QuadLink, a unified framework consisting of three stages for quad-dominant mesh generation by linking points into structured faces. QuadLink formulates polygonal mesh generation as a hybrid centroid-conditioned vertex linking model: it first predicts a unified set of anchors (vertices and face centroids), then learns centroid-conditioned links that associate vertices with face centroids, and finally assembles polygonal faces with a quad-first strategy guided by robust geometric verification strategies. This link-based formulation enables efficient generation of sparse and anisotropic quad-dominant meshes with coherent edge flow and meanwhile supporting hybrid polygonal topology. To construct training data for this model, we further introduce a Tri-to-Quad Operator that converts artistic triangle meshes into quad-dominant training data via global merge selection. Extensive experiments show that QuadLink produces production-ready quad-dominant meshes from point clouds and achieves improved geometric fidelity and topological quality compared to prior baselines. Our method natively supports hybrid polygonal topology, generalizing to arbitrary n-gon meshes without architectural changes.

In this paper, we introduce \textit{DecoRec}, a novel system designed to elevate single-view 2D images to a decomposed 3D scene mesh. Current methods for single-view scene reconstruction typically rely on object retrieval or the regression of coarse 3D voxels or surfaces, leading to inaccuracies in capturing the appearance and geometry of the input image. The lack of high-quality large-scale scene-level datasets further complicates direct 3D scene generation from single-view images. To achieve high-quality 3D scene generation from a single-view image, DecoRec takes advantage of recent diffusion-based single-view object reconstruction methods to reconstruct individual objects separately. Subsequently, a refinement pipeline is proposed to effectively merge these reconstructed objects, enhancing appearance and geometry through a differentiable rendering technique and diffusion-guided refinement. Our results demonstrate that DecoRec facilitates high-quality single-view scene reconstruction in both geometry and novel synthesis, offering significant benefits for downstream applications like room interior design.

We present ArtMesh, a mesh-native method for reconstructing articulated objects explicitly as connected triangle meshes with per-part rigid motion from multi-view images in start and end states. Existing 3D Gaussian Splatting pipelines for articulated reconstruction inherit the unstructured point-based geometry of their splatting base, which provides no surface topology for reasoning about part boundaries or enforcing motion consistency along the object's connectivity. ArtMesh instead builds on a mesh-based differentiable rendering backbone, enabling part-aware dynamics to act directly on the structured topology. To make the topology compatible with articulation, we introduce part-aware restricted Delaunay remeshing, producing connected submeshes whose triangles do not cross semantic part boundaries. The dynamic mesh field then optimizes articulation using bidirectional Vertex-wise Motion Consistency on transported mesh vertices and Pixel-wise Motion Consistency on rendered RGB-D observations. We introduce Articulate-100, a new benchmark of 100 articulated objects spanning 16 PartNet-Mobility categories. On this benchmark, ArtMesh outperforms prior 3DGS-based pipelines in joint parameter estimation and part-level geometric reconstruction, with the largest gains on objects with many movable parts.

Impossible objects, geometric constructions that humans can perceive but that cannot exist in real life, have been a topic of intrigue in visual arts, perception, and graphics, yet no satisfying computer representation of such objects exists. Previous work embeds impossible objects in 3D, cutting them or twisting/bending them in the depth axis. Cutting an impossible object changes its local geometry at the cut, which can hamper downstream graphics applications, such as smoothing, while bending makes it difficult to relight the object. Both of these can invalidate geometry operations, such as distance computation. As an alternative, we introduce Meschers, meshes capable of representing impossible constructions akin to those found in M.C. Escher's woodcuts. Our representation has a theoretical foundation in discrete exterior calculus and supports the use-cases above, as we demonstrate in a number of example applications. Moreover, because we can do discrete geometry processing on our representation, we can inverse-render impossible objects. We also compare our representation to cut and bend representations of impossible objects.

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative. Message-passing GNNs are widely used for mesh simulation, and their shared node and edge update functions are relatively generalisable across varying graph structures. By contrast, non-shareable edge-specific aggregation layers can capture nonlinear relationships more accurately but usually require fixed graph connectivity, which limits generalisability. This paper presents Mask-Morph Graph U-Net (MMGUNet), a practical approach to addressing the limitation of hierarchical Graph U-Net architectures that use edge-specific downsampling and upsampling layers. Fixed coarse graph connectivity is required for edge-specific layers. To retain this while improving spatial correspondence, the proposed method morphs the coarsened graph hierarchy to each input mesh using feature-aligned barycentric parameterisation before constructing cross-graph edges. It further applies node masking during supervised pretraining, followed by parameter-efficient fine-tuning in which high-parameter edge-specific layers are frozen. The proposed approach is evaluated in in-distribution, out-of-distribution, and cross-component transfer settings using mean Euclidean distance and maximum intrusion percentage error. Results show that coarse-graph morphing improves test accuracy relative to a fixed-coarse-graph baseline, while masked supervised pretraining reduces the train-test discrepancy and improves data efficiency during transfer. The proposed model also achieves lower prediction error compared with external baselines. These results demonstrate a practical route toward reusable, data-efficient mesh-based surrogate modelling for crashworthiness design exploration.

Video-guided 3D animation holds immense potential for content creation, offering intuitive and precise control over dynamic assets. However, practical deployment faces a critical yet frequently overlooked hurdle: the pose misalignment dilemma. In real-world scenarios, the initial pose of a user-provided static mesh rarely aligns with the starting frame of a reference video. Naively forcing a mesh to follow a mismatched trajectory inevitably leads to severe geometric distortion or animation failure. To address this, we present Rectified Dynamic Mesh (R-DMesh), a unified framework designed to generate high-fidelity 4D meshes that are ``rectified'' to align with video context. Unlike standard motion transfer approaches, our method introduces a novel VAE that explicitly disentangles the input into a conditional base mesh, relative motion trajectories, and a crucial rectification jump offset. This offset is learned to automatically transform the arbitrary pose of the input mesh to match the video's initial state before animation begins. We process these components via a Triflow Attention mechanism, which leverages vertex-wise geometric features to modulate the three orthogonal flows, ensuring physical consistency and local rigidity during the rectification and animation process. For generation, we employ a Rectified Flow-based Diffusion Transformer conditioned on pre-trained video latents, effectively transferring rich spatio-temporal priors to the 3D domain. To support this task, we construct Video-RDMesh, a large-scale dataset of over 500k dynamic mesh sequences specifically curated to simulate pose misalignment. Extensive experiments demonstrate that R-DMesh not only solves the alignment problem but also enables robust downstream applications, including pose retargeting and holistic 4D generation.

Intracranial aneurysms (IAs), characterized by unpredictable growth and risk of rupture, are a major cause of stroke and can lead to life-threatening hemorrhages with high mortality and long-term disability. With aging populations, the incidence and overall burden of cerebrovascular diseases are expected to increase, highlighting the need for scalable approaches to analyze complex medical data and improve population-level understanding of these conditions. While digital twins and deep learning offer promising avenues for improving diagnosis, prognosis, and treatment, their effectiveness is limited by the scarcity of large-scale, high-quality medical data and corresponding labels. We present Synthetic VAsculature (SynVA), a modular toolkit for vascular mesh generation and anatomically consistent aneurysm synthesis. SynVA combines novel flow-matching-based methods for generating healthy vessel meshes with learning-based approaches for anatomy-conditioned aneurysm mesh generation - aneurysms are computed from pre-existing vascular geometries rather than being generated in isolation. In addition, we introduce the SynVA procedural model for vascular and aneurysm synthesis based solely on physiological principles and statistical priors, which enables the generation of large-scale datasets (e.g., for the training of mesh-based generative models). To this end, we release a dataset of 50,000 fully labeled mesh samples for a variety of downstream vision tasks, such as semantic segmentation. Extensive quantitative and qualitative evaluations demonstrate that SynVA generates realistic vessel geometries and anatomically plausible aneurysms. Specifically, our experiments indicate that some methods produce aneurysm shapes more aligned with expert human perception while others perform better on quantitative similarity metrics with reconstructions of real aneurysms.

Autoregressive (AR) models can generate high-quality low-poly meshes from point clouds, but they still operate in an all-or-nothing manner: when a local region is unsatisfactory, the entire mesh must be regenerated, wasting computation and destroying satisfactory mesh structure elsewhere. We introduce MeshFIM, a Fill-in-the-Middle (FIM) framework that regenerates a target region of a low-poly mesh conditioned on the surrounding context. MeshFIM addresses three mesh-specific challenges: enforcing exact attachment along the exposed boundary, preserving topological order in the context, and suppressing overflow beyond the intended region. It does so with five complementary design choices: boundary vertex markers, context positional embeddings, expanded context width, context augmentation, and a low-poly geometry encoder whose gated subtraction mechanism focuses generation on the missing region by leveraging the difference between the reference surface and the existing mesh. Detailed ablation studies are presented to show the effectiveness of every introduced component. Based on MeshFIM, we demonstrate two applications: interactive brush-based editing and automatic defect repair on low-poly mesh (see Figure 1). Last but not least, experiments show that MeshFIM outperforms a range of baselines in mesh refinement, mesh repair and whole mesh generation plus stitch-back scheme.

We introduce a meshfree exterior calculus (MEEC) for learning structure-preserving descriptions of physics on point clouds, and use it to build MEEC-Net, a data-efficient surrogate that transfers across resolutions, geometries, and physical parameters. MEEC equips an $\varepsilon$-ball graph with virtual node and edge measures via a single sparse Schur complement solve; the resulting complex satisfies discrete conservation exactly, is end-to-end differentiable in the point positions, and exposes a direct geometry-to-physics link without the mesh-generation step required by conventional structure-preserving discretizations. MEEC-Net learns unknown physics as a shared edge-wise flux law in an SO($d$)-invariant local frame, so the same kernel produces compatible fluxes on any point cloud whose features lie in the training range. We prove a solution-error bound that splits into discretization and kernel-approximation terms which is independent of problem geometry, explaining the observed transfer from very few examples. We show that single-solution training transfers to unseen geometries, boundary conditions, and physical parameters. On five canonical PDE benchmarks MEEC-Net achieves 1-2 orders of magnitude lower out-of-distribution error than baseline neural-operator approaches. On the SimJEB structural-bracket benchmark it achieves competitive error while using substantially fewer training geometries.

The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, the location/values of the applied Dirichlet/Neumann boundary conditions, body forces and material properties, among others. We have previously introduced hybridization of classical linear iterative solvers with neural operators for specific geometries, but they tend to not perform well on geometries not previously seen during training. We partially addressed this challenge by introducing the deep operator network Geo-DeepONet and hybridizing it with Krylov-based iterative linear solvers, which, despite learning effectively across arbitrary unstructured meshes without requiring retraining, led to only modest reductions in iterations compared to state-of-the-art preconditioners. In this study we introduce Neural Subspace Proper Orthogonal Decomposition (NSPOD), a multigrid-like deep operator network-based preconditioner which can dramatically reduce the number of iterations needed for convergence in Krylov-based linear iterative solvers, even when compared to state-of-the-art methods such as algebraic multigrid preconditioners. We demonstrate its efficiency via numerical experiments on a linearized version of solid mechanics PDEs applied to unstructured domains obtained from complex CAD geometries. We expect that the findings in this study lead to more efficient hybrid preconditioners that can match, or possibly even surpass, the convergence properties of the current gold standard preconditioning methods for solid mechanics PDEs.

We present egenioussBench, a visual localisation benchmark built on geospatial reference data: a city-scale airborne 3D mesh and a CityGML LoD2 model. This pairing reflects deployable mapping assets and supports true scalability beyond traditional SfM-based approaches. The query data comprise smartphone images with centimetre-accurate, map-independent ground truth obtained via PPK and GCP/CP-aided adjustment. From 2,709 images, we derive a non-co-visible subset by estimating the full co-visibility matrix from rendered depth and selecting a maximum independent set; the released data include a test split of 42 non-co-visible images with withheld ground truth and a validation split of 412 sequential images with poses, e.g. for training of pose regressors and self-validation. The benchmark features a public leaderboard evaluated with binning metrics at multiple pose-error thresholds alongside global statistics (median, RMSE, outlier ratio), ensuring fair, like-for-like comparison across mesh- and LoD2-based methods. Together, these design choices expose realistic cross-view and cross-domain challenges while providing a rigorous, scalable path for advancing large-scale visual localisation. We make the evaluation code and data availeable at https://github.com/fratopa/egenioussBench and https://www.egeniouss.eu/

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular discretisations. However, practical implementations have struggled to fully realise these benefits. Existing backbones like Fourier neural operators are often biased towards regular grids and fail to generalise to complex domain topologies. We propose a novel architecture for function-space diffusion models that represents generalised graph convolutional kernels as finite element functions, enabling the model to naturally handle unstructured meshes and complex geometries. We demonstrate the efficacy of our network architecture through a series of unconditional and conditional sampling experiments across diverse geometries, including non-convex and multiply-connected domains. Our results show that the proposed method maintains resolution invariance and achieves high fidelity in capturing functional distributions on non-trivial geometries.

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical bottleneck in the field: while architectures have advanced significantly, the common underlying training paradigms remain bound to naive assumptions, such as node-wise supervision and explicit Euler time-stepping. These legacy choices ignore the stiff dynamics and local flux continuity inherent to numerous partial differential equations resolution methods, such as Finite Element, Difference, or Volume (FEM). In this work, we propose a unified framework to bridge the gap between geometric deep learning and rigorous numerical analysis. We introduce three key innovations: (1) Multi Node Prediction, a stencil-level objective that predicts field values for a node's full local topology, enforcing spatial derivative consistency; (2) Temporal Correction, replacing unstable explicit schemes with a predictor-corrector via temporal Cross-Attention; and (3) Geometric Inductive Biases, leveraging 3D Rotary Positional Embeddings (RoPE) to robustly capture rotational symmetries in unstructured meshes. We evaluate this framework across three architectures (MeshGraphNet, Transolver, and a Transformer) on diverse physics datasets. Our approach yields consistent improvements in accuracy and stability, particularly in long-horizon rollouts, while producing latent representations that generalize to unseen subtasks such as Wall Shear Stress or Pressure prediction. Code is available at https://github.com/DonsetPG/graph-physics.

Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets. We introduce CADFit, a hybrid optimization-based CAD reconstruction framework that recovers complex, editable CAD construction sequences from meshes by incrementally fitting and validating parametric operations using geometric feedback. Our approach is distinguished by formulating reconstruction as an IoU-driven optimization over structured CAD programs and supporting a rich set of operations, including extrusions, revolutions, fillets, and chamfers. Experiments on multiple CAD benchmarks show that CADFit outperforms state-of-the-art mesh-to-CAD methods in volumetric Intersection-over-Union and Chamfer Distance, while substantially reducing the Invalid Ratio of reconstructed CAD programs, particularly for complex designs. We further present a multimodal pipeline that enables end-to-end reconstruction of CAD construction sequences from images by combining image-based geometry reconstruction with CADFit. By enabling accurate reconstruction of higher-complexity CAD models, CADFit provides a practical foundation for generating richer datasets and advancing future learning-based approaches to CAD reverse engineering. The code is available at: https://github.com/ghadinehme/CADFit.

We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality), we prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port-Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation. This reduction clarifies what must be fixed and what should be learned, directly informing MeshFT-Net's design. Across evaluations on analytic and realistic datasets, physics-consistency tests, and out-of-distribution validation, MeshFT-Net achieves near-zero energy drift and strong physical fidelity (correct dispersion and momentum conservation) along with robust extrapolation and high data efficiency. By eliminating non-physical degrees of freedom and learning only metric-dependent structure, MeshFT provides a principled inductive bias for stable, faithful, and data-efficient learning-based physical simulation.

On-orbit inspection imagery is crucial as it enables characterization of non-cooperative resident space objects, providing the geometry and structural condition essential for active debris removal and on-orbit servicing mission planning. However, most existing neural implicit surface reconstruction methods have been confined to synthetic or hardware-in-the-loop data with known camera poses and controlled illumination. In this work, we present a pipeline for neural implicit surface reconstruction of non-cooperative space objects from monocular inspection imagery. We demonstrate it on publicly released ISS inspection footage from the STS-119 mission and publicly released on-orbit inspection footage of an H-IIA rocket upper stage. We find that segmentation-based background removal is essential for successful camera pose estimation from real on-orbit footage, where background variation between frames caused direct processing to fail entirely. We further incorporate photometric correction of per-frame exposure variations and analyze its behavior across datasets, finding that performance in shadowed regions varies with the illumination characteristics of the input footage.

3D shapes from scanning, reconstruction, or AI-generated content often lack simple quad mesh layouts -- critical for efficient editing and modeling. Existing quad-remeshing techniques typically produce complex layouts with irregular loops, leading to tedious manual cleanup and extensive algorithm tuning. We introduce SQuadGen, a diffusion-based generative framework that leverages Chart Distance Fields (CDF) to synthesize simple quad layouts on 3D shapes. Our approach addresses two key challenges: (1) the discrete nature of mesh connectivity, which hinders learning, and (2) the scarcity of large-scale datasets with simple quad meshes. To overcome the first, we propose CDF, a continuous surface-based representation enabling effective learning and synthesis of quad layouts. To address the second, we define loop-aware simplicity metrics and construct a large-scale dataset of high-quality quad layouts recovered from public 3D repositories through a robust quad-recovery pipeline. Extensive evaluations across diverse 3D inputs show that SQuadGen consistently outperforms existing methods, producing robust, artist-friendly simple quad layouts.

Recent advances in 4D content generation have attracted increasing attention, yet creating high-quality animated 3D models remains challenging due to the complexity of modeling spatio-temporal distributions and the scarcity of 4D training data. We present AnimateAnyMesh++, a feed-forward framework for text-driven animation of arbitrary 3D meshes with substantial upgrades in data, architecture, and generative capability. First, we expand the DyMesh-XL dataset by mining dynamic content from Objaverse-XL, increasing the number of unique identities from 60K to 300K and substantially broadening category and motion diversity. Second, we redesign DyMeshVAE-Flex with power-law topology-aware attention and vertex-normal enhanced features, which significantly improves trajectory reconstruction, local geometry preservation, and mitigates trajectory-sticking artifacts. Third, we introduce architectural changes to both DyMeshVAE-Flex and the rectified-flow (RF) generator to support variable-length sequence training and generation, enabling longer animations while preserving reconstruction fidelity. Extensive experiments demonstrate that AnimateAnyMesh++ generates semantically accurate and temporally coherent mesh animations within seconds, surpassing prior approaches in quality and efficiency. The enlarged DyMesh-XL, the upgraded DyMeshVAE-Flex, and variable-length RF together deliver consistent gains across benchmarks and in-the-wild meshes. We will release code, models, and the expanded DyMesh-XL upon acceptance of this manuscript to facilitate research in 4D content creation.

Kinematic rigs provide a structured interface for articulating 3D meshes but lack any associated pose space, i.e., an explicit representation of the plausible manifold of joint configurations for a given mesh. Without such a pose space, stochastic sampling or manual manipulation of raw rig parameters easily results in semantic and/or geometric violations, such as anatomical hyperextension and non-physical self-intersections. We propose Video-informed Pose Spaces (ViPS), a feedforward framework that discovers the latent distribution of valid articulations for auto-rigged meshes by distilling motion priors from a pretrained video diffusion model. Unlike existing methods that rely on scarce, artist-authored 4D datasets, or focus on reconstructing instances of individual motions, ViPS transfers generative video model priors into a universal distribution over the given rig parameterization. Differentiable geometric validators applied to the skinned mesh enforce shape-specific integrity without requiring manual regularizers. Our feedforward model reveals a smooth, compact, and controllable pose space. This, in turn, supports sampling for diverse shape variations, manifold projection for inverse kinematics, and temporally coherent trajectories for animation and keyframing. Further, the distilled 3D pose samples serve as semantic proxies to guide video diffusion, effectively closing the loop between generative 2D priors and structured 3D kinematic control. Our evaluations show that ViPS, trained solely using video priors, matches the performance of state-of-the-art models trained on synthetic artist-created 4D data in both plausibility and diversity. Additionally, as a universal model, ViPS exhibits robust zero-shot generalization to out-of-distribution species and unseen skeletal topologies.

Recent advances in 3D vision have led to specialized models for either 3D understanding (e.g., shape classification, segmentation, reconstruction) or 3D generation (e.g., synthesis, completion, and editing). However, these tasks are often tackled in isolation, resulting in fragmented architectures and representations that hinder knowledge transfer and holistic scene modeling. To address these challenges, we propose UniMesh, a unified framework that jointly learns 3D generation and understanding within a single architecture. First, we introduce a novel Mesh Head that acts as a cross model interface, bridging diffusion based image generation with implicit shape decoders. Second, we develop Chain of Mesh (CoM), a geometric instantiation of iterative reasoning that enables user driven semantic mesh editing through a closed loop latent, prompting, and re generation cycle. Third, we incorporate a self reflection mechanism based on an Actor Evaluator Self reflection triad to diagnose and correct failures in high level tasks like 3D captioning. Experimental results demonstrate that UniMesh not only achieves competitive performance on standard benchmarks but also unlocks novel capabilities in iterative editing and mutual enhancement between generation and understanding. Code: https://github.com/AIGeeksGroup/UniMesh. Website: https://aigeeksgroup.github.io/UniMesh.

Millimeter-wave (mmWave) radar has shown great potential for contactless, privacy-preserving, and robust human sensing, yet existing mmWave-based human mesh reconstruction (HMR) studies are still limited by the lack of benchmarks for generalization analysis under configuration shifts and fair comparison of different algorithms. To address the limitation, we present DGHMesh, a large-scale dual-radar mmWave dataset and generalization-focused benchmark for HMR. It contains data from 15 subjects performing 8 actions, with 360,000 synchronized frames collected from FMCW radar, SFCW radar, RGB images, and high-precision 3D HMR annotations. In addition, the dataset provides synchronized raw I/Q data from both radar modalities and accurately calibrated radar spatial positions. The benchmark is designed to evaluate HMR methods under diverse measurement configurations, including human position shifts, human orientation shifts, subarray size variations, and cross-subject settings. Based on DGHMesh, we also propose mmPTM, a query-based multi-radar fusion framework that jointly exploits point clouds and imaging tubes for HMR. Extensive experiments are conducted against representative baselines under different settings. The results demonstrate that mmPTM consistently achieves outstanding accuracy and competitive generalization capability across multiple sub-benchmarks, validating the effectiveness of multi-radar fusion and the practical value of the proposed dataset and benchmark for mmWave-based HMR research. DGHMesh and mmPTM are publicly available at https://github.com/SPIresearch/DGHMesh.(The complete benchmark and code will be released after paper publication)

Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network. However, pixel-based convolutions are restricted to static, uniform Cartesian grids, making them ill-suited to following evolving localized structures in an efficient manner. Graph neural networks (GNNs) naturally handle irregular spatial discretizations, but existing graph-based physics-aware deep learning (PADL) methods have difficulty handling extreme nonlinear regimes. To address these limitations, we propose Graph PARC (G-PARC), which uses moving least squares (MLS) kernels to approximate spatial derivatives on unstructured graphs, and embeds the derivatives of governing partial differential equations into the network's computational graph. G-PARC achieves better accuracy with 2-3x fewer parameters than MeshGraphNet, MeshGraphKAN, and GraphSAGE, replacing the traditional encoder-processor-decoder framework with analytically computed differential operators. We demonstrate that G-PARC (1) generalizes across nonuniform spatial and temporal discretizations; (2) handles moving meshes required for structural deformation; and (3) outperforms existing graph-based PADL methods on nonlinear benchmarks including fluvial hydrology, planar shock waves, and elastoplastic dynamics. By embedding explicit physical operators within the flexibility of GNNs, G-PARC enables accurate modeling of extreme nonlinear phenomena on complex computational domains, moving PADLbeyond idealized Cartesian grids.

Many CAD learning pipelines discretize Boundary Representations (B-Reps) into triangle meshes, discarding analytic surface structure and topological adjacency and thereby weakening consistent instance-level analysis. We present STEP-Parts, a deterministic CAD-to-supervision toolchain that extracts geometric instance partitions directly from raw STEP B-Reps and transfers them to tessellated carriers through retained source-face correspondence, yielding instance labels and metadata for downstream learning and evaluation. The construction merges adjacent B-Rep faces only when they share the same analytic primitive type and satisfy a near-tangent continuity criterion. On ABC, same-primitive dihedral angles are strongly bimodal, yielding a threshold-insensitive low-angle regime for part extraction. Because the partition is defined on intrinsic B-Rep topology rather than on a particular triangulation, the resulting boundaries remain stable under changes in tessellation. Applied to the DeepCAD subset of ABC, the pipeline processes approximately 180{,}000 models in under six hours on a consumer CPU. We release code and precomputed labels, and show that STEP-Parts serves both as a tessellation-robust geometric reference and as a useful supervision source in two downstream probes: an implicit reconstruction--segmentation network and a dataset-level point-based backbone.

Recent progress in image and video synthesis has inspired their use in advancing 3D scene generation. However, we observe that text-to-image and -video approaches struggle to maintain scene- and object-level consistency beyond a limited environment scale without a persistent, explicit geometric representation. We thus present a geometry-first approach that decouples this complex problem of large-scale 3D scene synthesis into its structural composition, represented as a mesh scaffold, and realistic appearance synthesis, which leverages powerful image synthesis models conditioned on the mesh scaffold. From an input text description, we first construct a mesh capturing the environment's geometry (walls, floors, etc.), and then use image synthesis, segmentation and object reconstruction to populate the mesh structure with objects in realistic layouts. This mesh scaffold is then rendered to condition image synthesis, providing a structural backbone for consistent appearance generation. This enables scalable, arbitrarily-sized 3D scenes of high object richness and diversity, combining robust 3D consistency with photorealistic detail. We believe this marks a significant step toward generating truly environment-scale, immersive 3D worlds.

We present Neural Image Space Tessellation effect (NIST), a lightweight screen-space post-processing approach for reducing the faceted silhouettes of low-poly renderings. Instead of tessellating primitives, creating new geometry, or modifying the underlying mesh, NIST uses the low-poly rendering result together with simple auxiliary G-buffer attributes to learn geometry-guided smoothing of object contours in image space. At its core, NIST first deforms image-space contours implicitly and then learns to reassign appearance in the whole image-space, including the deformed regions, preserving texture continuity and avoiding seam artifacts. Experiments show that NIST reduces visually apparent geometric faceting and produces smooth, coherent silhouettes close to tessellation-based smoothing references, with a nearly constant per-frame cost in our tested settings. To the best of our knowledge, NIST is the first work to move the solution of low-poly silhouette faceting from the pre-rendering geometry stage to a post-rendering screen-space stage.

Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers. However, scaling these solvers to industrial-scale geometries with over $10^8$ cells remains a fundamental challenge due to the prohibitive memory complexity of processing high-resolution meshes. We present Transolver-3, a new member of the Transolver family as a highly scalable framework designed for high-fidelity physics simulations. To bridge the gap between limited GPU capacity and the resolution requirements of complex engineering tasks, we introduce two key architectural optimizations: faster slice and deslice by exploiting matrix multiplication associative property and geometry slice tiling to partition the computation of physical states. Combined with an amortized training strategy by learning on random subsets of original high-resolution meshes and a physical state caching technique during inference, Transolver-3 enables high-fidelity field prediction on industrial-scale meshes. Extensive experiments demonstrate that Transolver-3 can handle meshes with over 160 million cells, achieving impressive performance across three challenging simulation benchmarks, including aircraft and automotive design tasks. Code is available at https://github.com/thuml/Transolver-3.

3D editing has emerged as a critical research area to provide users with flexible control over 3D assets. While current editing approaches predominantly focus on 3D Gaussian Splatting or multi-view images, the direct editing of 3D meshes remains underexplored. Prior attempts, such as VoxHammer, rely on voxel-based representations that suffer from limited resolution and necessitate labor-intensive 3D mask. To address these limitations, we propose \textbf{VecSet-Edit}, the first pipeline that leverages the high-fidelity VecSet Large Reconstruction Model (LRM) as a backbone for mesh editing. Our approach is grounded on a analysis of the spatial properties in VecSet tokens, revealing that token subsets govern distinct geometric regions. Based on this insight, we introduce Mask-guided Token Seeding and Attention-aligned Token Gating strategies to precisely localize target regions using only 2D image conditions. Also, considering the difference between VecSet diffusion process versus voxel we design a Drift-aware Token Pruning to reject geometric outliers during the denoising process. Finally, our Detail-preserving Texture Baking module ensures that we not only preserve the geometric details of original mesh but also the textural information. More details can be found in our project page: https://github.com/BlueDyee/VecSet-Edit/tree/main

While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures often employ feature dimensionality reduction strategies, which inadvertently induces Geometric Aliasing, resulting in the loss of critical physical boundary information. To address this, we propose the Physics-Geometry Operator Transformer (PGOT), designed to reconstruct physical feature learning through explicit geometry awareness. Specifically, we propose Spectrum-Preserving Geometric Attention (SpecGeo-Attention). Utilizing a ``physics slicing-geometry injection" mechanism, this module incorporates multi-scale geometric encodings to explicitly preserve multi-scale geometric features while maintaining linear computational complexity $O(N)$. Furthermore, PGOT dynamically routes computations to low-order linear paths for smooth regions and high-order non-linear paths for shock waves and discontinuities based on spatial coordinates, enabling spatially adaptive and high-precision physical field modeling. PGOT achieves consistent state-of-the-art performance across four standard benchmarks and excels in large-scale industrial tasks including airfoil and car designs.

Reconstructing cardiac motion from CMR sequences is critical for diagnosis, prognosis, and intervention. Existing methods rely on complete CMR stacks to infer full heart motion, limiting their applicability during intervention when only sparse observations are available. We present TetHeart, the first end-to-end framework for unified 4D heart mesh recovery from both offline full-stack and intra-procedural sparse-slice observations. Our method leverages deformable tetrahedra to capture shape and motion in a coherent space shared across cardiac structures. Before a procedure, it initializes detailed, patient-specific heart meshes from high-quality full stacks, which can then be updated using whatever slices can be obtained in real-time, down to a single one during the procedure. TetHeart incorporates several key innovations: (i) an attentive slice-adaptive 2D-3D feature assembly mechanism that integrates information from arbitrary numbers of slices at any position; (ii) a distillation strategy to ensure accurate reconstruction under extreme sparsity; and (iii) a weakly supervised motion learning scheme requiring annotations only at keyframes, such as the end-diastolic and end-systolic phases. Trained and validated on three large public datasets and evaluated zero-shot on additional private interventional and public datasets without retraining, TetHeart achieves state-of-the-art accuracy and strong generalization in both pre- and intra-procedural settings. Code and dataset is available at https://github.com/Scalsol/TetHeart.

Robot manipulation foundation models require scalable evaluation and data generation across diverse scenarios, with simulation providing an environment for both. Automated scene generation offers a promising path, yet prior work has largely emphasized coarse-grained scene layouts rather than fine-grained functional object compositions. Motivated by this gap, we present GIF, an agentic Generation framework for Interactive and Functional object compositions. In this framework, we recast this problem as disentangled reconstruction followed by relative pose recovery. CoGen produces instance-disentangled meshes with coarse initial poses leveraging complementary strengths of 2D and 3D generative models. GPRM refines the relative pose under joint geometric and physical guidance, and a VLM verifier selects the candidate that best matches the structured specification. We further construct a benchmark spanning eight representative contact-geometry classes and compare with state-of-the-art generators; GIF improves both asset quality and relation matching, while reducing collision rate to below 1%. Finally, we synthesize data for policy learning, revealing diversity scaling in both simulation and real-world deployment.