Daily Papers

The creation of photorealistic virtual worlds requires the accurate modeling of 3D surface geometry for a wide range of objects. For this, meshes are appealing since they 1) enable fast physics-based rendering with realistic material and lighting, 2) support physical simulation, and 3) are memory-efficient for modern graphics pipelines. Recent work on reconstructing and statistically modeling 3D shape, however, has critiqued meshes as being topologically inflexible. To capture a wide range of object shapes, any 3D representation must be able to model solid, watertight, shapes as well as thin, open, surfaces. Recent work has focused on the former, and methods for reconstructing open surfaces do not support fast reconstruction with material and lighting or unconditional generative modelling. Inspired by the observation that open surfaces can be seen as islands floating on watertight surfaces, we parameterize open surfaces by defining a manifold signed distance field on watertight templates. With this parameterization, we further develop a grid-based and differentiable representation that parameterizes both watertight and non-watertight meshes of arbitrary topology. Our new representation, called Ghost-on-the-Shell (G-Shell), enables two important applications: differentiable rasterization-based reconstruction from multiview images and generative modelling of non-watertight meshes. We empirically demonstrate that G-Shell achieves state-of-the-art performance on non-watertight mesh reconstruction and generation tasks, while also performing effectively for watertight meshes.

While recent advances in neural representations and generative models have revolutionized 3D content creation, the field remains constrained by significant data processing bottlenecks. To address this, we introduce HY3D-Bench, an open-source ecosystem designed to establish a unified, high-quality foundation for 3D generation. Our contributions are threefold: (1) We curate a library of 250k high-fidelity 3D objects distilled from large-scale repositories, employing a rigorous pipeline to deliver training-ready artifacts, including watertight meshes and multi-view renderings; (2) We introduce structured part-level decomposition, providing the granularity essential for fine-grained perception and controllable editing; and (3) We bridge real-world distribution gaps via a scalable AIGC synthesis pipeline, contributing 125k synthetic assets to enhance diversity in long-tail categories. Validated empirically through the training of Hunyuan3D-2.1-Small, HY3D-Bench democratizes access to robust data resources, aiming to catalyze innovation across 3D perception, robotics, and digital content creation.

Fast, reliable shape reconstruction is an essential ingredient in many computer vision applications. Neural Radiance Fields demonstrated that photorealistic novel view synthesis is within reach, but was gated by performance requirements for fast reconstruction of real scenes and objects. Several recent approaches have built on alternative shape representations, in particular, 3D Gaussians. We develop extensions to these renderers, such as integrating differentiable optical flow, exporting watertight meshes and rendering per-ray normals. Additionally, we show how two of the recent methods are interoperable with each other. These reconstructions are quick, robust, and easily performed on GPU or CPU. For code and visual examples, see https://leonidk.github.io/fmb-plus

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry processing, their irregular and combinatorial structure often make them unsuitable for learning-based applications. In this work, we present VoroMesh, a novel and differentiable Voronoi-based representation of watertight 3D shape surfaces. From a set of 3D points (called generators) and their associated occupancy, we define our boundary representation through the Voronoi diagram of the generators as the subset of Voronoi faces whose two associated (equidistant) generators are of opposite occupancy: the resulting polygon mesh forms a watertight approximation of the target shape's boundary. To learn the position of the generators, we propose a novel loss function, dubbed VoroLoss, that minimizes the distance from ground truth surface samples to the closest faces of the Voronoi diagram which does not require an explicit construction of the entire Voronoi diagram. A direct optimization of the Voroloss to obtain generators on the Thingi32 dataset demonstrates the geometric efficiency of our representation compared to axiomatic meshing algorithms and recent learning-based mesh representations. We further use VoroMesh in a learning-based mesh prediction task from input SDF grids on the ABC dataset, and show comparable performance to state-of-the-art methods while guaranteeing closed output surfaces free of self-intersections.

This paper introduces a method for simplifying textured surface triangle meshes in the wild while maintaining high visual quality. While previous methods achieve excellent results on manifold meshes by using the quadric error metric, they struggle to produce high-quality outputs for meshes in the wild, which typically contain non-manifold elements and multiple connected components. In this work, we propose a method for simplifying these wild textured triangle meshes. We formulate mesh simplification as a problem of decimating simplicial 2-complexes to handle multiple non-manifold mesh components collectively. Building on the success of quadric error simplification, we iteratively collapse 1-simplices (vertex pairs). Our approach employs a modified quadric error that converges to the original quadric error metric for watertight manifold meshes, while significantly improving the results on wild meshes. For textures, instead of following existing strategies to preserve UVs, we adopt a novel perspective which focuses on computing mesh correspondences throughout the decimation, independent of the UV layout. This combination yields a textured mesh simplification system that is capable of handling arbitrary triangle meshes, achieving to high-quality results on wild inputs without sacrificing the excellent performance on clean inputs. Our method guarantees to avoid common problems in textured mesh simplification, including the prevalent problem of texture bleeding. We extensively evaluate our method on multiple datasets, showing improvements over prior techniques through qualitative, quantitative, and user study evaluations.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

While state-of-the-art generative models produce high-fidelity 3D meshes, these outputs lack the physical properties required for interactive simulation, gaming, or robotics. We introduce Gen2Physics, a unified and automated framework that grounds generated meshes in physics by automatically decomposing them into their constituent material components. Unlike prior approaches, which focus on volumetric representations incompatible with standard physics engines, Gen2Physics operates directly on meshes to produce immediately simulation-ready assets. Our pipeline integrates a fine-tuned Vision Transformer for dense material segmentation, a robust 2D-to-3D consistency projection, and a Vision-Language Model (VLM) guided refinement that leverages contextual reasoning to assign physical properties and infer internal geometry (solid vs. hollow). By converting surface patches into volumes with distinct densities, our method enables physically plausible dynamic simulations. Experimental results on the ABO-500 and PartNet-Material benchmarks demonstrate that Gen2Physics more than doubles the material segmentation accuracy of prior physics-grounding pipelines (15.6 to 48.3 mIoU), while matching the mass-estimation accuracy of volumetric methods and being the only approach to output watertight per-material sub-meshes.

We introduce Mesh Silksong, a compact and efficient mesh representation tailored to generate the polygon mesh in an auto-regressive manner akin to silk weaving. Existing mesh tokenization methods always produce token sequences with repeated vertex tokens, wasting the network capability. Therefore, our approach tokenizes mesh vertices by accessing each mesh vertice only once, reduces the token sequence's redundancy by 50\%, and achieves a state-of-the-art compression rate of approximately 22\%. Furthermore, Mesh Silksong produces polygon meshes with superior geometric properties, including manifold topology, watertight detection, and consistent face normals, which are critical for practical applications. Experimental results demonstrate the effectiveness of our approach, showcasing not only intricate mesh generation but also significantly improved geometric integrity.

We present Home3D 1.0, a modular image-to-3D generation system that produces high-quality 3D assets from a single reference image, targeting interior design and e-commerce applications. Given a photograph of a furniture or decor item, the system outputs a mesh with physically-based rendering (PBR) materials, and the mesh can be decomposed into material-specific components. The pipeline is organized into four tightly coupled modules: Geometry reconstructs a watertight mesh through latent SDF modelling with a geometry VAE and a coarse-to-fine flow-matching DiT; Texture predicts multiview albedo observations, reprojects them onto the mesh, and completes unseen surface regions with a 3D texture field; Material uses MatWeaver to obtain component masks through video-based segmentation and UV-space voting, then retrieves and bakes PBR maps from a curated material library through hierarchical multi-modal matching; and Parts generates material-editable semantic part meshes with a PartVAE and PartDiT, decoding multi-head part-specific SDF fields in one pass. Each module is evaluated independently with dedicated metrics, highlighting both the current system capability and the remaining gaps toward broader deployment.

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define DeepMesh - an end-to-end differentiable mesh representation that can vary its topology. We validate our theoretical insight through several applications: Single view 3D Reconstruction via Differentiable Rendering, Physically-Driven Shape Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training. In all cases our end-to-end differentiable parameterization gives us an edge over state-of-the-art algorithms.

Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is not limited in resolution. Unfortunately, these methods are often not suitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Signed Distance Functions. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define MeshSDF, an end-to-end differentiable mesh representation which can vary its topology. We use two different applications to validate our theoretical insight: Single-View Reconstruction via Differentiable Rendering and Physically-Driven Shape Optimization. In both cases our differentiable parameterization gives us an edge over state-of-the-art algorithms.

City-scale 3D reconstruction from satellite imagery presents the challenge of extreme viewpoint extrapolation, where our goal is to synthesize ground-level novel views from sparse orbital images with minimal parallax. This requires inferring nearly 90^circ viewpoint gaps from image sources with severely foreshortened facades and flawed textures, causing state-of-the-art reconstruction engines such as NeRF and 3DGS to fail. To address this problem, we propose two design choices tailored for city structures and satellite inputs. First, we model city geometry as a 2.5D height map, implemented as a Z-monotonic signed distance field (SDF) that matches urban building layouts from top-down viewpoints. This stabilizes geometry optimization under sparse, off-nadir satellite views and yields a watertight mesh with crisp roofs and clean, vertically extruded facades. Second, we paint the mesh appearance from satellite images via differentiable rendering techniques. While the satellite inputs may contain long-range, blurry captures, we further train a generative texture restoration network to enhance the appearance, recovering high-frequency, plausible texture details from degraded inputs. Our method's scalability and robustness are demonstrated through extensive experiments on large-scale urban reconstruction. For example, in our teaser figure, we reconstruct a 4,km^2 real-world region from only a few satellite images, achieving state-of-the-art performance in synthesizing photorealistic ground views. The resulting models are not only visually compelling but also serve as high-fidelity, application-ready assets for downstream tasks like urban planning and simulation. Project page can be found at https://pku-vcl-geometry.github.io/Orbit2Ground/.

Triangle meshes are fundamental to 3D applications, enabling efficient modification and rasterization while maintaining compatibility with standard rendering pipelines. However, current automatic mesh generation methods typically rely on intermediate representations that lack the continuous surface quality inherent to meshes. Converting these representations into meshes produces dense, suboptimal outputs. Although recent autoregressive approaches demonstrate promise in directly modeling mesh vertices and faces, they are constrained by the limitation in face count, scalability, and structural fidelity. To address these challenges, we propose Nautilus, a locality-aware autoencoder for artist-like mesh generation that leverages the local properties of manifold meshes to achieve structural fidelity and efficient representation. Our approach introduces a novel tokenization algorithm that preserves face proximity relationships and compresses sequence length through locally shared vertices and edges, enabling the generation of meshes with an unprecedented scale of up to 5,000 faces. Furthermore, we develop a Dual-stream Point Conditioner that provides multi-scale geometric guidance, ensuring global consistency and local structural fidelity by capturing fine-grained geometric features. Extensive experiments demonstrate that Nautilus significantly outperforms state-of-the-art methods in both fidelity and scalability. The project page is at https://nautilusmeshgen.github.io.

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of our task-driven pooling on various learning tasks applied to 3D meshes.

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. In this paper, we present AnimateAnyMesh, the first feed-forward framework that enables efficient text-driven animation of arbitrary 3D meshes. Our approach leverages a novel DyMeshVAE architecture that effectively compresses and reconstructs dynamic mesh sequences by disentangling spatial and temporal features while preserving local topological structures. To enable high-quality text-conditional generation, we employ a Rectified Flow-based training strategy in the compressed latent space. Additionally, we contribute the DyMesh Dataset, containing over 4M diverse dynamic mesh sequences with text annotations. Experimental results demonstrate that our method generates semantically accurate and temporally coherent mesh animations in a few seconds, significantly outperforming existing approaches in both quality and efficiency. Our work marks a substantial step forward in making 4D content creation more accessible and practical. All the data, code, and models will be open-released.

Modern 3D engines and graphics pipelines require mesh as a memory-efficient representation, which allows efficient rendering, geometry processing, texture editing, and many other downstream operations. However, it is still highly difficult to obtain high-quality mesh in terms of detailed structure and time consistency from dynamic observations. To this end, we introduce Dynamic Gaussians Mesh (DG-Mesh), a framework to reconstruct a high-fidelity and time-consistent mesh from dynamic input. Our work leverages the recent advancement in 3D Gaussian Splatting to construct the mesh sequence with temporal consistency from dynamic observations. Building on top of this representation, DG-Mesh recovers high-quality meshes from the Gaussian points and can track the mesh vertices over time, which enables applications such as texture editing on dynamic objects. We introduce the Gaussian-Mesh Anchoring, which encourages evenly distributed Gaussians, resulting better mesh reconstruction through mesh-guided densification and pruning on the deformed Gaussians. By applying cycle-consistent deformation between the canonical and the deformed space, we can project the anchored Gaussian back to the canonical space and optimize Gaussians across all time frames. During the evaluation on different datasets, DG-Mesh provides significantly better mesh reconstruction and rendering than baselines. Project page: https://www.liuisabella.com/DG-Mesh

3D content generation technology has significantly advanced the work of designers, as well as the 3D printing and gaming industries. However, it remains difficult to produce lightweight, editable, and topologically clean artistic content that is directly production-ready. To achieve this, we present TaoFlowForge, an artistic mesh foundation model that generates production-ready meshes. Specifically, TaoFlowForge decomposes the mesh generation process into vertices generation and their connectivity prediction, i.e., edges. We formulate vertices generation as a two-stage coarse-to-fine process and incorporate several effective loss functions to further enhance its performance. In the connectivity prediction stage, we propose a simple yet effective method for estimating the connectivity affinity between vertices and additionally predict per-vertex normals, which determines the correct orientation of faces. Besides, we construct a large-scale dataset combining hand-crafted 3D assets with public high-quality topology datasets. Based on this, a carefully designed data curation pipeline is employed to filter the raw dataset, retaining only high-quality topology data for model training. Our model is trained on the combined dataset and tested on both out-of-distribution hand-crafted set of 3D assets and public datasets. Under image-conditioned generation, TaoFlowForge outperforms autoregressive methods and achieves state-of-the-art results among open-source mesh topology generators. We will release all the code and weights together with a portion of our test dataset.

We introduce OVOW, the first training-free system that reconstructs instance-level, simulation-ready 4D mesh scenes from a single monocular video. Recent 4D reconstruction achieves impressive rendering quality, but its outputs (\eg, implicit fields, Gaussian primitives, or point clouds) lack the watertight topology, instance separation, and standardized physical interfaces required by physics simulators and embodied AI. OVOW closes this gap with a four-stage pipeline: a vision-language model discovers, labels, and motion-classifies all instances; category-aware reconstruction yields per-instance meshes for rigid objects and topology-consistent mesh sequences for deformable ones; an iterative render-match-optimize procedure recovers metric scale and 6-DoF pose trajectories; and physics-grounded assembly enforces ground contact and inter-object support. Crucially, we model all motion, rigid and non-rigid, through direct vertex deformation without category-specific priors or skeleton rigging, producing watertight mesh scenes ready for downstream physics simulation and editing. We further establish the first benchmark for structured Video-to-4D evaluation, with metrics for geometric correctness, instance separation, and physical plausibility beyond visual fidelity; the same pipeline doubles as a scalable engine for synthesizing paired video-to-4D simulation data for future 4D world models and embodied AI. Across two synthetic benchmarks (static and 4D), OVOW attains the best overall layout and geometry accuracy and the lowest photometric and semantic error among all baselines, and on monocular video runs one to two orders of magnitude faster than the baselines, while downstream physics simulation confirms its physical stability.

We propose a compressive yet effective mesh representation, Blocked and Patchified Tokenization (BPT), facilitating the generation of meshes exceeding 8k faces. BPT compresses mesh sequences by employing block-wise indexing and patch aggregation, reducing their length by approximately 75\% compared to the original sequences. This compression milestone unlocks the potential to utilize mesh data with significantly more faces, thereby enhancing detail richness and improving generation robustness. Empowered with the BPT, we have built a foundation mesh generative model training on scaled mesh data to support flexible control for point clouds and images. Our model demonstrates the capability to generate meshes with intricate details and accurate topology, achieving SoTA performance on mesh generation and reaching the level for direct product usage.

In the domain of 3D content creation, achieving optimal mesh topology through AI models has long been a pursuit for 3D artists. Previous methods, such as MeshGPT, have explored the generation of ready-to-use 3D objects via mesh auto-regressive techniques. While these methods produce visually impressive results, their reliance on token-by-token predictions in the auto-regressive process leads to several significant limitations. These include extremely slow generation speeds and an uncontrollable number of mesh faces. In this paper, we introduce MeshCraft, a novel framework for efficient and controllable mesh generation, which leverages continuous spatial diffusion to generate discrete triangle faces. Specifically, MeshCraft consists of two core components: 1) a transformer-based VAE that encodes raw meshes into continuous face-level tokens and decodes them back to the original meshes, and 2) a flow-based diffusion transformer conditioned on the number of faces, enabling the generation of high-quality 3D meshes with a predefined number of faces. By utilizing the diffusion model for the simultaneous generation of the entire mesh topology, MeshCraft achieves high-fidelity mesh generation at significantly faster speeds compared to auto-regressive methods. Specifically, MeshCraft can generate an 800-face mesh in just 3.2 seconds (35times faster than existing baselines). Extensive experiments demonstrate that MeshCraft outperforms state-of-the-art techniques in both qualitative and quantitative evaluations on ShapeNet dataset and demonstrates superior performance on Objaverse dataset. Moreover, it integrates seamlessly with existing conditional guidance strategies, showcasing its potential to relieve artists from the time-consuming manual work involved in mesh creation.

Primitive-based splatting methods like 3D Gaussian Splatting have revolutionized novel view synthesis with real-time rendering. However, their point-based representations remain incompatible with mesh-based pipelines that power AR/VR and game engines. We present MeshSplatting, a mesh-based reconstruction approach that jointly optimizes geometry and appearance through differentiable rendering. By enforcing connectivity via restricted Delaunay triangulation and refining surface consistency, MeshSplatting creates end-to-end smooth, visually high-quality meshes that render efficiently in real-time 3D engines. On Mip-NeRF360, it boosts PSNR by +0.69 dB over the current state-of-the-art MiLo for mesh-based novel view synthesis, while training 2x faster and using 2x less memory, bridging neural rendering and interactive 3D graphics for seamless real-time scene interaction. The project page is available at https://meshsplatting.github.io/.

We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by recent advances in powerful large language models, we adopt a sequence-based approach to autoregressively generate triangle meshes as sequences of triangles. We first learn a vocabulary of latent quantized embeddings, using graph convolutions, which inform these embeddings of the local mesh geometry and topology. These embeddings are sequenced and decoded into triangles by a decoder, ensuring that they can effectively reconstruct the mesh. A transformer is then trained on this learned vocabulary to predict the index of the next embedding given previous embeddings. Once trained, our model can be autoregressively sampled to generate new triangle meshes, directly generating compact meshes with sharp edges, more closely imitating the efficient triangulation patterns of human-crafted meshes. MeshGPT demonstrates a notable improvement over state of the art mesh generation methods, with a 9% increase in shape coverage and a 30-point enhancement in FID scores across various categories.

Generating high-quality camera-controllable videos from monocular input is a challenging task, particularly under extreme viewpoint. Existing methods often struggle with geometric inconsistencies and occlusion artifacts in boundaries, leading to degraded visual quality. In this paper, we introduce EX-4D, a novel framework that addresses these challenges through a Depth Watertight Mesh representation. The representation serves as a robust geometric prior by explicitly modeling both visible and occluded regions, ensuring geometric consistency in extreme camera pose. To overcome the lack of paired multi-view datasets, we propose a simulated masking strategy that generates effective training data only from monocular videos. Additionally, a lightweight LoRA-based video diffusion adapter is employed to synthesize high-quality, physically consistent, and temporally coherent videos. Extensive experiments demonstrate that EX-4D outperforms state-of-the-art methods in terms of physical consistency and extreme-view quality, enabling practical 4D video generation.

Image-based 3D reconstruction has increasingly stunning results over the past few years with the latest improvements in computer vision and graphics. Geometry and topology are two fundamental concepts when dealing with 3D mesh structures. But the latest often remains a side issue in the 3D mesh-based reconstruction literature. Indeed, performing per-vertex elementary displacements over a 3D sphere mesh only impacts its geometry and leaves the topological structure unchanged and fixed. Whereas few attempts propose to update the geometry and the topology, all need to lean on costly 3D ground-truth to determine the faces/edges to prune. We present in this work a method that aims to refine the topology of any 3D mesh through a face-pruning strategy that extensively relies upon 2D alpha masks and camera pose information. Our solution leverages a differentiable renderer that renders each face as a 2D soft map. Its pixel intensity reflects the probability of being covered during the rendering process by such a face. Based on the 2D soft-masks available, our method is thus able to quickly highlight all the incorrectly rendered faces for a given viewpoint. Because our module is agnostic to the network that produces the 3D mesh, it can be easily plugged into any self-supervised image-based (either synthetic or natural) 3D reconstruction pipeline to get complex meshes with a non-spherical topology.

Convolutional neural networks (CNNs) have made great breakthroughs in 2D computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure, in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this paper presents SubdivNet, an innovative and versatile CNN framework for 3D triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g. variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers which uniformly merge four faces into one and an upsampling method which splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet's effectiveness and efficiency.

We present TriFlow, a new generative approach for producing compact 3D meshes with artist-like triangle topology directly from input geometry conditions such as signed distance fields. Our key insight is to represent mesh topology as a nearest-vertex vector field (NVF) defined over the surface, where each point encodes its association to the nearest triangle vertex in the local barycentric frame. We train a latent flow-matching model to synthesize this field, enabling topology generation conditioned on the input geometry. To extract a coherent mesh, we cluster surface regions using the generated NVF and guide a constrained quadric error metric (QEM) mesh simplification with topology-aware optimization. This yields output meshes that closely match the input geometry while exhibiting structured, artist-like connectivity. Experiments demonstrate that TriFlow achieves stronger generalization and significantly improved topology quality compared to state-of-the-art learning-based approaches, alongside 90% lower Chamfer Distance and an 8x speedup.

Generating high-quality triangle meshes is essential for film, gaming, and interactive 3D applications. Mainstream methods rely on mesh serialization and autoregressive processes, which stuggles in effective inference and is sensitive to error accumulation. In this paper, we present Nexus, a diffusion method that achieves holistic mesh generation via decoupled vertex and topology generation. First, we view mesh vertices as sparse voxels organized as an octree and adopt a diffusion model to generate the vertices in a coarse-to-fine manner. Second, for topology modeling, we propose Spacetime Interval, as an extension of Spacetime Distance to encode arbitrary edge and face topology into continuous per-vertex embeddings. It allows for a global and efficient recovery of complex topology. We then employ a diffusion model to generate the continuous embeddings on the generated vertices. Extensive experiments on the Objaverse and Toys4K datasets and in-the-wild images demonstrate that our method outperforms state-of-the-art autoregressive and two-stage baselines, effectively circumventing the inherent limitations of sequential mesh modeling. A blind user study from 3D practitioners confirms strong perceptual preference for our results.

Scaling artist-designed meshes to high triangle numbers remains challenging for autoregressive generative models. Existing transformer-based methods suffer from long-sequence bottlenecks and limited quantization resolution, primarily due to the large number of tokens required and constrained quantization granularity. These issues prevent faithful reproduction of fine geometric details and structured density patterns. We introduce MeshMosaic, a novel local-to-global framework for artist mesh generation that scales to over 100K triangles--substantially surpassing prior methods, which typically handle only around 8K faces. MeshMosaic first segments shapes into patches, generating each patch autoregressively and leveraging shared boundary conditions to promote coherence, symmetry, and seamless connectivity between neighboring regions. This strategy enhances scalability to high-resolution meshes by quantizing patches individually, resulting in more symmetrical and organized mesh density and structure. Extensive experiments across multiple public datasets demonstrate that MeshMosaic significantly outperforms state-of-the-art methods in both geometric fidelity and user preference, supporting superior detail representation and practical mesh generation for real-world applications.

Autoregressive Transformers dominate high-quality mesh generation by producing artist-worthy topologies, yet their inherent sequential decoding induces substantial computational overhead, falling orders of magnitude slower than parallel generative models. On the other hand, while continuous diffusion and flow-matching methods support efficient parallel synthesis across a variety of domains, they cannot be directly applied to meshes: mesh connectivity is inherently discrete and incompatible with standard continuous noise injection and denoising operations. To resolve this fundamental incompatibility, we introduce a compact topology embedder that projects discrete mesh vertex positions and normals into continuous per-vertex embeddings, where the original discrete adjacency information can be faithfully recovered via spacetime distance thresholding. After pretraining and freezing this embedder, any raw mesh can be fully converted into a continuous per-vertex state space unifying position, normal, and implicit topological attributes. Built upon this novel continuous mesh representation, we present PolyFlow, a Transformer-based flow-matching framework that achieves fully parallel vertex state denoising conditioned on extracted point-cloud features. During inference, our model completes generation rapidly via an ODE solver, and supports explicit, precise control over output mesh resolution by directly specifying the target vertex count. Extensive evaluations on the Toys4K benchmark demonstrate that PolyFlow surpasses state-of-the-art autoregressive baselines in both Chamfer Distance and Hausdorff Distance.

This paper presents a Surface-Aligned Gaussian representation for creating animatable human avatars from monocular videos,aiming at improving the novel view and pose synthesis performance while ensuring fast training and real-time rendering. Recently,3DGS has emerged as a more efficient and expressive alternative to NeRF, and has been used for creating dynamic human avatars. However,when applied to the severely ill-posed task of monocular dynamic reconstruction, the Gaussians tend to overfit the constantly changing regions such as clothes wrinkles or shadows since these regions cannot provide consistent supervision, resulting in noisy geometry and abrupt deformation that typically fail to generalize under novel views and poses.To address these limitations, we present SAGA,i.e.,Surface-Aligned Gaussian Avatar,which aligns the Gaussians with a mesh to enforce well-defined geometry and consistent deformation, thereby improving generalization under novel views and poses. Unlike existing strict alignment methods that suffer from limited expressive power and low realism,SAGA employs a two-stage alignment strategy where the Gaussians are first adhered on while then detached from the mesh, thus facilitating both good geometry and high expressivity. In the Adhered Stage, we improve the flexibility of Adhered-on-Mesh Gaussians by allowing them to flow on the mesh, in contrast to existing methods that rigidly bind Gaussians to fixed location. In the second Detached Stage, we introduce a Gaussian-Mesh Alignment regularization, which allows us to unleash the expressivity by detaching the Gaussians but maintain the geometric alignment by minimizing their location and orientation offsets from the bound triangles. Finally, since the Gaussians may drift outside the bound triangles during optimization, an efficient Walking-on-Mesh strategy is proposed to dynamically update the bound triangles.

Polygon meshes are an efficient representation of 3D geometry, and are of central importance in computer graphics, robotics and games development. Existing learning-based approaches have avoided the challenges of working with 3D meshes, instead using alternative object representations that are more compatible with neural architectures and training approaches. We present an approach which models the mesh directly, predicting mesh vertices and faces sequentially using a Transformer-based architecture. Our model can condition on a range of inputs, including object classes, voxels, and images, and because the model is probabilistic it can produce samples that capture uncertainty in ambiguous scenarios. We show that the model is capable of producing high-quality, usable meshes, and establish log-likelihood benchmarks for the mesh-modelling task. We also evaluate the conditional models on surface reconstruction metrics against alternative methods, and demonstrate competitive performance despite not training directly on this task.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

We present MeshTailor, the first mesh-native generative framework for synthesizing edge-aligned seams on 3D surfaces. Unlike prior optimization-based or extrinsic learning-based methods, MeshTailor operates directly on the mesh graph, eliminating projection artifacts and fragile snapping heuristics. We introduce ChainingSeams, a hierarchical serialization of the seam graph that orders chains from global structural cuts down to local details in a coarse-to-fine manner, and a dual-stream encoder that fuses topological and geometric context. Leveraging this hierarchical representation and dual-stream vertex embeddings, our MeshTailor Transformer utilizes an autoregressive pointer layer to trace seams vertex-by-vertex within local neighborhoods. Extensive evaluations show that MeshTailor produces more coherent and structurally regular seam layouts compared to recent optimization-based and learning-based baselines.

We present MeshFlow, a new method for generating artist-like 3D meshes. Current mesh generators often adopt Auto-Regressive (AR) next-token prediction, a natural choice given the discrete nature of mesh topology. However, AR methods scale poorly because the inference cost is quadratic in mesh size. They also require discretizing the vertex coordinates, which introduces quantization errors. To address these challenges, we introduce a Variational Autoencoder (VAE) that, supervised with a contrastive loss, represents both continuous vertex positions and discrete connectivity in a continuous latent space. This latent space is significantly more compact than prior token-based mesh representations. We then build a 3D generator based on a Rectified Flow transformer, generating all mesh vertices and edges in parallel. Our model generates meshes 18x faster than the fastest AR generator while also achieving excellent accuracy across standard mesh-generation metrics. Homepage: https://mesh-flow.github.io/, Code: https://github.com/facebookresearch/meshflow

Polygonal meshes are the standard surface representation of modern 3D pipelines, and generating high-quality meshes with artist-style topology is essential for film, gaming, and interactive 3D applications. Mainstream approaches serialize a mesh into a token sequence and decode it autoregressively, which is slow at inference and sensitive to error accumulation, making them impractical for interactive asset creation. We present Meshy T2, a fast native mesh generation framework built on flow matching. At its core is a vertex-set mesh VAE that encodes a mesh into one continuous latent token per vertex and decodes vertices, edge connectivity, and face winding order in a single pass, preserving high-precision geometry and artist-authored topology without vertex quantization or welding. Generation proceeds as a coarse-to-fine cascade of two flow-matching models: an image-conditioned voxel flow first sketches the overall shape as a coarse occupancy scaffold, and a mesh flow then populates the scaffold with per-vertex latent tokens, conditioned on the image, the scaffold, and a requested vertex budget. This design delivers three practical capabilities: interactive generation speed through parallel flow-based synthesis; effective face-count control through the requested vertex budget; and native support for multi-part assets, whose components emerge directly from the generated connectivity. In our experiments, Meshy T2 achieves state-of-the-art geometric fidelity and completes end-to-end image-to-mesh generation within a median of 6 seconds, over an order of magnitude faster than autoregressive baselines. Code and weights will be available at https://github.com/meshy-dev/meshy-t2.

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18times speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.

Image alignment by mesh warps, such as meshflow, is a fundamental task which has been widely applied in various vision applications(e.g., multi-frame HDR/denoising, video stabilization). Traditional mesh warp methods detect and match image features, where the quality of alignment highly depends on the quality of image features. However, the image features are not robust in occurrence of low-texture and low-light scenes. Deep homography methods, on the other hand, are free from such problem by learning deep features for robust performance. However, a homography is limited to plane motions. In this work, we present a deep meshflow motion model, which takes two images as input and output a sparse motion field with motions located at mesh vertexes. The deep meshflow enjoys the merics of meshflow that can describe nonlinear motions while also shares advantage of deep homography that is robust against challenging textureless scenarios. In particular, a new unsupervised network structure is presented with content-adaptive capability. On one hand, the image content that cannot be aligned under mesh representation are rejected by our learned mask, similar to the RANSAC procedure. On the other hand, we learn multiple mesh resolutions, combining to a non-uniform mesh division. Moreover, a comprehensive dataset is presented, covering various scenes for training and testing. The comparison between both traditional mesh warp methods and deep based methods show the effectiveness of our deep meshflow motion model.

We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents 3D shapes by deforming a collection of tetrahedral spheres, with geometric regularizations and constraints that effectively resolve common mesh issues such as irregular triangles, non-manifoldness, and floating artifacts. Experimental results on multi-view and single-view reconstruction highlight TetSphere splatting's superior mesh quality while maintaining competitive reconstruction accuracy compared to state-of-the-art methods. Additionally, TetSphere splatting demonstrates versatility by seamlessly integrating into generative modeling tasks, such as image-to-3D and text-to-3D generation.

We introduce Amortized Text-to-Mesh (AToM), a feed-forward text-to-mesh framework optimized across multiple text prompts simultaneously. In contrast to existing text-to-3D methods that often entail time-consuming per-prompt optimization and commonly output representations other than polygonal meshes, AToM directly generates high-quality textured meshes in less than 1 second with around 10 times reduction in the training cost, and generalizes to unseen prompts. Our key idea is a novel triplane-based text-to-mesh architecture with a two-stage amortized optimization strategy that ensures stable training and enables scalability. Through extensive experiments on various prompt benchmarks, AToM significantly outperforms state-of-the-art amortized approaches with over 4 times higher accuracy (in DF415 dataset) and produces more distinguishable and higher-quality 3D outputs. AToM demonstrates strong generalizability, offering finegrained 3D assets for unseen interpolated prompts without further optimization during inference, unlike per-prompt solutions.

Flow matching over carefully designed latent representations has recently emerged as a powerful paradigm for topology-aware mesh generation. Existing approaches, however, model vertices and connectivity jointly in a joint latent space, entangling continuous vertex geometry with discrete combinatorial structure; this complicates flow learning and manifests as drifting vertices and broken surfaces. We present LATO.2, a factorized flow matching framework that decomposes mesh generation into a vertex flow followed by a connectivity flow conditioned on the realized vertices, with both stages anchored to a shared coarse voxel scaffold. Dedicated VAEs underpin the two stages, recovering vertices at sub-voxel precision and embedding discrete connectivity into a continuous latent space. We demonstrate two advantages unique to this factorization: (i) part-wise generation, in which the scaffold is partitioned and each part synthesized at full latent capacity, yielding substantially higher-resolution meshes than a monolithic latent permits; and (ii) topology-adaptive editing, in which manipulating first-stage vertices induces the corresponding connectivity without re-optimization. Experiments show that LATO.2 surpasses state-of-the-art topology-aware mesh generators in geometric fidelity and connectivity quality.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

We present As-Plausible-as-Possible (APAP) mesh deformation technique that leverages 2D diffusion priors to preserve the plausibility of a mesh under user-controlled deformation. Our framework uses per-face Jacobians to represent mesh deformations, where mesh vertex coordinates are computed via a differentiable Poisson Solve. The deformed mesh is rendered, and the resulting 2D image is used in the Score Distillation Sampling (SDS) process, which enables extracting meaningful plausibility priors from a pretrained 2D diffusion model. To better preserve the identity of the edited mesh, we fine-tune our 2D diffusion model with LoRA. Gradients extracted by SDS and a user-prescribed handle displacement are then backpropagated to the per-face Jacobians, and we use iterative gradient descent to compute the final deformation that balances between the user edit and the output plausibility. We evaluate our method with 2D and 3D meshes and demonstrate qualitative and quantitative improvements when using plausibility priors over geometry-preservation or distortion-minimization priors used by previous techniques. Our project page is at: https://as-plausible-aspossible.github.io/

We present MeshLLM, a novel framework that leverages large language models (LLMs) to understand and generate text-serialized 3D meshes. Our approach addresses key limitations in existing methods, including the limited dataset scale when catering to LLMs' token length and the loss of 3D structural information during mesh serialization. We introduce a Primitive-Mesh decomposition strategy, which divides 3D meshes into structurally meaningful subunits. This enables the creation of a large-scale dataset with 1500k+ samples, almost 50 times larger than previous methods, which aligns better with the LLM scaling law principles. Furthermore, we propose inferring face connectivity from vertices and local mesh assembly training strategies, significantly enhancing the LLMs' ability to capture mesh topology and spatial structures. Experiments show that MeshLLM outperforms the state-of-the-art LLaMA-Mesh in both mesh generation quality and shape understanding, highlighting its great potential in processing text-serialized 3D meshes.

We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet instructions, which when knitted and stuffed result in a toy similar to the input geometry. Our approach relies on constructing the geometry and connectivity of a Crochet Graph, which is then translated into a crochet pattern. We segment the shape automatically into chrochetable components, which are connected using the join-as-you-go method, requiring no additional sewing. We demonstrate that our method is applicable to a large variety of shapes and geometries, and yields easily crochetable patterns.

Fitting a body to a 3D clothed human point cloud is a common yet challenging task. Traditional optimization-based approaches use multi-stage pipelines that are sensitive to pose initialization, while recent learning-based methods often struggle with generalization across diverse poses and garment types. We propose Equivariant Tightness Fitting for Clothed Humans, or ETCH, a novel pipeline that estimates cloth-to-body surface mapping through locally approximate SE(3) equivariance, encoding tightness as displacement vectors from the cloth surface to the underlying body. Following this mapping, pose-invariant body features regress sparse body markers, simplifying clothed human fitting into an inner-body marker fitting task. Extensive experiments on CAPE and 4D-Dress show that ETCH significantly outperforms state-of-the-art methods -- both tightness-agnostic and tightness-aware -- in body fitting accuracy on loose clothing (16.7% ~ 69.5%) and shape accuracy (average 49.9%). Our equivariant tightness design can even reduce directional errors by (67.2% ~ 89.8%) in one-shot (or out-of-distribution) settings. Qualitative results demonstrate strong generalization of ETCH, regardless of challenging poses, unseen shapes, loose clothing, and non-rigid dynamics. We will release the code and models soon for research purposes at https://boqian-li.github.io/ETCH/.

Creating high-fidelity 3D meshes with arbitrary topology, including open surfaces and complex interiors, remains a significant challenge. Existing implicit field methods often require costly and detail-degrading watertight conversion, while other approaches struggle with high resolutions. This paper introduces SparseFlex, a novel sparse-structured isosurface representation that enables differentiable mesh reconstruction at resolutions up to 1024^3 directly from rendering losses. SparseFlex combines the accuracy of Flexicubes with a sparse voxel structure, focusing computation on surface-adjacent regions and efficiently handling open surfaces. Crucially, we introduce a frustum-aware sectional voxel training strategy that activates only relevant voxels during rendering, dramatically reducing memory consumption and enabling high-resolution training. This also allows, for the first time, the reconstruction of mesh interiors using only rendering supervision. Building upon this, we demonstrate a complete shape modeling pipeline by training a variational autoencoder (VAE) and a rectified flow transformer for high-quality 3D shape generation. Our experiments show state-of-the-art reconstruction accuracy, with a ~82% reduction in Chamfer Distance and a ~88% increase in F-score compared to previous methods, and demonstrate the generation of high-resolution, detailed 3D shapes with arbitrary topology. By enabling high-resolution, differentiable mesh reconstruction and generation with rendering losses, SparseFlex significantly advances the state-of-the-art in 3D shape representation and modeling.

We propose an end-to-end deep learning architecture that produces a 3D shape in triangular mesh from a single color image. Limited by the nature of deep neural network, previous methods usually represent a 3D shape in volume or point cloud, and it is non-trivial to convert them to the more ready-to-use mesh model. Unlike the existing methods, our network represents 3D mesh in a graph-based convolutional neural network and produces correct geometry by progressively deforming an ellipsoid, leveraging perceptual features extracted from the input image. We adopt a coarse-to-fine strategy to make the whole deformation procedure stable, and define various of mesh related losses to capture properties of different levels to guarantee visually appealing and physically accurate 3D geometry. Extensive experiments show that our method not only qualitatively produces mesh model with better details, but also achieves higher 3D shape estimation accuracy compared to the state-of-the-art.

In this paper, we introduce MeshGen, an advanced image-to-3D pipeline that generates high-quality 3D meshes with detailed geometry and physically based rendering (PBR) textures. Addressing the challenges faced by existing 3D native diffusion models, such as suboptimal auto-encoder performance, limited controllability, poor generalization, and inconsistent image-based PBR texturing, MeshGen employs several key innovations to overcome these limitations. We pioneer a render-enhanced point-to-shape auto-encoder that compresses meshes into a compact latent space by designing perceptual optimization with ray-based regularization. This ensures that the 3D shapes are accurately represented and reconstructed to preserve geometric details within the latent space. To address data scarcity and image-shape misalignment, we further propose geometric augmentation and generative rendering augmentation techniques, which enhance the model's controllability and generalization ability, allowing it to perform well even with limited public datasets. For the texture generation, MeshGen employs a reference attention-based multi-view ControlNet for consistent appearance synthesis. This is further complemented by our multi-view PBR decomposer that estimates PBR components and a UV inpainter that fills invisible areas, ensuring a seamless and consistent texture across the 3D mesh. Our extensive experiments demonstrate that MeshGen largely outperforms previous methods in both shape and texture generation, setting a new standard for the quality of 3D meshes generated with PBR textures. See our code at https://github.com/heheyas/MeshGen, project page https://heheyas.github.io/MeshGen

Every Cartesian three-dimensional PDE solver hides a structural secret that production CFD codes have used for half a century and that graduate-level textbooks rarely state plainly. The derivative matrices, the compact Padé line solves, the Galerkin mass inversions, the alternating-direction-implicit substeps, and even the fast Poisson and Helmholtz diagonalization transforms all factor along the coordinate axes and collapse into repeated one-dimensional banded kernels executed along the grid lines. The three-dimensional operator exists only on paper; it is never assembled, factored, or stored. This paper is the manual for that collapse. We derive the Kronecker-product algebra that makes it exact, carry it cleanly through central differences, compact schemes, tensor-product Galerkin, B-spline and isogeometric methods, collocation, ADI time stepping, and direct Poisson and Helmholtz solves, and bring into the open the three production tricks that turn the reduction into hardware-conscious floating-point throughput on real machines: the multi-right-hand-side reshape that exposes a sweep as one batched line kernel (a dense BLAS-3 GEMM when the line factor is dense or element-local, a banded or stencil kernel when it is not), the sum factorization that rescues high-order Galerkin from the O(p^{2d}) quadrature trap, and the pencil decomposition that keeps every direction contiguous across an MPI cluster. For fixed stencil width or fixed polynomial degree, the compute cost stays O(N) in the total number of unknowns N = N_x N_y N_z; the operator storage drops to O(N_x + N_y + N_z) up to bandwidth constants; direct separable Poisson and Helmholtz solvers add the expected transform cost; the line kernels are embarrassingly parallel. These facts are familiar to practitioners but rarely assembled in one place; this paper collects them and shows how to use them.

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.

Diffusion-based 3D generation has made remarkable progress in recent years. However, existing 3D generative models often produce overly dense and unstructured meshes, which stand in stark contrast to the compact, structured, and sharply-edged Computer-Aided Design (CAD) models crafted by human designers. To address this gap, we introduce CADDreamer, a novel approach for generating boundary representations (B-rep) of CAD objects from a single image. CADDreamer employs a primitive-aware multi-view diffusion model that captures both local geometric details and high-level structural semantics during the generation process. By encoding primitive semantics into the color domain, the method leverages the strong priors of pre-trained diffusion models to align with well-defined primitives. This enables the inference of multi-view normal maps and semantic maps from a single image, facilitating the reconstruction of a mesh with primitive labels. Furthermore, we introduce geometric optimization techniques and topology-preserving extraction methods to mitigate noise and distortion in the generated primitives. These enhancements result in a complete and seamless B-rep of the CAD model. Experimental results demonstrate that our method effectively recovers high-quality CAD objects from single-view images. Compared to existing 3D generation techniques, the B-rep models produced by CADDreamer are compact in representation, clear in structure, sharp in edges, and watertight in topology.

This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method provides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.

We propose a remeshing-enhanced method for generatively deforming shapes with visual losses. It is intuitive that sufficiently drastic deformations of a mesh without changing its triangulation can easily compromise element quality, even if such large geometry changes may be semantically desired. Shape deformation methods could thus benefit from changing the triangulation; however, this is not done by most generative, text-based, visually-supervised mesh deformation methods. Remeshing is a discrete operation, proven to be especially challenging to couple with the notoriously noisy supervision signal provided by visual losses. We propose a vertex-based deformation optimization quantity capable of large deformations and robustness to such noise; we periodically remesh using an isotropic remesher that interpolates and carries forward the deformation optimization state. This enables continuous, geometry-informed progress in coarse-to-fine addition of resolution. The resulting shapes' triangulations fit their optimized geometry and have neat isotropic elements. Further, our method is localizable, able to grow new features on a base shape with expressive detail, leaving the rest unchanged. We showcase the effectiveness of our method on a variety of shapes and prompts, both local and global deformations, and demonstrate its superior visual quality and triangle efficiency. Our project page is at https://threedle.github.io/radmesh.

A triangular mesh is one of the most popular 3D data representations. As such, the deployment of deep neural networks for mesh processing is widely spread and is increasingly attracting more attention. However, neural networks are prone to adversarial attacks, where carefully crafted inputs impair the model's functionality. The need to explore these vulnerabilities is a fundamental factor in the future development of 3D-based applications. Recently, mesh attacks were studied on the semantic level, where classifiers are misled to produce wrong predictions. Nevertheless, mesh surfaces possess complex geometric attributes beyond their semantic meaning, and their analysis often includes the need to encode and reconstruct the geometry of the shape. We propose a novel framework for a geometric adversarial attack on a 3D mesh autoencoder. In this setting, an adversarial input mesh deceives the autoencoder by forcing it to reconstruct a different geometric shape at its output. The malicious input is produced by perturbing a clean shape in the spectral domain. Our method leverages the spectral decomposition of the mesh along with additional mesh-related properties to obtain visually credible results that consider the delicacy of surface distortions. Our code is publicly available at https://github.com/StolikTomer/SAGA.

Mesh generation has become a critical topic in recent years, forming the foundation of all 3D objects used across various applications, such as virtual reality, gaming, and 3D printing. With advancements in computational resources and machine learning, neural networks have emerged as powerful tools for generating high-quality 3D object representations, enabling accurate scene and object reconstructions. Despite these advancements, many methods produce meshes that lack realism or exhibit geometric and textural flaws, necessitating additional processing to improve their quality. This research introduces a convex optimization programming called disciplined convex programming to enhance existing meshes by refining their texture and geometry with a conic solver. By focusing on a sparse set of point clouds from both the original and target meshes, this method demonstrates significant improvements in mesh quality with minimal data requirements. To evaluate the approach, the classical dolphin mesh dataset from Facebook AI was used as a case study, with optimization performed using the CVXPY library. The results reveal promising potential for streamlined and effective mesh refinement.

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.

Recent progress in neural implicit functions has set new state-of-the-art in reconstructing high-fidelity 3D shapes from a collection of images. However, these approaches are limited to closed surfaces as they require the surface to be represented by a signed distance field. In this paper, we propose NeAT, a new neural rendering framework that can learn implicit surfaces with arbitrary topologies from multi-view images. In particular, NeAT represents the 3D surface as a level set of a signed distance function (SDF) with a validity branch for estimating the surface existence probability at the query positions. We also develop a novel neural volume rendering method, which uses SDF and validity to calculate the volume opacity and avoids rendering points with low validity. NeAT supports easy field-to-mesh conversion using the classic Marching Cubes algorithm. Extensive experiments on DTU, MGN, and Deep Fashion 3D datasets indicate that our approach is able to faithfully reconstruct both watertight and non-watertight surfaces. In particular, NeAT significantly outperforms the state-of-the-art methods in the task of open surface reconstruction both quantitatively and qualitatively.

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.

Learning radiance fields (NeRF) with powerful 2D diffusion models has garnered popularity for text-to-3D generation. Nevertheless, the implicit 3D representations of NeRF lack explicit modeling of meshes and textures over surfaces, and such surface-undefined way may suffer from the issues, e.g., noisy surfaces with ambiguous texture details or cross-view inconsistency. To alleviate this, we present DreamMesh, a novel text-to-3D architecture that pivots on well-defined surfaces (triangle meshes) to generate high-fidelity explicit 3D model. Technically, DreamMesh capitalizes on a distinctive coarse-to-fine scheme. In the coarse stage, the mesh is first deformed by text-guided Jacobians and then DreamMesh textures the mesh with an interlaced use of 2D diffusion models in a tuning free manner from multiple viewpoints. In the fine stage, DreamMesh jointly manipulates the mesh and refines the texture map, leading to high-quality triangle meshes with high-fidelity textured materials. Extensive experiments demonstrate that DreamMesh significantly outperforms state-of-the-art text-to-3D methods in faithfully generating 3D content with richer textual details and enhanced geometry. Our project page is available at https://dreammesh.github.io.