Daily Papers

Novel view synthesis and 3D reconstruction have advanced rapidly with radiance fields and splatting, yet their memory and computational demands limit their use in resource-constrained settings. We introduce Hexels: novel planar hexagonal surface elements with a first-order spatial color field for efficient 3D scene and 2D image representation. Hexels exploit locally planar regions with smoothly varying appearance using fewer, larger primitives. Their hexagonal support provides an area- and boundary-efficient domain, while the local color field captures appearance variation within each primitive. Across 34 scenes, Hexels improve PSNR over memory-matched 2DGS by 4.53-7.38 dB across datasets while requiring lower training VRAM. We further ablate Hexels by showing that per primitive, Hexels outperform 2DGS by upto 4.74 dB while using lower training VRAM and having 2.31 times faster FPS. Even in unconstrained settings, Hexels offers complementary quality-memory trade-offs. For efficient 3D surface reconstruction, Hexels reduce error by 28.9% compared with memory-matched 2DGS across 15 DTU scans. On 6 Tanks and Temples surface scenes, Hexels achieves the highest mean F1 among compared methods (34.38%, versus 31.72% for 2DGS). We further also show that Hexels, as a general primitive, improves 2D image representation over Image-GS. Hexels push the Pareto frontier on the quality-efficiency trade-off of surface-aligned primitives.

Constructing an adaptive hexahedral tessellation to fit an input triangle boundary is a key challenge in grid-based methods. The conventional method first removes outside elements (RO) and then projects the axis-aligned boundary onto the input triangle boundary, which has no guarantee on improving the initial Intersection over Union (IoU) and Hausdorff distance ratio (HR, w.r.t bounding box diagonal). The proposed MCHex approach replaces RO with a Marching Cubes method MCHex. Given the same computational budget (benchmarked using an identical precomputed Signed Distance Field, which dominates the runtime), MCHex provides better boundary approximation (higher IoU and lower HR) while guaranteeing a lower, yet still positive, minimum scaled Jacobian (>0 vs. RO's >0.48).

The Multiplane Image (MPI), containing a set of fronto-parallel RGBA layers, is an effective and efficient representation for view synthesis from sparse inputs. Yet, its fixed structure limits the performance, especially for surfaces imaged at oblique angles. We introduce the Structural MPI (S-MPI), where the plane structure approximates 3D scenes concisely. Conveying RGBA contexts with geometrically-faithful structures, the S-MPI directly bridges view synthesis and 3D reconstruction. It can not only overcome the critical limitations of MPI, i.e., discretization artifacts from sloped surfaces and abuse of redundant layers, and can also acquire planar 3D reconstruction. Despite the intuition and demand of applying S-MPI, great challenges are introduced, e.g., high-fidelity approximation for both RGBA layers and plane poses, multi-view consistency, non-planar regions modeling, and efficient rendering with intersected planes. Accordingly, we propose a transformer-based network based on a segmentation model. It predicts compact and expressive S-MPI layers with their corresponding masks, poses, and RGBA contexts. Non-planar regions are inclusively handled as a special case in our unified framework. Multi-view consistency is ensured by sharing global proxy embeddings, which encode plane-level features covering the complete 3D scenes with aligned coordinates. Intensive experiments show that our method outperforms both previous state-of-the-art MPI-based view synthesis methods and planar reconstruction methods.

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.

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.

A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. We first show that a representative example, the "hat" polykite, can form clusters called "metatiles", for which substitution rules can be defined. Because the metatiles admit tilings of the plane, so too does the hat. We then prove that generic members of our continuum of polygons are aperiodic, through a new kind of geometric incommensurability argument. Separately, we give a combinatorial, computer-assisted proof that the hat must form hierarchical -- and hence aperiodic -- tilings.

While structure-based relocalizers have long strived for point correspondences when establishing or regressing query-map associations, in this paper, we pioneer the use of planar primitives and 3D planar maps for lightweight 6-DoF camera relocalization in structured environments. Planar primitives, beyond being fundamental entities in projective geometry, also serve as region-based representations that encapsulate both structural and semantic richness. This motivates us to introduce PlanaReLoc, a streamlined plane-centric paradigm where a deep matcher associates planar primitives across the query image and the map within a learned unified embedding space, after which the 6-DoF pose is solved and refined under a robust framework. Through comprehensive experiments on the ScanNet and 12Scenes datasets across hundreds of scenes, our method demonstrates the superiority of planar primitives in facilitating reliable cross-modal structural correspondences and achieving effective camera relocalization without requiring realistically textured/colored maps, pose priors, or per-scene training. The code and data are available at https://github.com/3dv-casia/PlanaReLoc .

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in n-dimensional space, calculating the value of a sampled point requires interpolating the values of its 2^n neighboring vertices. The exponential scaling with dimension leads to significant computational overheads. To address this issue, we propose a simplex-based approach for encoding graphics primitives. The number of vertices in a simplex-based structure increases linearly with dimension, making it a more efficient and generalizable alternative to grid-based representations. Using the non-axis-aligned simplicial structure property, we derive and prove a coordinate transformation, simplicial subdivision, and barycentric interpolation scheme for efficient sampling, which resembles transformation procedures in the simplex noise algorithm. Finally, we use hash tables to store multiresolution features of all interest points in the simplicial grid, which are passed into a tiny fully connected neural network to parameterize graphics primitives. We implemented a detailed simplex-based structure encoding algorithm in C++ and CUDA using the methods outlined in our approach. In the 2D image fitting task, the proposed method is capable of fitting a giga-pixel image with 9.4% less time compared to the baseline method proposed by instant-ngp, while maintaining the same quality and compression rate. In the volumetric rendering setup, we observe a maximum 41.2% speedup when the samples are dense enough.

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.

Modeling and re-rendering dynamic 3D scenes is a challenging task in 3D vision. Prior approaches build on NeRF and rely on implicit representations. This is slow since it requires many MLP evaluations, constraining real-world applications. We show that dynamic 3D scenes can be explicitly represented by six planes of learned features, leading to an elegant solution we call HexPlane. A HexPlane computes features for points in spacetime by fusing vectors extracted from each plane, which is highly efficient. Pairing a HexPlane with a tiny MLP to regress output colors and training via volume rendering gives impressive results for novel view synthesis on dynamic scenes, matching the image quality of prior work but reducing training time by more than 100times. Extensive ablations confirm our HexPlane design and show that it is robust to different feature fusion mechanisms, coordinate systems, and decoding mechanisms. HexPlane is a simple and effective solution for representing 4D volumes, and we hope they can broadly contribute to modeling spacetime for dynamic 3D scenes.

Planar metasurfaces can profoundly control electromagnetic scattering. At microwave frequencies, such devices are typically implemented using multilayer cascades of patterned metallic sheets, whose design often requires time-consuming full-wave optimization. Here, we extend analytical models originally developed for sparse loaded-wire metagratings to accurately describe densely packed Jerusalem-cross meta-atoms embedded in standard printed circuit board (PCB) dielectric stacks. The model captures both near- and far-field coupling within and between layers, enabling efficient prediction of the dual-polarized response. Using this framework, we identify highly transmissive meta-atoms whose phase is controlled by the leg lengths of the Jerusalem crosses (microscopic design stage). This (phase)-(leg-length) "lookup table" allows rapid synthesis of Huygens' metasurfaces (macroscopic design stage), demonstrated through a full-wave-validated metalens exhibiting low-reflection beam manipulation. Notably, we implement a judicious scaling method to further extend the model to predict wideband meta-atom responses. In the companion paper (Part II), a hybrid machine-learning approach leverages this semianalytical framework to enhance accuracy without requiring the conventional exhaustive full-wave training, enabling ultrafast inverse design across the full parameter space. Overall, the presented methodology -- the standalone semianlytical scheme (Part I) and the machine-learning enhanced version (Part II) -- establishes an effective open-source toolkit for versatile, rapid, and highly accurate synthesis of fabrication-ready dual-polarized transmissive Huygens' meta-atoms and metasurfaces.

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.

Video world models that generate and explore environments at scale need a persistent 3D memory of what they have produced. Plane primitives offer a natural candidate: a compact set of oriented planes captures the dominant structural elements (e.g., walls, floors, facades) of indoor and outdoor scenes, while requiring only 7 parameters per primitive. We present PPMem, a video world model that adopts plane primitives as its persistent 3D memory. PPMem augments a video diffusion transformer with a planar prediction head and a Depth Token Fusion (DTF) module: each autoregressive chunk jointly produces RGB video and planar geometry, which merges into a persistent plane memory that conditions subsequent chunks via rendered depth. The resulting memory is three orders of magnitude more compact than per-pixel point clouds (~100K primitives, 5MB for a full scene), geometrically explicit (metric depth, normals, exportable surfaces), cross-view consistent (jointly predicted by the shared backbone), and adaptive (refined by the merging procedure as generation proceeds). On DL3DV and RealEstate10K, PPMem outperforms prior 3D-grounded world models in video quality while jointly producing metric-scale depth, surface normals, and exportable planar geometry, sustaining coherence across hundreds of frames under large viewpoint changes. Project page: https://hyzcluster.github.io/ppmem.

We introduce AlphaTablets, a novel and generic representation of 3D planes that features continuous 3D surface and precise boundary delineation. By representing 3D planes as rectangles with alpha channels, AlphaTablets combine the advantages of current 2D and 3D plane representations, enabling accurate, consistent and flexible modeling of 3D planes. We derive differentiable rasterization on top of AlphaTablets to efficiently render 3D planes into images, and propose a novel bottom-up pipeline for 3D planar reconstruction from monocular videos. Starting with 2D superpixels and geometric cues from pre-trained models, we initialize 3D planes as AlphaTablets and optimize them via differentiable rendering. An effective merging scheme is introduced to facilitate the growth and refinement of AlphaTablets. Through iterative optimization and merging, we reconstruct complete and accurate 3D planes with solid surfaces and clear boundaries. Extensive experiments on the ScanNet dataset demonstrate state-of-the-art performance in 3D planar reconstruction, underscoring the great potential of AlphaTablets as a generic 3D plane representation for various applications. Project page is available at: https://hyzcluster.github.io/alphatablets

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.

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.

This paper studies implicit surface reconstruction leveraging differentiable ray casting. Previous works such as IDR and NeuS overlook the spatial context in 3D space when predicting and rendering the surface, thereby may fail to capture sharp local topologies such as small holes and structures. To mitigate the limitation, we propose a flexible neural implicit representation leveraging hierarchical voxel grids, namely Neural Deformable Anchor (NeuDA), for high-fidelity surface reconstruction. NeuDA maintains the hierarchical anchor grids where each vertex stores a 3D position (or anchor) instead of the direct embedding (or feature). We optimize the anchor grids such that different local geometry structures can be adaptively encoded. Besides, we dig into the frequency encoding strategies and introduce a simple hierarchical positional encoding method for the hierarchical anchor structure to flexibly exploit the properties of high-frequency and low-frequency geometry and appearance. Experiments on both the DTU and BlendedMVS datasets demonstrate that NeuDA can produce promising mesh surfaces.

The success of deep learning is frequently described as the ability to train all parameters of a network on a specific application in an end-to-end fashion. Yet, several design choices on the camera level, including the pixel layout of the sensor, are considered as pre-defined and fixed, and high resolution, regular pixel layouts are considered to be the most generic ones in computer vision and graphics, treating all regions of an image as equally important. While several works have considered non-uniform, \eg, hexagonal or foveated, pixel layouts in hardware and image processing, the layout has not been integrated into the end-to-end learning paradigm so far. In this work, we present the first truly end-to-end trained imaging pipeline that optimizes the size and distribution of pixels on the imaging sensor jointly with the parameters of a given neural network on a specific task. We derive an analytic, differentiable approach for the sensor layout parameterization that allows for task-specific, local varying pixel resolutions. We present two pixel layout parameterization functions: rectangular and curvilinear grid shapes that retain a regular topology. We provide a drop-in module that approximates sensor simulation given existing high-resolution images to directly connect our method with existing deep learning models. We show that network predictions benefit from learnable pixel layouts for two different downstream tasks, classification and semantic segmentation.

We introduce a new approach for generating realistic 3D models with UV maps through a representation termed "Object Images." This approach encapsulates surface geometry, appearance, and patch structures within a 64x64 pixel image, effectively converting complex 3D shapes into a more manageable 2D format. By doing so, we address the challenges of both geometric and semantic irregularity inherent in polygonal meshes. This method allows us to use image generation models, such as Diffusion Transformers, directly for 3D shape generation. Evaluated on the ABO dataset, our generated shapes with patch structures achieve point cloud FID comparable to recent 3D generative models, while naturally supporting PBR material generation.

Despite the latest remarkable advances in generative modeling, efficient generation of high-quality 3D assets from textual prompts remains a difficult task. A key challenge lies in data scarcity: the most extensive 3D datasets encompass merely millions of assets, while their 2D counterparts contain billions of text-image pairs. To address this, we propose a novel approach which harnesses the power of large, pretrained 2D diffusion models. More specifically, our approach, HexaGen3D, fine-tunes a pretrained text-to-image model to jointly predict 6 orthographic projections and the corresponding latent triplane. We then decode these latents to generate a textured mesh. HexaGen3D does not require per-sample optimization, and can infer high-quality and diverse objects from textual prompts in 7 seconds, offering significantly better quality-to-latency trade-offs when comparing to existing approaches. Furthermore, HexaGen3D demonstrates strong generalization to new objects or compositions.

The Berge-Fulkerson conjecture states that every bridgeless cubic graph can be covered with six perfect matchings such that each edge is covered exactly twice. An equivalent reformulation is that it's possible to find a 6-cycle 4-cover. In this paper we discuss the oriented version (o6c4c) of the latter statement, pose it as a conjecture and prove it for the family of Isaacs flower snarks. Similarly to the case of oriented cycle double cover, we can always construct an orientable surface (possibly with boundary) from an o6c4c solution. If the o6c4c solution itself splits into two (not necessarily oriented) cycle double covers, then it's also possible to build another pair of orientable surfaces (also possibly with boundaries). Finally we show how to build a ribbon graph, and for some special o6c4c cases we show that this ribbon graph corresponds to an oriented 6-cycle double cover. Github: https://github.com/gexahedron/cycle-double-covers

Parametric computer-aided design (CAD) modeling is fundamental to industrial design, but existing datasets often lack explicit geometric constraints and fine-grained functional semantics, limiting editable, constraint-compliant generation. We present HistCAD, a large-scale dataset featuring constraint-aware modeling sequences that compactly represent procedural operations while ensuring compatibility with native CAD software, encompassing five aligned modalities: modeling sequences, multi-view renderings, STEP-format B-reps, native parametric files, and textual annotations. We develop AM\(_HistCAD\), an annotation module that extracts geometric and spatial features from modeling sequences and uses a large language model to generate complementary annotations of the modeling process, geometric structure, and functional type. Extensive evaluations demonstrate that HistCAD's explicit constraints, flattened sequence format, and multi-type annotations improve robustness, parametric editability, and accuracy in text-driven CAD generation, while industrial parts included in HistCAD further support complex real-world design scenarios. HistCAD thus provides a unified benchmark for advancing editable, constraint-aware, and semantically enriched generative CAD modeling.

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.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

Hexagonal oxide perovskites, in contrast to the more familiar perovskites, allow for face-sharing of metal-oxygen octahedra or trigonal prisms within their structural frameworks. This results in dimers, trimers, tetramers, or longer fragments of chains of face-sharing octahedra in the crystal structures, and consequently in much shorter metal-metal distances and lower metal-oxygen-metal bond angles than are seen in the more familiar perovskites. The presence of the face-sharing octahedra can have a dramatic impact on magnetic properties of these compounds, and dimer-based materials, in particular, have been the subjects of many quantum-materials-directed studies in materials physics. Hexagonal oxide perovskites are of contemporary interest due to their potential for geometrical frustration of the ordering of magnetic moments or orbital occupancies at low temperatures, which is especially relevant to their significance as quantum materials. As such, several hexagonal oxide perovskites have been identified as potential candidates for hosting the quantum spin liquid state at low temperatures. In our view, hexagonal oxide perovskites are fertile ground for finding new quantum materials. This review briefly describes the solid state chemistry of many of these materials.

Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and topologically simpler, including also Boy surface (real projective plane), using a family of ruled surfaces. We show their usefulness in visualizing the process using commonly available modeling software.

Shrinking pattern dimensions leads to an increased variety of defect types in semiconductor devices. This has spurred innovation in patterning approaches such as Directed self-assembly (DSA) for which no traditional, automatic defect inspection software exists. Machine Learning-based SEM image analysis has become an increasingly popular research topic for defect inspection with supervised ML models often showing the best performance. However, little research has been done on obtaining a dataset with high-quality labels for these supervised models. In this work, we propose a method for obtaining coherent and complete labels for a dataset of hexagonal contact hole DSA patterns while requiring minimal quality control effort from a DSA expert. We show that YOLOv8, a state-of-the-art neural network, achieves defect detection precisions of more than 0.9 mAP on our final dataset which best reflects DSA expert defect labeling expectations. We discuss the strengths and limitations of our proposed labeling approach and suggest directions for future work in data-centric ML-based defect inspection.

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.

Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph representation learning. Specifically, constructing graphs that effectively capture the complete geometric information of crystals and handle chiral crystals remains an unsolved and challenging problem. In this paper, we introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom, enabling efficient and expressive graph representations of crystals. Furthermore, we propose ComFormer, a SE(3) transformer designed specifically for crystalline materials. ComFormer includes two variants; namely, iComFormer that employs invariant geometric descriptors of Euclidean distances and angles, and eComFormer that utilizes equivariant vector representations. Experimental results demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks across three widely-used crystal benchmarks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Three-dimensional Gaussian Splatting (3DGS) has recently emerged as an efficient representation for novel-view synthesis, achieving impressive visual quality. However, in scenes dominated by large and low-texture regions, common in indoor environments, the photometric loss used to optimize 3DGS yields ambiguous geometry and fails to recover high-fidelity 3D surfaces. To overcome this limitation, we introduce PlanarGS, a 3DGS-based framework tailored for indoor scene reconstruction. Specifically, we design a pipeline for Language-Prompted Planar Priors (LP3) that employs a pretrained vision-language segmentation model and refines its region proposals via cross-view fusion and inspection with geometric priors. 3D Gaussians in our framework are optimized with two additional terms: a planar prior supervision term that enforces planar consistency, and a geometric prior supervision term that steers the Gaussians toward the depth and normal cues. We have conducted extensive experiments on standard indoor benchmarks. The results show that PlanarGS reconstructs accurate and detailed 3D surfaces, consistently outperforming state-of-the-art methods by a large margin. Project page: https://planargs.github.io

A quadrilateral block decomposition of a planar domain is judged by whether it is complete, whether its elements are well shaped, and how many of its vertices are irregular. The last has a provable floor: the discrete Gauss-Bonnet identity enforces a lower bound on the total vertex irregularity of any all-quadrilateral mesh of a given domain purely based on its topology and corner angles. We train a reinforcement learning agent to build decompositions that reach this bound, which we call par. It acts directly on the mesh's half-edge data structure through local edits, with a policy network whose convolutions follow the mesh's own connectivity, so it applies unchanged to domains larger than any seen in training. The reward targets the floor directly, and it is sparse: random play reaches it on no domain with more than eight sides. We overcome this exploration barrier via behaviour cloning on optimal meshes that are trivial to construct, walked backward into demonstrations, before training it with PPO. On 96 held-out domains the agent produces an all-quadrilateral mesh on every one, a usable one on 95.7 on average, and a provably optimal one on 90; Gmsh's strongest configuration at the same element count completes 51, is usable on 38 and optimal on none, and even at three to fourteen times the elements never produces a more regular mesh. On 64 domains twice the training size the agent completes all, is usable on 62, and keeps a median excess over par below one against Gmsh's 39 at the same element count.

Parts manufactured with Fused Deposition Modeling (FDM) often require Design for Additive Manufacturing (DFAM) modifications to ensure printability, structural integrity, and reduced post-processing. Current slicers identify defects such as steep overhangs but are unable to modify the underlying geometry. This work presents AgentsCAD, a multi-agent system that bridges raw boundary-representation (B-Rep) geometry and Large Language Model (LLM) reasoning to automate targeted DFM. The workflow begins by parsing a STEP file. The agentic system detects overhangs above a 45°threshold, constructs a face-adjacency topology graph, and optionally injects semantic feature labels from a GraphSAGE model trained on MFCAD++ (59,665 parts), before dispatching a Claude Sonnet design-reasoning agent that recommends reorientations, fillets, chamfers, and similar modifications. A GPT-4o vision-language verifier inspects rendered views to confirm geometric integrity. Outputs include a modified STEP file and a human-readable report. A test case on a birdhouse model demonstrates that the system correctly diagnoses overhangs, selects appropriate defect mitigation strategies, and proposes physically valid corrections, partially solving the geometry-to-language translation problem central to LLM-driven CAD modification.

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.

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.

Large Language Models (LLMs) have demonstrated impressive capabilities in a wide range of code generation tasks. However, generating code for certain domains remains challenging. One such domain is Computer-Aided Design (CAD) program, where the goal is to produce scripted parametric models that define object geometry for precise design and manufacturing applications. A key challenge in LLM-based CAD program generation is the limited geometric complexity of generated shapes compared to those found in real-world industrial designs. This shortfall is in part due to the lack of diversity in the available CAD program training data. To address this, we propose a novel data augmentation paradigm that prompts an LLM to generate CAD programs conditioned on a reference surface program and a modeling procedure - an idea inspired by practices in industrial design. By varying the reference surface using a collection of organic shapes, our method enriches the geometric distribution of generated CAD models. In particular, it introduces edges and faces defined by spline-based curvature, which are typically missing or underrepresented in existing open-source CAD program datasets. Experiments show that our method produces CAD samples with significantly greater geometric diversity and a higher resemblance to industry-grade CAD designs in terms of the proportion of organic shape primitives. This enhancement makes our CAD data augmentation approach a useful tool for training LLMs and other deep learning models in CAD generation.

The coexistence of multiple moire lattices in van der Waals heterostructures raises a fundamental question: how do distinct moire patterns interact and reconstruct? Here, we investigate twisted bilayer graphene (tBG) on hexagonal boron nitride (h-BN), where tBG and graphene/h-BN moire structures coexist, using conductive atomic force microscopy combined with continuum-model simulations. We show that reconstruction between these moire lattices-moire-moire reconstruction-manifests across multiple length scales, giving rise to diverse commensurate double-moire phases. Locally, the stacking registry between the two moire lattices is uniquely selected by the global twist configuration (helical or alternate), mediated by rotational relaxation of the shared graphene layer. This registry, together with twist angle and strain, governs commensurate domains from C3z-symmetric to strained symmetry-modified structures. These results establish moire-moire reconstruction as a general framework for engineering structural and electronic order -- including theoretically predicted topological flat bands below the magic angle -- in multilayer moire materials.

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.

The honeycomb and Kelvin problems ask how space can be partitioned into cells of equal volume with the least surface area. We resolve this question in four dimensions for convex bodies that tile space by translations, showing that the regular 24-cell uniquely minimizes surface area at fixed volume. We develop a framework combining an exact deficit identity, valid in every dimension, with a descent argument. As a consequence, the regular 24-cell also minimizes surface area among such tiles containing a fixed ball.

Identifying and grounding precise geometric entities, such as edges, planar regions, and curved surfaces within 3D objects, is foundational to computer-aided design (CAD), robotic manipulation, and scientific simulation. Although modern Vision Language Models (VLMs) have advanced referring segmentation (RIS) in the image domain, extending such language-driven localization to structured 3D geometry is substantially harder. The 3D object appearance is highly sensitive to viewpoints; a single perspective may render a target entity clearly observable, while another may suffer from severe occlusion or foreshortening. In this work, we attempt to solve these challenges with MV-GEL (Multi-View Geometric Entity Localization), a framework for localizing fine-grained geometric entities on polygon meshes from natural language queries. Our key insight is that reliable CAD entity (i.e., faces, edges or solids) localization depends on selecting views that make the queried entity maximally interpretable. We introduce GELviews, a prompt-conditioned ranking module that prioritizes viewpoints based on language prompted observability of geometric CAD entities. Selected views are processed by a VLM-based reasoning segmentation backbone, and predicted masks are lifted to the corresponding meshes via geometry-aware ray casting. Our framework is completely CAD agnostic and relies only on 3D meshes. Experiments show up to a 1.7X improvement in face-level IoU and over 4.5X gains in edge-level F1 compared to vanilla baselines, substantially outperforming CLIP-based and random view sampling, particularly for thin and view-sensitive structures. The dataset, code and trained checkpoints are available at https://github.com/kbali1297/MV-GEL.

We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets.

In computer-aided design (CAD) systems, 2D line drawings are commonly used to illustrate 3D object designs. To reconstruct the 3D models depicted by a single 2D line drawing, an important key is finding the edge loops in the line drawing which correspond to the actual faces of the 3D object. In this paper, we approach the classical problem of face identification from a novel data-driven point of view. We cast it as a sequence generation problem: starting from an arbitrary edge, we adopt a variant of the popular Transformer model to predict the edges associated with the same face in a natural order. This allows us to avoid searching the space of all possible edge loops with various hand-crafted rules and heuristics as most existing methods do, deal with challenging cases such as curved surfaces and nested edge loops, and leverage additional cues such as face types. We further discuss how possibly imperfect predictions can be used for 3D object reconstruction.

We introduce a differentiable 3D representation that unifies the ray tracing capabilities of foam-based ray tracing with the efficiency of modern rasterization pipelines. While prior foam representations enable constant-time ray traversal through an explicit volumetric partition of space, their potentially unbounded cells hinder efficient tile-based rasterization. We address this limitation by generalizing Voronoi foams to bounded power diagrams with controllable cell extents, enabling spatially bounded primitives without requiring expensive Delaunay triangulations during training. We further introduce an oriented surface formulation that explicitly models interfaces between interior and exterior regions, and decouple geometry from appearance by embedding differentiable texture directly on these surfaces. Together, these contributions yield a representation that preserves state-of-the-art ray tracing efficiency while achieving rasterization performance competitive with current generation 3DGS, providing a practical path toward unified real-time differentiable rendering.

We prepared Na_xTO_2 (T = Mn, Co) nanostructures to use as cathode material in Na-ion batteries. The Rietveld refinement of x-ray diffraction data confirms the hexagonal symmetry. Scanning and transmission electron microscopy measurements show hexagonal and rod-shape morphology for T = Co and Mn, respectively. The magnetic measurements indicate the presence of variable oxidation states of Mn/Co ions, but no long range ordering till 5~K. We find that the Na_{0.6}MnO_2 is highly insulating whereas Na_{0.7}CoO_2 is semiconducting in nature. The conduction in Na_{0.7}CoO_2 takes place through both variable range hopping (VRH) as well as activation mechanisms in different temperature ranges. However, for Na_{0.6}MnO_2 the VRH prevails at elevated temperatures. Furthermore, the coin cells have been fabricated and tested the electrochemical behavior using cyclic voltammetry, which confirms the reversibility of Na--ions during intercalation/de-intercalation.

This paper aims to generate materials for 3D meshes from text descriptions. Unlike existing methods that synthesize texture maps, we propose to generate segment-wise procedural material graphs as the appearance representation, which supports high-quality rendering and provides substantial flexibility in editing. Instead of relying on extensive paired data, i.e., 3D meshes with material graphs and corresponding text descriptions, to train a material graph generative model, we propose to leverage the pre-trained 2D diffusion model as a bridge to connect the text and material graphs. Specifically, our approach decomposes a shape into a set of segments and designs a segment-controlled diffusion model to synthesize 2D images that are aligned with mesh parts. Based on generated images, we initialize parameters of material graphs and fine-tune them through the differentiable rendering module to produce materials in accordance with the textual description. Extensive experiments demonstrate the superior performance of our framework in photorealism, resolution, and editability over existing methods. Project page: https://zhanghe3z.github.io/MaPa/

The most widely used method for obtaining high-quality two-dimensional materials is through mechanical exfoliation of bulk crystals. Manual identification of suitable flakes from the resulting random distribution of crystal thicknesses and sizes on a substrate is a time-consuming, tedious task. Here, we present a platform for fully automated scanning, detection, and classification of two-dimensional materials, the source code of which we make openly available. Our platform is designed to be accurate, reliable, fast, and versatile in integrating new materials, making it suitable for everyday laboratory work. The implementation allows fully automated scanning and analysis of wafers with an average inference time of 100 ms for images of 2.3 Mpixels. The developed detection algorithm is based on a combination of the flakes' optical contrast toward the substrate and their geometric shape. We demonstrate that it is able to detect the majority of exfoliated flakes of various materials, with an average recall (AR50) between 67% and 89%. We also show that the algorithm can be trained with as few as five flakes of a given material, which we demonstrate for the examples of few-layer graphene, WSe_2, MoSe_2, CrI_3, 1T-TaS_2 and hexagonal BN. Our platform has been tested over a two-year period, during which more than 10^6 images of multiple different materials were acquired by over 30 individual researchers.

Text and image conditioned 3D models now generate convincing assets, but they still offer little direct control over the space an object should occupy or avoid. In authoring, this spatial intent is often known before generation starts. A chair should fit a seating envelope, a prop should leave clearance for motion, or a part should expose a contact surface. Prompts and image views are poor carriers for such constraints, requiring the need for an explicit control interface. We present Arbor, a trainable attachment for text conditioned latent 3D generation. Arbor introduces constraint meshes as a native 3D control interface. The interface uses hull regions where geometry should exist, avoidance regions that should remain empty, and touch regions the object should contact. Unlike completion or whole object scaffold control, these meshes are not target evidence. They are local typed requirements and can include regions where no surface should appear. Arbor keeps this signal as geometry by converting constraint meshes into tokens and learning a routed attachment inside a frozen denoiser. Each latent region can therefore receive the part of the constraint that matters for its spatial location. We evaluate Arbor on automatic and artist curated control benchmarks with hull, avoidance, and touch constraints, and compare the metric trends to a user preference study. Even without dedicated compliance losses, Arbor improves constraint obedience while preserving object quality and variation under fixed constraints.

Constructing computer-aided design (CAD) models is labor-intensive but essential for engineering and manufacturing. Recent advances in Large Language Models (LLMs) have inspired the LLM-based CAD generation by representing CAD as command sequences. But these methods struggle in practical scenarios because command sequence representation does not support entity selection (e.g. faces or edges), limiting its ability to support complex editing operations such as chamfer or fillet. Further, the discretization of a continuous variable during sketch and extrude operations may result in topological errors. To address these limitations, we present Pointer-CAD, a novel LLM-based CAD generation framework that leverages a pointer-based command sequence representation to explicitly incorporate the geometric information of B-rep models into sequential modeling. In particular, Pointer-CAD decomposes CAD model generation into steps, conditioning the generation of each subsequent step on both the textual description and the B-rep generated from previous steps. Whenever an operation requires the selection of a specific geometric entity, the LLM predicts a Pointer that selects the most feature-consistent candidate from the available set. Such a selection operation also reduces the quantization error in the command sequence-based representation. To support the training of Pointer-CAD, we develop a data annotation pipeline that produces expert-level natural language descriptions and apply it to build a dataset of approximately 575K CAD models. Extensive experimental results demonstrate that Pointer-CAD effectively supports the generation of complex geometric structures and reduces segmentation error to an extremely low level, achieving a significant improvement over prior command sequence methods, thereby significantly mitigating the topological inaccuracies introduced by quantization error.

Text-to-CAD generation aims to create parametric CAD models from natural language, enabling rapid prototyping and intuitive design workflows. However, existing benchmarks focus on basic primitives and simple sketch-extrude sequences, lacking advanced features essential for real-world applications and covering only traditional mechanical parts. We introduce Text2CAD-Bench, the first benchmark systematically evaluating text-to-CAD across geometric complexity and application diversity. Our benchmark comprises 600 human-curated examples spanning four levels: L1-L2 cover fundamental geometry with standard features, L3 introduces complex topology and freeform surfaces, and L4 extends to real-world domains beyond mechanical parts. Each example pairs dual-style prompts -- geometric descriptions mimicking non-expert users, and procedural sequences aligned with expert-level conventions. Evaluating mainstream general LLMs and domain-specific models, we find that current models perform reasonably on basic geometry but degrade substantially on complex topology and advanced features. We release our benchmark to drive progress in text-to-CAD research.

We study the relation between equal-weight circle quadrature, Gauss--Chebyshev quadrature, and planar Minkowski reconstruction. The regular N-point grid is an mathbb S^1-design of strength N-1; a half-step rotation of the 2M-point grid projects to the classical M-point Gauss--Chebyshev rule. A common family of quadrature-error functionals gives exact identities for integration error, mixed-area error, and support-function error. For Nge3, the centered Minkowski polygon P_N with perimeter 2π has the exact Hausdorff distance from the unit disk B^2 \[ d_H(P_N,B^2)=1-\fracπ{N}\cot\fracπ{N} =π^2{3N^2}+O(N^{-4}). \] With Steiner centering, we obtain d_H(K_μ,K_ν)leπW_1(μ,ν) for balanced, nondegenerate probability measures, where W_1 uses geodesic distance. Its exponent is sharp even for smooth positive densities near the uniform measure. The identity W_1(ν_N,σ)=π/(2N) yields a general O(N^{-1}) bound for the regular grid. The sharper O(N^{-2}) rate follows from the sparse discrepancy spectrum and the inverse multiplier (1-k^2)^{-1}. Finally, a perturbation estimate gives sufficient conditions for preserving the quadratic rate and its leading constant.

Recent advances in general-purpose AI models and agentic systems have enabled them to perform some CAD tasks. A systematic assessment is now needed to establish what these systems can accomplish and how well their outputs meet engineering requirements. This paper presents an empirical study of GPT-6 Astra, a SOTA general-purpose AI model, across four basic CAD tasks: model understanding, generation, editing, and evaluation. We design test cases spanning different levels of complexity and engineering requirements. The results show that GPT-6 Astra can support multiple stages of CAD workflows, with successful outcomes in cases involving nontrivial geometric complexity. This suggests that general-purpose AI is beginning to offer practical value in almost all steps in CAD workflow. However, gaps remain between generating visually plausible geometry and producing valid, functional, and editable CAD models. Recurring errors in freeform geometry, parameter dependencies, and mating relationships between parts limit engineering usefulness. Agentic iterative refinement can improve results but does not consistently resolve critical errors; long completion times further constrain practical use.

Current 3D generative models mostly produce a final surface: a visually strong but largely opaque mesh. Interactive 3D worlds need more than a surface. They need named parts, an assembly hierarchy, measurable constraints, local edit handles, and joints for articulation. We present Nova3D, a system that generates 3D assets as executable Blender source code; the compiled mesh, a binary glTF (GLB), is treated as the artifact, not the asset. Because the output is a program, semantic handles exist at generation time rather than being recovered afterward by segmentation or rigging. We evaluate on Nova3D-Bench, a frozen, spec-grounded benchmark of 54 items across six domains and three difficulty levels with text and image inputs, against eleven baselines in four families (mesh-native, part-structured, code-native, and CAD) plus a same-LLM ablation. Nova3D produces an executable program and a valid artifact for 54/54 items. Every asset exposes named parts organized in a parent-child assembly tree; no mesh-native, CAD, or segmentation baseline exposes either. It satisfies 51/52 prompt-stated numeric and count constraints (best baseline: 11/52), passes 14/18 blinded local edits with locality preserved in 18/18, and articulates 59 joints across 12 assets at 98.3% geometric validity, where every baseline exposes zero native joints. Its geometry is competitive: it wins the structured domains in a pairwise shape-quality tournament and is second only to the strongest mesh-native model, while conceding texture realism to baked-PBR systems. The central result is representational: code-native generation turns a generated 3D object from an opaque surface into a programmable asset that downstream systems can inspect, measure, edit, and animate.

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.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

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.

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.

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions. Focusing on trilinear interpolating methods as positional encoding, we present theoretical insights and an analytical mesh extraction, showing the transformation of hypersurfaces to flat planes within the trilinear region under the eikonal constraint. Moreover, we introduce a method for approximating intersecting points among three hypersurfaces contributing to broader applications. We empirically validate correctness and parsimony through chamfer distance and efficiency, and angular distance, while examining the correlation between the eikonal loss and the planarity of the hypersurfaces.

Single-image piece-wise planar 3D reconstruction aims to simultaneously segment plane instances and recover 3D plane parameters from an image. Most recent approaches leverage convolutional neural networks (CNNs) and achieve promising results. However, these methods are limited to detecting a fixed number of planes with certain learned order. To tackle this problem, we propose a novel two-stage method based on associative embedding, inspired by its recent success in instance segmentation. In the first stage, we train a CNN to map each pixel to an embedding space where pixels from the same plane instance have similar embeddings. Then, the plane instances are obtained by grouping the embedding vectors in planar regions via an efficient mean shift clustering algorithm. In the second stage, we estimate the parameter for each plane instance by considering both pixel-level and instance-level consistencies. With the proposed method, we are able to detect an arbitrary number of planes. Extensive experiments on public datasets validate the effectiveness and efficiency of our method. Furthermore, our method runs at 30 fps at the testing time, thus could facilitate many real-time applications such as visual SLAM and human-robot interaction. Code is available at https://github.com/svip-lab/PlanarReconstruction.

Shape abstraction is an important task for simplifying complex geometric structures while retaining essential features. Sweep surfaces, commonly found in human-made objects, aid in this process by effectively capturing and representing object geometry, thereby facilitating abstraction. In this paper, we introduce \papername, a novel approach to shape abstraction through sweep surfaces. We propose an effective parameterization for sweep surfaces, utilizing superellipses for profile representation and B-spline curves for the axis. This compact representation, requiring as few as 14 float numbers, facilitates intuitive and interactive editing while preserving shape details effectively. Additionally, by introducing a differentiable neural sweeper and an encoder-decoder architecture, we demonstrate the ability to predict sweep surface representations without supervision. We show the superiority of our model through several quantitative and qualitative experiments throughout the paper. Our code is available at https://mingrui-zhao.github.io/SweepNet/

We study the task of panoptic symbol spotting, which involves identifying both individual instances of countable things and the semantic regions of uncountable stuff in computer-aided design (CAD) drawings composed of vector graphical primitives. Existing methods typically rely on image rasterization, graph construction, or point-based representation, but these approaches often suffer from high computational costs, limited generality, and loss of geometric structural information. In this paper, we propose VecFormer, a novel method that addresses these challenges through line-based representation of primitives. This design preserves the geometric continuity of the original primitive, enabling more accurate shape representation while maintaining a computation-friendly structure, making it well-suited for vector graphic understanding tasks. To further enhance prediction reliability, we introduce a Branch Fusion Refinement module that effectively integrates instance and semantic predictions, resolving their inconsistencies for more coherent panoptic outputs. Extensive experiments demonstrate that our method establishes a new state-of-the-art, achieving 91.1 PQ, with Stuff-PQ improved by 9.6 and 21.2 points over the second-best results under settings with and without prior information, respectively, highlighting the strong potential of line-based representation as a foundation for vector graphic understanding.

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.

A recent experiment has reported that body-centered cubic (bcc)-structured Ag is realized by bending face-centered cubic (fcc)-structured Ag nanowires [S. Sun {\it et al}., Phys. Rev. Lett. {\bf 128}, 015701 (2022)]. However, the bcc phase has been observed only near the Ag surface. Here, we explore how the bcc phase is stabilized near the surface by compressions. Our first-principles calculations for noble metals, Cu, Ag, and Au, indicate that body-centered tetragonal (bct) rather than bcc structure is preferred due to the surface effect. The bct-fcc boundary treated as a fixed boundary condition is necessary to thermodynamically stabilize the bct phase of Ag nanowire. The correlation between crystal structure and electron density-of-states is also discussed for three noble metals.

Native 3D generators now recover impressive mesh geometry from a single image. However, a dense mesh stays soft where a machined object should be sharp, it carries no part decomposition, and it exposes no parameter a user could edit. To address this, we explore the paradigm of 3D shape as code, leveraging and scaling the coding ability of an LLM for 3D modeling. We introduce Procedura, a novel 3D modeling agent framework that writes an object as a procedural assembly, a parametric program whose named parts are joined by typed, machine-checkable mates. From a text prompt, the agent plans the object as an assembly graph and writes the program part by part, solving each placement from the mated frames rather than guessing it, and admitting a part only once compile, mate, and connectivity checks pass. A decoupled vision critic then refines the assembly one diagnosed fix at a time. Moreover, the same graph carries per-part materials and a simulator-validated articulation. We evaluate on P3D-Bench under its assembly judge, and with the same judge on MechBench-36, our hard-surface benchmark. On both, Procedura outperforms state-of-the-art native 3D generators and every prior 3D-code agent on judged quality, produces the sharpest edges of any method we evaluate, and is the only one whose output is an editable, part-structured program.

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural representations. This mismatch leaves no suitable method to solve surface PDEs directly within the neural domain, forcing explicit mesh extraction or per-instance residual training, preventing end-to-end workflows. We present a novel, mesh-free formulation that learns a local update operator conditioned on neural (local) shape attributes, enabling surface PDEs to be solved directly where the (neural) data lives. The operator integrates naturally with prevalent neural surface representations, is trained once on a single representative shape, and generalizes across shape and topology variations, enabling accurate, fast inference without explicit meshing or per-instance optimization while preserving differentiability. Across analytic benchmarks (heat equation and Poisson solve on sphere) and real neural assets across different representations, our method slightly outperforms CPM while remaining reasonably close to FEM, and, to our knowledge, delivers the first end-to-end pipeline that solves surface PDEs on both neural and classical surface representations. Code will be released on acceptance.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

The task of synthesizing novel views from a single image has useful applications in virtual reality and mobile computing, and a number of approaches to the problem have been proposed in recent years. A Multiplane Image (MPI) estimates the scene as a stack of RGBA layers, and can model complex appearance effects, anti-alias depth errors and synthesize soft edges better than methods that use textured meshes or layered depth images. And unlike neural radiance fields, an MPI can be efficiently rendered on graphics hardware. However, MPIs are highly redundant and require a large number of depth layers to achieve plausible results. Based on the observation that the depth complexity in local image regions is lower than that over the entire image, we split an MPI into many small, tiled regions, each with only a few depth planes. We call this representation a Tiled Multiplane Image (TMPI). We propose a method for generating a TMPI with adaptive depth planes for single-view 3D photography in the wild. Our synthesized results are comparable to state-of-the-art single-view MPI methods while having lower computational overhead.

Manual modeling of material parameters and 3D geometry is a time consuming yet essential task in the gaming and film industries. While recent advances in 3D reconstruction have enabled accurate approximations of scene geometry and appearance, these methods often fall short in relighting scenarios due to the lack of precise, spatially varying material parameters. At the same time, diffusion models operating on 2D images have shown strong performance in predicting physically based rendering (PBR) properties such as albedo, roughness, and metallicity. However, transferring these 2D material maps onto reconstructed 3D geometry remains a significant challenge. We propose a framework for fusing 2D material data into 3D geometry using a combination of novel learning-based and projection-based approaches. We begin by reconstructing scene geometry via Gaussian Splatting. From the input images, a diffusion model generates 2D maps for albedo, roughness, and metallic parameters. Any existing diffusion model that can convert images or videos to PBR materials can be applied. The predictions are further integrated into the 3D representation either by optimizing an image-based loss or by directly projecting the material parameters onto the Gaussians using Gaussian ray tracing. To enhance fine-scale accuracy and multi-view consistency, we further introduce a light-weight neural refinement step (Neural Merger), which takes ray-traced material features as input and produces detailed adjustments. Our results demonstrate that the proposed methods outperform existing techniques in both quantitative metrics and perceived visual realism. This enables more accurate, relightable, and photorealistic renderings from reconstructed scenes, significantly improving the realism and efficiency of asset creation workflows in content production pipelines.

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 propose a method, named DualMesh-UDF, to extract a surface from unsigned distance functions (UDFs), encoded by neural networks, or neural UDFs. Neural UDFs are becoming increasingly popular for surface representation because of their versatility in presenting surfaces with arbitrary topologies, as opposed to the signed distance function that is limited to representing a closed surface. However, the applications of neural UDFs are hindered by the notorious difficulty in extracting the target surfaces they represent. Recent methods for surface extraction from a neural UDF suffer from significant geometric errors or topological artifacts due to two main difficulties: (1) A UDF does not exhibit sign changes; and (2) A neural UDF typically has substantial approximation errors. DualMesh-UDF addresses these two difficulties. Specifically, given a neural UDF encoding a target surface S to be recovered, we first estimate the tangent planes of S at a set of sample points close to S. Next, we organize these sample points into local clusters, and for each local cluster, solve a linear least squares problem to determine a final surface point. These surface points are then connected to create the output mesh surface, which approximates the target surface. The robust estimation of the tangent planes of the target surface and the subsequent minimization problem constitute our core strategy, which contributes to the favorable performance of DualMesh-UDF over other competing methods. To efficiently implement this strategy, we employ an adaptive Octree. Within this framework, we estimate the location of a surface point in each of the octree cells identified as containing part of the target surface. Extensive experiments show that our method outperforms existing methods in terms of surface reconstruction quality while maintaining comparable computational efficiency.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

Finite element simulations carried out on meshes issued from real-world geometries - patient-specific anatomies, scanned industrial parts, fractured media - almost never satisfy the shape-regularity assumptions under which classical a posteriori error analysis is written. Practitioners are therefore left without a quantitative answer to a very legitimate question: how wrong is my simulation when my mesh is coarse and contains badly shaped elements? In this work, we study to which extent equilibrated flux estimators can provide such an answer. Indeed, they deliver a guaranteed and fully computable upper bound of the energy-norm discretization error, with a constant equal to one; and, crucially for the present study, its derivation uses no shape-regularity, quasi-uniformity or angle condition. The only geometric ingredient is the Poincaré constant on a single cell, which Payne and Weinberger showed to be at most hK /pi on any convex cell K, however distorted (hK being the cell size). Mesh quality affects the local efficiency - the sharpness of the estimator - but never its reliability, so that the failure mode under distortion is pessimism rather than false confidence.

Computer-Aided Design (CAD) model reconstruction from point clouds is an important problem at the intersection of computer vision, graphics, and machine learning; it saves the designer significant time when iterating on in-the-wild objects. Recent advancements in this direction achieve relatively reliable semantic segmentation but still struggle to produce an adequate topology of the CAD model. In this work, we analyze the current state of the art for that ill-posed task and identify shortcomings of existing methods. We propose a hybrid analytic-neural reconstruction scheme that bridges the gap between segmented point clouds and structured CAD models and can be readily combined with different segmentation backbones. Moreover, to power the surface fitting stage, we propose a novel implicit neural representation of freeform surfaces, driving up the performance of our overall CAD reconstruction scheme. We extensively evaluate our method on the popular ABC benchmark of CAD models and set a new state-of-the-art for that dataset. Project page: https://www.obukhov.ai/point2cad}{https://www.obukhov.ai/point2cad.

We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling strategy. Additionally, by using an interpolated version of SelectionConv, we can operate on the sphere while using existing 2D CNNs and their weights. Since our method leverages existing graph implementations, it is also fast and can be fine-tuned efficiently. Our method is also general enough to be applied to any surface type, even those that are topologically non-simple. We demonstrate the effectiveness of our technique on the tasks of style transfer and segmentation for spheres as well as stylization for 3D meshes. We provide a thorough ablation study of the performance of various spherical sampling strategies.

Let λ_{mathbb K}(m) denote the maximal absolute projection constant among m-dimensional Banach spaces over mathbb K=mathbb R or mathbb C. Its exact value is known only in a few cases, and determining it remains a challenging problem. In this note, we investigate several structured vector configurations that naturally arise in this context. We first recall the connection between maximal projection constants and tight frames, then consider biangular tight frames, and show that their relative and quasimaximal projection constants coincide. A particularly interesting example is provided by the midpoints of the edges of a regular simplex, which yield natural lower bounds for λ_{mathbb R}(m). Numerical evidence suggests that these bounds may be sharp in dimensions 6 and 8. We also discuss weighted spherical (2,2)-designs with a small number of vectors and their connection with maximal projection constants. Examples in dimensions 4 and 5 indicate that the sign patterns of their Gram matrices may play an important role. These observations lead us to formulate several conjectures concerning maximal absolute projection constants and the vector configurations associated with them.

We address 2D floorplan reconstruction from 3D scans. Existing approaches typically employ heuristically designed multi-stage pipelines. Instead, we formulate floorplan reconstruction as a single-stage structured prediction task: find a variable-size set of polygons, which in turn are variable-length sequences of ordered vertices. To solve it we develop a novel Transformer architecture that generates polygons of multiple rooms in parallel, in a holistic manner without hand-crafted intermediate stages. The model features two-level queries for polygons and corners, and includes polygon matching to make the network end-to-end trainable. Our method achieves a new state-of-the-art for two challenging datasets, Structured3D and SceneCAD, along with significantly faster inference than previous methods. Moreover, it can readily be extended to predict additional information, i.e., semantic room types and architectural elements like doors and windows. Our code and models are available at: https://github.com/ywyue/RoomFormer.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly competitive baseline results from combining popular clustering algorithms with recent improvements in 3D geometry estimation. However, such purely geometric methods are understandably oblivious to plane semantics, which are crucial to discerning distinct planes. To overcome this limitation, we propose a method that predicts multi-view consistent plane embeddings that complement geometry when clustering points into planes. We show through extensive evaluation on the ScanNetV2 dataset that our new method outperforms existing approaches and our strong geometric baseline for the task of plane estimation.

In this paper, we propose Img2CAD, the first approach to our knowledge that uses 2D image inputs to generate CAD models with editable parameters. Unlike existing AI methods for 3D model generation using text or image inputs often rely on mesh-based representations, which are incompatible with CAD tools and lack editability and fine control, Img2CAD enables seamless integration between AI-based 3D reconstruction and CAD software. We have identified an innovative intermediate representation called Structured Visual Geometry (SVG), characterized by vectorized wireframes extracted from objects. This representation significantly enhances the performance of generating conditioned CAD models. Additionally, we introduce two new datasets to further support research in this area: ABC-mono, the largest known dataset comprising over 200,000 3D CAD models with rendered images, and KOCAD, the first dataset featuring real-world captured objects alongside their ground truth CAD models, supporting further research in conditioned CAD model generation.

Generating editable 3D CAD models from natural language remains challenging, as existing text-to-CAD systems either produce meshes or rely on scarce design-history data. We present NURBGen, the first framework to generate high-fidelity 3D CAD models directly from text using Non-Uniform Rational B-Splines (NURBS). To achieve this, we fine-tune a large language model (LLM) to translate free-form texts into JSON representations containing NURBS surface parameters (i.e, control points, knot vectors, degrees, and rational weights) which can be directly converted into BRep format using Python. We further propose a hybrid representation that combines untrimmed NURBS with analytic primitives to handle trimmed surfaces and degenerate regions more robustly, while reducing token complexity. Additionally, we introduce partABC, a curated subset of the ABC dataset consisting of individual CAD components, annotated with detailed captions using an automated annotation pipeline. NURBGen demonstrates strong performance on diverse prompts, surpassing prior methods in geometric fidelity and dimensional accuracy, as confirmed by expert evaluations. Code and dataset will be released publicly.

Recent advances in radiance field reconstruction, such as 3D Gaussian Splatting (3DGS), have achieved high-quality novel view synthesis and fast rendering by representing scenes with compositions of Gaussian primitives. However, 3D Gaussians present several limitations for scene reconstruction. Accurately capturing hard edges is challenging without significantly increasing the number of Gaussians, creating a large memory footprint. Moreover, they struggle to represent flat surfaces, as they are diffused in space. Without hand-crafted regularizers, they tend to disperse irregularly around the actual surface. To circumvent these issues, we introduce a novel method, named 3D Convex Splatting (3DCS), which leverages 3D smooth convexes as primitives for modeling geometrically-meaningful radiance fields from multi-view images. Smooth convex shapes offer greater flexibility than Gaussians, allowing for a better representation of 3D scenes with hard edges and dense volumes using fewer primitives. Powered by our efficient CUDA-based rasterizer, 3DCS achieves superior performance over 3DGS on benchmarks such as Mip-NeRF360, Tanks and Temples, and Deep Blending. Specifically, our method attains an improvement of up to 0.81 in PSNR and 0.026 in LPIPS compared to 3DGS while maintaining high rendering speeds and reducing the number of required primitives. Our results highlight the potential of 3D Convex Splatting to become the new standard for high-quality scene reconstruction and novel view synthesis. Project page: convexsplatting.github.io.

Meshes are fundamental representations of 3D surfaces. However, creating high-quality meshes is a labor-intensive task that requires significant time and expertise in 3D modeling. While a delicate object often requires over 10^4 faces to be accurately modeled, recent attempts at generating artist-like meshes are limited to 1.6K faces and heavy discretization of vertex coordinates. Hence, scaling both the maximum face count and vertex coordinate resolution is crucial to producing high-quality meshes of realistic, complex 3D objects. We present Meshtron, a novel autoregressive mesh generation model able to generate meshes with up to 64K faces at 1024-level coordinate resolution --over an order of magnitude higher face count and 8{times} higher coordinate resolution than current state-of-the-art methods. Meshtron's scalability is driven by four key components: (1) an hourglass neural architecture, (2) truncated sequence training, (3) sliding window inference, (4) a robust sampling strategy that enforces the order of mesh sequences. This results in over 50{%} less training memory, 2.5{times} faster throughput, and better consistency than existing works. Meshtron generates meshes of detailed, complex 3D objects at unprecedented levels of resolution and fidelity, closely resembling those created by professional artists, and opening the door to more realistic generation of detailed 3D assets for animation, gaming, and virtual environments.

Mesh quality assessment (MQA) models play a critical role in the design, optimization, and evaluation of mesh operation systems in a wide variety of applications. Current MQA models, whether model-based methods using topology-aware features or projection-based approaches working on rendered 2D projections, often fail to capture the intricate interactions between texture and 3D geometry. We introduce HybridMQA, a first-of-its-kind hybrid full-reference colored MQA framework that integrates model-based and projection-based approaches, capturing complex interactions between textural information and 3D structures for enriched quality representations. Our method employs graph learning to extract detailed 3D representations, which are then projected to 2D using a novel feature rendering process that precisely aligns them with colored projections. This enables the exploration of geometry-texture interactions via cross-attention, producing comprehensive mesh quality representations. Extensive experiments demonstrate HybridMQA's superior performance across diverse datasets, highlighting its ability to effectively leverage geometry-texture interactions for a thorough understanding of mesh quality. Our implementation will be made publicly available.

While surface-based view synthesis algorithms are appealing due to their low computational requirements, they often struggle to reproduce thin structures. In contrast, more expensive methods that model the scene's geometry as a volumetric density field (e.g. NeRF) excel at reconstructing fine geometric detail. However, density fields often represent geometry in a "fuzzy" manner, which hinders exact localization of the surface. In this work, we modify density fields to encourage them to converge towards surfaces, without compromising their ability to reconstruct thin structures. First, we employ a discrete opacity grid representation instead of a continuous density field, which allows opacity values to discontinuously transition from zero to one at the surface. Second, we anti-alias by casting multiple rays per pixel, which allows occlusion boundaries and subpixel structures to be modelled without using semi-transparent voxels. Third, we minimize the binary entropy of the opacity values, which facilitates the extraction of surface geometry by encouraging opacity values to binarize towards the end of training. Lastly, we develop a fusion-based meshing strategy followed by mesh simplification and appearance model fitting. The compact meshes produced by our model can be rendered in real-time on mobile devices and achieve significantly higher view synthesis quality compared to existing mesh-based approaches.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

Networks of atom-centered coordination octahedra commonly occur in inorganic and hybrid solid-state materials. Characterizing their spatial arrangements and characteristics is crucial for relating structures to properties for many materials families. The traditional method using case-by-case inspection becomes prohibitive for discovering trends and similarities in large datasets. Here, we operationalize chemical intuition to automate the geometric parsing, quantification, and classification of coordination octahedral networks. We find axis-resolved tilting trends in ABO_{3} perovskite polymorphs, which assist in detecting oxidation state changes. Moreover, we develop a scale-invariant encoding scheme to represent these networks, which, combined with human-assisted unsupervised machine learning, allows us to taxonomize the inorganic framework polytypes in hybrid iodoplumbates (A_xPb_yI_z). Consequently, we uncover a violation of Pauling's third rule and the design principles underpinning their topological diversity. Our results offer a glimpse into the vast design space of atomic octahedral networks and inform high-throughput, targeted screening of specific structure types.

We present Hunyuan3D 2.0, an advanced large-scale 3D synthesis system for generating high-resolution textured 3D assets. This system includes two foundation components: a large-scale shape generation model -- Hunyuan3D-DiT, and a large-scale texture synthesis model -- Hunyuan3D-Paint. The shape generative model, built on a scalable flow-based diffusion transformer, aims to create geometry that properly aligns with a given condition image, laying a solid foundation for downstream applications. The texture synthesis model, benefiting from strong geometric and diffusion priors, produces high-resolution and vibrant texture maps for either generated or hand-crafted meshes. Furthermore, we build Hunyuan3D-Studio -- a versatile, user-friendly production platform that simplifies the re-creation process of 3D assets. It allows both professional and amateur users to manipulate or even animate their meshes efficiently. We systematically evaluate our models, showing that Hunyuan3D 2.0 outperforms previous state-of-the-art models, including the open-source models and closed-source models in geometry details, condition alignment, texture quality, and etc. Hunyuan3D 2.0 is publicly released in order to fill the gaps in the open-source 3D community for large-scale foundation generative models. The code and pre-trained weights of our models are available at: https://github.com/Tencent/Hunyuan3D-2

The study of twisted two-dimensional (2D) materials, where twisting layers create moiré superlattices, has opened new opportunities for investigating topological phases and strongly correlated physics. While systems such as twisted bilayer graphene (TBG) and twisted transition metal dichalcogenides (TMDs) have been extensively studied, the broader potential of a seemingly infinite set of other twistable 2D materials remains largely unexplored. In this paper, we define "theoretically twistable materials" as single- or multi-layer structures that allow for the construction of simple continuum models of their moiré structures. This excludes, for example, materials with a "spaghetti" of bands or those with numerous crossing points at the Fermi level, for which theoretical moiré modeling is unfeasible. We present a high-throughput algorithm that systematically searches for theoretically twistable semimetals and insulators based on the Topological 2D Materials Database. By analyzing key electronic properties, we identify thousands of new candidate materials that could host rich topological and strongly correlated phenomena when twisted. We propose representative twistable materials for realizing different types of moiré systems, including materials with different Bravais lattices, valleys, and strength of spin-orbital coupling. We provide examples of crystal growth for several of these materials and showcase twisted bilayer band structures along with simplified twisted continuum models. Our results significantly broaden the scope of moiré heterostructures and provide a valuable resource for future experimental and theoretical studies on novel moiré systems.

LLM-based agents are increasingly capable of generating complex 3D structures, with the potential to reshape how objects are designed and realized in the physical world. Yet, producing elegant geometry is fundamentally different from producing objects that can be built and perform their intended functions. Existing evaluations largely focus on geometric quality while overlooking physical realizability. We introduce LMBuild, a benchmark for evaluating LLM agents on generating buildable and functional structures. LMBuild represents generated objects as assembled structures comprising part decompositions, joints, materials, and sequences. To support reproducible evaluation, we provide a unified framework consisting of: (1) an interactive environment in which agents can use tools to retrieve, create, and place components to construct objects; (2) a curated benchmark that repurposes established CAD datasets and augments them with knowledge from Wikipedia; and (3) a evaluation framework covering structural soundness, functional affordance, design quality, and physical realization. Evaluations across 30 systems reveal several intriguing findings: (a) Soundness and alignment are no longer the primary bottlenecks for frontier closed-source models, while functional affordance and physical operability remain substantially more challenging; (b) stronger models more effectively create new components, whereas weaker models tend to rely on retrieval; and (c) providing functional specifications substantially improves part completeness, kinematics, and physical operability. These results show that generating real-world structures requires deeper reasoning about functional affordances, mechanics, and designing and creating novel components. We expect LMBuild to provide a foundation for measuring progress and incentivizing research toward agents that generate buildable and functional structures.

Representing and rendering dynamic scenes has been an important but challenging task. Especially, to accurately model complex motions, high efficiency is usually hard to maintain. We introduce the 4D Gaussian Splatting (4D-GS) to achieve real-time dynamic scene rendering while also enjoying high training and storage efficiency. An efficient deformation field is constructed to model both Gaussian motions and shape deformations. Different adjacent Gaussians are connected via a HexPlane to produce more accurate position and shape deformations. Our 4D-GS method achieves real-time rendering under high resolutions, 70 FPS at a 800times800 resolution on an RTX 3090 GPU, while maintaining comparable or higher quality than previous state-of-the-art methods. More demos and code are available at https://guanjunwu.github.io/4dgs/.

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.

We present MeshSegmenter, a simple yet effective framework designed for zero-shot 3D semantic segmentation. This model successfully extends the powerful capabilities of 2D segmentation models to 3D meshes, delivering accurate 3D segmentation across diverse meshes and segment descriptions. Specifically, our model leverages the Segment Anything Model (SAM) model to segment the target regions from images rendered from the 3D shape. In light of the importance of the texture for segmentation, we also leverage the pretrained stable diffusion model to generate images with textures from 3D shape, and leverage SAM to segment the target regions from images with textures. Textures supplement the shape for segmentation and facilitate accurate 3D segmentation even in geometrically non-prominent areas, such as segmenting a car door within a car mesh. To achieve the 3D segments, we render 2D images from different views and conduct segmentation for both textured and untextured images. Lastly, we develop a multi-view revoting scheme that integrates 2D segmentation results and confidence scores from various views onto the 3D mesh, ensuring the 3D consistency of segmentation results and eliminating inaccuracies from specific perspectives. Through these innovations, MeshSegmenter offers stable and reliable 3D segmentation results both quantitatively and qualitatively, highlighting its potential as a transformative tool in the field of 3D zero-shot segmentation. The code is available at https://github.com/zimingzhong/MeshSegmenter.

Illuminating the surface of a convex body with parallel beams of light in a given direction generates a shadow region. We prove sharp regularity results for the boundary of this shadow in every direction of illumination. Moreover, techniques are developed for investigating the regularity of the region generated by orthogonally projecting a convex set onto another. As an application we study the geometry and Hausdorff dimension of the singular set corresponding to a Monge-Ampere equation.

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased, perceptually distorted surfaces and lack scalability to high-resolution 3D shapes. We present a data-driven approach for automatic feature detection and remeshing that requires only a coarse, aliased mesh as input and scales to arbitrary resolution reconstructions. We define and learn a collection of surface-based fields to (1) capture sharp geometric features in the shape with an implicit vertexwise model and (2) approximate improvements in normals alignment obtained by applying edge-flips with an edgewise model. To support scaling to arbitrary complexity shapes, we learn our fields using local triangulated patches, fusing estimates on complete surface meshes. Our feature remeshing algorithm integrates the learned fields as sharp feature priors and optimizes vertex placement and mesh connectivity for maximum expected surface improvement. On a challenging collection of high-resolution shape reconstructions in the ABC dataset, our algorithm improves over state-of-the-art by 26% normals F-score and 42% perceptual RMSE_{v}.

We propose a novel point-based representation, Gaussian surfels, to combine the advantages of the flexible optimization procedure in 3D Gaussian points and the surface alignment property of surfels. This is achieved by directly setting the z-scale of 3D Gaussian points to 0, effectively flattening the original 3D ellipsoid into a 2D ellipse. Such a design provides clear guidance to the optimizer. By treating the local z-axis as the normal direction, it greatly improves optimization stability and surface alignment. While the derivatives to the local z-axis computed from the covariance matrix are zero in this setting, we design a self-supervised normal-depth consistency loss to remedy this issue. Monocular normal priors and foreground masks are incorporated to enhance the quality of the reconstruction, mitigating issues related to highlights and background. We propose a volumetric cutting method to aggregate the information of Gaussian surfels so as to remove erroneous points in depth maps generated by alpha blending. Finally, we apply screened Poisson reconstruction method to the fused depth maps to extract the surface mesh. Experimental results show that our method demonstrates superior performance in surface reconstruction compared to state-of-the-art neural volume rendering and point-based rendering methods.

Computer-aided design (CAD) tools are utilized in the manufacturing industry for modeling everything from cups to spacecraft. These programs are complex to use and typically require years of training and experience to master. Structured and well-constrained 2D sketches and 3D constructions are crucial components of CAD modeling. A well-executed CAD model can be seamlessly integrated into the manufacturing process, thereby enhancing production efficiency. Deep generative models of 3D shapes and 3D object reconstruction models have garnered significant research interest. However, most of these models produce discrete forms of 3D objects that are not editable. Moreover, the few models based on CAD operations often have substantial input restrictions. In this work, we fine-tuned pre-trained models to create OpenECAD models (0.55B, 0.89B, 2.4B and 3.1B), leveraging the visual, logical, coding, and general capabilities of visual language models. OpenECAD models can process images of 3D designs as input and generate highly structured 2D sketches and 3D construction commands, ensuring that the designs are editable. These outputs can be directly used with existing CAD tools' APIs to generate project files. To train our network, we created a series of OpenECAD datasets. These datasets are derived from existing public CAD datasets, adjusted and augmented to meet the specific requirements of vision language model (VLM) training. Additionally, we have introduced an approach that utilizes dependency relationships to define and generate sketches, further enriching the content and functionality of the datasets.

Recent advances in synthetic methods enable designing subunits that self-assemble into structures with well-defined sizes and architectures, but yields are frequently suppressed by the formation of off-target metastable structures. Increasing the complexity (number of distinct inter-subunit interaction types) can inhibit off-target structures, but leads to slower kinetics and higher synthesis costs. Here, we use icosahedral shells formed of programmable triangular subunits as a model system, and identify design principles that produce the highest target yield at the lowest complexity. We use a symmetry-based construction to create a range of design complexities, starting from the maximal symmetry Caspar-Klug assembly up to the fully addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal that the most prominent defects leading to off-target assemblies are a class of disclinations. We derive symmetry-based rules for identifying the optimal (lowest-complexity, highest-symmetry) design that inhibits these disclinations, leading to robust, high-fidelity assembly of targets with arbitrarily large sizes. Optimal complexity varies non-monotonically with target size, with `magic' sizes appearing for high-symmetry designs in which symmetry axes do not intersect vertices of the triangular net. The optimal designs at magic sizes require 12 times fewer inequivalent interaction-types than the (minimal symmetry) fully addressable construction.

The recently discovered "hat" aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. We show that a close relative of the hat -- the equilateral member of the continuum to which it belongs -- is a weakly chiral aperiodic monotile: it admits only non-periodic tilings if we forbid reflections by fiat. Furthermore, by modifying this polygon's edges we obtain a family of shapes called Spectres that are strictly chiral aperiodic monotiles: they admit only chiral non-periodic tilings based on a hierarchical substitution system.

Neural radiance fields achieve unprecedented quality for novel view synthesis, but their volumetric formulation remains expensive, requiring a huge number of samples to render high-resolution images. Volumetric encodings are essential to represent fuzzy geometry such as foliage and hair, and they are well-suited for stochastic optimization. Yet, many scenes ultimately consist largely of solid surfaces which can be accurately rendered by a single sample per pixel. Based on this insight, we propose a neural radiance formulation that smoothly transitions between volumetric- and surface-based rendering, greatly accelerating rendering speed and even improving visual fidelity. Our method constructs an explicit mesh envelope which spatially bounds a neural volumetric representation. In solid regions, the envelope nearly converges to a surface and can often be rendered with a single sample. To this end, we generalize the NeuS formulation with a learned spatially-varying kernel size which encodes the spread of the density, fitting a wide kernel to volume-like regions and a tight kernel to surface-like regions. We then extract an explicit mesh of a narrow band around the surface, with width determined by the kernel size, and fine-tune the radiance field within this band. At inference time, we cast rays against the mesh and evaluate the radiance field only within the enclosed region, greatly reducing the number of samples required. Experiments show that our approach enables efficient rendering at very high fidelity. We also demonstrate that the extracted envelope enables downstream applications such as animation and simulation.

We present SplatFace, a novel Gaussian splatting framework designed for 3D human face reconstruction without reliance on accurate pre-determined geometry. Our method is designed to simultaneously deliver both high-quality novel view rendering and accurate 3D mesh reconstructions. We incorporate a generic 3D Morphable Model (3DMM) to provide a surface geometric structure, making it possible to reconstruct faces with a limited set of input images. We introduce a joint optimization strategy that refines both the Gaussians and the morphable surface through a synergistic non-rigid alignment process. A novel distance metric, splat-to-surface, is proposed to improve alignment by considering both the Gaussian position and covariance. The surface information is also utilized to incorporate a world-space densification process, resulting in superior reconstruction quality. Our experimental analysis demonstrates that the proposed method is competitive with both other Gaussian splatting techniques in novel view synthesis and other 3D reconstruction methods in producing 3D face meshes with high geometric precision.

Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is encoded not only via geometric primitives, but also by parameterized constraints between the elements. This relational specification can be viewed as the construction of a constraint program, allowing edits to coherently propagate to other parts of the design. Machine learning offers the intriguing possibility of accelerating the design process via generative modeling of these structures, enabling new tools such as autocompletion, constraint inference, and conditional synthesis. In this work, we present such an approach to generative modeling of parametric CAD sketches, which constitute the basic computational building blocks of modern mechanical design. Our model, trained on real-world designs from the SketchGraphs dataset, autoregressively synthesizes sketches as sequences of primitives, with initial coordinates, and constraints that reference back to the sampled primitives. As samples from the model match the constraint graph representation used in standard CAD software, they may be directly imported, solved, and edited according to downstream design tasks. In addition, we condition the model on various contexts, including partial sketches (primers) and images of hand-drawn sketches. Evaluation of the proposed approach demonstrates its ability to synthesize realistic CAD sketches and its potential to aid the mechanical design workflow.

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

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.

3D Gaussian Splatting techniques have enabled efficient photo-realistic rendering of static scenes. Recent works have extended these approaches to support surface reconstruction and tracking. However, tracking dynamic surfaces with 3D Gaussians remains challenging due to complex topology changes, such as surfaces appearing, disappearing, or splitting. To address these challenges, we propose GSTAR, a novel method that achieves photo-realistic rendering, accurate surface reconstruction, and reliable 3D tracking for general dynamic scenes with changing topology. Given multi-view captures as input, GSTAR binds Gaussians to mesh faces to represent dynamic objects. For surfaces with consistent topology, GSTAR maintains the mesh topology and tracks the meshes using Gaussians. In regions where topology changes, GSTAR adaptively unbinds Gaussians from the mesh, enabling accurate registration and the generation of new surfaces based on these optimized Gaussians. Additionally, we introduce a surface-based scene flow method that provides robust initialization for tracking between frames. Experiments demonstrate that our method effectively tracks and reconstructs dynamic surfaces, enabling a range of applications. Our project page with the code release is available at https://eth-ait.github.io/GSTAR/.

Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/.

In this paper, we present Surf-D, a novel method for generating high-quality 3D shapes as Surfaces with arbitrary topologies using Diffusion models. Specifically, we adopt Unsigned Distance Field (UDF) as the surface representation, as it excels in handling arbitrary topologies, enabling the generation of complex shapes. While the prior methods explored shape generation with different representations, they suffer from limited topologies and geometry details. Moreover, it's non-trivial to directly extend prior diffusion models to UDF because they lack spatial continuity due to the discrete volume structure. However, UDF requires accurate gradients for mesh extraction and learning. To tackle the issues, we first leverage a point-based auto-encoder to learn a compact latent space, which supports gradient querying for any input point through differentiation to effectively capture intricate geometry at a high resolution. Since the learning difficulty for various shapes can differ, a curriculum learning strategy is employed to efficiently embed various surfaces, enhancing the whole embedding process. With pretrained shape latent space, we employ a latent diffusion model to acquire the distribution of various shapes. Our approach demonstrates superior performance in shape generation across multiple modalities and conducts extensive experiments in unconditional generation, category conditional generation, 3D reconstruction from images, and text-to-shape tasks.

Subwavelength atomic lattices have emerged as a promising platform for quantum applications, leveraging collective superradiant and subradiant effects to enhance light-matter interactions. Integrating atomic lattices into nanostructures is at the front of effort toward any application with atomic lattices, but is still a challenging theoretical task, as the dipole interactions are hard to model in arbitrary dielectric environment. Here, we develop a formalism that allows the embedding of emitters to a wide class of thin curved waveguides, by greatly simplifying the wave equation and consequentially the dipole interactions. We demonstrate the formalism for locally constant positive curved surfaces, where we derive a new surface Green function that allows exact computation of the collective superradiant and subradiant states. We also show how the curvature and the thickness of the waveguides affects the collective states through an effective surface wavelength.

Recent methods for neural surface representation and rendering, for example NeuS, have demonstrated the remarkably high-quality reconstruction of static scenes. However, the training of NeuS takes an extremely long time (8 hours), which makes it almost impossible to apply them to dynamic scenes with thousands of frames. We propose a fast neural surface reconstruction approach, called NeuS2, which achieves two orders of magnitude improvement in terms of acceleration without compromising reconstruction quality. To accelerate the training process, we parameterize a neural surface representation by multi-resolution hash encodings and present a novel lightweight calculation of second-order derivatives tailored to our networks to leverage CUDA parallelism, achieving a factor two speed up. To further stabilize and expedite training, a progressive learning strategy is proposed to optimize multi-resolution hash encodings from coarse to fine. We extend our method for fast training of dynamic scenes, with a proposed incremental training strategy and a novel global transformation prediction component, which allow our method to handle challenging long sequences with large movements and deformations. Our experiments on various datasets demonstrate that NeuS2 significantly outperforms the state-of-the-arts in both surface reconstruction accuracy and training speed for both static and dynamic scenes. The code is available at our website: https://vcai.mpi-inf.mpg.de/projects/NeuS2/ .

Surface cutting is a fundamental task in computer graphics, with applications in UV parameterization, texture mapping, and mesh decomposition. However, existing methods often produce technically valid but overly fragmented atlases that lack semantic coherence. We introduce SeamGPT, an auto-regressive model that generates cutting seams by mimicking professional workflows. Our key technical innovation lies in formulating surface cutting as a next token prediction task: sample point clouds on mesh vertices and edges, encode them as shape conditions, and employ a GPT-style transformer to sequentially predict seam segments with quantized 3D coordinates. Our approach achieves exceptional performance on UV unwrapping benchmarks containing both manifold and non-manifold meshes, including artist-created, and 3D-scanned models. In addition, it enhances existing 3D segmentation tools by providing clean boundaries for part decomposition.

Representing 3D surfaces as level sets of continuous functions over R^3 is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision tasks. In order to represent 3D motion within this framework, it is often assumed (either explicitly or implicitly) that the transformations which a surface may undergo are homeomorphic: this is not necessarily true, for instance, in the case of fluid dynamics. In order to represent more general classes of deformations, we propose to apply this theoretical framework as regularizers for the optimization of simple 4D implicit functions (such as signed distance fields). We show that our representation is capable of capturing both homeomorphic and topology-changing deformations, while also defining correspondences over the continuously-reconstructed surfaces.

A large transverse thermoelectric response, known as anomalous Nernst effect (ANE) has been recently observed in several topological magnets. Building a thermopile employing this effect has been the subject of several recent propositions. Here, we design and build a thermopile with an array of tilted adjacent crystals of Mn_3Sn. The design employs a single material and replaces pairs of P and N thermocouples of the traditional design with hermaphroditic legs. The design exploits the large lag angle between the applied field and the magnetization, which we attribute to the interruption of magnetic octupoles at the edge of xy-plane. Eliminating extrinsic contacts between legs will boost the efficiency, simplify the process and pave the way for a new generation of thermopiles.

Texture modeling and synthesis are essential for enhancing the realism of virtual environments. Methods that directly synthesize textures in 3D offer distinct advantages to the UV-mapping-based methods as they can create seamless textures and align more closely with the ways textures form in nature. We propose Mesh Neural Cellular Automata (MeshNCA), a method that directly synthesizes dynamic textures on 3D meshes without requiring any UV maps. MeshNCA is a generalized type of cellular automata that can operate on a set of cells arranged on non-grid structures such as the vertices of a 3D mesh. MeshNCA accommodates multi-modal supervision and can be trained using different targets such as images, text prompts, and motion vector fields. Only trained on an Icosphere mesh, MeshNCA shows remarkable test-time generalization and can synthesize textures on unseen meshes in real time. We conduct qualitative and quantitative comparisons to demonstrate that MeshNCA outperforms other 3D texture synthesis methods in terms of generalization and producing high-quality textures. Moreover, we introduce a way of grafting trained MeshNCA instances, enabling interpolation between textures. MeshNCA allows several user interactions including texture density/orientation controls, grafting/regenerate brushes, and motion speed/direction controls. Finally, we implement the forward pass of our MeshNCA model using the WebGL shading language and showcase our trained models in an online interactive demo, which is accessible on personal computers and smartphones and is available at https://meshnca.github.io.

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.

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.

Computer-aided design (CAD) significantly enhances the efficiency, accuracy, and innovation of design processes by enabling precise 2D and 3D modeling, extensive analysis, and optimization. Existing methods for creating CAD models rely on latent vectors or point clouds, which are difficult to obtain and costly to store. Recent advances in Multimodal Large Language Models (MLLMs) have inspired researchers to use natural language instructions and images for CAD model construction. However, these models still struggle with inferring accurate 3D spatial location and orientation, leading to inaccuracies in determining the spatial 3D starting points and extrusion directions for constructing geometries. This work introduces CAD-GPT, a CAD synthesis method with spatial reasoning-enhanced MLLM that takes either a single image or a textual description as input. To achieve precise spatial inference, our approach introduces a 3D Modeling Spatial Mechanism. This method maps 3D spatial positions and 3D sketch plane rotation angles into a 1D linguistic feature space using a specialized spatial unfolding mechanism, while discretizing 2D sketch coordinates into an appropriate planar space to enable precise determination of spatial starting position, sketch orientation, and 2D sketch coordinate translations. Extensive experiments demonstrate that CAD-GPT consistently outperforms existing state-of-the-art methods in CAD model synthesis, both quantitatively and qualitatively.

Recent advances in radiance fields and novel view synthesis enable creation of realistic digital twins from photographs. However, current methods struggle with flat, texture-less surfaces, creating uneven and semi-transparent reconstructions, due to an ill-conditioned photometric reconstruction objective. Surface reconstruction methods solve this issue but sacrifice visual quality. We propose a novel hybrid 2D/3D representation that jointly optimizes constrained planar (2D) Gaussians for modeling flat surfaces and freeform (3D) Gaussians for the rest of the scene. Our end-to-end approach dynamically detects and refines planar regions, improving both visual fidelity and geometric accuracy. It achieves state-of-the-art depth estimation on ScanNet++ and ScanNetv2, and excels at mesh extraction without overfitting to a specific camera model, showing its effectiveness in producing high-quality reconstruction of indoor scenes.

Automated construction of surface geometries of cardiac structures from volumetric medical images is important for a number of clinical applications. While deep-learning-based approaches have demonstrated promising reconstruction precision, these approaches have mostly focused on voxel-wise segmentation followed by surface reconstruction and post-processing techniques. However, such approaches suffer from a number of limitations including disconnected regions or incorrect surface topology due to erroneous segmentation and stair-case artifacts due to limited segmentation resolution. We propose a novel deep-learning-based approach that directly predicts whole heart surface meshes from volumetric CT and MR image data. Our approach leverages a graph convolutional neural network to predict deformation on mesh vertices from a pre-defined mesh template to reconstruct multiple anatomical structures in a 3D image volume. Our method demonstrated promising performance of generating whole heart reconstructions with as good or better accuracy than prior deep-learning-based methods on both CT and MR data. Furthermore, by deforming a template mesh, our method can generate whole heart geometries with better anatomical consistency and produce high-resolution geometries from lower resolution input image data. Our method was also able to produce temporally consistent surface mesh predictions for heart motion from CT or MR cine sequences, and therefore can potentially be applied for efficiently constructing 4D whole heart dynamics. Our code and pre-trained networks are available at https://github.com/fkong7/MeshDeformNet

The twist-grain-boundary (TGB) phases, characterized by a periodic, helical arrangement of blocks made of polar smectic phases, SmAF and SmCF, have been discovered. They have been observed for rod-like molecules with a strong longitudinal dipole moment, featuring an (S)-2-methylbutyl end group having only weak twisting power, and emerge below the antiferroelectric SmAAF phase, where the lamellar structure is already well established. It is suggested that the structure is governed by electrostatic interactions amplified by weak chiral forces, in striking contrast to the mechanism of TGB phase formation found in non-polar materials. The TGB phases exhibit light selective reflection in the visible range, while the value of electric polarization confirms an almost perfectly ordered dipole alignment.

The Gaussian splatting for radiance field rendering method has recently emerged as an efficient approach for accurate scene representation. It optimizes the location, size, color, and shape of a cloud of 3D Gaussian elements to visually match, after projection, or splatting, a set of given images taken from various viewing directions. And yet, despite the proximity of Gaussian elements to the shape boundaries, direct surface reconstruction of objects in the scene is a challenge. We propose a novel approach for surface reconstruction from Gaussian splatting models. Rather than relying on the Gaussian elements' locations as a prior for surface reconstruction, we leverage the superior novel-view synthesis capabilities of 3DGS. To that end, we use the Gaussian splatting model to render pairs of stereo-calibrated novel views from which we extract depth profiles using a stereo matching method. We then combine the extracted RGB-D images into a geometrically consistent surface. The resulting reconstruction is more accurate and shows finer details when compared to other methods for surface reconstruction from Gaussian splatting models, while requiring significantly less compute time compared to other surface reconstruction methods. We performed extensive testing of the proposed method on in-the-wild scenes, taken by a smartphone, showcasing its superior reconstruction abilities. Additionally, we tested the proposed method on the Tanks and Temples benchmark, and it has surpassed the current leading method for surface reconstruction from Gaussian splatting models. Project page: https://gs2mesh.github.io/.

High fidelity 3D reconstruction and rendering hinge on capturing precise geometry while preserving photo realistic detail. Most existing methods either fuse these goals into a single cumbersome model or adopt hybrid schemes whose uniform primitives lead to a trade off between efficiency and fidelity. In this paper, we introduce HaloGS, a dual representation that loosely couples coarse triangles for geometry with Gaussian primitives for appearance, motivated by the lightweight classic geometry representations and their proven efficiency in real world applications. Our design yields a compact yet expressive model capable of photo realistic rendering across both indoor and outdoor environments, seamlessly adapting to varying levels of scene complexity. Experiments on multiple benchmark datasets demonstrate that our method yields both compact, accurate geometry and high fidelity renderings, especially in challenging scenarios where robust geometric structure make a clear difference.

Computer-Aided Design (CAD) relies on structured and editable geometric representations, yet existing generative methods are constrained by small annotated datasets with explicit design histories or boundary representation (BRep) labels. Meanwhile, millions of unannotated 3D meshes remain untapped, limiting progress in scalable CAD generation. To address this, we propose DreamCAD, a multi-modal generative framework that directly produces editable BReps from point-level supervision, without CAD-specific annotations. DreamCAD represents each BRep as a set of parametric patches (e.g., Bézier surfaces) and uses a differentiable tessellation method to generate meshes. This enables large-scale training on 3D datasets while reconstructing connected and editable surfaces. Furthermore, we introduce CADCap-1M, the largest CAD captioning dataset to date, with 1M+ descriptions generated using GPT-5 for advancing text-to-CAD research. DreamCAD achieves state-of-the-art performance on ABC and Objaverse benchmarks across text, image, and point modalities, improving geometric fidelity and surpassing 75% user preference. Code and dataset will be publicly available.

In the field of graphic design, automating the integration of design elements into a cohesive multi-layered artwork not only boosts productivity but also paves the way for the democratization of graphic design. One existing practice is Graphic Layout Generation (GLG), which aims to layout sequential design elements. It has been constrained by the necessity for a predefined correct sequence of layers, thus limiting creative potential and increasing user workload. In this paper, we present Hierarchical Layout Generation (HLG) as a more flexible and pragmatic setup, which creates graphic composition from unordered sets of design elements. To tackle the HLG task, we introduce Graphist, the first layout generation model based on large multimodal models. Graphist efficiently reframes the HLG as a sequence generation problem, utilizing RGB-A images as input, outputs a JSON draft protocol, indicating the coordinates, size, and order of each element. We develop new evaluation metrics for HLG. Graphist outperforms prior arts and establishes a strong baseline for this field. Project homepage: https://github.com/graphic-design-ai/graphist