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    Mint: Discretely Integrable Moments for Symmetric Frame Fields
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Vekhter, Josh; Chen, Zhen; Vouga, Etienne; Attene, Marco; Sellán, Silvia
    This paper studies the problem of unconstrained (e.g. not orthogonal or unit) symmetric frame field design in volumes. Our principal contribution is a novel (and theoretically well-founded) local integrability condition for frame fields represented as a triplet of symmetric tensors of second, fourth, and sixth order. We also formulate a novel smoothness energy for this representation. To validate our discritization, we study the problem of seamless parameterization of volumetric objects. We compare against baseline approaches by formulating a smooth, integrable, and approximately octahedral frame objective in our discritization. Our method is the first to solve these problems with automatic placement of singularities while also enforcing a symmetric proxy for local integrability as a hard constraint, achieving significantly higher quality parameterizations, in expectation, relative to other frame field design based approaches.
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    Symmetrized Poisson Reconstruction
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Kohlbrenner, Maximilian; Liu, Hongyi; Alexa, Marc; Kazhdan, Misha; Attene, Marco; Sellán, Silvia
    Many common approaches for reconstructing surfaces from point clouds leverage normal information to fit an implicit function to the points. Normals typically play two roles: the direction provides a planar approximation to the surface and the sign distinguishes inside from outside. When the sign is missing, reconstructing a surface with globally consistent sidedness is challenging. In this work, we investigate the idea of squaring the Poisson Surface Reconstruction, replacing the normals with their outer products, making the approach agnostic to the signs of the input/estimated normals. Squaring results in a quartic optimization problem, for which we develop an iterative and hierarchical solver, based on setting the cubic partial derivatives to zero. We show that this technique significantly outperforms standard L-BFGS solver and demonstrate reconstruction of surfaces from unoriented noisy input in linear time.
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    MDNF: Multi-Diffusion-Nets for Neural Fields on Meshes
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Rimon, Avigail Cohen; Shnitzer, Tal; Ben-Chen, Mirela; Attene, Marco; Sellán, Silvia
    We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial and frequency domains by associating finer spatial resolution levels with higher frequency bands, while coarser resolutions are mapped to lower frequencies. To achieve geometry-aware spatial decomposition we leverage multiple DiffusionNet components, each associated with a different spatial resolution level. Subsequently, we apply a Fourier feature mapping to encourage finer resolution levels to be associated with higher frequencies. The final signal is composed in a wavelet-inspired manner using a sine-activated MLP, aggregating higher-frequency signals on top of lower-frequency ones. Our architecture attains high accuracy in learning complex neural fields and is robust to discontinuities, exponential scale variations of the target field, and mesh modification. We demonstrate the effectiveness of our approach through its application to diverse neural fields, such as synthetic RGB functions, UV texture coordinates, and vertex normals, illustrating different challenges. To validate our method, we compare its performance against two alternatives, showcasing the advantages of our multi-resolution architecture.
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    Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Matching Algorithms
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Ehm, Viktoria; Amrani, Nafie El; Xie, Yizheng; Bastian, Lennart; Gao, Maolin; Wang, Weikang; Sang, Lu; Cao, Dongliang; Weißberg, Tobias; Lähner, Zorah; Cremers, Daniel; Bernard, Florian; Attene, Marco; Sellán, Silvia
    Finding correspondences between 3D deformable shapes is an important and long-standing problem in geometry processing, computer vision, graphics, and beyond. While various shape matching datasets exist, they are mostly static or limited in size, restricting their adaptation to different problem settings, including both full and partial shape matching. In particular the existing partial shape matching datasets are small (fewer than 100 shapes) and thus unsuitable for data-hungry machine learning approaches. Moreover, the type of partiality present in existing datasets is often artificial and far from realistic. To address these limitations, we introduce a generic and flexible framework for the procedural generation of challenging full and partial shape matching datasets. Our framework allows the propagation of custom annotations across shapes, making it useful for various applications. By utilising our framework and manually creating cross-dataset correspondences between seven existing (complete geometry) shape matching datasets, we propose a new large benchmark BeCoS with a total of 2543 shapes. Based on this, we offer several challenging benchmark settings, covering both full and partial matching, for which we evaluate respective state-of-the-art methods as baselines. Visualisations and code of our benchmark can be found at: https://nafieamrani.github.io/BeCoS/.
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    OctFusion: Octree-based Diffusion Models for 3D Shape Generation
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Xiong, Bojun; Wei, Si-Tong; Zheng, Xin-Yang; Cao, Yan-Pei; Lian, Zhouhui; Wang, Peng-Shuai; Attene, Marco; Sellán, Silvia
    Diffusion models have emerged as a popular method for 3D generation. However, it is still challenging for diffusion models to efficiently generate diverse and high-quality 3D shapes. In this paper, we introduce OctFusion, which can generate 3D shapes with arbitrary resolutions in 2.5 seconds on a single Nvidia 4090 GPU, and the extracted meshes are guaranteed to be continuous and manifold. The key components of OctFusion are the octree-based latent representation and the accompanying diffusion models. The representation combines the benefits of both implicit neural representations and explicit spatial octrees and is learned with an octree-based variational autoencoder. The proposed diffusion model is a unified multi-scale U-Net that enables weights and computation sharing across different octree levels and avoids the complexity of widely used cascaded diffusion schemes. We verify the effectiveness of OctFusion on the ShapeNet and Objaverse datasets and achieve state-of-the-art performances on shape generation tasks. We demonstrate that OctFusion is extendable and flexible by generating high-quality color fields for textured mesh generation and high-quality 3D shapes conditioned on text prompts, sketches, or category labels. Our code and pre-trained models are available at https://github.com/octree-nn/octfusion.
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    Robust Construction of Polycube Segmentations via Dual Loops
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Snoep, Maxim; Speckmann, Bettina; Verbeek, Kevin; Attene, Marco; Sellán, Silvia
    Polycube segmentations for 3D models effectively support a wide variety of applications such as seamless texture mapping, spline fitting, structured multi-block grid generation, and hexahedral mesh construction. However, the automated construction of valid polycube segmentations suffers from robustness issues: state-of-the-art methods are not guaranteed to find a valid solution. In this paper we present DualCube: an iterative algorithm which is guaranteed to return a valid polycube segmentation for 3D models of any genus. Our algorithm is based on a dual representation of polycubes. Starting from an initial simple polycube of the correct genus, together with the corresponding dual loop structure and polycube segmentation, we iteratively refine the polycube, loop structure, and segmentation, while maintaining the correctness of the solution. DualCube is robust by construction: at any point during the iterative process the current segmentation is valid. Its iterative nature furthermore facilitates a seamless trade-off between quality and complexity of the solution. DualCube can be implemented using comparatively simple algorithmic building blocks; our experimental evaluation establishes that the quality of our polycube segmentations is on par with, or exceeding, the state-of-the-art.
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    One-Shot Method for Computing Generalized Winding Numbers
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Martens, Cedric; Bessmeltsev, Mikhail; Attene, Marco; Sellán, Silvia
    The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to compute a generalized winding number, based only on the surface boundary and the intersections of a single ray with the surface, supporting any oriented surface representations that support a ray intersection query. Due to the focus on the boundary, our algorithm has a unique set of properties. For 2D parametric curves, on a regular grid of query points, our method is up to 4× faster than the current state of the art, maintaining the same precision. In 3D, our method can compute a winding number of a surface without discretizing it, including parametric surfaces. For some meshes with many triangles and a simple boundary, our method is faster than the hierarchical evaluation of the generalized winding number while still being precise. Similarly, on some parametric surfaces with a simple boundary, our method can be faster than adaptive quadrature. We validate our algorithms theoretically, numerically, and by demonstrating a gallery of results on a variety of parametric surfaces and meshes, as well uses in a variety of applications, including voxelizations and boolean operations.
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    Bayesian 3D Shape Reconstruction from Noisy Points and Normals
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Pujol, Eduard; Chica, Antonio; Attene, Marco; Sellán, Silvia
    Reconstructing three-dimensional shapes from point clouds remains a central challenge in geometry processing, particularly due to the inherent uncertainties in real-world data acquisition. In this work, we introduce a novel Bayesian framework that explicitly models and propagates uncertainty from both input points and their estimated normals. Our method incorporates the uncertainty of normals derived via Principal Component Analysis (PCA) from noisy input points. Building upon the Smooth Signed Distance (SSD) reconstruction algorithm, we integrate a smoothness prior based on the curvatures of the resulting implicit function following Gaussian behavior. Our method reconstructs a shape represented as a distribution, from which sampling and statistical queries regarding the shape's properties are possible. Additionally, because of the high cost of computing the variance of the resulting distribution, we develop efficient techniques for variance computation. Our approach thus combines two common steps of the geometry processing pipeline, normal estimation and surface reconstruction, while computing the uncertainty of the output of each of these steps.
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    Exact and Efficient Mesh-Kernel Generation
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) Nehring-Wirxel, Julius; Kern, Paul; Trettner, Philip; Kobbelt, Leif; Attene, Marco; Sellán, Silvia
    The mesh kernel for a star-shaped mesh is a convex polyhedron given by the intersection of all half-spaces defined by the faces of the input mesh. For all non-star-shaped meshes, the kernel is empty. We present a method to robustly and efficiently compute the kernel of an input triangle mesh by using exact plane-based integer arithmetic to compute the mesh kernel. We make use of several ways to accelerate the computation time. Since many applications just require information if a non-empty mesh kernel exists, we also propose a method to efficiently determine whether a kernel exists by developing an exact plane-based linear program solver. We evaluate our method on a large dataset of triangle meshes and show that in contrast to previous methods, our approach is exact and robust while maintaining a high performance. It is on average two orders of magnitude faster than other exact state-of-the-art methods and often about one order of magnitude faster than non-exact methods.
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    An Efficient Global-to-Local Rotation Optimization Approach via Spherical Harmonics
    (The Eurographics Association and John Wiley & Sons Ltd., 2025) He, Zihang; Yang, Yuezhi; Deng, Congyue; Lu, Jiaxin; Guibas, Leonidas; Huang, Qixing; Attene, Marco; Sellán, Silvia
    This paper studies the classical problem of 3D shape alignment, namely computing the relative rotation between two shapes (centered at the origin and normalized by scale) by aligning spherical harmonic coefficients of their spherical function representations. Unlike most prior work, which focuses on the regime in which the inputs have approximately the same shape, we focus on the more general and challenging setting in which the shapes may differ. Central to our approach is a stability analysis of spherical harmonic coefficients, which sheds light on how to align them for robust rotation estimation. We observe that due to symmetries, certain spherical harmonic coefficients may vanish. As a result, using a robust norm for alignment that automatically discards such coefficients offers more accurate rotation estimates than the widely used L2 norm. To enable efficient continuous optimization, we show how to analytically compute the Jacobian of spherical harmonic coefficients with respect to rotations. We also introduce an efficient approach for rotation initialization that requires only a sparse set of rotation samples. Experimental results show that our approach achieves better accuracy and efficiency compared to baseline approaches.