44-Issue 5

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https://diglib.eg.org/handle/10.2312/3607200

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The Affine Heat Method
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Soliman, Yousuf; Sharp, Nicholas; Attene, Marco; Sellán, Silvia
This work presents the Affine Heat Method for computing logarithmic maps. These maps are local surface parameterizations defined by the direction and distance along shortest geodesic paths from a given source point, and arise in many geometric tasks from local texture mapping to geodesic distance-based optimization. Our main insight is to define a connection Laplacian with a homogeneous coordinate accounting for the translation between tangent coordinate frames; the action of short-time heat flow under this Laplacian gives both the direction and distance from the source, along shortest geodesics. The resulting numerical method is straightforward to implement, fast, and improves accuracy compared to past approaches. We present two variants of the method, one of which enables pre-computation for fast repeated solves, while the other resolves the map even near the cut locus in high detail. As with prior heat methods, our approach can be applied in any dimension and to any spatial discretization, including polygonal meshes and point clouds, which we demonstrate along with applications of the method.
Anisotropic Gauss Reconstruction and Global Orientation with Octree-based Acceleration
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Ma, Yueji; Shen, Jialu; Meng, Yanzun; Xiao, Dong; Shi, Zuoqiang; Wang, Bin; Attene, Marco; Sellán, Silvia
Unoriented surface reconstruction is an important task in computer graphics. Recently, methods based on the Gauss formula or winding number have achieved state-of-the-art performance in both orientation and surface reconstruction. The Gauss formula or winding number, derived from the fundamental solution of the Laplace equation, initially found applications in calculating potentials in electromagnetism. Inspired by the practical necessity of calculating potentials in diverse electromagnetic media, we consider the anisotropic Laplace equation to derive the anisotropic Gauss formula and apply it to surface reconstruction, called ''anisotropic Gauss reconstruction''. By leveraging the flexibility of anisotropic coefficients, additional constraints can be introduced to the indicator function. This results in a stable linear system, eliminating the need for any artificial regularization. In addition, the oriented normals can be refined by computing the gradient of the indicator function, ultimately producing high-quality normals and surfaces. Regarding the space/time complexity, we propose an octree-based acceleration algorithm to achieve a space complexity of O(N) and a time complexity of O(NlogN). Our method can reconstruct ultra-large-scale models (exceeding 5 million points) within 4 minutes on an NVIDIA RTX 4090 GPU. Extensive experiments demonstrate that our method achieves state-of-the-art performance in both orientation and reconstruction, particularly for models with thin structures, small holes, or high genus. Both CuPy-based and CUDA-accelerated implementations are made publicly available at https://github.com/mayueji/AGR.
Arrange and Traverse Algorithm for Computation of Reeb Spaces of Piecewise Linear Maps
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Hristov, Petar; Sakurai, Daisuke; Carr, Hamish; Hotz, Ingrid; Masood, Talha Bin; Attene, Marco; Sellán, Silvia
We present the first combinatorial algorithm for efficiently computing the Reeb space in all dimensions. The Reeb space is a higher-dimensional generalization of the Reeb graph, which is standard practice in the analysis of scalar fields, along with other computational topology tools such as persistent homology and the Morse-Smale complex. One significant limitation of topological tools for scalar fields is that data often involves multiple variables, where joint analysis is more insightful. Generalizing topological data structures to multivariate data has proven challenging and the Reeb space is one of the few available options. However, none of the existing algorithms can efficiently compute the Reeb space in arbitrary dimensions and there are no available implementations which are robust with respect to numerical errors. We propose a new algorithm for computing the Reeb space of a generic piecewise linear map over a simplicial mesh of any dimension called arrange and traverse. We implement a robust specialization of our algorithm for tetrahedral meshes and evaluate it on real-life data.
Atomizer: Beyond Non-Planar Slicing for Fused Filament Fabrication
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Chermain, Xavier; Cocco, Giovanni; Zanni, Cédric; Garner, Eric; Hugron, Pierre-Alexandre; Lefebvre, Sylvain; Attene, Marco; Sellán, Silvia
Fused filament fabrication (FFF) enables users to quickly design and fabricate parts with unprecedented geometric complexity, fine-tuning both the structural and aesthetic properties of each object. Nevertheless, the full potential of this technology has yet to be realized, as current slicing methods fail to fully exploit the deposition freedom offered by modern 3D printers. In this work, we introduce a novel approach to toolpath generation that moves beyond the traditional layer-based concept. We use frames, referred to as atoms, as solid elements instead of slices. We optimize the distribution of atoms within the part volume to ensure even spacing and smooth orientation while accurately capturing the part's geometry. Although these atoms collectively represent the complete object, they do not inherently define a fabrication plan. To address this, we compute an extrusion toolpath as an ordered sequence of atoms that, when followed, provides a collision-free fabrication strategy. This general approach is robust, requires minimal user intervention compared to existing techniques, and integrates many of the best features into a unified framework: precise deposition conforming to non-planar surfaces, effective filling of narrow features - down to a single path - and the capability to locally print vertical structures before transitioning elsewhere. Additionally, it enables entirely new capabilities, such as anisotropic appearance fabrication on curved surfaces.
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.
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/.
Controlling Quadric Error Simplification with Line Quadrics
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Liu, Hsueh-Ti Derek; Rahimzadeh, Mehdi; Zordan, Victor; Attene, Marco; Sellán, Silvia
This work presents a method to control the output of mesh simplification algorithms based on iterative edge collapses. Traditional mesh simplification focuses on preserving the visual appearance. Despite still being an important criterion, other geometric properties also play critical roles in different applications, such as triangle quality for computations. This motivates our work to stay under the umbrella of the popular quadric error mesh simplification, while proposing different ways to control the simplified mesh to possess other geometric properties. The key ingredient of our work is another quadric error, called line quadrics, which can be seamlessly added to the vanilla quadric error metric. We show that, theoretically and empirically, adding our line quadrics can improve the numerics and encourage the simplified mesh to have uniformly distributed vertices. If we spread the line quadric adaptively to different regions, it can easily lead to soft preservation of feature vertices and edges. Our method is simple to implement, requiring only a few lines of code change on top of the original quadric error simplification, and can lead to a variety of user controls.
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.
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.
FRIDU: Functional Map Refinement with Guided Image Diffusion
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Rimon, Avigail Cohen; Ben-Chen, Mirela; Litany, Or; Attene, Marco; Sellán, Silvia
We propose a novel approach for refining a given correspondence map between two shapes. A correspondence map represented as a functional map, namely a change of basis matrix, can be additionally treated as a 2D image. With this perspective, we train an image diffusion model directly in the space of functional maps, enabling it to generate accurate maps conditioned on an inaccurate initial map. The training is done purely in the functional space, and thus is highly efficient. At inference time, we use the pointwise map corresponding to the current functional map as guidance during the diffusion process. The guidance can additionally encourage different functional map objectives, such as orthogonality and commutativity with the Laplace-Beltrami operator. We show that our approach is competitive with state-of-the-art methods of map refinement and that guided diffusion models provide a promising pathway to functional map processing.
GreenCloud: Volumetric Gradient Filtering via Regularized Green's Functions
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Tojo, Kenji; Umetani, Nobuyuki; Attene, Marco; Sellán, Silvia
Gradient-based optimization is a fundamental tool in geometry processing, but it is often hampered by geometric distortion arising from noisy or sparse gradients. Existing methods mitigate these issues by filtering (i.e., diffusing) gradients over a surface mesh, but they require explicit mesh connectivity and solving large linear systems, making them unsuitable for point-based representation. In this work, we introduce a gradient filtering method tailored for point-based geometry. Our method bypasses explicit connectivity by leveraging regularized Green's functions to directly compute the filtered gradient field from discrete spatial points. Additionally, our approach incorporates elastic deformation based on Green's function of linear elasticity (known as Kelvinlets), reproducing various elastic behaviors such as smoothness and volume preservation while improving robustness in affine transformations. We further accelerate computation using a hierarchical Barnes-Hut style approximation, enabling scalable optimization of one million points. Our method significantly improves convergence across a wide range of applications, including reconstruction, editing, stylization, and simplified optimization experiments with Gaussian splatting.
High-Resolution 3D Shape Matching with Global Optimality and Geometric Consistency
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Amrani, Nafie El; Roetzer, Paul; Bernard, Florian; Attene, Marco; Sellán, Silvia
3D shape matching plays a fundamental role in applications such as texture transfer and 3D animation. A key requirement for many scenarios is that matchings exhibit geometric consistency, which ensures that matchings preserve neighbourhood relations across shapes. Despite the importance of geometric consistency, few existing methods explicitly address it, and those that do are either local optimisation methods requiring accurate initialisation, or are severely limited in terms of shape resolution, handling shapes with only up to 3,000 triangles. In this work, we present a scalable approach for geometrically consistent 3D shape matching that, for the first time, scales to high-resolution meshes with up to 10,000 triangles. Our method follows a two-stage procedure: (i) we compute a globally optimal and geometrically consistent mapping of surface patches on the source shape to the target shape via a novel integer linear programming formulation. (ii) we find geometrically consistent matchings of corresponding surface patches which respect correspondences of boundaries of patches obtained from stage (i). With this, we obtain dense, smooth, and guaranteed geometrically consistent correspondences between high-resolution shapes. Empirical evaluations demonstrate that our method is scalable and produces highquality, geometrically consistent correspondences across a wide range of challenging shapes. Our code is publicly available: https://github.com/NafieAmrani/SuPa-Match.
Im2SurfTex: Surface Texture Generation via Neural Backprojection of Multi-View Images
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Georgiou, Yiangos; Loizou, Marios; Averkiou, Melinos; Kalogerakis, Evangelos; Attene, Marco; Sellán, Silvia
We present Im2SurfTex, a method that generates textures for input 3D shapes by learning to aggregate multi-view image outputs produced by 2D image diffusion models onto the shapes' texture space. Unlike existing texture generation techniques that use ad hoc backprojection and averaging schemes to blend multiview images into textures, often resulting in texture seams and artifacts, our approach employs a trained neural module to boost texture coherency. The key ingredient of our module is to leverage neural attention and appropriate positional encodings of image pixels based on their corresponding 3D point positions, normals, and surface-aware coordinates as encoded in geodesic distances within surface patches. These encodings capture texture correlations between neighboring surface points, ensuring better texture continuity. Experimental results show that our module improves texture quality, achieving superior performance in high-resolution texture generation.
MatAIRials: Isotropic Inflatable Metamaterials for Freeform Surface Design
(The Eurographics Association and John Wiley & Sons Ltd., 2025) He, Siyuan; Wu, Meng-Jan; Lebée, Arthur; Skouras, Mélina; Attene, Marco; Sellán, Silvia
Inflatable pads, such as those used as mattresses or protective equipment, are structures made of two planar membranes sealed according to periodic patterns, typically parallel lines or dots. In this work, we propose to treat these inflatables as metamaterials. By considering novel sealing patterns with 6-fold symmetry, we are able to generate a family of inflatable materials whose macroscale contraction is isotropic and can be modulated by controlling the parameters of the seals. We leverage this property of our inflatable materials family to propose a simple and effective algorithm based on conformal mapping that allows us to design the layout of inflatable structures that can be fabricated flat and whose inflated shapes approximate those of given target freeform surfaces.
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.
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.
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.
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.
Real-Time Secondary Animation with Spring Decomposed Skinning
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Akyürek, Bartu; Sahillioglu, Yusuf; Attene, Marco; Sellán, Silvia
We present a framework to integrate secondary motion into the existing animation pipelines. Skinning provides fast computation for real-time animation and intuitive control over the deformation. Despite the benefits, traditional skinning methods lack secondary dynamics such as the jiggling of fat tissues. We address the rigidity of skinning methods by physically simulating the deformation handles with spring forces. Most studies introduce secondary motion into skinning by employing FEM simulation on volumetric mesh vertices, coupling their computational complexity with mesh resolution. Unlike these approaches, we do not require any volumetric mesh input. Our method scales to higher mesh resolutions by directly simulating deformation handles. The simulated handles, namely the spring bones, enrich rigid skinning deformation with a diverse range of secondary animation for subjects including rigid bodies, elastic bodies, soft tissues, and cloth simulation. In essence, we leverage the benefits of physical simulations in the scope of deformation handles to achieve controllable real-time dynamics on a wide range of subjects while remaining compatible with existing skinning pipelines. Our method avoids tetrahedral remeshing and it is significantly faster compared to FEM-based volumetric mesh simulations.
Representing Animatable Avatar via Factorized Neural Fields
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Song, Chunjin; Wu, Zhijie; Wandt, Bastian; Sigal, Leonid; Rhodin, Helge; Attene, Marco; Sellán, Silvia
For reconstructing high-fidelity human 3D models from monocular videos, it is crucial to maintain consistent large-scale body shapes along with finely matched subtle wrinkles. This paper explores how per-frame rendering results can be factorized into a pose-independent component and a corresponding pose-dependent counterpart to facilitate frame consistency at multiple scales. Pose adaptive texture features are further improved by restricting the frequency bands of these two components. Pose-independent outputs are expected to be low-frequency, while high-frequency information is linked to pose-dependent factors. We implement this with a dual-branch network. The first branch takes coordinates in the canonical space as input, while the second one additionally considers features outputted by the first branch and pose information of each frame. A final network integrates the information predicted by both branches and utilizes volume rendering to generate photo-realistic 3D human images. Through experiments, we demonstrate that our method consistently surpasses all state-of-the-art methods in preserving high-frequency details and ensuring consistent body contours. Our code is accessible at https://github.com/ChunjinSong/facavatar.

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