SGP25: Eurographics Symposium on Geometry Processing (CGF 44-5)

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https://diglib.eg.org/handle/10.2312/3607286

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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.
SGP 2025 CGF 44-5: Frontmatter
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Attene, Marco; Sellán, Silvia; Attene, Marco; Sellán, Silvia
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.
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.
Volume Preserving Neural Shape Morphing
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Buonomo, Camille; Digne, Julie; Chaine, Raphaelle; Attene, Marco; Sellán, Silvia
Shape interpolation is a long standing challenge of geometry processing. As it is ill-posed, shape interpolation methods always work under some hypothesis such as semantic part matching or least displacement. Among such constraints, volume preservation is one of the traditional animation principles. In this paper we propose a method to interpolate between shapes in arbitrary poses favoring volume and topology preservation. To do so, we rely on a level set representation of the shape and its advection by a velocity field through the level set equation, both shape representation and velocity fields being parameterized as neural networks. While divergence free velocity fields ensure volume and topology preservation, they are incompatible with the Eikonal constraint of signed distance functions. This leads us to introduce the notion of adaptive divergence velocity field, a construction compatible with the Eikonal equation with theoretical guarantee on the shape volume preservation. In the non constant volume setting, our method is still helpful to provide a natural morphing, by combining it with a parameterization of the volume change over time. We show experimentally that our method exhibits better volume preservation than other recent approaches, limits topological changes and preserves the structures of shapes better without landmark correspondences.
Shape Approximation by Surface Reuse
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Baas, Berend; Bommes, David; Bousseau, Adrien; Attene, Marco; Sellán, Silvia
The manufacturing industry faces an urgent need to transition from the linear ''make-take-use-dispose'' production model towards more sustainable circular models that retain resources in the production chain. Motivated by this need, we introduce the new problem of approximating 3D surfaces by reusing panels from other surfaces. We present an algorithm that takes as input one or several existing shapes and relies on partial shape registration to identify a small set of simple panels that, once cut from the existing shapes and transformed rigidly, approximate a target shape within a user-defined distance threshold. As a proof of concept, we demonstrate our algorithm in the context of rapid prototyping, where we harvest curved panels from plastic bottles and assemble them with custom connectors to fabricate medium-size freeform structures.
Uniform Sampling of Surfaces by Casting Rays
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Ling, Selena; Madan, Abhishek; Sharp, Nicholas; Jacobson, Alec; Attene, Marco; Sellán, Silvia
Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used implicit surfaces. This work studies a simple and general scheme for sampling points on a surface, which is derived from a connection to the intersections of random rays with the surface. Concretely, given a subroutine to cast a ray against a surface and find all intersections, we can use that subroutine to uniformly sample white noise points on the surface. This approach is particularly effective in the context of implicit signed distance functions, where sphere marching allows us to efficiently cast rays and sample points, without needing to extract an intermediate mesh. We analyze the basic method to show that it guarantees uniformity, and find experimentally that it is significantly more efficient than alternative strategies on a variety of representations. Furthermore, we show extensions to blue noise sampling and stratified sampling, and applications to deform neural implicit surfaces as well as moment estimation.
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.
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.
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.
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.
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.
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.
Resolving Self-intersections in 3D Meshes while Preserving Floating-point Coordinates
(The Eurographics Association and John Wiley & Sons Ltd., 2025) Valque, Léo; Lazard, Sylvain; Attene, Marco; Sellán, Silvia
We present a straightforward and robust method for resolving the mesh intersection problem. We focus specifically on the challenge caused by the intersections resulting from the conversion of the vertices coordinates from their exact mathematical values to a fixed-precision floating-point format. Our method takes as input a soup of triangles and outputs intersection-free models whose vertices coordinates are all represented with double-precision floating-point format. We evaluated our approach thoroughly, considering a large collection of meshes. In particular, we can process all the 4 524 models in Thingi10K [ZJ16] that contain self-intersections. This outperforms previous state-of-the-art approaches: On the 527 models of Thingi10K for which naive rounding fails, Zhou et al.'s approach [ZGZJ16] is capable of handling 91% of them, and Valque's 94% [Val24]. In terms of time efficiency, our approach handles about 50k vertices per second on average, which is faster to that of Zhou et al. by a factor 1.4 on these non-trivial models and is faster than that of Valque by several order of magnitude.
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.
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.
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.
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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