SGP: Eurographics Symposium on Geometry Processing

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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.
Entropy-driven Progressive Compression of 3D Point Clouds
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Zampieri, Armand; Delarue, Guillaume; Bakr, Nachwa Abou; Alliez, Pierre; Hu, Ruizhen; Lefebvre, Sylvain
3D point clouds stand as one of the prevalent representations for 3D data, offering the advantage of closely aligning with sensing technologies and providing an unbiased representation of a measured physical scene. Progressive compression is required for real-world applications operating on networked infrastructures with restricted or variable bandwidth. We contribute a novel approach that leverages a recursive binary space partition, where the partitioning planes are not necessarily axis-aligned and optimized via an entropy criterion. The planes are encoded via a novel adaptive quantization method combined with prediction. The input 3D point cloud is encoded as an interlaced stream of partitioning planes and number of points in the cells of the partition. Compared to previous work, the added value is an improved rate-distortion performance, especially for very low bitrates. The latter are critical for interactive navigation of large 3D point clouds on heterogeneous networked infrastructures.
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.
Fabricable Multi-Scale Wang Tiles
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Liu, Xiaokang; Li, Chenran; Lu, Lin; Deussen, Oliver; Tu, Changhe; Campen, Marcel; Spagnuolo, Michela
Wang tiles, also known as Wang dominoes, are a jigsaw puzzle system with matching edges. Due to their compactness and expressiveness in representing variations, they have become a popular tool in the procedural synthesis of textures, height fields, 3D printing and representing other large and non-repetitive data. Multi-scale tiles created from low-level tiles allow for a higher tiling efficiency, although they face the problem of combinatorial explosion. In this paper, we propose a generation method for multi-scale Wang tiles that aims at minimizing the amount of needed tiles while still resembling a tiling appearance similar to low-level tiles. Based on a set of representative multi-scale Wang tiles, we use a dynamic generation algorithm for this purpose. Our method can be used for rapid texture synthesis and image halftoning. Respecting physical constraints, our tiles are connected, lightweight, independent of the fabrication scale, able to tile larger areas with image contents and contribute to "mass customization".
On Shape Design and Optimization of Gerotor Pumps
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Pareja-Corcho, Juan C.; Barton, Michael; Pedrera-Busselo, Asier; Mejia-Parra, Daniel; Moreno, Aitor; Posada, Jorge; Hu, Ruizhen; Lefebvre, Sylvain
A gerotor pump is a two-piece mechanism where two rotational components, interior and exterior, engage each other via a rotational motion to transfer a fluid in a direction parallel to their rotational axes. A natural question arises on what shape of the gerotor is the optimal one in the sense of maximum fluid being pumped for a unit of time, given the constraint of a fixed material needed to manufacture the pump. As there is no closed-formula to answer this question, we propose a new algorithm to design and optimize the shape of gerotor pumps to be as efficient as possible. The proposed algorithm is based on a fast construction of the envelope of the interior component and subsequent optimization. We demonstrate our algorithm on a benchmark gerotor and show that the optimized solution increases the estimated flowrate by 16%. We also use our algorithm to study the effect of the number of teeth on the cavity area of a gerotor.
Rational Bézier Guarding
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Khanteimouri, Payam; Mandad, Manish; Campen, Marcel; Campen, Marcel; Spagnuolo, Michela
We present a reliable method to generate planar meshes of nonlinear rational triangular elements. The elements are guaranteed to be valid, i.e. defined by injective rational functions. The mesh is guaranteed to conform exactly, without geometric error, to arbitrary rational domain boundary and feature curves. The method generalizes the recent Bézier Guarding technique, which is applicable only to polynomial curves and elements. This generalization enables the accurate handling of practically important cases involving, for instance, circular or elliptic arcs and NURBS curves, which cannot be matched by polynomial elements. Furthermore, although many practical scenarios are concerned with rational functions of quadratic and cubic degree only, our method is fully general and supports arbitrary degree. We demonstrate the method on a variety of test cases.
SimJEB: Simulated Jet Engine Bracket Dataset
(The Eurographics Association and John Wiley & Sons Ltd., 2021) Whalen, Eamon; Beyene, Azariah; Mueller, Caitlin; Digne, Julie and Crane, Keenan
This paper introduces the Simulated Jet Engine Bracket Dataset (SimJEB) [WBM21]: a new, public collection of crowdsourced mechanical brackets and accompanying structural simulations. SimJEB is applicable to a wide range of geometry processing tasks; the complexity of the shapes in SimJEB offer a challenge to automated geometry cleaning and meshing, while categorical labels and structural simulations facilitate classification and regression (i.e. engineering surrogate modeling). In contrast to existing shape collections, SimJEB's models are all designed for the same engineering function and thus have consistent structural loads and support conditions. On the other hand, SimJEB models are more complex, diverse, and realistic than the synthetically generated datasets commonly used in parametric surrogate model evaluation. The designs in SimJEB were derived from submissions to the GrabCAD Jet Engine Bracket Challenge: an open engineering design competition with over 700 hand-designed CAD entries from 320 designers representing 56 countries. Each model has been cleaned, categorized, meshed, and simulated with finite element analysis according to the original competition specifications. The result is a collection of 381 diverse, high-quality and application-focused designs for advancing geometric deep learning, engineering surrogate modeling, automated cleaning and related geometry processing tasks.
Structural Design Using Laplacian Shells
(The Eurographics Association and John Wiley & Sons Ltd., 2019) Ulu, Erva; McCann, Jim; Kara, Levent Burak; Bommes, David and Huang, Hui
We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally-sound minimum weight shell object. Our approach works by altering the local shell thickness repeatedly based on the stresses that develop inside the object. A key issue in shell design is that large thickness values might result in self-intersections on the inner boundary creating a significant computational challenge during optimization. To address this, we propose a shape parametrization based on the solution to the Laplace's equation that guarantees smooth and intersection-free shell boundaries. Combined with our gradient-free optimization algorithm, our method provides a practical solution to the structural design of hollow objects with a single inner cavity. We demonstrate our method on a variety of problems with arbitrary 3D models under complex force configurations and validate its performance with physical experiments.

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Browsing SGP: Eurographics Symposium on Geometry Processing by Subject "aided design"

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