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Now showing 1 - 10 of 13
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    An Approach to the Decomposition of Solids with Voids via Morse Theory
    (The Eurographics Association, 2023) Pareja-Corcho, Juan; Montoya-Zapata, Diego; Moreno, Aitor; Cadavid, Carlos; Posada, Jorge; Arenas-Tobon, Ketzare; Ruiz-Salguero, Oscar; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, Gilda
    The decomposition of solids is a problem of interest in areas of engineering such as feature recognition or manufacturing planning. The problem can be stated as finding a set of smaller and simpler pieces that glued together amount to the initial solid. This decomposition can be guided by geometrical or topological criteria and be applied to either surfaces or solids (embedded manifolds). Most topological decompositions rely on Morse theory to identify changes in the topology of a manifold. A Morse function f is defined on the manifold and the manifold's topology is studied by studying the behaviour of the critical points of f . A popular structure used to encode this behaviour is the Reeb graph. Reeb graph-based decompositions have proven to work well for surfaces and for solids without inner voids, but fail to consider solids with inner voids. In this work we present a methodology based on the handle-decomposition of a manifold that can encode changes in the topology of solids both with and without inner voids. Our methodology uses the Boundary Representation of the solid and a shape similarity criteria to identify changes in the topology of both the outer and inner boundary(ies) of the solid. Our methodology is defined for Morse functions that produce parallel planar level sets and we do not consider the case of annidated solids (i.e. solids within other solids). We present an algorithm to implement our methodology and execute experiments on several datasets. Future work includes the testing of the methodology with functions different to the height function and the speed up of the algorithm's data structure.
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    Kernel-Based Sampling of Arbitrary Data
    (The Eurographics Association, 2020) Cammarasana, Simone; Patanè, Giuseppe; Biasotti, Silvia and Pintus, Ruggero and Berretti, Stefano
    Point sampling is widely used in several Computer Graphics' applications, such as point-based modelling and rendering, image and geometric processing. Starting from the kernel-based sampling of signals defined on a regular grid, which generates adaptive distributions of samples with blue-noise property, we specialise this sampling to arbitrary data in terms of dimension and structure, such as signals, vector fields, curves, and surfaces. To demonstrate the novelties and benefits of the proposed approach, we discuss its applications to the resampling of 2D/3D domains according to the distribution of physical quantities computed as solutions to PDEs, and to the sampling of vector fields, 2D curves and 3D point sets. According to our experiments, the proposed sampling achieves a high approximation accuracy, preserves the features of the input data, and is computationally efficient.
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    The Py3DViewer Project: A Python Library for fast Prototyping in Geometry Processing
    (The Eurographics Association, 2019) Cherchi, Gianmarco; Pitzalis, Luca; Frongia, Giovanni Laerte; Scateni, Riccardo; Agus, Marco and Corsini, Massimiliano and Pintus, Ruggero
    Fast research and prototyping, nowadays, is shifting towards languages that allow interactive execution and quick changes. Python is very widely used for rapid prototyping. We introduce Py3DViewer, a new Python library that allows researchers to quickly prototype geometry processing algorithms by interactively editing and viewing meshes. Polygonal and polyhedral meshes are both supported. The library is designed to be used in conjunction with Jupyter environments, which allow interactive Python code execution and data visualization in a browser, thus opening up the possibility of viewing a mesh while editing the underlying geometry and topology.
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    Digital Terrain Model From UAV Photogrammetric Data
    (The Eurographics Association, 2020) Morel, Jules; Bac, Alexandra; Kanai, Takashi; Biasotti, Silvia and Pintus, Ruggero and Berretti, Stefano
    This paper presents a method designed to finely approximate ground surfaces from UAV photogrammetric point clouds by relying on statistical filters to separate vegetation from potential ground points, dividing the whole plot in similar complexity sub-plots through an optimized tilling, and filling holes by blending multiple local approximations through the partition of unity principle. Experiments on very different terrain topology show that our approach leads to significant improvement over the state-of-the-art method.
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    Mesh Comparison Using Regular Grids
    (The Eurographics Association, 2024) Kaye, Patrizia; Ivrissimtzis, Ioannis; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    A symmetric grid-based approach to mesh comparison is proposed, providing intuitive visual results alongside an objective measure of the local differences between meshes. The difference function is defined on the nodes of a regular 3D lattice, making it suitable as input for a variety of analysis algorithms. The visual results are compared and comparable to the Metro tool.
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    Simplification of Shapes for Fabrication with V-Groove Milling Tools
    (The Eurographics Association, 2018) Muntoni, A.; Scalas, A.; Nuvoli, S.; Scateni, R.; Livesu, Marco and Pintore, Gianni and Signoroni, Alberto
    We introduce here a pipeline for simplifying digital 3D shapes with the aim of fabricating them using 2D polygonal flat parts. Our method generates shapes that, once unfolded, can be fabricated with CNC milling machines using special tools called V-Grooves. These tools make V-shaped furrows at given angles depending on the shape of the used tool. Milling the edges of each flat facet simplifies the manual assembly that consists only in folding the facets at the desired angle between the adjacent facets. Our method generates simplified shapes where every dihedral angle between adjacent facets belongs to a restricted set, thus making the assembly process quicker and more straightforward. Firstly, our method automatically computes a simplification of the model, iterating local changes on a triangle mesh generated by applying the Marching Cubes algorithm on the original mesh. The user performs a second manual simplification using a tool that removes spurious facets. Finally, we use a simple unfolding algorithm which flattens the polygonal facets onto the 2D plane, so that a CNC milling machine can fabricate it with a sheet of rigid material.
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    Topological Initialization of Injective Integer Grid Maps
    (The Eurographics Association, 2022) Livesu, Marco; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, Riccardo
    Integer Grid Maps (IGM) are a class of mappings characterized by integer isolines that align up to unit translations and rotations of multiples of 90 degrees. They are widely used in the context of remeshing, to lay a quadrilateral grid onto the mapped surface. Computing an IGM is notoriously a challenging task, because it requires to solve a numerical problem with mixed discrete and continuous variables which is known to be NP-Hard. As a result, state of the art methods rely on heuristics that may occasionally fail to produce a valid quadrilateral mesh. Existing pipelines incorporate a final sanitization step which attempts to fix such defects, but no guaranteees can be given in this regard. In this paper we propose a simple topological construction that allows to reduce the problem of computing an IGM to the one of mapping a topological disk to a convex domain. This is a much easier problem to deal with, because it does not endow integer translational and rotational constraints, permitting to obtain a parameterization that is guaranteed to incorporate all the correct integer transitions and to not contain degenerate or inverted elements. Despite provably correct, the so generated maps contain a considerable amount of geometric distortion and a poor quad connectivity, making this technique more suitable for a robust initialization rather than for the computation of an application-ready IGM. In the article we present the details of our construction, also analyzing its geometric and topological properties.
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    Outside-in Priority-based Approximation of 3D Models in LEGO Bricks
    (The Eurographics Association, 2022) Fanni, Filippo Andrea; Rossi, Elisa De; Giachetti, Andrea; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, Riccardo
    In this paper, we discuss the problem of converting a 3D mesh into an assembly of LEGO blocks. The major challenge of this task is how to aggregate the voxels derived by the shape discretization into a set of standard bricks guaranteeing global connectivity. We propose an outside-in priority-based heuristic method based on the analysis of the critical regions that are more likely to cause the creation of a legal assembly to fail. We show that our graph-building heuristic provides relevant advantages, making it easier to obtain a connected graph with good properties with respect to the layer-based or random aggregation strategies applied in most of the optimization approaches. We also propose BRICKS, a novel dataset for the evaluation of aggregation strategies. It includes voxelizations at 3 different resolutions of 33 shapes and allows the easy comparison of different voxel aggregation strategies independently of the shape discretization step and also considering their scalability. We use it to evaluate our approach with respect to graph-based connectivity measures, showing the advantages of the proposed strategy.
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    Split and Mill: User Assisted Height-field Block Decomposition for Fabrication
    (The Eurographics Association, 2019) Muntoni, Alessandro; SPANO, LUCIO DAVIDE; Scateni, Riccardo; Agus, Marco and Corsini, Massimiliano and Pintus, Ruggero
    We present here Split and Mill: an interactive system for the manual volume decomposition of free form shapes. Our primary purpose is to generate portions respecting the properties allowing to mill them with a 3-axis milling machine. We show that a manual decomposition is competitive with the automatic partitioning when the user is skilled enough. We, thus, think that our tool can be beneficial for the practitioners in the field, and we release it as free software.
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    Meshtrics: Objective Quality Assessment of Textured 3D Meshes for 3D Reconstruction
    (The Eurographics Association, 2024) Madeira, Tiago; Oliveira, Miguel; Dias, Paulo; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    In the context of 3D reconstruction, the pursuit of photorealistic models requires precise, objective quality evaluation methods. In this work, we investigate several potential objective metrics for the quality assessment of textured 3D meshes by evaluating their correlation with human perception of visual quality. We conduct experiments using a publicly available, subjectively-rated database of textured 3D meshes containing various types of geometry and texture distortions. Based on these experiments, we discuss the characteristics and limitations of the evaluated metrics. Notably, image-based metrics demonstrated the strongest correlation with subjective scores in most tested scenarios, suggesting that 2D image metrics are reliable predictors of 3D model visual quality. We then introduce a framework designed to facilitate the analysis of various characteristics of 3D models and their fidelity, with a particular focus on image-based metrics leveraging photographs of real-world environments as reference. Our toolkit streamlines the generation of renders and the application of quality metrics, enabling manual annotation in 2D and 3D spaces, while incorporating an automatic alignment refinement step for precise registration of reference photographs. We evaluate the proposed approach using a dataset generated through the 3D reconstruction of a complex indoor environment. Our experiments support the efficacy of the solution in benchmarking 3D reconstruction results, enabling timely informed adjustments to the reconstruction methodology. Source code is available at https://github.com/tiagomfmadeira/Meshtrics.