Eurographics Digital Library

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Recent Submissions

Item
Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Wang, Zimeng; Dou, Zhiyang; Xu, Rui; Lin, Cheng; Liu, Yuan; Long, Xiaoxiao; Xin, Shiqing; Komura, Taku; Yuan, Xiaoming; Wang, Wenping; Hu, Ruizhen; Lefebvre, Sylvain
We introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state-of-the-art approaches for this task often rely on the watertightness of the input [LWS*15; PWG*19; PWG*19] or suffer from substantial computational costs [DLX*22; CD23], thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high-accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water-tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis.
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Stability for Inference with Persistent Homology Rank Functions
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Wang, Qiquan; García-Redondo, Inés; Faugère, Pierre; Henselman-Petrusek, Gregory; Monod, Anthea; Hu, Ruizhen; Lefebvre, Sylvain
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the ''shape'' of a wide range of complex data structures, such as point clouds, networks, and functions. However, their use in statistical settings is challenging due to their complex geometric structure. In this paper, we revisit the persistent homology rank function, which is mathematically equivalent to a barcode and persistence diagram, as a tool for statistics and machine learning. Rank functions, being functions, enable the direct application of the statistical theory of functional data analysis (FDA)-a domain of statistics adapted for data in the form of functions. A key challenge they present over barcodes in practice, however, is their lack of stability-a property that is crucial to validate their use as a faithful representation of the data and therefore a viable summary statistic. In this paper, we fill this gap by deriving two stability results for persistent homology rank functions under a suitable metric for FDA integration. We then study the performance of rank functions in functional inferential statistics and machine learning on real data applications, in both single and multiparameter persistent homology. We find that the use of persistent homology captured by rank functions offers a clear improvement over existing non-persistence-based approaches.
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Winding Number Features for Vector Sketch Colorization
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Scrivener, Daniel; Coldren, Ellis; Chien, Edward; Hu, Ruizhen; Lefebvre, Sylvain
Vector sketch software (e.g. Adobe Illustrator, Inkscape) and touch-interactive technologies have long aided artists in the creation of resolution-independent digital drawings that mimic the unconstrained nature of freehand sketches. However, artist intent behind stroke topology is often ambiguous, complicating traditional segmentation tasks such as coloring. For inspiration, we turn to the winding number, a classic geometric property of interest for binary segmentation in the presence of boundary data. Its direct application for multi-region segmentation poses two main challenges: (1) strokes may not be consistently oriented to best identify perceptually salient regions; (2) for interior strokes there is no ''correct'' orientation, as either choice better distinguishes one of two neighboring regions. Thus, we form a harmonic feature space from multiple winding number fields and perform segmentation via Voronoi/power diagrams in this domain. Our perspective allows both for automatic fill region detection and for a semi-automatic framework that naturally incorporates user hints and interactive sculpting of results, unlike competing automatic methods. Our method is agnostic to curve orientation and gracefully handles varying gap sizes in the sketch boundary, outperforming state-of-the-art colorization methods on these ''gappy'' inputs. Moreover, it inherits the ability of winding numbers to specify ''fuzzy'' boundaries, leading to simple strategies for color diffusion and single-parameter-driven growing and shrinking of regions.
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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.
Item
Cut-Cell Microstructures for Two-scale Structural Optimization
(The Eurographics Association and John Wiley & Sons Ltd., 2024) Tozoni, Davi Colli; Huang, Zizhou; Panozzo, Daniele; Zorin, Denis; Hu, Ruizhen; Lefebvre, Sylvain
Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is essential. Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with tiles adapted to the geometry of the cut-cell. We propose a fully automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.