Eurographics Digital Library

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Recent Submissions

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Exploring the Geometry of Swarm Intelligence: Negative Inertia and Ellipsoidal Search Space Evolution in PSO
(The Eurographics Association, 2025) Krämer, Katharina; Müller, Stefan; Kosterhon, Michael; Egger, Bernhard; Günther, Tobias
This paper introduces a geometry-aware method for analyzing swarm behavior in Particle Swarm Optimization (PSO) based on ellipsoidal modeling. Inspired by the n-ball hitting probability, we propose an abstraction of the search space covered by particles over time. Using principal component analysis (PCA), we approximate the particle distribution at each iteration with ellipsoids, enabling a visual and quantitative assessment of how well the swarm explores and concentrates its search effort. We apply this technique to investigate a PSO variant with negative inertia weights, which has shown promising performance in prior empirical analysis. While negative inertia may appear counterintuitive, our ellipsoidal analysis reveals that it introduces oscillatory search dynamics that balance exploration and exploitation more effectively than standard strategies such as constant inertia or linear decreasing inertia. Our experiments include a six-dimensional medical image registration task and an illustrative two-dimensional Rastrigin function, which serves to visually demonstrate how the swarm structure evolves. The proposed analysis framework provides new insight into swarm dynamics and offers a tool for understanding and comparing the behavior of PSO variants beyond conventional performance metrics.
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Bin-VBSR: Variable Block Size Binned Block-Compressed Sparse Row for Efficient GPU-Accelerated Finite Element Analysis
(The Eurographics Association, 2025) Pfeil, Florian; Ferreira, Stephanie; Mueller-Roemer, Johannes Sebastian; Egger, Bernhard; Günther, Tobias
We present Binned Variable Block Compressed Sparse Row (Bin-VBSR), a novel GPU-optimized sparse matrix data structure and associated sparse matrix-vector multiplication algorithm for matrices with variable-size dense blocks. This includes a novel approach to handling long rows in the Binned Compressed Sparse Row (Bin-CSR) family of GPU-optimized sparse matrix data structures. We demonstrate speedups of up to 9.9× over Bin-BCSR* and extend its data compression advantages over compressed sparse row (CSR) to variable block size, resulting in an improvement of up to 50%.
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Differentiable XPBD for Gradient-Based Learning of Physical Parameters from Motion
(The Eurographics Association, 2025) Drysch, Simone; Stotko, David; Klein, Reinhard; Egger, Bernhard; Günther, Tobias
Accurate cloth simulation is a vital component in computer graphics, virtual reality, and fashion design. Position-Based Dynamics (PBD) and its extension (XPBD) offer robust and efficient methods for simulating deformable objects like cloth. This paper details the evaluation and comparison of cloth simulations based on XPBD, including its ''small steps'' variant and an Energy- Aware (EA) modification. The XPBD variants are evaluated for their physical plausibility and energy conservation to analyze their suitability for inverse problems. Furthermore, we explore the implementation of a differentiable XPBD simulator, enabling the estimation of material properties and external forces. The differentiable simulator is assessed for its capability to estimate parameters in scenarios of increasing complexity. Results indicate that small time steps with single iterations in XPBD offer good energy behavior, while the EA modification exhibits undesired characteristics. The differentiable simulator successfully estimates single parameters but identifies challenges with multi-parameter optimization due to compensatory effects.
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Bijective Feature-Aware Contour Matching
(The Eurographics Association, 2025) Selman, Zain; Speetzen, Nils; Kobbelt, Leif; Egger, Bernhard; Günther, Tobias
Computing maps between data sequences is a fundamental problem with various applications in the fields of geometry and signal processing. As such, a multitude of approaches exist, that make trade-offs between flexibility, performance, and accuracy. Even recent approaches cannot be applied to periodic data, such as contours, without significant compromises due to their map representation or method of optimization. We propose a universal method to optimize maps between periodic and non periodic univariate sequences. By continuously optimizing a piecewise linear approximation of the smooth map on a common intermediate domain, we decouple the map and input resolution. Our optimization offers bijectivity guarantees and flexibility with regards to applications and data modality. To robustly converge towards a high quality solution we initially apply a lowpass filter to the input. This creates a scale space that suppresses local features in the early phase of the optimization (global phase) and gradually adds them back later (local phase). We demonstrate the versatility of our method on various scenarios with different types of sequences, including multi-contour morphing, signature prototypes, symmetry detection, and 3D motioncapture- data alignment.
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Robust Discrete Differential Operators for Wild Geometry
(The Eurographics Association, 2025) Wagner, Sven Dominik; Botsch, Mario; Egger, Bernhard; Günther, Tobias
Many geometry processing algorithms rely on solving PDEs on discrete surface meshes. Their accuracy and robustness crucially depend on the mesh quality, which oftentimes cannot be guaranteed - in particular when automatically processing geometries extracted from arbitrary implicit representations. Through extensive numerical experiments, we evaluate the robustness of various Laplacian implementations across geometry processing libraries on synthetic and ''in-the-wild'' surface meshes with degenerate or near-degenerate elements, revealing their strengths, weaknesses, and failure cases. To improve numerical stability, we extend the recently proposed tempered finite elements method (TFEM) to meshes with strongly varying element sizes, to arbitrary polygonal elements, and to gradient and divergence operators. Our resulting differential operators are simple to implement, efficient to compute, and robust even in the presence of fully degenerate mesh elements.