Multi-scale Cycle Tracking in Dynamic Planar Graphs
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866912020978204672 |
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| author | Rasheed, Farhan Naseer, Abrar Nilsson, Emma Masood, Talha Bin Hotz, Ingrid |
| author_facet | Rasheed, Farhan Naseer, Abrar Nilsson, Emma Masood, Talha Bin Hotz, Ingrid |
| contents | This paper presents a nested tracking framework for analyzing cycles in 2D force networks within granular materials. These materials are composed of interacting particles, whose interactions are described by a force network. Understanding the cycles within these networks at various scales and their evolution under external loads is crucial, as they significantly contribute to the mechanical and kinematic properties of the system. Our approach involves computing a cycle hierarchy by partitioning the 2D domain into segments bounded by cycles in the force network. We can adapt concepts from nested tracking graphs originally developed for merge trees by leveraging the duality between this partitioning and the cycles. We demonstrate the effectiveness of our method on two force networks derived from experiments with photoelastic disks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-scale Cycle Tracking in Dynamic Planar Graphs Rasheed, Farhan Naseer, Abrar Nilsson, Emma Masood, Talha Bin Hotz, Ingrid Graphics Computational Geometry Computer Vision and Pattern Recognition I.3.5; I.3.6; I.3.8; J.2 This paper presents a nested tracking framework for analyzing cycles in 2D force networks within granular materials. These materials are composed of interacting particles, whose interactions are described by a force network. Understanding the cycles within these networks at various scales and their evolution under external loads is crucial, as they significantly contribute to the mechanical and kinematic properties of the system. Our approach involves computing a cycle hierarchy by partitioning the 2D domain into segments bounded by cycles in the force network. We can adapt concepts from nested tracking graphs originally developed for merge trees by leveraging the duality between this partitioning and the cycles. We demonstrate the effectiveness of our method on two force networks derived from experiments with photoelastic disks. |
| title | Multi-scale Cycle Tracking in Dynamic Planar Graphs |
| topic | Graphics Computational Geometry Computer Vision and Pattern Recognition I.3.5; I.3.6; I.3.8; J.2 |
| url | https://arxiv.org/abs/2409.06476 |