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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.08626 |
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| _version_ | 1866915920729866240 |
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| author | Vincze, Csaba Nagy, Ábris |
| author_facet | Vincze, Csaba Nagy, Ábris |
| contents | A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics' theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08626 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On taxicab distance mean functions and their geometric applications: methods, implementations and examples Vincze, Csaba Nagy, Ábris Optimization and Control Discrete Mathematics G.2.3 A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics' theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well. |
| title | On taxicab distance mean functions and their geometric applications: methods, implementations and examples |
| topic | Optimization and Control Discrete Mathematics G.2.3 |
| url | https://arxiv.org/abs/2304.08626 |