Variance of the distance to the boundary of convex domains in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$
| Autor: | Fletcher, Alastair N., Fletcher, Alexander G. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we give for the first time a systematic study of the variance of the distance to the boundary for arbitrary bounded convex domains in $\mathbb{R}^2$ and $\mathbb{R}^3$. In dimension two, we show that this function is strictly convex, which leads to a new notion of the centre of such a domain, called the variocentre. In dimension three, we investigate the relationship between the variance and the distance to the boundary, which mathematically justifies claims made for a recently developed algorithm for classifying interior and exterior points with applications in biology. Comment: 26 pages, 6 figures |
| Databáze: | arXiv |
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