Average and Expected Distortion of Voronoi Paths and Scapes
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866913365933162496 |
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| author | Edelsbrunner, Herbert Nikitenko, Anton |
| author_facet | Edelsbrunner, Herbert Nikitenko, Anton |
| contents | The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about $\tfrac{4}π$. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_03350 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Average and Expected Distortion of Voronoi Paths and Scapes Edelsbrunner, Herbert Nikitenko, Anton Metric Geometry Probability 60D05 Geometric probability and stochastic geometry, 68U05 Computer graphics, computational geometry The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about $\tfrac{4}π$. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes. |
| title | Average and Expected Distortion of Voronoi Paths and Scapes |
| topic | Metric Geometry Probability 60D05 Geometric probability and stochastic geometry, 68U05 Computer graphics, computational geometry |
| url | https://arxiv.org/abs/2012.03350 |