Grid Peeling of Parabolas
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911783723204608 |
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| author | Rote, Günter Rüber, Moritz Saghafian, Morteza |
| author_facet | Rote, Günter Rüber, Moritz Saghafian, Morteza |
| contents | Grid peeling is the process of repeatedly removing the convex hull vertices of the grid-points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Grid Peeling of Parabolas Rote, Günter Rüber, Moritz Saghafian, Morteza Computational Geometry Numerical Analysis G.1 Grid peeling is the process of repeatedly removing the convex hull vertices of the grid-points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes. |
| title | Grid Peeling of Parabolas |
| topic | Computational Geometry Numerical Analysis G.1 |
| url | https://arxiv.org/abs/2402.15787 |