How many points in a point cloud is sufficient for accurate estimation of the curvature
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913921866137600 |
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| author | Mirzaie, R. |
| author_facet | Mirzaie, R. |
| contents | We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the curvature in a given point of a curve. Then, we extend it to estimate the Gaussian curvature of the surfaces. In the proposed algorithms, we use a relation between the number of selected points in the point cloud and the probability that a given point has a suffcient number of nearby points. This relation allows us to control the required number of points in the point cloud. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_06779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How many points in a point cloud is sufficient for accurate estimation of the curvature Mirzaie, R. Differential Geometry 53C21, 53C23, 62D05 We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the curvature in a given point of a curve. Then, we extend it to estimate the Gaussian curvature of the surfaces. In the proposed algorithms, we use a relation between the number of selected points in the point cloud and the probability that a given point has a suffcient number of nearby points. This relation allows us to control the required number of points in the point cloud. |
| title | How many points in a point cloud is sufficient for accurate estimation of the curvature |
| topic | Differential Geometry 53C21, 53C23, 62D05 |
| url | https://arxiv.org/abs/2506.06779 |