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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.09692 |
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| _version_ | 1866910487133814784 |
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| author | Zou, Qiang Zhu, Lizhen |
| author_facet | Zou, Qiang Zhu, Lizhen |
| contents | This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does not assume ordered or fixed-size data points as input. There is also no need for manually setting the number of knots. It casts the parameterization and knot placement problems as a sequence-to-sequence translation problem, a generative process automatically determining the number of knots, their placement, parameter values, and their ordering. Once trained, SplineGen demonstrates a notable improvement over existing methods, with a one to two orders of magnitude increase in approximation accuracy on test data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SplineGen: a generative model for B-spline approximation of unorganized points Zou, Qiang Zhu, Lizhen Computational Engineering, Finance, and Science Computational Geometry This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does not assume ordered or fixed-size data points as input. There is also no need for manually setting the number of knots. It casts the parameterization and knot placement problems as a sequence-to-sequence translation problem, a generative process automatically determining the number of knots, their placement, parameter values, and their ordering. Once trained, SplineGen demonstrates a notable improvement over existing methods, with a one to two orders of magnitude increase in approximation accuracy on test data. |
| title | SplineGen: a generative model for B-spline approximation of unorganized points |
| topic | Computational Engineering, Finance, and Science Computational Geometry |
| url | https://arxiv.org/abs/2406.09692 |