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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2604.14400 |
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| _version_ | 1866915939465822208 |
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| author | Zhang, Bingwei Chen, Thomas Hormann, Kai Yap, Chee |
| author_facet | Zhang, Bingwei Chen, Thomas Hormann, Kai Yap, Chee |
| contents | Range functions are a fundamental tool for certified computations in
geometric modeling, computer graphics, and robotics,
but traditional range functions have only quadratic convergence order
($m=2$). For ``superior'' convergence order (i.e., $m>2$), we exploit the
Cornelius--Lohner framework in order to
introduce new bivariate range functions based
on Taylor, Lagrange, and Hermite interpolation.
In particular, we focus on practical
range functions with cubic and quartic convergence order.
We implemented them in Julia and provide experimental
validation of their performance in terms
of efficiency and efficacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14400 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bivariate range functions with superior convergence order Zhang, Bingwei Chen, Thomas Hormann, Kai Yap, Chee Numerical Analysis Computational Geometry Range functions are a fundamental tool for certified computations in geometric modeling, computer graphics, and robotics, but traditional range functions have only quadratic convergence order ($m=2$). For ``superior'' convergence order (i.e., $m>2$), we exploit the Cornelius--Lohner framework in order to introduce new bivariate range functions based on Taylor, Lagrange, and Hermite interpolation. In particular, we focus on practical range functions with cubic and quartic convergence order. We implemented them in Julia and provide experimental validation of their performance in terms of efficiency and efficacy. |
| title | Bivariate range functions with superior convergence order |
| topic | Numerical Analysis Computational Geometry |
| url | https://arxiv.org/abs/2604.14400 |