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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/2405.11123 |
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| _version_ | 1866916251292401664 |
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| author | Hu, Tsung-Wei Lai, Ming-Jun |
| author_facet | Hu, Tsung-Wei Lai, Ming-Jun |
| contents | This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. The construction involves four essential components: local functions, blending functions, redistributing functions, and gluing functions. The resulting curve possesses favorable attributes, including $G^2$ geometric smoothness, locality, the absence of cusps, and no self-intersection. Moreover, the algorithm is adaptable to various scenarios, such as preserving convexity, interpolating sharp corners, and ensuring sphere preservation. The paper substantiates the efficacy of the proposed method through the presentation of numerous numerical examples, offering a practical demonstration of its capabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Construction of Interpolating Space Curves with Any Degree of Geometric Continuity Hu, Tsung-Wei Lai, Ming-Jun Numerical Analysis 31A05, 35J25, 30C60, 53A10 This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. The construction involves four essential components: local functions, blending functions, redistributing functions, and gluing functions. The resulting curve possesses favorable attributes, including $G^2$ geometric smoothness, locality, the absence of cusps, and no self-intersection. Moreover, the algorithm is adaptable to various scenarios, such as preserving convexity, interpolating sharp corners, and ensuring sphere preservation. The paper substantiates the efficacy of the proposed method through the presentation of numerous numerical examples, offering a practical demonstration of its capabilities. |
| title | A Construction of Interpolating Space Curves with Any Degree of Geometric Continuity |
| topic | Numerical Analysis 31A05, 35J25, 30C60, 53A10 |
| url | https://arxiv.org/abs/2405.11123 |