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一个五重七点对偶插值型细分
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Abstract:
对偶插值型细分方法通过结合对偶型细分的拓扑特性与插值型细分的几何精确性，逐步成为细分领域的研究热点。该方法的关键在于生成的曲线或曲面既能保持初始控制多边形插值特性，又具备光滑性等特点。本文阐述了一种基于两个参数的五重七点对偶插值细分格式，针对该细分格式的多项式再生性和连续性开展了计算与讨论。为提升对偶插值型细分方法的灵活性和适用性提供了新思路。
Dual interpolatory subdivision scheme, by combining the topological properties of dual subdivision with the geometric precision of interpolatory subdivision, has gradually become a research hotspot in the subdivision field. The key to this scheme lies in generating curves or surfaces that both preserve the interpolation characteristics of the initial control polygon and exhibit smoothness. This paper proposes a five-arity seven-point dual interpolatory subdivision scheme with two parameters, and analyzes its continuity and regeneration. This provides new ideas to enhance the flexibility and applicability of dual interpolatory subdivision schemes.
| [1] | Loop, C. (1987) Smooth Subdivision Surfaces Based on Triangles. Master’s Thesis. University of Utah. |
| [2] | Dyn, N., Levin, D. and Gregory, J.A. (1987) A 4-Point Interpolatory Subdivision Scheme for Curve Design. Computer Aided Geometric Design, 4, 257-268. https://doi.org/10.1016/0167-8396(87)90001-x |
| [3] | Catmull, E. and Clark, J. (1978) Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes. Computer-Aided Design, 10, 350-355. https://doi.org/10.1016/0010-4485(78)90110-0 |
| [4] | Dyn, N., Levine, D. and Gregory, J.A. (1990) A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control. ACM Transactions on Graphics, 9, 160-169. https://doi.org/10.1145/78956.78958 |
| [5] | Deng, C., Xu, H., Ma, W. and Li, Y. (2019) Repeated Local Operations and Associated Interpolation Properties of Dual 2n-Point Subdivision Schemes. Journal of Computational and Applied Mathematics, 349, 344-353. https://doi.org/10.1016/j.cam.2018.09.030 |
| [6] | Romani, L. (2019) Interpolating M-Refinable Functions with Compact Support: The Second Generation Class. Applied Mathematics and Computation, 361, 735-746. https://doi.org/10.1016/j.amc.2019.06.018 |
| [7] | Gemignani, L., Romani, L. and Viscardi, A. (2022) Bezout-Like Polynomial Equations Associated with Dual Univariate Interpolating Subdivision Schemes. Advances in Computational Mathematics, 48, Article No. 4. https://doi.org/10.1007/s10444-021-09912-4 |
| [8] | Viscardi, A. (2023) Optimized Dual Interpolating Subdivision Schemes. Applied Mathematics and Computation, 458, Article 128215. https://doi.org/10.1016/j.amc.2023.128215 |
| [9] | Aspert, N. (2003) Non-Linear Subdivision of Univariate Signals and Discrete Surfaces. Swiss Federal Institute of Technology in Lausanne. |
