Extremal Scattered Data Interpolation in $$\mathbb {R}^3$$ Using Triangular Bézier Surfaces

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• 刊名：Lecture Notes in Computer Science
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：8962
• 期：1
• 页码：304-311
• 全文大小：231 KB
• 参考文献：1. Andersson, L.-E., Elfving, T., Iliev, G., Vlachkova, K.: Interpolation of convex scattered data in \(\mathbb{R}^3\) based upon an edge convex minimum norm network. J. Approx. Theory 80(3), 299-20 (1995) CrossRef
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  8. Nielson, G.M.: A method for interpolating scattered data based upon a minimum norm network. Math. Comput. 40(161), 253-71 (1983) CrossRef
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  11. Vlachkova, K.: A Newton-type algorithm for solving an extremal constrained interpolation problem. Num. Linear Algebra Appl. 7(3), 133-46 (2000) CrossRef
  
• 作者单位：Krassimira Vlachkova (16)
  
  16. Faculty of Mathematics and Informatics, Sofia University, “St. Kliment Ohridski-Blvd. James Bourchier 5, 1164, Sofia, Bulgaria
  
• 丛书名：Numerical Methods and Applications
• ISBN：978-3-319-15585-2
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

We consider the problem of extremal scattered data interpolation in \(\mathbb {R}^3\) . Using our previous work on minimum \(L_2\) -norm interpolation curve networks, we construct a bivariate interpolant \(F\) with the following properties: \(F\) is \(G^1\) -continuous, \(F\) consists of triangular Bézier surfaces, each Bézier surface satisfies the tetra-harmonic equation \(\varDelta ^4 F=0\) . Hence \(F\) is an extremum to the corresponding energy functional. We also discuss the case of convex scattered data in \(\mathbb {R}^3\) .