Extremal Interpolation of Convex Scattered Data in \(\mathbb {R}^3\) Using Tensor Product 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：9374
• 期：1
• 页码：435-442
• 全文大小：248 KB
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  11.Monterde, J., Ugail, H.: On harmonic and biharmonic Bézier surfaces. Comput. Aided Geom. Des. 21, 697–715 (2004)MathSciNet CrossRef MATH
  12.Monterde, J., Ugail, H.: A general 4th-order PDE method to generate Bézier surfaces from the boundary. Comput. Aided Geom. Des. 23, 208–225 (2006)MathSciNet CrossRef MATH
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  15.Peters, J.: Smooth interpolation of a mesh of curves. Constr. Approx. 7(1), 221–246 (1991)MathSciNet CrossRef MATH
  16.Vlachkova, K.: Interpolation of convex scattered data in \(\mathbb{R}^3\) based upon a convex minimum \(L_p\) -norm network. C. R. Acad. Bulg. Sci. 45, 13–15 (1992)MathSciNet MATH
  17.Vlachkova, K.: A Newton-type algorithm for solving an extremal constrained interpolation problem. Num. Linear Algebra Appl. 7(3), 133–146 (2000)MathSciNet CrossRef MATH
  18.Vlachkova, K.: Extremal scattered data interpolation using tensor product Bézier surfaces. In: Ivanov, K., Nikolov, G., Uluchev, R. (eds.) Constructive Theory of Functions Sozopol 2013, pp. 253–264. Marin Drinov Academic Publishing House, Sofia (2014)
  
• 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：Large-Scale Scientific Computing
• ISBN：978-3-319-26520-9
• 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 interpolation of convex scattered data in \(\mathbb {R}^3\) and propose a feasible solution. Using our previous work on edge convex minimum \(L_p\)-norm interpolation curve networks, \(1<p\le \infty \), we construct a bivariate interpolant F with the following properties:(i) F is \(G^1\)-continuous;