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Spline Interpolation and Fitting in $$\mathbb {R}^{n}$$ R n

In: Regression and Fitting on Manifold-valued Data

Author

Listed:
  • Ines Adouani

    (University of Sousse, Higher Institute of Applied Sciences and Technology of Sousse (ISSAT))

  • Chafik Samir

    (University of Clermont Auvergne (UCA))

Abstract

This chapter unfolds a comprehensive exploration of the fitting and interpolation problem in $$\mathbb {R}^{n}$$ R n . We present a formal definition of the fitting problem, simultaneously addressing the core challenge of accurately interpolating time-labeled data in Euclidean space. Subsequently, a thorough review of key definitions related to Bézier splines ensues, highlighting the prerequisites for achieving $$C^{m}$$ C m continuity, ( $$m=0,1,2$$ m = 0 , 1 , 2 ). The chapter culminates in the introduction of an innovative method for solving the interpolation problem in $$\mathbb {R}^{n}$$ R n through the use of $$C^{m}$$ C m Bézier splines. This approach adeptly navigates the complexities of fitting data in multiple dimensions, ensuring the desired continuity up to the mth order and providing a nuanced and effective solution to this intricate problem.

Suggested Citation

  • Ines Adouani & Chafik Samir, 2024. "Spline Interpolation and Fitting in $$\mathbb {R}^{n}$$ R n," Springer Books, in: Regression and Fitting on Manifold-valued Data, chapter 0, pages 9-26, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61712-6_2
    DOI: 10.1007/978-3-031-61712-6_2
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