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Fitting Smooth Paths to Spherical Data

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  • Peter E. Jupp
  • John T. Kent

Abstract

Given a set of data points on the sphere at known times, one often wishes to fit a smooth path to the data. In this paper we propose a unified approach to deal with such problems. Our method can be described as “unwrapping” the data onto the plane, where standard curve fitting techniques can then be applied. As an important example of our approach, we define and fit “spherical spline functions”.

Suggested Citation

  • Peter E. Jupp & John T. Kent, 1987. "Fitting Smooth Paths to Spherical Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(1), pages 34-46, March.
    • Handle: RePEc:bla:jorssc:v:36:y:1987:i:1:p:34-46
    DOI: 10.2307/2347843
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    Cited by:

    1. Hanna, Martin S. & Chang, Ted, 2000. "Fitting Smooth Histories to Rotation Data," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 47-61, October.
    2. Kwang‐Rae Kim & Ian L. Dryden & Huiling Le & Katie E. Severn, 2021. "Smoothing splines on Riemannian manifolds, with applications to 3D shape space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 108-132, February.
    3. Samir, Chafik & Adouani, Ines, 2019. "C1 interpolating Bézier path on Riemannian manifolds, with applications to 3D shape space," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 371-384.
    4. Meisam Moghimbeygi & Mousa Golalizadeh, 2019. "A longitudinal model for shapes through triangulation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 99-121, March.
    5. García-Morales, Vladimir, 2021. "A constructive theory of shape," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Beran, Rudolf, 2016. "Nonparametric estimation of trend in directional data," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3808-3827.
    7. Ian L. Dryden & Kwang-Rae Kim & Huiling Le, 2019. "Bayesian Linear Size-and-Shape Regression with Applications to Face Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 83-103, February.

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