$C^1$ surface interpolation for scattered data on a sphere

@article{Lawson1984C1SI,
  title={\$C^1\$ surface interpolation for scattered data on a sphere},
  author={Charles L. Lawson},
  journal={Rocky Mountain Journal of Mathematics},
  year={1984},
  volume={14},
  pages={177-202}
}
  • C. Lawson
  • Published 1 March 1984
  • Mathematics
  • Rocky Mountain Journal of Mathematics
An algorithm is described for constructing a smooth computable function, f, defined over the surface of a sphere and interpolating a set of n data values, u sub i, associated with n locations, P sub i, on the surface of the sphere. The interpolation function, f, will be continuous and have continuous first partial derivatives. The locations, p sub i, are not required to lie on any type of regular grid. 
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Methods and software that extend the C ~ interpolant of data values associated with arbitrarily distributed nodes on the surface of a sphere method are described and test results are presented.
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We discuss several approaches to the problem of interpolating or approximating data given at scattered points lying on the surface of the sphere. These include methods based on spherical harmonics,
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