$C^1$ 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}
}

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.

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.Expand

Proceedings Pacific Graphics '98. Sixth Pacific Conference on Computer Graphics and Applications (Cat. No.98EX208)

1998

TLDR

The basis of this work is a hybrid interpolant which is a convex combination of three quintic Bezier schemes which is of degree 9 over degree 4 and it requires the evaluation of 27 control points.Expand

The C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ω embedded into R3 confirm the O(h3) order of convergence as the data becomes dense.Expand

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,… Expand