\(\mathcal {C}^2\) Composite Spline Methods for Fitting Data on the Sphere

The aim of this paper is to build two spherical interpolation schemes of class \(\mathcal {C}^2 \) by using the tensor product and the boolean sum of cubic composite algebraic splines and cubic \( 2\pi \) -periodic composite Uniform Algebraic Trigonometric splines where a sphere-like surface is identified by a rectangular domain. In this paper, a general theory is developed and a high order of convergence is obtained. A comparison with similar methods introduced in the literature, confirms that the proposed methods are more robust and efficient. A numerical application using 3D real data approximating a human head is provided.