Interpolation of discrete spherical image

A divisible geodesic dome's image is often used for the representation of a spherical image in a digital computer. In the spherical image, any points are enclosed by a triangle facet whose vertices correspond to the position of the pixels. In this paper we propose two novel algorithms of interpolating a point on a sphere based on the values of the three vertices. One is the spherical Barycentric interpolation obtained by modifying the conventional Barycentric interpolation for a planar image; the other is the trilinear interpolation deduced from three linear equations. The proposed method outperforms the conventional nearest neighboring interpolation in the quality of the interpolated image.