Spline Interpolation on the Special Orthogonal Group SO(n)

In the preceding chapter, we developed and scrutinized a methodology for curve fitting to data on the sphere. The spherical manifold proved advantageous due to its inherent visualizability, enabling an intuitive understanding of the proposed algorithm. While \(\mathbb {S}^{2}\) served as an excellent preliminary example to assess the concepts, the need to extend the work to more intricate manifolds becomes imperative to substantiate the complexity of the approach.