An Adjustable Spherical Spline Interpolation with Shape Parameters

A class of Bezier curves with shape parameters in R³ is generalized to the unitsphere S³. Anevaluation algorithm of the curve is given and the smooth joining conditions between two curves are considered in terms of quaternions and the generalized Bernstein basis functions.Then an adjustable spherical spline interpolation method is presented as an application. Specific impact of changing parameters on the shape of the curve is illustrated in the numerical experiments results.The results show that the proposed method is effective.