Lagrange geometric interpolation by rational spatial cubic Bézier curves

In the paper, the Lagrange geometric interpolation by spatial rational cubic Bezier curves is studied. It is shown that under some natural conditions the solution of the interpolation problem exists and is unique. Furthermore, it is given in a simple closed form which makes it attractive for practical applications. Asymptotic analysis confirms the expected approximation order, i.e., order six. Numerical examples pave the way for a promising nonlinear geometric subdivision scheme.