An explicit formula for the control points of periodic uniform spline interpolants and its application

Usually we obtain the B-spline control points of a cubic uniform spline interpolant by solving a system of linear equations. In this paper, we derive an explicit formula for the control points of periodic spline interpolants. As an application of this formula, we derive the least possible bound for the deviation of the periodic cubic spline interpolant to the data polygon.

► An explicit formula for the control points of the periodic cubic uniform spline interpolants.
► The least possible bound for the deviation from the periodic uniform cubic spline interpolant to its data polygon.
► The conditions for achieving the least possible bound.