A scheme for interpolation with trigonometric spline curves

摘要

We present a method for the interpolation of a given sequence of data points with Cn continuous trigonometric spline curves of order n+1 (n≥1) that are produced by blending elliptical arcs. Ready to use explicit formulae for the control points of the interpolating arcs are also provided. Each interpolating arc depends on a global parameter α∈(0,π) that can be used for global shape modification. Associating non-negative weights with data points, rational trigonometric interpolating spline curves can be obtained, where weights can be used for local shape modification. The proposed interpolation scheme is a generalization of the Overhauser spline, and it includes a Cn Bézier spline interpolation method as the limiting case α→0.