Construction of G3 Conic Spline Interpolation

Abstract

In this paper, a new method to interpolate a sequence of ordered points with conic splines is presented. The degree of continuity at joints of the resulting splines can reach G3 while the number of curvature extrema is reduced to a minimum. The construction process is not based on parametrization, but basic geometric elements. A new geometric concept called Chord-Tangent Ratio which is vital to determine the shape of conic splines is proposed. The main idea of the construction is to merge the constraints of continuity into a function of tangent arguments and Chord-Tangent Ratios, and construct an optimization function to eliminate the curvature extrema, then through an iterative process, for the constraint function to reach its zero point and for the optimization function to reach its minimum. Experiments show that splines constructed by the new method performs well not only in terms of continuity, but also in smoothness.