Shape Representation of Polynomial Curves with Adjustable Interpolation Points

Abstract

Piecewise cubic and quartic polynomial curves with adjustable interpolation points are presented in this paper. The adjustable interpolation points are represented by local shape parameters and the given control points. Based on the choice of endpoint tangents of curve segments, piecewise cubic $C^1$, piecewise cubic $G^2$ and piecewise quartic $C^2$ curves are given. The representations of the piecewise cubic $C^1$ curves and the piecewise quartic $C^2$ curves are integrated representations of approximating and interpolating curves. By changing the values of the local shape parameters, local approximating curves and local interpolating curves can be generated respectively.