Shape Representation of Polynomial Curves with Adjustable Interpolation Points

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 C¹, piecewise cubic G² and piecewise quartic C² curves are given. The representations of the piecewise cubic C¹ curves and the piecewise quartic C² 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.