Approximating polynomial bezier curves using harmonic rational bezier curves

摘要

This paper deals with the problem of approximating polynomial Bezier curves withlow-harmonic rational Bezier curves. It is shown that a polynomial Bezier curve is representable as a hybrid curve consisting of a low-harmonic curve with a moving control point. This hybrid representation leads directly to a low-harmonic approximation of a given polynomial curve. The approximation error is also analyzed. The result can be used to fine tune a polynomial trajectory for high-speed machinery to remove high harmonics from the trajectory.