Analysis of B-spline curve using discrete Fourier transform (Q710426)

Summary: We apply the discrete Fourier transform to the construction of B-spline curves to gain more insight into their structure. As a B-spline curve is determined by its control polygon, this analysis is intimately linked to the Fourier analysis of the control polygon. To do this we apply the fast Fourier transform algorithm to the structure of the B-spline curve and its rational form. We get the inner structure of the original B-spline curve in the transform domain, again in the form of the B-spline curve, having the control polygon as a regular or star polygon. Using the technique mentioned in the paper, we get the same curve without a change of the shape in the transformed case of polygon points. We also extend the idea for the interval form of B-spline curves.