High-quality Approximation of the Fermat Spiral with Polynomial Function

To make the Fermat Spiral suitable for the needs of industrial design systems, a high-quality polynomial approximation method is given. The new algorithm is based on s power series. First, the definition of s-power series is reviewed, and the conversion matrix between s-Power and Bézier forms is discussed; then the hermite interpolation approximation algorithm of Fermat's spiral is given using s-power, and finally the algorithm is described in detail. The correctness and validity of this approximation algorithm are verified by an example, and it can be used in computer aided design.