The best sextic approximation of hyperbola with order twelve

Abstract

In this article, the best uniform approximation for the hyperbola of degree 6 that has approximation order 12 is found. The associated error function vanishes 12 times and equioscillates 13 times. For an arc of the hyperbola, the error is bounded by 2:4 x 10-4. We explain the details of the derivation and show how to apply the method. The method is simple and this encourages and motivates people working in CG and CAD to apply it in their works.