On the Bertrand Nurbs curves

In the section of researchs, results and discussions of this study is divided into 5 subsections.In the first section, the second and third derivatives of open B-spline curves at the points t=t_dandt=t_(m-d) and the Frenet vector fields and curvatures of these curves are given. In the second section,the control points of the second B-spline curve are given in terms of the control points of the first B-spline curve when given two B-spline curves occured a Bertrand curve pairs. In the third section the first,thesecond and the third derivatives of a NURBS curve at the points t=t_dandt=t_(m-d)are given with Frenet vector fields and curvatures at arbitrary point. In the 4th, the conditions of providing Bertrand curve pairs of given two NURBS curves are given. In the last section the numerical examples are given with the Frenet vector fields and curvatures and the conditions of being Bertrand curve pairs