A General Construction Scheme for Unit Quaternion Curves with Simple High Order Derivatives

This paper proposes a newclass of unit quaternion curves in SO(3).A general method is developed that transforms a curve in R3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to well-known spline curves (such as B´ezier, Hermite, and B-spline curves), we are able to construct var..