Interpolation of Unit Quaternion Curve with High Order Continuity

This paper presents a method of designing a unit quaternion curve which is C^k continuous. The curve interpolates not only a given sequence of 3D orientations but also a sequence of angle velocities. This method is based on the mappings between S³ and R³ which ensures the property of interpolating the given orientations. The property of interpolating the given angle velocities is ensured by the differential formula of the exponential mapping.