Interpolating solid orientations with a C-2-continuous B-spline quaternion curve

An algorithm is presented to construct a C-2-continuous B-spline quaternion curve which interpolates a given sequence of unit quatertrions on the rotation group SO(3). We present a method to extend a B-spline interpolation curve to SO(3). The problem is essentially to find the quaternion control points of the quaternion B-spline interpolation curve. Although the associated constraint equation is non-linear, we can get the accurate quaternion control points according to two additional rules for quaternion computations in S-3. In addition, we provide a point insertion method to construct interpolation curves that have local modification property. The effectiveness of the algorithm is verified by applying it to some examples.Computer Science, Artificial IntelligenceComputer Science, Information SystemsComputer Science, Theory & MethodsImaging Science & Photographic TechnologyCPCI-S(ISTP)