Interpolating solid orientations with a C2 -Continuous B-spline quaternion curve

Abstract

An algorithm is presented to construct a C2-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group 50(3). We present a method to extend a B-spline interpolation curve to 50(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 S3. 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. © Springer-Verlag Berlin Heidelberg 2007.