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

Authors:
Wenbing Ge;Zhangjin Huang;Guoping Wang
Affiliations:
Dept. of Computer Science and Technology, Peking University, Beijing, China;Dept. of Computer Science and Technology, Peking University, Beijing, China;Dept. of Computer Science and Technology, Peking University, Beijing, China
Venue:
Edutainment'07 Proceedings of the 2nd international conference on Technologies for e-learning and digital entertainment
Year:
2007

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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 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 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.