Interpolating Solid Orientations with a C2-Continuous B-Spline Quaternion Curve

  • Wenbing Ge
  • Zhangjin Huang
  • Guoping Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4469)


An algorithm is presented to construct a C 2-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 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.


C2-continuous interpolation quaternion  B-spline curve computer animation 


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Wenbing Ge
    • 1
  • Zhangjin Huang
    • 1
  • Guoping Wang
    • 1
  1. 1.Dept. of Computer Science and Technology, Peking University, BeijingChina

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