This paper deals with the problem of automatic fairing (or fine-tuning) of two-parameter rational B-spline spherical and spatial motions. The results presented in this paper extend the previous results on fine-tuning of one-parameter rational B-spline motions. A dual quaternion representation of spatial displacements is employed and the problem of fairing two-parameter motions is studied as a surface fairing problem in the space of dual quaternions. By combining surface fairing techniques from the field of computer aided geometric design with the computer aided synthesis of freeform rational motions, smoother (C3 continuous) two-parameter rational B-spline motions are generated. Several examples are presented to illustrate the effectiveness of the proposed method. Techniques for motion smoothing have important applications in the Cartesian motion planning, camera motion synthesis, and spatial navigation in virtual reality systems. In particular, smoother two-parameter freeform motions have applications in the development of a kinematic based approach to geometric shape design and in five-axis NC tool path planning.

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