Rational control of orientation for animation *

The smooth interpolation of keyframes of a rigid body, in particular their orientations, is an important problem in animation . Using the quaternion as a representation for orientation, several papers have solved this problem through the generation of smooth curves on the quaternion sphere. However, none of these methods have constructed rational curves. This paper develops a method for generating true rational Bezier curves on the quaternion sphere that interpolate a given set of orientations. The control of orientation by a rational Bezier curve has all of the typical advantages of Bezier curves, such as efficient computation, subdivision, and variation diminution. We also discuss control of the speed of rotation, and cusp avoidance, both of which are simpler with our method. This paper can be viewed as an extension of the classical work on interpolation of points (i. e., position) to the interpolation of orientations.