Orientation Interpolation in Quatemion Space Using Spherical Biarcs

We consider the problem of interpolating a smooth curve to a point sequence in the unit quaternion space U. This problem has application to object orientation interpolation in computer animation , sweep surface generation in solid modeling[7, 6]. Since the unit quaternions form the unit sphere 8 3 in p;4, a simple curve scheme using spherical biarcs is presented to solve this problem. The spherical biarc is a curve on a sphere consisting of two smoothly joining circular arcs. It is shown that for any two given points and two tangents specified at the two points on the unit sphere S'3 , there always exist spherical biarcs interpolating these data and these biarcs are easy to construct. This leads to an algorithm for constructing a smooth and locally controllable circular arc spline curve to interpolate a sequence of unit quaternions in U. We also discuss how to compute in-between quaternions efficiently on the resulting spline curve.