Ken Shoemake’s 1985 Siggraph paper “Animation Rotation with Quaternion Curves”, that brought quaternions to computer graphics, covered this. The idea is to use quaternions as control points in a spline the same way you would use 3d points in a spline. You could have a series of quaternion orientations, and connect them with C_2 continuity by using a connected series of piecewise cubic Bezier splines.
The abstract mentions it: “This paper gives one answer by presenting a new kind of spline curve, created on a sphere, suitable for smoothly in-hetweening (i.e. interpolating) sequences of arbitrary rotations.” And the final punch line is section 4.3, then you can work through the details in the earlier sections.
The abstract mentions it: “This paper gives one answer by presenting a new kind of spline curve, created on a sphere, suitable for smoothly in-hetweening (i.e. interpolating) sequences of arbitrary rotations.” And the final punch line is section 4.3, then you can work through the details in the earlier sections.
https://www.cs.cmu.edu/~kiranb/animation/p245-shoemake.pdf