ABSTRACT
One of the advantages of using unit quaternions instead of rotation matrices to represent rotations in 3-dimensions is that the authors can use spherical linear interpolation to interpolate between two unit quaternions. Since every rigid motion can be represented by a screw transformation, the authors shall use screw linear interpolation (ScLERP) to interpolate between two rigid motions. They could use SLERP to interpolate between the unit quaternions p0 and q0, but it is not so clear how to interpolate between p1 and q1 so that the interpolant for p1 and q1 always remains orthogonal to the interpolant between p0 and q0. However, they need this orthogonality condition to ensure that every value of ScLERP is a unit dual quaternion and therefore represents a screw transformation.
