G1 motion interpolation using cubic PH biarcs with prescribed length

In this paper the G1 interpolation scheme for motion data, i.e., interpolation of data points and rotations at the points, with cubic PH biarcs is presented. The rotational part of the motion is determined by the Euler-Rodrigues frame which matches the given boundary positions. In addition, the length of the biarc is prescribed. It is shown that the interpolant exists for any data and any chosen length greater than the difference between the interpolation points. The interpolant is given in a closed form and depends on some free shape parameters, which are determined so that the curve is of a nice shape and the twist of the Euler-Rodrigues frame is minimized. The spline construction is provided and numerical examples that confirm the derived theoretical results are included.