ScrewBender: Smoothing Piecewise Helical Motions

Although a piecewise helical (polyscrew) motion is continuous, velocities are typically discontinuous at control poses when the motion switches between screws. We obtain a smooth motion through polyscrew 4-point, B-spline, or Jarek subdivision, which are trivial to implement and can be animated in real time. To overcome this problem, we use screw, or helical, motions to interpolate between poses. A screw is fully defined by the initial and final control poses. It combines a minimum-angle linear rotation around a fixed axis of direction S with a minimum-distance linear translation along S.