ABSTRACT

Helix splines are spline curves with piecewise constant curvature and constant torsion. Therefore helix splines might be of interest for milling machines. Al­ though interpolation has been addressed in [3], an approach for approximation is unknown. A helix can be interpreted as the trajectory of a screw motion of a point P: P rotates around an axis a while it additionally is translated proportional to the rotation angle into the direction of the axis. The helix lies on a circular cylinder with axis a. The projection of a helix segment into a plane which is perpendicular to the axis yields a circular arc. If it contains the first point of the helix segment, we refer to this circular arc as a basis cir­ cle. In this paper these circular arcs are restricted to have an opening angle 2<p < 27r. We call 2(p the opening angle of the helix segment.