Optimal contour orientations for machining of free{form surfaces

In contour machining of free{form surfaces with a ball{end cutter, the tool contacts the surface along loci that correspond to sections by a set of parallel planes, with equidistant spacing and common normal N. For a given tool radius, the greatest scallop height between successive tool paths is suppressed by choosing an orientation for the contouring planes that will maximize, over the entire surface, the minimum angle between N and the local surface normal n. This optimization problem is solved by computing the (symmetrized) Gauss map for the surface, projecting it stereographically onto a plane, and using the medial axis transform for the complement of its image to identify the contouring orientation N that is \most distant" from the symmetrized Gauss map boundary. Invoking a Gauss map algorithm described elsewhere, the method is implemented in the context of bicubic B ezier surfaces, with tool paths on the ooset surface approximated by PH space curves that can be directly passed to real{time CNC interpolators. Empirical tests show signiicant improvements in the quality of machined surfaces over cases where the contouring orientation is chosen in an ad hoc manner.