IGB-offset for plane curves loop removal by scanning of interval sequences

The generation of NC-tool paths for 2 1/2-axes machining is based on offset curves to arbitrary simple piecewise smooth G(0) generator curves. Global and local properties that are of interest for the offset generation from the NC and the differential geometric viewpoint are discussed and described in this paper. These properties lead to an approach for generating global offset curves in a more direct and technological way. The key point of this approach is the restriction of the offset image to nonsingular parts of the generator curve with respect to the given offset distance. In general, this restricted offset image is discontinuous, but the restriction guarantees a minimal number of self-intersection points. The correspondence of self-intersections to parameter intervals is used to describe uniquely a set of relevant trim intervals. The result after the trimming of these intervals is a continuous offset curve that is, up to some technological constraints, equal to the offset curve of the right-or left-sided rolling ball blend of the generator curve. This offset carries the Gauss-Bonnet values of the generator as invariants and is, therefore, called IGB-offset. Global loops of the IGB-offset are classified by the superposition of remaining self-intersection intervals and are described by the union of elements with even index of finite interval sequences in the parameter space of the IGB-offset. (C) 1998 Elsevier Science B.V.