One-sided arc approximation of B-spline curves for interference-free offsetting

An algorithm is presented to generate a piecewise curve with G(1) continuity using area, which approximates a B-spline curve without crossing the curve. Initially, the B-spline curve in database is decomposed into piecewise Bezier curves. Using convex hulls of the Bezier curves to protect the original curve from interference, the line segments are chosen all on the same side of the B-spline curve to give a one-sided approximating curve. Based on the obtained approximating line segments, biarc fitting and single are fitting methods are applied to construct a smooth, G(1) continuous curve which does not cross the original curve. If the resulting curve is offset to generate tool paths for pocketing boundaries with B-spline curves, the over-cutting problem can be eliminated completely, and abrupt direction changes on tool paths can be greatly reduced. This method can also be applied to generate collision free paths for robot arms. (C) 1999 Elsevier Science Ltd. All rights reserved.