A novel approach for computing C{sup}2-continuous offset of NURBS curves

摘要

Computing offset curves is an important geometric operation in areas of CAD/CAM, robotics, cam design and many industrial applications. In this paper, an algorithm for computing offsets of NURBS curves using C{sup}2-continuous B-spline curves is presented. The progenitor curve in database is initially approximated by a line-fitting curve, and then the exact offset of this line-fitting curve is introduced as an initial offset. Based on the initial offset and a set of selected knots, an intended C{sup}2-continuous B-spline curve is subsequently constructed. The method uses a new error-measuring scheme, which is based on the convex hull property of Bezier curves and the idea of cumulative errors, to calculate the global error bound of offset approximation. The method obtains offset curves with C{sup}2 continuity and guarantees that the actual error bound is precisely within the prescribed tolerance. In addition, it also allows one to selectively parametrize the offset curve.