Curve offsetting based on Legendre series

Curve offsetting is one of the most important geometric operations in CAD/CAM systems due to its immediate applications to NC machining. Although offset curves to Pythagorean hodograph curves are rational, offset curves to generic rational curves are non-rational and hence incompatible with B-spline representation. For this reason, approximation techniques have been widely used for curve offsetting. From the Neumann theorem it is known that an analytic function defined over [−1. 1] has a converging Legendre series. Based on the use of the Legendre series, we present a stable and efficient method for offsetting planar B-spline curves. Our approach provides users with easy control of approximation accuracy and flexibility to determine the degree of an offset curve.