Approximation of planar offset curves using quadratic trigonometric splines with shape parameter

Abstract

This paper presents a new method for generating the approximation offset of freeform planar curves using quadratic trigonometric splines with shape parameter. Although the input is higher-degree NURBS curves, only knot insertion at the inflexion and end points of the self-intersecting loop are required for initial offsetting. Based on the obtained new control polygon and its offsets, the quadratic trigonometric spline was constructed to approximate the exact offset curves. Because of the great controllability, the proposed method could generate a completely overestimating offset curve by adjusting the value of the shape parameter, which guarantees no overcutting in NC machining. Furthermore, it also produces the lowest number of control points compared with other works. Experimental results demonstrated the usefulness and effectiveness of this method.