Computing offsets of B-spline curves

Abstract

This paper presents a general offset technique valid for non-uniform rational B-spline curves. The offset curve is defined by a new control polygon where each new control point is the offset of a control point of the original curve in a direction given by the normal at the closest point of the curve. The offset factor is related to both the curvature and the distance between the control point and its closest point. Straight lines and inflection points are considered as well as the offset in a direction other than the normal one. One of the main advantages of this technique is to provide a good approximation when the offset cannot be described by a B-spline and an exact result otherwise (for circles, for example).