Arbitrary point displacement on B-spline curve

Curvilinear formats store straight lines as polygonal segments, while curved parts are encoded as a set of control points, following the formalism of Bézier curves or B-Splines. These formats have been proposed by multibeam mask-writers, and a work group was formed to extend the standard Oasis format, retaining four types of curves. Among them, Implicit Bézier and B-Splines are of special interest, due to their compactness and potential for file conversion and geometric operations. However, sizing-like operations are not straightforward on B-Splines, as the curve is locally controlled by multiple control points in general. This paper presents different methods to move a point on a B-Spline curve to a desired location, discussing their advantages and disadvantages.