Convexity-preserving B-spline modification

Abstract

This report discusses the problem of modifying the shape of a cubic B-spline curve while retaining its convexity. This is achieved by moving control points in such a way as to maintain the appropriate shape of the corresponding control polygon. The problem is formulated as a linear programming problem, which may be solved using the simplex method. Two examples, taken from cross-sections of a ship hull, are discussed.