Modifying curvatures at design points for convex B-spline curves

The curvature of a curve at a point expresses the roundness of the curve at that position. Interactive modifications to it can, produce many shapes similar to the intended one, among which the most satisfying can be chosen. In this paper, we discuss how to interactively modify the curvature of a convex B-spline curve at a feature point while preserving nice characteristics of the curve. Constraint equations in terms of the control vertices for the curve are given to determine the associated properties. Based on these constraints, we present a simple and efficient design scheme capable of repositioning the control vertices into more appropriate positions. This enables a designer to rapidly manipulate the shape of a curve in real time.