B-spline Curve Generation and Modification based on Specified Radius of Curvature

A method to generate a quintic B-spline curve which passes through given points is described. In this case, there are four more equations than there are control point positions. Two methods have been developed to compensate for the difference between the number of unknowns and that of the equations. These are assuming that the curvatures at both ends of the curve are zero, and assigning four gradients to the given points. In addition to this method, another method to generate a quintic B-spline curve which passes close to given points, and which has the first derivative at these given points is described. In this case, a linear system will be underdetermined, determined or overdetermined depending on the number of given points with gradients. A method to modify a quintic B-spline curve shape according to the specified radius of curvature distribution to realize an aesthetically pleasing freeform curve is described. The difference between the B-spline curve radius of curvature and the specified radius of curvature is minimized by introducing the least-squares method. Examples of curve generation are given. Key-Words: B-spline curve generation, curvature vector, curve shape modification, given points, given points with gradients, underdetermined system, overdetermined system