Curve generation and modification based on radius of curvature smoothing

A method to generate a quintic B-spline curve which passes through the given points is described. In this case, there are four more equations than there are control point positions. Therefore, four gradients which are the first derivative of a quintic B-spline equation are assigned to the given points. In addition to this method, another method to generate a quintic B-spline curve which passes through the 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 differences between the B-spline curve radius of curvature and the specified radius of curvature is minimized by introducing the least-squares method.

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