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Efficient Degree Elevation and Knot Insertion for B-spline Curves using Derivatives

AbstractThis paper presents a new algorithm for raising the degree of a B-spline curve which can also insert new knots at the same time. The new algorithm is faster than existing algorithms, and is much easier to understand and to implement. The new control points are computed using the following three simple steps: computing derivatives from control points, resampling the knot vector, and computing new control points from derivatives. Comparisons with previous methods and examples are given.