B-Spline Curves
B-splines were investigated as early as the nineteenth century by N. Lobachevsky (see Renyi [506], p. 165); they were constructed as convolutions of certain probability distributions.1 In 1946, I. J. Schoenberg [542] used B-splines for statistical data smoothing, and his paper started the modern theory of spline approximation. For the purposes of this book, the discovery of the recurrence relations for B-splines by C. de Boor [137], M. Cox [129], and L. Mansfield was one of the most important developments in this theory. The recurrence relations were first used by Gordon and Riesenfeld [284] in the context of parametric B-spline curves.
This chapter presents a theory for arbitrary degree B-spline curves. The original development ...
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