Abstract
The B-splines introduced in 5 can also be constructed by projecting simplices onto the real line. The density function of a simplex shadow is a B-spline. Schoenberg found this geometric interpretation in 1965, and de Boor used it in 1976 to define multivariate B-splines, see [de Boor ’76b]. This beautiful geometric construction of B-splines allows us to immediately see or to derive in a straightforward manner properties, such as smoothness and recursion, the knot insertion and degree elevation formulas.
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© 2002 Springer-Verlag Berlin Heidelberg
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Prautzsch, H., Boehm, W., Paluszny, M. (2002). Simplex splines. In: Bézier and B-Spline Techniques. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04919-8_18
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DOI: https://doi.org/10.1007/978-3-662-04919-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07842-2
Online ISBN: 978-3-662-04919-8
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