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In the mathematical subfield of numerical analysis, a Bspline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Bsplines were investigated as early as the nineteenth century by Nikolai Lobachevsky from Kazan State University, Russia. A fundamental theorem states that every spline function of a given degree, smoothness, and domain partition, can be represented as a linear combination of Bsplines of that same degree and smoothness, and over that same partition.^{[1]} The term Bspline was coined by Isaac Jacob Schoenberg and is short for basis spline.^{[2]} Bsplines can be evaluated in a numerically stable way by the de Boor algorithm. Simplified, potentially faster variants of the de Boor algorithm have been created but they suffer from comparatively lower stability.^{[3]}^{[4]}
In the computer science subfields of computeraided design and computer graphics, the term Bspline frequently refers to a spline curve parametrized by spline functions that are expressed as linear combinations of Bsplines (in the mathematical sense above). A Bspline is simply a generalisation of a Bézier curve, and it can avoid the Runge phenomenon without increasing the degree of the Bspline.
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