Splines are curves,
usually in 2-dimensional or 3-dimensional space, that are defined by
connecting a sequence of points together with parts that are piecewise
polynomials, where the derivatives of the piecewise polynomials agree at
the joining points to produce a smooth curve at every point.
Splines are used in industrial design, most notably in automotive
design, to produce eye-pleasing shapes that are also aerodynamic.
The B-splines are a
basis for all splines, so that any spline can be made as a finite linear
combination of B-splines.
There are several ways to define the B-splines,
including this one that contains the binomial coefficients.
For more information on the topic, you can visit this website by Alena
Scott which defines B-splines.
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