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Was (wer) ist Non-Uniform Rational B Spline - definition
![NURBS have the ability to exactly describe circles. Here, the black triangle is the control polygon of a NURBS curve (shown at w=1). The Blue dotted line shows the corresponding control polygon of a B-spline curve in 3D [[homogeneous coordinates]], formed by multiplying the NURBS by the control points by the corresponding weights. The blue parabolas are the corresponding B-spline curve in 3D, consisting of three parabolas. By choosing the NURBS control points and weights, the parabolas are parallel to the opposite face of the gray cone (with its tip at the 3D origin), so dividing by ''w'' to project the parabolas onto the ''w''=1 plane results in circular arcs (red circle; see [[conic section]]).](https://commons.wikimedia.org/wiki/Special:FilePath/NURBS-circle-3D.svg?width=200 "NURBS have the ability to exactly describe circles. Here, the black triangle is the control polygon of a NURBS curve (shown at w=1). The Blue dotted line shows the corresponding control polygon of a B-spline curve in 3D [[homogeneous coordinates]], formed by multiplying the NURBS by the control points by the corresponding weights. The blue parabolas are the corresponding B-spline curve in 3D, consisting of three parabolas. By choosing the NURBS control points and weights, the parabolas are parallel to the opposite face of the gray cone (with its tip at the 3D origin), so dividing by ''w'' to project the parabolas onto the ''w''=1 plane results in circular arcs (red circle; see [[conic section]]).")
![animated creation of a NURBS spline]].)](https://commons.wikimedia.org/wiki/Special:FilePath/NURBstatic.svg?width=200 "animated creation of a NURBS spline]].)")
![spline as a mathematical concept]]](https://commons.wikimedia.org/wiki/Special:FilePath/Spline (PSF).png?width=200 "spline as a mathematical concept]]")
Wikipedia
In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree. Cardinal B-splines have knots that are equidistant from each other. B-splines can be used for curve-fitting and numerical differentiation of experimental data.
In computer-aided design and computer graphics, spline functions are constructed as linear combinations of B-splines with a set of control points.
