Translations:B-Splines/44/en

The derivation of B-splines from Bézier curves have the mathematical consequence that in B-splines every polynomial piece has the same length. Such B-splines are called uniform. The more general case is that they can but must not have the same length. Such non-uniform splines have the advantage that one can control how close the splines cross its control point. Mathematically this is achieved by defining the different $$N_{i,n}$$ pieces at different intervals. If for example a B-spline is defined for the interval [0, 1], it is uniform if all its e.g. 5 pieces are also defined in this interval. If now $$N_{1,4}$$ is only defined in the interval [0, 0.6] (outside the interval it is set to zero), it is shorter and thus the spline becomes non-uniform.