Translations:B-Splines/100/en

As several Bézier curves are combined to form a spline, we get a set of Bernstein polynomials forming the spline (they are the basis). As we want to overcome the mentioned limitations of Bézier curves, we don't geometrically combine the different Bernstein polynomials of the Bézier curves, but define Bernstein polynomials over the whole geometrical range of the spline. So we don't combine the Bézier curves with its Bernstein polynomials, which would be
 * $$\textrm{Bezier-combination}=\begin{cases}

\sum_{i=0}^{n}P_{i}\cdot B_{i,n}(t), & 0\le t\le1\\ \sum_{i=0}^{n}P_{i+n}\cdot B_{i,n}(t-1), & 1\le t\le2\\ \cdots \end{cases}$$