Editing De Casteljau's algorithm (section)

=== Notation ===
When doing the calculation by hand it is useful to write down the coefficients in a triangle scheme as
<math display="block">
\begin{matrix}
\beta_0     & = \beta_0^{(0)}     &                   &         &               \\
            &                     & \beta_0^{(1)}     &         &               \\
\beta_1     & = \beta_1^{(0)}     &                   &         &               \\
            &                     &                   & \ddots  &               \\
\vdots      &                     & \vdots            &         & \beta_0^{(n)} \\
            &                     &                   &         &               \\
\beta_{n-1} & = \beta_{n-1}^{(0)} &                   &         &               \\
            &                     & \beta_{n-1}^{(1)} &         &               \\
\beta_n     & = \beta_n^{(0)}     &                   &         &               \\
\end{matrix}
</math>
When choosing a point ''t''<sub>0</sub> to evaluate a Bernstein polynomial we can use the two diagonals of the triangle scheme to construct a division of the polynomial
<math display="block">B(t) = \sum_{i=0}^n \beta_i^{(0)} b_{i,n}(t), \quad t \in [0,1]</math>
into
<math display="block">B_1(t) = \sum_{i=0}^n \beta_0^{(i)} b_{i,n}\left(\frac{t}{t_0}\right)\!, \quad t \in [0,t_0]</math>
and
<math display="block">B_2(t) = \sum_{i=0}^n \beta_i^{(n-i)} b_{i,n}\left(\frac{t-t_0}{1-t_0}\right)\!, \quad t \in [t_0,1].</math>