Editing De Casteljau's algorithm (section)

== Bézier curve ==
[[File:Bézier 2 big.gif|thumb|right|A second order Bézier curve.]]
[[File:Bezier cubic anim.gif|thumb|right|A third order Bézier curve.]]
[[File:Bezier forth anim.gif|thumb|right|A fourth order Bézier curve.]]

When evaluating a Bézier curve of degree ''n'' in 3-dimensional space with ''n'' + 1 control points '''P'''<sub>''i''</sub>
<math display="block">\mathbf{B}(t) = \sum_{i=0}^{n} \mathbf{P}_i b_{i,n}(t),\ t \in [0,1]</math>
with
<math display="block">\mathbf{P}_i := \begin{pmatrix} x_i \\ y_i \\ z_i \end{pmatrix},</math>
we split the Bézier curve into three separate equations
<math display="block">\begin{align}
B_1(t) &= \sum_{i=0}^{n} x_i b_{i,n}(t), & t \in [0,1] \\[1ex]
B_2(t) &= \sum_{i=0}^{n} y_i b_{i,n}(t), & t \in [0,1] \\[1ex]
B_3(t) &= \sum_{i=0}^{n} z_i b_{i,n}(t), & t \in [0,1]
\end{align}</math>
which we evaluate individually using De Casteljau's algorithm.