linear Bézier curves

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For linear Bézier curves, there are only two control points which are the endpoints of the curve,

and

. The Bernshtein polynomial and its first derivatives are:

$\begin{equation*}\left\{\begin{aligned}B_1(t) &= (1-t) P_1 + t P_2 \\ B_1'(t) &= P_2 - P_1 \\ B_1''(t) &= 0 \end{aligned}\right.\end{equation*}$

**Figure 2:** linear Bézier curve
$\begin{picture}(60,24) \textcolor[rgb]{0.09,0.32,0.12}{ \qbezier(10,10)(30,16)(... ...\mbox{$P_1$}} \put(50,22){\circle{2}}\put(52,20){\mbox{$P_2$}} }% \end{picture}$

Luc Maisonobe 2005-05-29