gistfile1.tex

\begin{tikzpicture}
\coordinate [label=left:$P_0$] (P0) at (0,0);
\coordinate [label=left:$P_1$] (P1) at (3,5);
\coordinate [label=right:$P_2$] (P2) at (6,5);
\coordinate [label=right:$P_3$] (P3) at (9,0);
\coordinate (X1) at ($(P0) !.5! (P2)$);
\coordinate (X2) at ($(P1) !.5! (P3)$);
\coordinate [label=below:$0$] (0) at (4,2);
\coordinate [label=left:$P(0)$] (p0) at (3,4.166667);
\coordinate [label=below:$a$] (a) at (4.5,2);
\coordinate [label=above:$P(a)$] (pa) at (4.5,4.791667);
\coordinate [label=below:$1$] (1) at (5,2);
\coordinate [label=right:$P(1)$] (p1) at (6,4.166667);

\draw (P0) -- (P2);
\draw (P1) -- (P3);
\draw (X1) -- (P1);
\draw (X2) -- (P2);

\draw [red] plot [smooth] coordinates {(p0) (3.3,4.391667) (3.6,4.566667) (3.9,4.691667) (4.2,4.7666667) (pa) (4.8,4.766667) (5.1,4.691667) (5.4,4.5666667) (5.7,4.391667) (p1)};

\filldraw (0) circle (1pt) -- (a) circle (1pt) -- (1) circle (1pt);
\draw [->,dashed] (0) -- (p0);
\draw [->,dashed] (a) -- (pa);
\draw [->,dashed] (1) -- (p1);
\end{tikzpicture}