Quadratic Bézier Curves

\setlength{\unitlength}{1cm}
\begin{picture}(6, 4)
  \linethickness{0.075mm}
  \multiput(0, 0)(1, 0){7}{\line(0, 1){4}}
  \multiput(0, 0)(0, 1){5}{\line(1, 0){6}}  
  \put(.5, .5){\circle*{.1}}
  \put(1, 3){\circle*{.1}}
  \put(3, 3.5){\circle*{.1}}  
  \thicklines
  \put(.5, .5){\line(1, 5){.5}}
  \put(1, 3){\line(4, 1){2}}
  \qbezier(.5, .5)(1, 3)(3, 3.5)
  \thinlines
  \put(2.5, 2){\circle*{.1}}
  \put(5.5, .5){\circle*{.1}}
  \put(5, 3){\circle*{.1}}  
  \put(2.5, 2){\line(2, -1){3}}
  \put(5.5, .5){\line(-1, 5){.5}}
  \linethickness{1mm}
  \qbezier(2.5, 2)(5.5, .5)(5, 3)
  \thinlines
  \qbezier(4, 2)(4, 3)(3, 3)
  \qbezier(3, 3)(2, 3)(2, 2)
  \qbezier(2, 2)(2, 1)(3, 1)
  \qbezier(3, 1)(4, 1)(4, 2)
\end{picture}