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\input preamble.tex

% ---------------------------------------------------------------------------
\begin{document}
\begin{center}
{\Huge \bf{I. Rational Quadratic Bezier Curves}}
\bigskip

\begin{lapdf}(16,20)(-8,-10)
 \Dgray
 \Dash(1)
 \Polygon(-8,0)(0,10)(8,0) \Stroke
 \Dash(0)
 \Red
 \Rcurve(64)(-8,0,7)(0,10,1)(8,0,7) \Stroke
 \Green
 \Rcurve(64)(-8,0,6)(0,10,1)(8,0,6) \Stroke
 \Blue
 \Rcurve(64)(-8,0,5)(0,10,1)(8,0,5) \Stroke
 \Cyan
 \Rcurve(64)(-8,0,4)(0,10,1)(8,0,4) \Stroke
 \Magenta
 \Rcurve(64)(-8,0,3)(0,10,1)(8,0,3) \Stroke
 \Yellow
 \Rcurve(64)(-8,0,2)(0,10,1)(8,0,2) \Stroke
 \Black
 \Rcurve(64)(-8,0,1)(0,10,1)(8,0,1) \Stroke
 \Red
 \Rcurve(64)(-8,0,1)(0,10,2)(8,0,1) \Stroke
 \Green
 \Rcurve(64)(-8,0,1)(0,10,3)(8,0,1) \Stroke
 \Blue
 \Rcurve(64)(-8,0,1)(0,10,4)(8,0,1) \Stroke
 \Cyan
 \Rcurve(64)(-8,0,1)(0,10,5)(8,0,1) \Stroke
 \Magenta
 \Rcurve(64)(-8,0,1)(0,10,6)(8,0,1) \Stroke
 \Yellow
 \Rcurve(64)(-8,0,1)(0,10,7)(8,0,1) \Stroke
 \Black
 \Rcurve(64)(-8,0,1)(0,10,0)(8,0,1) \Stroke
 \Red
 \Rcurve(64)(-8,0,7)(0,10,-1)(8,0,7) \Stroke
 \Green
 \Rcurve(64)(-8,0,6)(0,10,-1)(8,0,6) \Stroke
 \Blue
 \Rcurve(64)(-8,0,5)(0,10,-1)(8,0,5) \Stroke
 \Cyan
 \Rcurve(64)(-8,0,4)(0,10,-1)(8,0,4) \Stroke
 \Magenta
 \Rcurve(64)(-8,0,3)(0,10,-1)(8,0,3) \Stroke
 \Yellow
 \Rcurve(64)(-8,0,2)(0,10,-1)(8,0,2) \Stroke
 \Point(1)(-8,0)
 \Point(1)(+0,10)
 \Point(1)(+8,0)
 \Text(-8.0,0.2,rb){$P_0$}
 \Text(+0.2,+10.3,rb){$P_1$}
 \Text(+8.0,0.2,lb){$P_2$}
\end{lapdf}
\end{center}
All curves share the same Bezier points, but they differ in the weights of
the points. The black curve is a parabola {$w = 1$}. Above of this all
curves are hyperbolas with increasing weigts, below of this are elliptic curves
with decreasing weights. The line has a weight of {$w = 0$}. After this
the weights are negative increasing. The curves are the complementare
elliptical arcs to the positive counterparts.

\newpage
\unitlength1.16cm

\begin{center}
{\Huge \bf{II. Conic Curves}}
\bigskip

\begin{lapdf}(16,16)(0,0)
 \Dgray
 \Rcurve(64)(4,10.333,2)(0,3.4,1)(8,3.4,2)
 \Rcurve(80)(4,10.333,2)(0,3.4,-1)(8,3.4,2) \Stroke
 \Red
 \Rcurve(64)(4,9.7,2)(0,4.7,1)(8,4.7,2)
 \Rcurve(80)(4,9.7,2)(0,4.7,-1)(8,4.7,2) \Stroke
 \Green
 \Rcurve(64)(9.7,4,2)(4.7,0,1)(4.7,8,2)
 \Rcurve(80)(9.7,4,2)(4.7,0,-1)(4.7,8,2) \Stroke
 \Blue
 \Rcurve(64)(16,16,1)(8,8,5)(16,0,1) \Stroke
 \Cyan
 \Rcurve(64)(0,16,1)(8,8,5)(0,0,1) \Stroke
 \Magenta
 \Rcurve(64)(0,16,1)(8,0,1)(16,16,1) \Stroke
 \Yellow
 \Rcurve(64)(0,0,1)(8,16,1)(16,0,1) \Stroke
\end{lapdf}

\large Circle, Ellipse, Parabola, Hyperbola
\end{center}
\end{document}