[pstricks] Quartic Bezier curves (of fourth order)

[Herbert Voss]

a solution created with hot needles ...

Herbert


\documentclass{article}
\usepackage{pst-plot}

\makeatletter
\pst at def{BezierQuartic}<
   ] /Points ED %                y4 x4 y3 x3 y2 x2 y1 x1 y0 x0
   /GetBezierCoor {
   /t ED				% t on stack
   /t1 1 t sub def
%  the x coordinate
   Points 8 get t 4 exp mul                              % x0*B0(t)
   Points 6 get t 3 exp 4 mul mul t1 mul add             % x1*B1(t)
   Points 4 get t 2 exp 6 mul mul t1 2 exp mul add       % x2*B2(t)
   Points 2 get t 4 mul mul t1 3 exp mul add             % x3*B3(t)
   Points 0 get t1 4 exp mul add                         % x4*B4(t)
%  the y coordinate
   Points 9 get t 4 exp mul                              % y0*B0(t)
   Points 7 get t 3 exp 4 mul mul t1 mul add             % y1*B1(t)
   Points 5 get t 2 exp 6 mul mul t1 2 exp mul add       % y2*B2(t)
   Points 3 get t 4 mul mul t1 3 exp mul add             % y3*B3(t)
   Points 1 get t1 4 exp mul add                         % y4*B4(t)
} def
   /epsilon 0.01 def
   /n 5 def
   epsilon GetBezierCoor         % next Bezier point
   Points 0 get Points 1 get     % starting point
   ArrowA moveto
   epsilon epsilon 1 {
     /t ED
     t GetBezierCoor
     t 0.9999 lt { lineto }{ 1 epsilon sub GetBezierCoor 4 2 roll ArrowB 
pop pop pop pop } ifelse
   } for >
%\def\tx at BezierQuartic{BezierQuartic }
\def\psbezierIV{\pst at object{psbezierIV}}
\def\psbezierIV at i{%
   \pst at getarrows{%
     \begin at OpenObj
     \pst at getcoors[\psbezierIV at ii%
   }}
\def\psbezierIV at ii{%
   \addto at pscode{%
     \tx at BezierQuartic
     \ifshowpoints \tx at BezierShowPoints \fi
   }%
   \end at OpenObj}
%
\makeatother

\begin{document}
\psset{xunit=0.2cm}
\begin{pspicture}(40,15)
\psbezierIV[linewidth=2pt,showpoints=true]{<->}(0,0)(10,5)(20,13)(30,5)(40,0)
\end{pspicture}

\end{document}