[pstricks] Draw a vector field

[Michael Sharpe]

On Nov 8, 2010, at 6:40 PM, David Tarazona wrote:

> Hi again and thanks for the support
> 
> My question is simple, how i can to draw a vector field of the gradient of a z=f(x,y) function???
> 
> i mean, the gradient of z is:
> 
> ∇Z=(∂z/∂x) î + (∂z/∂y) ĵ
> 
> so i want to graph the vector field as seen on pages 9 and 23 on this PDF: 
> http://www.math.msu.edu/~hensh/latex/pstricks/seminarSS08.pdf
> 
> i think that i could use simply a "double multido" for x and y and graph the vectors, but i dont know how to get the color effect shown in the PDF...
> 
> thanks for the support again
> 

Well, since no-one else is stepping up, here's an example that goes part way to what you want. It isn't limited to the gradient of a function but works for any vector field (vx,vy). The color range is not correct (this example goes from black to green), and the line thickness isn't either.

\psset{unit=3cm}%
\begin{pspicture}[showgrid=true](-.5,-.5)(1.5,1.5)
% assume vector field magnitude in range [0,20]
\multido{\nx=0+.2}{6}{
  \multido{\ny=0+.2}{6}{% specify vx vy in PostScript code
  \pstVerb{ \nx\space dup mul 20 mul neg /vx exch def \ny
    \space dup mul 20 mul /vy exch def vx dup mul vy dup mul add sqrt /radius exch def /ndx radius .5 add cvi def }\definecolor[ps]{thecolor}{rgb}{0 ndx 20 div 0}
      \psrline[linecolor=thecolor]{->}(\nx,\ny)(10pt;{(! vx vy )})}}
\end{pspicture}

Michael