In maxima, the default behavior when invoking the plot3d() function is to show the resulting manifold from the side in perspective. For instance, running
(%i0) wxplot3d(cos(x)*cos(y),[x,-%pi,%pi],[y,-%pi,%pi]);
yields
Such plots can be very pretty but tend to biaise our interpretation of it and also sometimes parts of the manifold are hidden. How do I get a "bird's view" of the same plot?
This can be achieved by asking Maxima to run gnuplot's set view map command before drawing the plot. Indeed, calling
(%i0) wxplot3d(cos(x)*cos(y),[x,-%pi,%pi],[y,-%pi,%pi], [gnuplot_preamble, "set view map"]);
yields
An alternative to the color plot is the contour plot. For instance,
(%i1) wxplot3d(cos(x)*cos(y),[x,-%pi,%pi],[y,-%pi,%pi], [gnuplot_preamble,
"set view map; set size square;unset surface;set contour;set cntrparam levels 10;set clabel '%.1f';set isosamples 150"])
yields
Those parameters are the ones recommended by the "Gnuplot in Action" book, page 145, Listing 8.1. Here is a description of what each does (from the very same listing):
set view map #Choose birds-eye view
set size square #Choose equal units in both directions
unset surface #Switch off the surface...
set contour #... but switch on contours lines
set cntrparam levels 10 #Increase the number of contour lines
set clabel "%.1f" #Choose format of contour labels in key
set isosamples 150 #Increase sampling frequency