## Parametric

The set parametric command changes the meaning of plot (splot) from normal functions to parametric functions. The command unset parametric restores the plotting style to normal, single-valued expression plotting.

Syntax:

         set parametric
         unset parametric
         show parametric

For 2D plotting, a parametric function is determined by a pair of parametric functions operating on a parameter. An example of a 2D parametric function would be plot sin(t),cos(t), which draws a circle (if the aspect ratio is set correctly — see set size (p. )). gnuplot will display an error message if both functions are not provided for a parametric plot.

For 3D plotting, the surface is described as x=f(u,v), y=g(u,v), z=h(u,v). Therefore a triplet of functions is required. An example of a 3D parametric function would be cos(u)*cos(v),cos(u)*sin(v),sin(u), which draws a sphere. gnuplot will display an error message if all three functions are not provided for a parametric splot.

The total set of possible plots is a superset of the simple f(x) style plots, since the two functions can describe the x and y values to be computed separately. In fact, plots of the type t,f(t) are equivalent to those produced with f(x) because the x values are computed using the identity function. Similarly, 3D plots of the type u,v,f(u,v) are equivalent to f(x,y).

Note that the order the parametric functions are specified is xfunction, yfunction (and zfunction) and that each operates over the common parametric domain.

Also, the set parametric function implies a new range of values. Whereas the normal f(x) and f(x,y) style plotting assume an xrange and yrange (and zrange), the parametric mode additionally specifies a trange, urange, and vrange. These ranges may be set directly with set trange, set urange, and set vrange, or by specifying the range on the plot or splot commands. Currently the default range for these parametric variables is [-5:5]. Setting the ranges to something more meaningful is expected.