not so FAQ

• Legend
• Tics
• Label
• 2-D Plot
• 3-D Plot
• Polar Coordinate
• Parametric Functions
  • 
    parameters

  • 
    vertical line

  • 
    circle, polygons

  • 
    exchange X and Y-axes
• Data File
• After Plotting
• Miscellaneous Stuff

About Parametric Functions

use of parameters

In the usual 2-dimensional plot of gnuplot, the Y coordinate is
expressed by y=f(x), however you can also use a parametric
expression which uses the parameter t,

x = f(t)
y = g(t)

With this expression, more complicated functions can be plotted with
gnuplot. Note that the 3-dim. plot with two parameters u,v
is given in the
spherical harmonics section.

First of all, you need to use the command set parametric
to tell gnuplot that the function is defined by a parameter.
Then, the plot command followed by a function f(t) which
is the X-coordinate and a function g(t) for Y-coordinate, is give
like, plot f(t),g(t) .

to draw a vertical line

The most simple but it is impossible to express by the y=f(x) form
is a vertical line which is x=const. This function can be written as:

x=const
y=t

with the parameter t, when t is varied. The range of
t is controlled by the command set trange .

gnuplot> set parametric

dummy variable is t for curves, u/v for surfaces
gnuplot> const=3
gnuplot> set trange [1:4]
gnuplot> set xrange [0:5]
gnuplot> set yrange [0:5]
gnuplot> plot const,t

In this case the vertical line is draw at x=3. Since we used set
trange [1:4] , the range of this truncated line is from 1 to 4.
If trange not set, the vertical line is drawn from the bottom
to top border lines.

to draw a circle, polygons

The parametric expression of a circle is

x=sin(t)
y=cos(t)

and the circle can be drawn if one changes the t parameter
from 0 to 2pi. The graph is “squared” here, and the t range
is given by an option of plot command.

gnuplot> set parametric

dummy variable is t for curves, u/v for surfaces
gnuplot> set size square
gnuplot> set xrange [-1:1]
gnuplot> set yrange [-1:1]
gnuplot> plot [0:2*pi] sin(t),cos(t)

The parameter t is not changing continuously, and actually
this is controlled by the value which is set by the set
samples command. The default value is 100. In the case of
set samples 8 , gnuplot generates eight t values
from zero to 2*pi, and the graph becomes a regular heptagon. If
you need a regular N-gon, just type set samples
N+1.

The 2-dim. parametric representation is convenient to draw a
function which is in a polar coordinate.
The 2-dim. polar coordinate has two variables which are radius
r and angle theta. The gnuplot parameter t is
for the theta, and the radius r is expressed by a
function of angle, namely r(t). A (x,y) coordinate is given
by

x=r(t)*cos(t)
y=r(t)*sin(t)

The circle is a special case of which r(t)=const. When the radius of
circle is proportional to t, you get a spiral.

gnuplot> set xrange [-10*pi:10*pi]
gnuplot> set yrange [-10*pi:10*pi]
gnuplot> plot [0:10*pi] t*sin(t),t*cos(t)

The following example shows r(t)=const*(1+cos(t)), which is called
Cardioid.

gnuplot> set parametric

dummy variable is t for curves, u/v for surfaces
gnuplot> r(t) = 1+cos(t)
gnuplot> plot [0:2*pi] r(t)*cos(t),r(t)*sin(t)

exchange X and Y-axes

Functions are normaly expressed by y=f(x), but the parametric
expression allows us to make a graph of x=f(y). The y values are
the same as t, and the x values are calculated
with a function of f(t).

gnuplot> set parametric

dummy variable is t for curves, u/v for surfaces
gnuplot> c=2*pi
gnuplot> set size square
gnuplot> set trange [-c:c]
gnuplot> set xrange [-c:c]
gnuplot> set yrange [-c:c]
gnuplot> plot c*sin(t),t with lines, t,c*cos(t) with impulses

Two functions are shown, one (green stripe) is y=2pi*cos(x), and the other
(red solid line) is x=f(t)=2pi*sin(y).

The option with impulse draws a vertical line from the
Y=0 axis. If you use with impulses for the red curve
which is x=2pi*sin(y), you still get a vertical stripe, not a
horizontal one.