Of the two simple plugins, the first takes as input a parametric curve
and draws an approximate Bézier curve. (Mathematically, a parametric
curve is of the form *f(t)=(x(t),y(t))* in Cartesian coordinates,
where *t* is the parameter.) The second plugin does the same for a
curve given in the polar form.

The central aim of the plugins is to achieve a reasonably good approximation by resorting to only a small number of control points. This is contrary to the naive idea of just inserting control points more densely on the curve in order to reach the desired accuracy.

To install the simple plugins, start by downloading the zip file. Unzip it. It contains three items, two files and one folder:

- file
*simple_parametric_curve.py* - file
*doc.pdf* - folder
*example_files*(containing subfolders*param*and*polar*)

The file *simple_parametric_curve.py* is the most
important. It creates the two simple plugins when you insert it in your
user folder for Gimp plugins, called *<something>/plug-ins*,
and restart Gimp. The second file, *doc.pdf*, is the documentation
(instructions), and you had better first at least have a look at it and
when you have time to read it more closely. The folder *example_files
*contains some example files. Namely, there are two ways to
feed inputs to the plugins: from the GUI, or from a user-written file, and
the example files are examples of the latter method.

When you have put the file *simple_parametric_curve.py*
in your *plug-ins* folder and restarted Gimp, the two plugins should
appear in Gimp's menu as

__Simple polar
curve__, except that instead of two functions **x(t)**and
**y(t)**, you need to
input one function **r(t)**.
### How to apply the plugins from the GUI

## Download

__Image >
Filters > Render > Parametric Curves > Simple parametric
curve__

and

__Image >
Filters > Render > Parametric Curves > Simple polar curve__

In the file *doc.pdf * you will find detailed instructions
about the usage of the plugins, but a brief overview is given here to
make the start easier.

We talk first of the plugin __Simple parametric curve__. There are
two ways to apply it:

- The plugin can be launched straight from its GUI in Gimp, which
offers a
*simple*set of settings to choose from and a*simple*way to input the parametric curve as a pair of functions**x(t)**and**y(t)**in Python syntax; see below for more details. - It is also possible to apply the plugin more efficiently by
launching it from the same GUI but telling it to read the inputs from
a file. This enables the user to work with more complicated parametric
curves. In principle, any continuous parametric curve, implemented in
Python, can be used. (But the plugin
*is*simple and may fail with some curves.) Furthermore, in this way the inputs become automatically saved.Such a file can be written from scratch, but you can start more easily by editing some of the example files. What the input file can or should contain, is explained in

*doc.pdf*, and there you can find also examples.

Never mind at start about the example files. You can get acquainted
with the plugins by trying what you can do with the GUI. At the location
at Gimp's menu mentioned above you find the two simple plugins. Choose
the first one, __Simple parametric curve__: Clicking its name you
open its GUI. If you then click the OK button at the lower edge, the
plugin should draw a half circle. (Not very remarkable: that's just what
the built-in default inputs do.) Then go ahead and try to run the plugin
again, changing some of the settings to see what they do. Note that some
of the inputs, such as the starting value and ending value for the
parameter **t**, should be in Python
syntax: For example, the default value for the ending values is **"pi"** (that is 180 degrees
in radians), but if you wish to try 360 degrees, instead, you should
enter **"2*pi**"
(without the apostrophes!).

One entry asks to input a list of values of **t**,
but you had better ignore this until you have read from *doc.pdf*
what it means (but if you want to try, go ahead!). The same advice goes
for reading inputs from a file.

You will soon be wishing to draw some other curve. To this end you have
to input your curve as a parametric curve by typing a pair of functions
**x(t)**and **y(t)**
in Python syntax into the corresponding slots in the GUI. The standard
mathematical functions of Python are available.

For example, to draw the exponential function *y* = *e*^{
x}, you would write "t" in
the slot for the function **x(t)**,
and "exp(t)" in the slot for the function
**y(t)** (omitting the
apostrophes!). Then hit OK. If you are not satisfied with the result,
you can try setting the **starting ** and **ending** values for **t**
to "-2" and "2",
respectively, or whatever values you like. Make sure that **closed
**is set to "No".

Another example could be the *astroid*: The functions **x(t)**and
**y(t)** are "cos(t)**3"
and "sin(t)**3", respectively, and
the **starting**
and **ending**
values are "0" and "2*pi",
respectively. Click also the button for **closed**
to set it to "Yes"; the purpose is to
instruct Gimp to make the path closed.

More examples you can find in the file *doc.pdf* and in the
folder *example_files/param.*

Everything said above is true, with obvious modifications, for the
other plugin __Simple polar curve__. Open its GUI and try the
default curve there: just click OK. A logarithmic spiral arc will appear
on the screen. Experimenting further should now be easy if you just know
what a curve in a polar form means.

At this point it is probably__ __advisable to have a closer glance
at the file *doc.pdf*, and then you are ready to really try what
the plugins can and what they cannot do.