* THE INPUT PAGE

The Input page contains two selectors, the first one in the form
of a couple of radio buttons, the second one in the form of a combo.

The radio buttons are labeled with "2D" and "3D", respectively. 
As the labels say, they allow to switch between two- and three-dimensional
graphic mode by clicking on them. Mind that GTKMathplot allows you
to plot both two- and three-dimensional shapes, but not together at once.
Thus, you can not mix two- and three-dimensional objects in the same graphic
but you should choose each time in which graphic mode you want to operate.
The default graphic mode, i.e. the one selected after the start of the program,
is the two-dimensional one.

The combo selector lets you pick up the mathematical shape you want to define 
or whose definition you want to change.
GTKMathplot allows you to display several mathematical shapes at a time, namely
up to 10 in two-dimensional mode and up to 5 in three-dimensional mode. 
Each shape is defined by its own equation or set of equations.

The shapes are identified by numbers (from 1 to 10 or from 1 to 5) and the combo
always shows the currently selected shape. Immediately after the start of the
program the selected shape is the number 1.
You can switch to another shape by clicking on the combo: a menu
opens and from there you can select another shape by clicking on the 
corresponding entry.

The most important element of the Input page is the input mask containing the
"Object definition". In the input mask you should enter the mathematical 
definition of a curve or surface. This consists of one or more equations
and of the variation interval(s) of the parameter(s) appearing in those 
equations.

GTKMathplot lets you define an object either by means of a single cartesian 
equation or by means of a set of parametric equations.
The default definition type is "Cartesian", meaning that GTKMathplot expects 
you define a mathematical shape by means of a single cartesian equation. 
To switch to the "Parametric" mode, you should click on the radio button with 
this label.
To switch back to the cartesian definition type, just click on the "Cartesian"
radio button.

The actual aspect of the input mask depends on the chosen definition type.

If the active definition type is "Cartesian", then you can see one long text
entry where you are supposed to enter the cartesian equation describing 
the object. Near to this entry, on the left side, there is either the label
"y(x) = " or the label "z(x,y) = " depending whether the current graphic
mode is either 2D (two-dimensional) or 3D (three-dimensional).
If the definition type is set to "Parametric", you will see three long
text entries marked with the labels "x(s,t) =", "y(s,t) =", and "z(s,t) =",
respectively (although the "z(s,t) =" entry is disabled in two-dimensional
graphic mode). In these entries you should type the parametric equations
defining the object you would like to visualize. If you do not know
what parametric equations are, then you will probably never need to work
with the "Parametric" definition type. Anyway, if you are curious, you can know
more about parametric equations by reading the section [[EXAMPLES]].  

Under the text entry/entries for the equation(s) you can see one or two rows
of three text entries each.
Here you should enter the minimum and the maximum value that the parameter(s)
appearing in the equation can take.
If you need it, you can also specify for each parameter the number of 
subintervals into which the variation interval (i.e. the interval between 
minimum and maximum of the parameter) has to be split. 
The default value, either 200 or 50, is adequate for the greatest part of
use cases. A higher value means a smoother appearance of the displayed
object, a too low value produces rough shapes with artificial edges. 
Mind that what 'too low' exactly means depends on the particular
equation(s) defining the mathematical object.
If this is visualized in a too rough way, then you should definitely increase
the number of subintervals for one or both parameters.

To every mathematical object you can associate a caption,
which is going to be shown in a legend near to the canvas;
the caption can be entered in the text entry labeled with "caption:".

A mathematical object can be drawn by GTKMathplot in different plot styles, 
namely dotted, stroked, or filled.
The  plot style can be chosen by clicking on the corresponding radio button 
within the "Plot style" frame.
The filled style applies only to surfaces: filled surfaces are visualized 
by means of filled facets (in 3D) or triangles (in 2D).
Stroked curves and surfaces are visualized as metal wire skeletons formed by 
many, and possibly very small, segments.
Dotted curves and surfaces are displayed on the canvas as sets of vertices; 
if these ones are displaced tightly enough, you can reconstruct from their 
displacement the shape of the curve or surface they belong to.

Finally, the input mask contains four buttons.
The "Clear" button can be used to clear all text entries of the input mask.

If you click on the "Save to..." button, a file selector appears.
Here you should choose a file where to save the current mathematical definition.
The file can have an arbitrary name, but its extension should always be ".mdef", 
like in "ArbitraryName.mdef".
If the file name you choose corresponds to an already existent file, you will be 
asked for confirmation before the file is overwritten with the information 
forming the current mathematical definition.
If the current mathematical definition is not entirely correct, for example
because of an error in the equation or since the maximum of a parameter 
is not greater than its minimum, then GTKMathplot will refuse to save anything
in the chosen file and will show you a suitable error message.

What has been told about the "Save to..." function, can be repeated for
the "Evaluate & Save" button. There are however two important differences.
In the file you choose after clicking on "Evaluate & Save" GTKMathplot
will not save the definition in the input mask, but a sequence of
points coordinates separated by empty lines.
GTKMathplot evaluates indeed the mathematical object defined in the input
mask: it uses the entered information to compute the coordinates of the points
forming the shape that it would draw on the canvas if you pressed the button 
"Display/Update graphic", instead of "Evaluate & Save".
Mind that the file where the results of these computations will be stored
should have extension ".gdat", like in like in "ArbitraryName.gdat".

The file produced by GTKMathplot when you request to evaluate and save
a mathematical definition is compatible with GNUplot, meaning that
you can visualize also in GNUplot the stored curve or surface by using
either the `plot` command (for curves) or `splot` (for surfaces).
To know more abot the format of these files, see the section 
[[FORMAT OF GDAT FILES]].

If you click on the "Load from..." button, a file selector is shown on 
the screen.
Here you should choose a file from where to load a previously saved 
mathematical definition.
The files selector always shows you all files with ".mdef" extension contained
in the selected directory. If you choose a file whose name does not end with 
the extension ".mdef", GTKMathplot will refuse to open it and display an error
message.

** SHORTCUTS FOR THE INPUT PAGE

- Alt+l  : Open file selector to load a mathematical definition from a file
- Alt+s  : Open file selector to save the current definition to a file
- Alt+v  : Same as clicking on the "Evaluate & Save" button
- Alt+c  : Clear the input mask
- Alt+d  : Display/Update graphic (switch to the Output page)
