Documentation

LANGUAGE /COLORS / SPACE / PARAMETERS / VARIABLES / FUNCTIONS / CONTROLS /
EQUATIONS / POINTS / SEGMENTS / CURVES / ARCS / TEXTS/ BUTTONS

It is not necessary for the user of Descartes to study in detail the documentation of all its tools. The purpose of the documentation is to clarify some possible doubts that may arise when he or she uses Desacrtes to the limit of its possibilities. In order to start using Descartes it is enough to study the appetizer and look briefly at the examples. This section is intended more as a reference than as something to be read in detail.

There are fourteen tools to configure Descartes. These tools allow the user to show a wide variety of interactive graphs and to decide some additional aspects like the language and colours.

Each tool corresponds to one of the "parameters" understood by Descartes as an applet. These "parameters" are the applet parameters. This means that they appear on the html code where a call to the applet is made on a Web page. This is an example of such a call to the applet Descartes:

And this is the result of the applet call:

The reader will observe that there are 14 lines between the <applet>  and  </applet> tags. Each line starts with <param name= and then it has the name of parm between double quotes. Then it comes value=  and a string between double quotes. Most of these strings are empty (they have only one space to prevent the html editors from eliminating it), which means that the corresponding parameters are not being used in this particular call. These names and values are what in the Java-applet terminology are called the applet parameters. In other words, Desacrtes as an applet has 14 parameters. In order to avoid confusion with the mathematical use of the word parameter, throughout these pages we use the word tools for the Descartes parameters. The contents of this section of the document is a detailed  explanation of how each of these tools (the Descartes parameters) may be configurated.

We start with some general comments.

The strings used as a value in the applet Descartes use the character   ;  as a separator between configurations of different objects of the same type. In other words, each value string may contain the configurations of several objects separated by ; . A click on the config button of Descartes makes the  Descartes configuration window to pop out. On the upper left of this window there is a choice control with the fourteen Descartes tools as options. When the user selects one of these tools, the configuration panel for that tool appears in the middle of the configuration window and on it one can see the contents of the value string separated into several lines. These lines correspond to the substrings obtained with   ;  as separator. This presentation simplyfies the editing of the configuration by making it possible to concentrate on one object at a time thanks to the fact that each line contains the configuration of one and only one object. The character   ;  should never be used inside the configuration panel of a tool because it would be interpreted as a separator in the applet call.

The Descartes tools may be classified in three groups: the graphic, the auxiliary and the mixed tools. The graphic tools generate objects that have a distinct graphic representation on the coordinate system. They are: EQUATIONS, POINTS, SEGMENTS, CURVES and ARCS. The auxiliary tools generate objects that do not have a graphic representation on the coordinate system. They are: COLORS, TEXTS, PARAMETERS, VARIABLES and FUNCTIONS. The mixed tools are: SPACE and CONTROLS. SPACE itself does have a graphic representation but its objects are essentialy three PARAMETERS with fixed names. The CONTROLS on the other hand are POINTS which may be dragged by the user while their coordinates may be used as PARAMETERS.

The auxiliary tools are presented first because they are simpler. Follow the links to gain access to the documentation of each tool.

Auxiliary tools:

LANGUAGE.

BUTTONS.

COLORS.

TEXTS.

PARAMETERS.

VARIABLES.

FUNCTIONS.

Mixed tools:

SPACE.

CONTROLS.

Graphic tools:

We present here some general aspects of graphic tools.

In order to define the colour of any graph you must add an expression of the form: colour=red separated by : from the other configuration expressions.  The word red may be substituted by any of the predefined colours or by a hexadecimal expression (see COLORS for a list of the predefined colours and an explanation of the hexadecimal representation of colours).

EQUATIONS.

POINTS.

SEGMENTS.

CURVES.

ARCS.

All graphic tools have these three common features besides color: background, trace and sequence. They may be considered "advanced features". Their explanations are presented below. The reader must keep in mind that these features may be applied on any of the graphic tools.

background

If background is set to true then the graph is drawn only once on the coordinate system and it is kept there just as the coordinate axes or the net. In order to activate this feature you must write background=true. separated by : from the other features of the graphic object. background is also a feature of TEXTS. The graphic tools and the TEXTS that have background=true specified, are drawn only at the start, when the Init button is clicked or when the SPACE parameters are modified. This feature is very useful to speed up the interactions with the applet by leaving as fixed elements on the background some graphs that take time to draw but they never change because they do not depend on the parameters or on the CONTROLS.  Such graphs are frequently used as visual references for the other graphs. This feature is applied on the conic sections construction and their reflection properties. The graphic objects and the TEXTS which don't have the specification background=true, are drawn every time a parameter is changed or a control is moved. The default value of this feature is of course background=false and may be omited.

trace

The feature trace is used to leave a trace on the screen of the previously drawn graphs. To activate this feature an expression like this: trace=red must be added on the configuration line of the object, separated by : from the other features. Of course the word red may be substituted by any other valid colour expression. The specified colour is used to draw the graphs left as the trace of the graphic object. The trace graphs become background graphs. If the user writes trace=false then no trace is left. If trace=true is written then the trace graphs are drawn in  gray. In order to erase the traces left by the various graphs the user may either click the right mouse button on the applet or click the Clear button. Look at the Introduction for an example of the trace feature.

sequence

The sequence feature may be used on any graphic tool to create a family of graphs. In order to draw  families of EQUATIONS, SEGMENTS, POINTS, ARCS or CURVES, one should add an expression of the form:

sequence=s[a,b]n

(separated by : from the other features). s is the name of the variable which will be used to generate the family of graphs,  [a,b] is the interval of values which s will sweep and  n is the number of subintervals into which [a,b] will be divided. Such expression generates  n+1 graphs, unless  a=b, in which case only one graph is drawn. The example families of curves illustrates the use of the   sequence feature on EQUATIONS and ARCS. The example parabolic throw illustrates the use of  sequence on CURVES.

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	Ministerio de Educación, Cultura y Deporte. Aņo 2000