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<book id="GeometriaUsersGuide" lang="en">

<title>Geometria 3.2</title>
<subtitle>User's Guide</subtitle>

<chapter id="General">
<title>General</title>

<!-- Help page start -->

<sect1 id="Overview">
<title>Overview</title>

<para>
<emphasis>Geometria</emphasis>
provides a graphic interface
for creating and solving problems in solid geometry.
</para>

<para>
At any given time, the Geometria user is either a problem
<emphasis>creator</emphasis>
(a.k.a. teacher) or a problem
<emphasis>solver</emphasis>
(a.k.a. student).
</para>

<para>
Both problems and solutions are called
<emphasis>documents</emphasis>.
Documents are saved in files. Users engage in a Geometria process as follows:
</para>

<itemizedlist>

<listitem>
The creator creates a problem, provides it with an
<link linkend="Answer">answer</link>
and
<link linkend="SaveProblem">saves</link>
the problem to a file.
</listitem>

<listitem>
The solver
<link linkend="OpenProblem">opens</link>
the problem file and starts a
<link linkend="CreateSolution">new solution</link> to the problem.
</listitem>

<listitem>
The solution consists of a number of actions. The actions are recorded in
the solution
<link linkend="SolutionLog">log</link>.
</listitem>

<listitem>
The solver
<link linkend="Answer">answers</link>
the problem. The solver's answer is considered correct if it matches
the creator's. A correct answer concludes the solution
<link linkend="SolutionLog">log</link>.
The solver
<link linkend="SaveSolution">saves</link>
the solution to a file.
</listitem>

<listitem>
The solution can be
<link linkend="SolutionLog">played back</link>
by
<link linkend="OpenSolution">opening</link>
the file and following the solver's actions.
</listitem>

</itemizedlist>

<para>
Note that Geometria performs no semantic analysis of the problem in order
to determine if the creator's answer is actually correct. The answer
may be incorrect or even make no sense at all.
The problem may make no sense either. The problem might ask:
</para>

<para>
<emphasis>
What is the highest point in Monkey's Brow County, KY?
</emphasis>
</para>

<para>
and be answered as:
</para>

<para>
<emphasis>
Point Z in figure MyPyramid.
</emphasis>
</para>

<para>
If that is what the creator considers a correct answer to the problem,
it's fine with Geometria. However, it is unlikely that his problem
will get much attention from solvers.
</para>

<para>
Every document contains the problem text, an
<link linkend="Envelope">envelope</link>,
a number of figures and a number of notepad
<link linkend="Notepad">records</link>.
Figures are limited to convex polyhedra. Figures can be
measured, drawn upon, transformed,
<link linkend="RotateFigure">rotated</link>,
<link linkend="ViewModes">viewed</link>
transparent or opaque.
</para>

<para>
Measurements and drawings can only be made on the surface of a figure.
Actions in the figure's interior are possible by
<link linkend="CutFigure">cutting</link>
the figure with a suitable plane.
</para>

<para>
Labels and
<link linkend="Variables">variables</link>
provide a convenient abstraction over numeric coordinates
and measurements.
<link linkend="Variables">Variables</link>
are used in
<link linkend="Calculator">calculations</link>
and referenced in drawings. Labels and variables are also used to
<link linkend="Answer">answer</link>
the problem.
</para>

<para>
The
<link linkend="Answer">answer</link>
is not necessarily numeric. In fact, some of the most challenging
problems cannot be answered with a number. The problem may ask for a certain
point, segment, path or plane to be constructed. For example:
</para>

<para>
<emphasis>
Find a plane that is parallel to the diagonal of the cube and cuts off
the cube twice the volume of the pyramid.
</emphasis>
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Calculator">Calculator</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="Variables">
<title>Variables</title>

<sect2 id="CreatingAVariable">
<title>Creating a Variable</title>

<para>
A <emphasis>variable</emphasis> is created as a result
of a measurement or a calculation. A newly created variable has
a name and a definition. For instance, the variable myDistance in the
example below is defined as the distance between points P and W in figure
MyCube:
</para>

<programlisting>
myDistance = |PW| : MyCube
</programlisting>

<para>
In another example, variable myArea is a result of a calculation upon
previously defined variables myVolume and myDistance:
</para>

<programlisting>
myArea = 2 * myVolume / myDistance
</programlisting>

<para>
Newly created variables are automatically recorded,
along with their definitions, on the
<link linkend="Notepad">notepad</link>.
</para>

<para>
Variable names can contain alphanumeric characters alone.
Special and accented characters are not allowed. A variable name cannot
contain spaces.
</para>

<para>
Variable names are case sensitive. Thus,
<emphasis>myArea</emphasis>
and
<emphasis>MyArea</emphasis>
will reference two distinct variables.
</para>

<para>
<emphasis>PI</emphasis>
is reserved for the corresponding constant and cannot be used for newly
created variables. However, it can be used in
<link linkend="Calculator">calculations</link>.
</para>

</sect2>

<sect2 id="ValueOfAVariable">
<title>Value of a Variable</title>

<para>
Each variable has a numeric value. However, in most cases, this value
remains transparent to the user. The user can create and solve
Geometria problems without ever knowing the underlying values of the
variables he or she has defined. To see the numerical value of a variable,
type the variable in the
<link linkend="Calculator">calculator</link>
and click the <emphasis>Evaluate</emphasis> button.
Due to roundup errors, the numeric values may slightly vary over the process
of creating or solving the problem.
</para>

<para>
The value of a variable may change as a result of certain actions upon
figures. If, in the example above, MyCube is
<link linkend="ScaleFigure">scaled</link>
by the factor of 3,
the value of myDistance will be implicitly multiplied by 3.
The values of any variables that depend on myDistance, such as
myArea, will be automatically updated as well.
</para>

<para>
However, the numerical value of the
<link linkend="Answer">answer</link>
will be unaffected by actions upon
figures. If, in the example above, the problem creator enters myDistance
as the problem answer
<emphasis>before</emphasis>
scaling the figure, the value of the answer will not change, even though
myDistance will carry a new value in all subsequent calculations. This
note applies to all types of answer.
</para>

<para>
Therefore, the problem creator should consider (re)entering the answer
before making the problem available to solvers.
</para>

</sect2>

<sect2 id="PinnedVariable">
<title>Pinned Variable</title>

<para>
After certain actions, the definition of a variable may become obsolete.
For example, if point P or point W is
<link linkend="EraseElements">erased</link>,
the definition of the variable myDistance above will become obsolete.
Same if figure MyCube is
<link linkend="RemoveFigure">removed</link>.
Such a variable is called <emphasis>pinned</emphasis>.
</para>

<para>
A pinned variable is no longer dependent upon its
original definition and its value will no longer be updated.
For example,
<link linkend="EraseElements">erasing</link>
point P in figure MyCube will pin variable myDistance.
If MyCube is subsequently scaled as described above,
the value of myDistance will nevertheless stay the same.
</para>

<para>
If the action that pinned a variable is
<link linkend="UndoActions">undone</link>,
the definition of the variable is restored and the variable
becomes again targeted for updates.
</para>

</sect2>

<sect2 id="LifetimeOfAVariable">
<title>Lifetime of a Variable</title>

<para>
Once a variable is defined, it can be used in
<link linkend="Calculator">calculations</link> and
referenced in actions, such as measuring, drawing
and transforming figures. A variable can also be used to
<link linkend="Answer">answer</link> a problem. A pinned variable
can still be used in calculations and references.
</para>

<para>
A variable exists as long as it is recorded on the
<link linkend="Notepad">notepad</link>.
Clearing the
<link linkend="Notepad">notepad</link>
is the only way to remove a variable. Use caution since this
action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
When the document, such as a problem or a solution, is saved,
all the variables recorded on the
<link linkend="Notepad">notepad</link>
are saved, too. 
</para>

</sect2>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>
<listitem>
<link linkend="Calculator">Calculator</link>
</listitem>
<listitem>
<link linkend="SaveProblem">Save Problem</link>
</listitem>
<listitem>
<link linkend="SaveSolution">Save Solution</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

<sect2 id="RenameVariable">
<title>Rename Variable</title>

<para>
To rename a variable, select
<emphasis>Rename Variable</emphasis>
from the
<emphasis>Edit</emphasis>
menu. Alternatively, select the notepad
<link linkend="Notepad">record</link>
that defines the variable, right click and select
<emphasis>Rename Variable</emphasis>
from the popup menu.
</para>

<para>
A dialog will pop up. Select the variable you wish to rename from the drop-down list,
enter the new name for the variable and click
<emphasis>OK</emphasis>.
The new name must be a
<link linkend="CreatingAVariable">valid</link>
variable name.
</para>

<para>
Click on the record that defines the variable on the
<link linkend="Notepad">notepad</link>
ahead of time, to have it automatically selected in the input box.
</para>

<para>
Renaming a variable will result in some of the notepad
<link linkend="Notepad">records</link>
being updated accordingly.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>

</itemizedlist>

</sect2>

</sect1>

<sect1 id="Calculator">
<title>Calculator</title>

<sect2 id="Expressions">
<title>Expressions</title>

<para>
Calculations are performed upon valid expressions. Expressions can contain
numbers,
<link linkend="Variables">variables</link>,
the constant
<emphasis>PI</emphasis>,
operators, functions and parentheses.
</para>

</sect2>

<sect2 id="Assignment">
<title>Assignment</title>

<para>
The calculator operates in the context of the currently open document.
</para>

<para>
To calculate an expression myExpression and assign the result
to a new variable myVariable, type in:
</para>

<programlisting>
myVariable = myExpression
</programlisting>

<para>
and click
<emphasis>Evaluate</emphasis>.
The variable name must be unique in the context of the currently
open document. A new record will be added to the
<link linkend="Notepad">notepad</link>. The newly created variable can be
used in subsequent calculations and references.
</para>

<para>
If no document is open, the numeric result of the calculation
will be displayed. No new variable will be created.
</para>

</sect2>

<sect2 id="Operators">
<title>Operators</title>

<para>
The following operators are supported:
</para>

<itemizedlist>	

<listitem>
+ (add)
</listitem>

<listitem>
- (negate, subtract)
</listitem>

<listitem>
* (multiply)
</listitem>

<listitem>
/ (divide)
</listitem>

<listitem>
^ (power operator)
</listitem>

</itemizedlist>

</sect2>

<sect2 id="Functions">
<title>Functions</title>

<para>
The following functions are supported:
</para>

<itemizedlist>

<listitem>
sqrt (square root)
</listitem>

<listitem>
sin
</listitem>

<listitem>
cos
</listitem>

<listitem>
tan
</listitem>

<listitem>
asin
</listitem>

<listitem>
acos
</listitem>

<listitem>
atan
</listitem>

</itemizedlist>

<para>
Arguments to functions are taken into parentheses.
</para>

</sect2>

<sect2 id="Examples">
<title>Examples</title>

<para>
Calculate the side of a cube whose volume is myVolume:
</para>

<programlisting>
mySide = myVolume ^ (1 / 3)
</programlisting>

<para>
Calculate the side adjacent to angle myAngle
in a right triangle whose hypothenuse is myHypothenuse:
</para>

<programlisting>
mySide = myHypothenuse * cos(myAngle)
</programlisting>

</sect2>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="Notepad">
<title>Notepad</title>

<para>
Each time a new
<link linkend="CreatingAVariable">variable</link>
is created as a result of a measurement or a
<link linkend="Calculator">calculation</link>,
a record is added to the notepad automatically.
Each record consists of a unique variable name and,
possibly, a definition. Measurement records may also contain the name of
the figure where the measurement was taken. For example, the following record:
</para>

<programlisting>
myDistance = |AB| : MyCube
</programlisting>

<para>
is the result of measuring the distance between
points A and B in a figure named MyCube. The distance has been assigned
the variable myDistance. The record:
</para>

<programlisting>
myAngle = &lt;PLX
</programlisting>

<para>
is a result of measuring an angle. The figure name is not shown since
the document currently contains a single figure. The record:
</para>

<programlisting>
myVolume = volume : Figure1
</programlisting>

<para>
is the result of measuring the volume of a figure named Figure1.
The following record was added after a
<link linkend="Calculator">calculation</link>:
</para>

<programlisting>
h = 2 * myVolume / myArea
</programlisting>

<para>
If a variable is
<link linkend="PinnedVariable">pinned</link>,
its definition no longer shows on the notepad. For example,
if point X is
<link linkend="EraseElements">erased</link>,
the variable myAngle will be stripped of its definition and
the second example above will read:
</para>

<programlisting>
myAngle
</programlisting>

<para>
Notepad records are owned by the current document, whether it is
a problem or a solution. When the document is saved to a file,
the records will likewise be saved to that file.
</para>

<para>
If the current document is
<link linkend="CloseDocument">closed</link>,
the notepad will be cleared of records. If another document is
opened, its notepad records will be displayed instead.
</para>

<para>
To erase all records from the notepad, select
<emphasis>Clear Notepad</emphasis>
from the <emphasis>Edit</emphasis> menu.
Use caution since this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
To deselect the notepad records, right click and choose
<emphasis>Clear Selection</emphasis>
from the popup menu.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Calculator">Calculator</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="UndoActions">
<title>Undo Actions</title>

<para>
To undo the last action performed on a figure or a document, select
<emphasis>Undo</emphasis>
from the <emphasis>Edit</emphasis>
menu or click the

<inlinemediaobject> 
<imageobject>
<imagedata fileref="../../images/24x24/Undo.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar. In a solution, the action will be also
erased from the
<link linkend="SolutionLog">log</link>.
The actions are undone in the reverse order
as they have been performed.
</para>

<para>
To view a short description of the action that would be undone,
pause the mouse over the 

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Undo.png"/>
</imageobject> 
</inlinemediaobject>

button.
</para>

<para>
Any undone action can be
<link linkend="RedoActions">redone</link>.
</para>

<para>
Some of the actions cannot be undone. A warning is displayed when such
an action is about to take place.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="RedoActions">Redo Actions</link>
</listitem>
<listitem>
<link linkend="SolutionLog">Log</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="RedoActions">
<title>Redo Actions</title>

<para>
To redo the last undone action on a figure or a document, select
<emphasis>Redo</emphasis>
from the <emphasis>Edit</emphasis>
menu or click the

<inlinemediaobject> 
<imageobject>
<imagedata fileref="../../images/24x24/Redo.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar. In a solution, the action will be added to the
<link linkend="SolutionLog">log</link>.
The actions are redone in the reverse order as they have been undone.
</para>

<para>
To view a short description of the action that would be redone,
pause the mouse over the 

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Redo.png"/>
</imageobject> 
</inlinemediaobject>

button.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>
<listitem>
<link linkend="SolutionLog">Log</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="Options">
<title>Options</title>

<sect2 id="Font">
<title>Font</title>

<para>
To make the characters larger or smaller, select
<emphasis>Font</emphasis>
from the
<emphasis>Options</emphasis>
menu, then select the desired font size.
</para>

</sect2>

<sect2 id="Language">
<title>Language</title>

<para>
To switch to a different language, select
<emphasis>Language</emphasis>
from the
<emphasis>Options</emphasis>
menu, then select the desired language.
</para>

</sect2>

</sect1>

<sect1 id="KnownLimitations">
<title>Known Limitations</title>

<sect2 id="InordinateSizeOrShape">
<title>Inordinate Size or Shape</title>

<para>
The application may behave erratically if the figures contain excessively
sized or oddly shaped elements. Here are some guidelines for keeping the
figures safe:
</para>

<itemizedlist>

<listitem>
Avoid both very large (over 100) and very small (under 0.01)
<link linkend="ScaleFigure">scaling</link>
factors. 
</listitem>

<listitem>
When creating a prism or a pyramid using the
<link linkend="FigureGallery">figure gallery</link>,
keep the number of sides within reasonable limit (under 100).
By design, Geometria cannot handle any solids but convex polyhedra.
However
<link linkend="ToggleTransparency">opaque</link>
prisms and pyramids with a large number of sides do look like
cylinders and cones respectively. Unfortunately, actions upon such figures
may be slow and unimpressive. The application may become unstable and
fail to respond to user actions.
</listitem>

</itemizedlist>

</sect2>

<sect2 id="PreviousVersionsOfGeometria">
<title>Previous Versions of Geometria</title>

<para>
Problems, solutions and figures created with Geometria versions prior
to 3.0 are no longer supported. However,
we plan to have all future versions of Geometria backward compatible
with 3.0.
</para>

</sect2>

<sect2 id="SolutionLanguage">
<title>Solution Language</title>

<para>
Solution files created with Geometria versions prior to 3.1 must be
<link linkend="OpenSolution">opened</link>
using the same
<link linkend="Language">language</link>
in which they were
<link linkend="SaveSolution">saved</link>.
</para>

</sect2>

</sect1>

</chapter>

<chapter id="Documents">
<title>Documents</title>

<sect1 id="Envelope">
<title>Envelope</title>

<para>
The envelope of a document, such as a problem or a solution, consists
of the name, email address and web page of the author and
some comments. All fields are optional.
</para>

<para>
To edit the envelope, select <emphasis>Envelope</emphasis>
from the <emphasis>Edit</emphasis> menu or click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Envelope.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
A dialog will pop up. Fill in the fields and click
<emphasis>OK</emphasis>.
</para>

<para>
Envelope changes can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="Answer">
<title>Answer</title>

<para>
A problem is not ready to be solved until the creator supplies it with
an answer. The solver's answer is considered correct if it matches the
creator's (see
<link linkend="Overview">Overview</link>
for details).
</para>

<sect2 id="CreatorsAnswer">
<title>Creator's Answer</title>

<para>
To define the answer to the currently open problem, select
<emphasis>Answer</emphasis> from the 
<emphasis>Edit</emphasis> menu.
Select the answer type:
</para>

<itemizedlist>

<listitem>
Number
</listitem>

<listitem>
Point Set
</listitem>

<listitem>
Segment Set
</listitem>

<listitem>
Fixed Plane
</listitem>

<listitem>
Condition Plane, or
</listitem>

<listitem>
Multiple choice
</listitem>

</itemizedlist>

<para>
Open the
<emphasis>Value</emphasis> pane.
</para>

</sect2>

<sect2 id="AnswerTypes">
<title>Answer Types</title>

<sect3 id="ANumber">
<title>Number</title>

<para>
Enter a valid
<link linkend="Expressions">expression</link>.
Click
<emphasis>OK</emphasis>.
To minimize the input, have a notepad
<link linkend="Notepad">record</link>
selected ahead of time.
</para>

</sect3>

<sect3 id="PointSet">
<title>Point Set</title>

<para>
The term
<emphasis>point set</emphasis>
refers to a single point, end points of a segment (2 points) or a path
(2 or more points).
</para>

<para>
Enter one or more labels separated by commas. Click
<emphasis>OK</emphasis>.
To minimize the input, have the points
<link linkend="SelectElements">selected</link>
ahead of time in the selected figure.
</para>

</sect3>

<sect3 id="SegmentSet">
<title>Segment Set</title>

<para>
The segments must satisfy a certain condition. Currently, the following conditions are supported:
</para>

<itemizedlist>

<listitem>
The segments form a
<ulink url="http://en.wikipedia.org/wiki/Hamiltonian_path">Hamiltonian cycle</ulink>
in the selected figure
</listitem>

</itemizedlist>

</sect3>

<sect3 id="FixedPlane">
<title>Fixed Plane</title>

<para>
Reference the plane by 3 comma-separated labels. Click
<emphasis>OK</emphasis>.
To minimize the input, have some reference elements, such as 3 points,
a point and a segment, or a face
<link linkend="SelectElements">selected</link>
ahead of time in the selected figure.
</para>

</sect3>

<sect3 id="ConditionPlane">
<title>Condition Plane</title>

<para>
Unlike a fixed plane, that is a plane occupying a fixed position in space, a
<emphasis>condition plane</emphasis>
must satisfy a number of conditions. Generally, a
condition plane is not unique.
</para>

<para>
There are three groups of conditions. Select a condition in at least one
of the groups. Click
<emphasis>OK</emphasis>.
</para>

<para>
The first group contains the following conditions:
</para>

<itemizedlist>

<listitem>
Plane contains a given point
</listitem>

<listitem>
Plane contains a given line
</listitem>

<listitem>
Plane does not contain a given point
</listitem>

<listitem>
Plane does not contain a given line
</listitem>

<listitem>
Plane contains no vertex of the selected figure
</listitem>

<listitem>
Plane contains no edge of the selected figure
</listitem>

<listitem>
Plane is parallel to a given line
</listitem>

<listitem>
Plane is parallel to a given plane
</listitem>

<listitem>
Plane is perpendicular to a given line
</listitem>

<listitem>
Plane is perpendicular to a given plane
</listitem>

</itemizedlist>

<para>
Reference the given point, line or plane, as required, by
comma-separated labels. To minimize the input, have the elements
<link linkend="SelectElements">selected</link>
ahead of time in the selected figure.
</para>

<para>
The second group consists of the following condition:
</para>

<itemizedlist>

<listitem>
Plane divides the volume of selected figure in given ratio
</listitem>

</itemizedlist>

<para>
Enter a valid
<link linkend="Expressions">expression</link>.
The expression will be interpreted as the numerator of a ratio whose
denominator is 1. For example, a + 1 means that the volume
should be cut in ratio a + 1 : 1.
Select a notepad
<link linkend="Notepad">record</link>
ahead of time to have it copied automatically to the input box.
</para>

<para>
The third group refers to the way the plane cuts the figure.
The section may be shaped like an:
</para>

<itemizedlist>

<listitem>
Isoscelles triangle
</listitem>

<listitem>
Right triangle
</listitem>

<listitem>
Equilateral (regular) triangle
</listitem>

<listitem>
Parallelogram
</listitem>

<listitem>
Rhombus
</listitem>

<listitem>
Rectangle
</listitem>

<listitem>
Square
</listitem>

</itemizedlist>

<para>
The answer definition can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
Note that, although, as a rule, the problem creator enters the answer
symbolically, Geometria stores all answers numerically. Once entered,
the answer will be unaffected by all subsequent actions upon figures.
Therefore it is a good idea to (re)enter the answer as a last action
before saving the problem and making it available to solvers.
</para>

</sect3>

<sect3 id="MultipleChoice">
<title>Multiple choice</title>

<para>
Enter an option. Click the
<emphasis>Add</emphasis>
button to add another option. Click the
<emphasis>Remove</emphasis>
button to remove an option. Each option must be unique. Select the correct option. Click
<emphasis>OK</emphasis>.
</para>

</sect3>

</sect2>

<sect2 id="SolversAnswer">
<title>Solver's Answer</title>

<para>
The solver concludes the solution by providing a correct answer.
Note, again, that the solver's answer is considered correct
if it matches the creator's.
</para>

<para>
Have the solution
<link linkend="OpenSolution">opened</link>.
Select
<emphasis>Answer</emphasis> from the
<emphasis>Edit</emphasis> menu.
Enter a valid
<link linkend="Expressions">expression</link>
or comma-separated labels, as appropriate.
To minimize the input, have a notepad
<link linkend="Notepad">record</link>
and/or some elements, such as points, segments or a face,
<link linkend="SelectElements">selected</link>
ahead of time in the selected figure. Click
<emphasis>OK</emphasis>.
</para>

<para>
An evaluation of the answer (corect or incorrect) will pop up.
</para>

<para>
If the answer is correct, it will conclude the solution
<link linkend="SolutionLog">log</link>.
No more actions will be possible unless the answer is
<link linkend="UndoActions">undone</link>.
You may want to
<link linkend="SaveSolution">save</link> the solution to a file.
A saved solution can later be
<link linkend="SolutionLog">played back</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Overview">Overview</link>
</listitem>
<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>
<listitem>
<link linkend="SelectElements">Select</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

</sect1>

<sect1 id="CreateProblem">
<title>Create Problem</title>

<para>
Create a problem by either selecting
<emphasis>Create Document-&gt;Problem</emphasis> from the
<emphasis>Document</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/NewProblem.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
If there are unsaved modifications in the current document,
a dialog will be displayed asking
if the current document should be saved before it is closed.
</para>

<para>
Click <emphasis>Yes</emphasis> to save
the current document. 
</para>

<para>
Click <emphasis>No</emphasis> to close
the current document without saving. Note that all unsaved modifications
to the current document will be lost.
</para>

<para>
Click <emphasis>Cancel</emphasis> to dismiss the dialog
with no action taken.
</para>

<para>
If concluded, this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="OpenProblem">Open Problem</link>
</listitem>
<listitem>
<link linkend="SaveProblem">Save Problem</link>
</listitem>
<listitem>
<link linkend="CloseDocument">Close Document</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="OpenProblem">
<title>Open Problem</title>

<para>
Open a problem from a file by either selecting
<emphasis>Open Document-&gt;Problem</emphasis> from
the <emphasis>Document</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/OpenProblem.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar. Alternatively, drag the file into the Geometria window. 
</para>

<para>
If there are unsaved modifications in the current document,
whether it is a problem or a solution,
a dialog will be displayed asking
if the current document should be saved before it is closed.
</para>

<para>
Click <emphasis>Yes</emphasis> to save
the current document. 
</para>

<para>
Click <emphasis>No</emphasis> to close
the current document without saving. Note that all unsaved modifications
to the current document will be lost.
</para>

<para>
Click <emphasis>Cancel</emphasis> to dismiss the dialog
with no action taken.
</para>

<para>
If concluded, this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="CreateProblem">Create Problem</link>
</listitem>
<listitem>
<link linkend="SaveProblem">Save Problem</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>
<listitem>
<link linkend="CloseDocument">Close Document</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="SaveProblem">
<title>Save Problem</title>

<para>
Save the currently open problem to a file by either selecting
<emphasis>Save Document</emphasis> from
the <emphasis>Document</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/SaveDocument.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
To save the problem under a different name, select
<emphasis>Save Document As</emphasis> from
the <emphasis>Document</emphasis> menu.
</para>

<para>
This action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
If this is a final revision of the problem, you may consider
<link linkend="Notepad">erasing</link>
all working calculations and measurements from the notepad.
The records will not show on the notepad to the problem's solver,
however, unless cleared, they will still be present in the file.
</para>

<para>
Beware, though, that the action of clearing the notepad cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
A final revision of the problem should also be provided with an
<link linkend="Answer">answer</link>.
</para>

<para>
To prevent any further editing of the problem, select
<emphasis>Save Locked Problem As</emphasis>
from the <emphasis>Document</emphasis> menu. When the solver opens
a locked problem file, Geometria will automatically start a new
solution. The solver will not be able to modify the problem itself.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="CreateProblem">Create Problem</link>
</listitem>
<listitem>
<link linkend="OpenProblem">Open Problem</link>
</listitem>
<listitem>
<link linkend="CloseDocument">Close Document</link>
</listitem>
<listitem>
<link linkend="Answer">Answer</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="CreateSolution">
<title>Create Solution</title>

<para>
Create solution to the currently opened problem by either selecting
<emphasis>Create Document-&gt;Solution</emphasis> from
the <emphasis>Document</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/NewSolution.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
If the problem you wish to solve is not opened,
<link linkend="OpenProblem">open</link> it first.
</para>

<para>
If there are unsaved modifications in the current problem,
a dialog will be displayed asking
if the current problem should be saved before it is closed.
</para>

<para>
Click <emphasis>Yes</emphasis> to save
the current problem. Note that you will be solving the version of
the problem you just saved.
</para>

<para>
Click <emphasis>No</emphasis> to close
the current problem without saving. Note that all unsaved modifications
to the current problem will be lost and you will be solving
the last saved version of the problem.
</para>

<para>
Click <emphasis>Cancel</emphasis> to dismiss the dialog
with no action taken.
</para>

<para>
If concluded, this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="OpenProblem">Open Problem</link>
</listitem>
<listitem>
<link linkend="OpenSolution">Open Solution</link>
</listitem>
<listitem>
<link linkend="SaveSolution">Save Solution</link>
</listitem>
<listitem>
<link linkend="CloseDocument">Close Document</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="OpenSolution">
<title>Open Solution</title>

<para>
Open a solution from a file by either selecting
<emphasis>Open Document-&gt;Solution</emphasis> from
the <emphasis>Document</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/OpenSolution.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar. Alternatively, drag the file into the Geometria window.
</para>

<para>
If there are unsaved modifications in the current document,
whether it is a solution or a problem,
a dialog will be displayed asking
if the current document should be saved before it is closed.
</para>

<para>
Click <emphasis>Yes</emphasis> to save
the current document. 
</para>

<para>
Click <emphasis>No</emphasis> to close
the current document without saving. Note that all unsaved modifications
to the current document will be lost.
</para>

<para>
Click <emphasis>Cancel</emphasis> to dismiss the dialog
with no action taken.
</para>

<para>
If concluded, this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="CreateSolution">Create Solution</link>
</listitem>
<listitem>
<link linkend="SaveSolution">Save Solution</link>
</listitem>
<listitem>
<link linkend="CloseDocument">Close Document</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="SaveSolution">
<title>Save Solution</title>

<para>
Save the currently open solution to a file by either selecting
<emphasis>Save Document</emphasis> from
the <emphasis>Document</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/SaveDocument.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
To save the solution under a different name, select
<emphasis>Save Document As</emphasis> from
the <emphasis>Document</emphasis> menu.
</para>

<para>
This action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
If this is a final revision of the solution, do not forget to conclude it
with a correct
<link linkend="Answer">answer</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="CreateSolution">Create Solution</link>
</listitem>
<listitem>
<link linkend="OpenSolution">Open Solution</link>
</listitem>
<listitem>
<link linkend="CloseDocument">Close Document</link>
</listitem>
<listitem>
<link linkend="Answer">Answer</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="CloseDocument">
<title>Close Document</title>

<para>
Close the currently opened document, whether it is a problem or a solution,
by either selecting
<emphasis>Close Document</emphasis> from
the <emphasis>Document</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/CloseDocument.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
If there are unsaved modifications in the current document,
a dialog will be displayed asking
if the current document should be saved before it is closed.
</para>

<para>
Click <emphasis>Yes</emphasis> to save
the current document. 
</para>

<para>
Click <emphasis>No</emphasis> to close
the current document without saving. Note that all unsaved modifications
to the current document will be lost.
</para>

<para>
Click <emphasis>Cancel</emphasis> to dismiss the dialog
with no action taken.
</para>

<para>
If concluded, this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
Notepad
<link linkend="Notepad">records</link>
and figures belong to the currently open document. When the document is
closed, the notepad is cleared and the figures closed.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SaveProblem">Save Problem</link>
</listitem>
<listitem>
<link linkend="SaveSolution">Save Solution</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="SolutionLog">
<title>Solution Log</title>

<sect2 id="PlayBack">
<title>Play Back</title>

<para>
As the solver progresses through the solution,
his or her actions are recorded in the solution log.
A
<link linkend="SaveSolution">saved</link>
solution can later be opened and played back.
</para>

<para>
To start playing back the solution, click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/LogPlay.png"/>
</imageobject> 
</inlinemediaobject>

button.
</para>

<para>
To play back the next step, click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/LogNext.png"/>
</imageobject> 
</inlinemediaobject>

button.
</para>

<para>
To jump forward or backward, select an arbitrary record in the log.
</para>

<para>
To erase all records from the log, click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/LogClear.png"/>
</imageobject> 
</inlinemediaobject>

button. Use caution since this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
To erase all records following the selected record, click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/LogCut.png"/>
</imageobject> 
</inlinemediaobject>

button. Use caution since this action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
To stop playing back the solution, click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/LogStop.png"/>
</imageobject> 
</inlinemediaobject>

button.
</para>

<para>
While the solution is being played back, it is freezed.
To modify the solution, stop the play back first.
</para>

</sect2>

<sect2 id="SolutionComments">
<title>Solution Comments</title>

<para>
To comment on a solution step, right click on the corresponding record and select
<emphasis>Comment</emphasis>
from the popup menu. A dialog will be displayed. Type in your comments and click
<emphasis>OK</emphasis>.
</para>

<para>
To view the comments, pause the mouse over the corresponding record.
Commented records are highlighted in the solution log.
</para>

</sect2>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Overview">Overview</link>
</listitem>
<listitem>
<link linkend="SaveSolution">Save Document</link>
</listitem>
<listitem>
<link linkend="OpenSolution">Open Solution</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

</chapter>

<chapter id="Figures">
<title>Figures</title>

<sect1 id="FigureGallery">
<title>Figure Gallery</title>

<para>
The figure gallery contains regular prisms, regular pyramids
and the five platonic solids, namely, the tetrahedron, cube,
octahedron, dodecahedron and icosahedron.
</para>

<para>
To create a prism, select an item from the
<emphasis>Figure-&gt;Gallery-&gt;Prism</emphasis> menu.
</para>

<para>
To create a pyramid, select an item from the
<emphasis>Figure-&gt;Gallery-&gt;Pyramid</emphasis> menu.
</para>

<para>
To create a platonic solid, select an item from the
<emphasis>Figure-&gt;Gallery-&gt;Platonic Solid</emphasis> menu.
</para>

<para>
The figure will be added to the currently opened
document. If no document is opened, you may want to
<link linkend="CreateProblem">create a problem</link>
first.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="OpenFigure">Open Figure</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="OpenFigure">
<title>Open Figure</title>

<para>
Open a figure from a file by either selecting
<emphasis>Open Figure</emphasis> from
the <emphasis>Figure</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/OpenFigure.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar. Alternatively, drag the file into the Geometria window.
</para>

<para>
The figure will be added to the currently opened
document. If no document is opened, you may want to
<link linkend="CreateProblem">create a problem</link>
first.
</para>

<para>
A
<link linkend="FigureGallery">gallery</link>
of figures is available to choose from,
including prisms, pyramids and platonic solids.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="FigureGallery">Figure Gallery</link>
</listitem>
<listitem>
<link linkend="SaveFigure">Save Figure</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="CloneFigure">
<title>Clone Figure</title>

<para>
Clone a figure by either selecting
<emphasis>Clone Figure</emphasis>
from the
<emphasis>Figure</emphasis>
menu or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/CloneFigure.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="SaveFigure">
<title>Save Figure</title>

<para>
Save a figure to a file by either selecting
<emphasis>Save Figure</emphasis> from
the <emphasis>Figure</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/SaveFigure.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
This action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="OpenFigure">Open Figure</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="RemoveFigure">
<title>Remove Figure</title>

<para>
Remove a figure from the current document by either selecting
<emphasis>Remove Figure</emphasis> from
the <emphasis>Figure</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/RemoveFigure.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
Removing a figure that has been measured will result in some of the
variables being
<link linkend="PinnedVariable">pinned</link>.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
The solver cannot remove a figure that is part of the problem. However,
any figures that have been created in the process of solving the problem
may be removed.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="ExportImage">
<title>Export Image</title>

<para>
To export a figure to an image file, select
<emphasis>Export Image</emphasis>
from the
<emphasis>Figure</emphasis>
menu. A dialog will pop up. Choose an image file type,
enter a file name and click
<emphasis>Save</emphasis>.
</para>

<para>
This action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="ExportOFFFile">
<title>Export OFF File</title>

<para>
<emphasis>OFF</emphasis> is a popular file format for
polyhedra. It is used by Geomview (http://www.geomview.org) and
other geometry software. To export a figure to a file in OFF
format, select
<emphasis>Export OFF File</emphasis>
from the
<emphasis>Figure</emphasis>
menu. A dialog will pop up. Choose an file name and click
<emphasis>Save</emphasis>.
</para>

<para>
This action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="RenameFigure">
<title>Rename Figure</title>

<para>
To rename a figure, select
<emphasis>Rename Figure</emphasis> from
the <emphasis>Figure</emphasis> menu.
</para>

<para>
Some special characters and spaces are not allowed in figure names.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
The solver cannot rename a figure that is part of the problem. However,
any figures that have been created in the process of solving the problem
may be renamed.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="PrintFigure">
<title>Print Figure</title>

<para>
Print a figure by either selecting
<emphasis>Print Figure</emphasis> from
the <emphasis>Figure</emphasis> menu
or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Print.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
This action cannot be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect1>

<sect1 id="View">
<title>View</title>

<sect2 id="Attitude">
<title>Attitude</title>

<para>
<emphasis>Geometria</emphasis> employs a fixed right-hand reference
system. The Z axis of the reference system is parallel
to the vertical edge of the screen.
No knowledge of the reference system is necessary to manipulate figures,
create and solve problems.
</para>

<para>
At any given time, the figure has a certain attitude. The attitude can be
described in terms of angles the figure forms with the reference system.
When a figure is created, it has the
<emphasis>default</emphasis> attitude.
The figure's attitude changes as the figure is rotated.
</para>

<para>
To revert a figure to the initial attitude, select
<emphasis>Initial Attitude</emphasis>
from the
<emphasis>View</emphasis>
menu or right click and select
<emphasis>Initial Attitude</emphasis>
from the popup menu.
</para>

<para>
When a figure is saved, its current attitude becomes its initial attitude.
To revert to the attitude the figure had when it was created, before
any subsequent rotations, select 
<emphasis>Default Attitude</emphasis>
from the <emphasis>View</emphasis> menu.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="RotateFigure">Rotate Figure</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="RotateFigure">
<title>Rotate Figure</title>

<para>
<link linkend="ToggleSelector">Toggle</link>
the selector off
and stroke a figure with the mouse to rotate the figure. The rotation speed
and angle will depend on the stroke.
</para>

<para>
To pin a rotating figure, click on it.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Attitude">Attitude</link>
</listitem>
<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="SelectElements">
<title>Select Elements</title>

<sect3 id="ToggleSelector">
<title>Toggle Selector</title>

<para>
Right click on a figure and select
<emphasis>Toggle Selector</emphasis> from the popup menu.
Alternatively, click the selector button

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/SelectorOn.png"/>
</imageobject> 
</inlinemediaobject>

on the tool bar.
</para>

<para>
When the selector
is on (white selector icon), elements can be selected by clicking on them.
When the selector is off
(dimmed selector icon), dragging the mouse will
<link linkend="RotateFigure">rotate</link> the figure.
</para>

<para>
The selector is off by default.
</para>

</sect3>

<sect3 id="SelectElementsOneByOne">
<title>Select Elements One By One</title>

<para>
Click an element, such as a point, a segment or a face, to select (highlight) it.
To select more than one element, hold down the Ctrl key. Faces can only be
selected in
<link linkend="ViewModes">non-transparent</link>
view mode.
</para>

<para>
Click on an empty space inside a figure
to clear the selection. Hold down the Ctrl key
and click on a selected element to clear that element alone.
</para>

</sect3>

<sect3 id="SelectAllElements">
<title>Select All Elements</title>

<para>
To select all points and segments in a figure (with the exception of vertices and edges),
select
<emphasis>Select All</emphasis>
from the
<emphasis>Edit</emphasis>
menu. This action offers a convenient way to
<link linkend="EraseSelection">erase all elements</link>
at once.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="RotateFigure">Rotate Figure</link>
</listitem>
<listitem>
<link linkend="ViewModes">View Modes</link>
</listitem>
<listitem>
<link linkend="EraseSelection">Erase Selection</link>
</listitem>

</itemizedlist>

</sect3>

</sect2>

<sect2 id="ViewModes">
<title>View Modes</title>

<sect3 id="ToggleTransparency">
<title>Toggle Transparency</title>

<para>
To toggle the view mode of a figure between transparent and opaque, select
<emphasis>Toggle Transparency</emphasis> from the
<emphasis>View</emphasis>
menu. Alternatively, click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Transparency.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
In a transparent figure, visible segments are solid,
whereas invisible segments are dashed. Any point or
segment can be selected,
whether it is visible or not. Faces can only be selected in an opaque figure.
</para>

<para>
In an opaque figure, invisible segments and points are not shown. Points,
segments and faces can be selected only if they are visible.
</para>

</sect3>

<sect3 id="SetColor">
<title>Set Color</title>

<para>
To change the color of an opaque figure, select
<emphasis>Set Color</emphasis> from the 
<emphasis>View</emphasis> menu or click the color selector button

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Color.png"/>
</imageobject> 
</inlinemediaobject>

on the tool bar.
Select a color in the popup dialog and click
<emphasis>OK</emphasis>.
</para>

</sect3>

<sect3 id="ToggleLabels">
<title>Toggle Labels</title>

<para>
To show or hide point labels, select
<emphasis>Toggle Labels</emphasis> from the
<emphasis>View</emphasis>
menu. Alternatively, click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Labels.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar. Labels will only show in
<link linkend="ToggleTransparency">transparent</link> figures.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>

</itemizedlist>

</sect3>

</sect2>

<sect2 id="ZoomFigure">
<title>Zoom Figure</title>

<para>
To zoom in on a figure, select <emphasis>Zoom In</emphasis> from
the <emphasis>View</emphasis> menu or click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/ZoomIn.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
To zoom out, select <emphasis>Zoom Out</emphasis> from
the <emphasis>View</emphasis> menu or click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/ZoomOut.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
To resize a figure so it fits into the window,
select <emphasis>Fit To View</emphasis> from
the <emphasis>View</emphasis> menu or click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/FitToView.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>

</itemizedlist>

</sect2>

</sect1>

<sect1 id="Measure">
<title>Measure</title>

<sect2 id="MeasureDistance">
<title>Measure Distance</title>

<para>
To measure the distance between two points, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Distance</emphasis> from the
<emphasis>Measure</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/MeasureDistance.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
both points or the segment that joins them, right click and select
<emphasis>Distance</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The two points must belong to the same face.
</para>

<para>
A dialog will pop up. Fill in, if necessary, the
points, assign a unique
<link linkend="Variables">variable</link>
and click <emphasis>OK</emphasis>.
A record will appear on the
<link linkend="Notepad">notepad</link>, as below:
</para>

<programlisting>
myDistance = |AB| : MyCube
</programlisting>

<para>
where myDistance is the variable assigned to the distance between points A and
B in figure MyCube. If MyCube is currently the only figure,
the record will read:
</para>

<programlisting>
myDistance = |AB|
</programlisting>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="MeasureAngle">
<title>Measure Angle</title>

<para>
To measure an angle, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Angle</emphasis> from the
<emphasis>Measure</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/MeasureAngle.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
two segments that make the angle in question, right click and select
<emphasis>Angle</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The segments that make the angle must belong to the same face
and not be collinear.
</para>

<para>
A dialog will pop up. Fill in, if necessary, the
points, assign a unique
<link linkend="Variables">variable</link>
and click <emphasis>OK</emphasis>.
A record will appear on the
<link linkend="Notepad">notepad</link>, as below:
</para>

<programlisting>
myAngle = &lt;ABC : MyPyramid
</programlisting>

<para>
where myAngle is the variable assigned to the angle between AB and AC
in figure MyPyramid. If MyPyramid is currently the only figure,
the record will read:
</para>

<programlisting>
myAngle = &lt;ABC
</programlisting>

<para>
All angles are expressed in radians.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="MeasureArea">
<title>Measure Area</title>

<para>
To measure the area of a face proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Area</emphasis> from the
<emphasis>Measure</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Area.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the face, right click and select
<emphasis>Area</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
A dialog will pop up. Select, if necessary, the face from the list,
assign a unique
<link linkend="Variables">variable</link>
and click <emphasis>OK</emphasis>.
A record will appear on the
<link linkend="Notepad">notepad</link>, as below:
</para>

<programlisting>
myArea = area[ABC] : MyCube
</programlisting>

<para>
where myArea is the variable assigned to the area of the face
that contains vertices A, B, C
in figure MyCube. If MyCube is currently the only figure,
the record will read:
</para>

<programlisting>
myArea = area[ABC]
</programlisting>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="MeasureVolume">
<title>Measure Volume</title>

<para>
To measure the volume of a figure proceed,
alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Volume</emphasis> from the
<emphasis>Measure</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Volume.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</listitem>

</itemizedlist>

<para>
A dialog will pop up. Assign a unique
<link linkend="Variables">variable</link>
and click <emphasis>OK</emphasis>. A record will appear on the
<link linkend="Notepad">notepad</link>, as below:
</para>

<programlisting>
myVolume = volume : MyCube
</programlisting>

<para>
where myVolume is the variable assigned to the volume of
figure MyCube. If MyCube is currently the only figure,
the record will read:
</para>

<programlisting>
myVolume = volume
</programlisting>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

</sect1>

<sect1 id="Draw">
<title>Draw</title>

<sect2 id="DrawSegment">
<title>Draw Segment</title>

<para>
To join two points with a segment, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Draw Segment</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/DrawLine.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the two points, right click and select
<emphasis>Draw Segment</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The two points must belong to the same face.
</para>

<para>
If a dialog pops up, fill in the points and click
<emphasis>OK</emphasis>.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="DrawPerpendicular">
<title>Draw Perpendicular</title>

<para>
To draw a perpendicular through a point to a segment,
proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Draw Perpendicular</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Perpendicular.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the point and the segment, right click and select
<emphasis>Draw Perpendicular</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The point and the segment must belong to the same face. The point may or may not
belong to the segment.
</para>

<para>
If a dialog pops up, fill in the points and click
<emphasis>OK</emphasis>.
</para>

<para>
If the point and the segment belong to two different faces at the same time,
a second dialog may pop up. Select a face from the list and click
<emphasis>OK</emphasis>.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="DivideSegment">
<title>Divide Segment</title>

<para>
To divide a segment in a given ratio, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Divide Segment</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/DivideLine.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the segment, right click and select
<emphasis>Divide Segment</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
A dialog will pop up. Fill in, if necessary, the points and
valid
<link linkend="Expressions">expressions</link>
for the numerator and denominator of the ratio. Click
<emphasis>OK</emphasis>.
</para>

<para>
The ratio is defined as AX : XB, where
X is the division point, AB the segment. For example, if the ratio is 1 : 2,
X will be twice closer to A than to B. If the ratio is 3 : 1, X will be
three times closer to B than to A.
</para>

<para>
The midpoint divides the segment in ratio 1 : 1 and therefore can be
drawn as shown above. However, a convenience
<link linkend="DrawMidpoint">Draw Midpoint</link>
action offers a shortcut.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="DrawMidpoint">Draw Midpoint</link>
</listitem>
<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="DrawMidpoint">
<title>Draw Midpoint</title>

<para>
To draw the midpoint of a segment, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Draw Midpoint</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the segment, right click and select
<emphasis>Draw Midpoint</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
A dialog may pop up. Fill in, if necessary, the points. Click
<emphasis>OK</emphasis>.
</para>

<para>
Note that drawing the midpoint is equivalent to
<link linkend="DivideSegment">dividing</link> the segment in ratio 1 : 1.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="DivideSegment">Divide Segment</link>
</listitem>
<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="DivideAngle">
<title>Divide Angle</title>

<para>
To divide an angle in a given ratio, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Divide Angle</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/DivideAngle.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
two segments that make the angle, right click and select
<emphasis>Divide Angle</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The segments that make the angle must belong to the same face
and not be collinear.
</para>

<para>
A dialog will pop up. Fill in, if necessary, the
points and valid
<link linkend="Expressions">expressions</link>
for the numerator and denominator of the ratio. Click
<emphasis>OK</emphasis>.
</para>

<para>
The ratio is defined as &lt;AOX : &lt;XOB, where
OX is the division segment, &lt;AOB the angle. For example, if the ratio is 1 : 2,
OX will make with OB a twice greater angle than with OA.
If the ratio is 3 : 1,
OX will make with OA three times greater an angle than with OB.
</para>

<para>
The bisector divides the angle in ratio 1 : 1, therefore can be
drawn as shown above. However, the convenience
<link linkend="DrawBisector">Draw Bisector</link>
action offers a shortcut.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="DrawBisector">Draw Bisector</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="DrawBisector">
<title>Draw Bisector</title>

<para>
To draw the bisector of an angle, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Draw Bisector</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
two segments that make the angle, right click and select
<emphasis>Draw Bisector</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The segments that make the angle must belong to the same face
and not be collinear.
</para>

<para>
A dialog may pop up. Fill in, if necessary, the points. Click
<emphasis>OK</emphasis>.
</para>

<para>
Note that drawing the bisector is equivalent to
<link linkend="DivideAngle">dividing</link> the angle in ratio 1 : 1.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="DivideAngle">Divide Angle</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="IntersectLines">
<title>Intersect Lines</title>

<para>
To draw the intersection point of the lines containing two given segments,
proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Intersect Lines</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Intersect.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the segments, right click and select
<emphasis>Intersect Lines</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
Both segments, as well as the intersection point of their lines,
must belong to the same face.
</para>

<para>
A dialog may pop up. Fill in, if necessary, the points. Click
<emphasis>OK</emphasis>.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="LayDistance">
<title>Lay Distance</title>

<para>
To draw a point on a given segment at a given distance from a given point,
proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Lay Distance</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/LayDistance.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the point and the segment, right click and select
<emphasis>Lay Distance</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The point and the segment must belong to the same face.
The point may or may not belong to the segment.
</para>

<para>
A dialog will pop up. Fill in, if necessary, the points and a valid 
<link linkend="Expressions">expression</link>
for the distance. Click
<emphasis>OK</emphasis>.
Select a notepad
<link linkend="Notepad">record</link>
ahead of time to have it copied automatically to the distance input box.
</para>

<para>
This action may result in the construction of one or two distinct points.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="LayAngle">
<title>Lay Angle</title>

<para>
To draw a segment from the end point of another segment so that
the two segments make a given angle, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Lay Angle</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/LayAngle.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the segment and its end point, right click and select
<emphasis>Lay Angle</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
A dialog will pop up. Fill in, if necessary, the points and a valid 
<link linkend="Expressions">expression</link>
for the angle. Click
<emphasis>OK</emphasis>.
Select a notepad
<link linkend="Notepad">record</link>
ahead of time to have it copied automatically to the angle input box.
</para>

<para>
The angle must be greater than 0 and less than 180 degrees and be entered
in radians, as opposed to degrees. For example, to lay an angle of 60 degrees,
enter PI/3.
</para>

<para>
If the segment belongs to two different faces at the same time,
a second dialog may pop up. Select a face from the list and click
<emphasis>OK</emphasis>.
</para>

<para>
This action may result in the construction of one or two distinct segments.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="RenamePoint">
<title>Rename Point</title>

<para>
The problem creator can rename a point in a figure by selecting
<emphasis>Rename Point</emphasis>
from the
<emphasis>Draw</emphasis>
menu.
</para>

<para>
A dialog will pop up. Enter the old and the new labels for the point
in question and click
<emphasis>OK</emphasis>.
A valid label consists of a capital letter, which may be
followed by one or more digits.
</para>

<para>
<link linkend="SelectElements">Select</link>
a point ahead of time to have it automatically copied into
the input box.
</para>

<para>
Renaming a point may result in some of the notepad
<link linkend="Notepad">records</link>
being updated accordingly.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>
<listitem>
<link linkend="Notepad">Notepad</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="EraseElements">
<title>Erase Elements</title>

<sect3 id="EraseSegment">
<title>Erase Segment</title>

<para>
To erase a segment or its part, select
<emphasis>Erase Segment</emphasis>
from the
<emphasis>Draw</emphasis>
menu. The segment cannot belong to an edge.
</para>

<para>
If a dialog pops up, fill in the points and click
<emphasis>OK</emphasis>.
</para>

<para>
Note that a whole segment can be more conveniently erased by selecting it
and performing the
<link linkend="EraseSelection">Erase Selection</link> action.
</para>

<para>
Erasing a segment that has been referenced in measurements
will result in some of the variables being
<link linkend="PinnedVariable">pinned</link>.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

</sect3>

<sect3 id="EraseSelection">
<title>Erase Selection</title>

<para>
To erase one or more elements, such as points and/or segments,
<link linkend="SelectElementsOneByOne">select</link>
them and proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Erase Selection</emphasis> from the
<emphasis>Draw</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Erase.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</listitem>

</itemizedlist>

<para>
Vertices and segments that belong to edges will not be erased.
</para>

<para>
To erase all points and segments in a figure (with the exception of vertices and edges),
<link linkend="SelectAllElements">select them all</link>
first.
</para>

<para>
To erase only a part of a drawn segment, use the
<link linkend="EraseSegment">Erase Segment</link> action.
</para>

<para>
Erasing elements that have been referenced in measurements
will result in some of the variables being
<link linkend="PinnedVariable">pinned</link>.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect3>

</sect2>

</sect1>

<sect1 id="Transform">
<title>Transform</title>

<sect2 id="ScaleFigure">
<title>Scale Figure</title>

<para>
To scale a figure along a given segment by a given positive factor, proceed,
alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select
<emphasis>Scale Figure</emphasis> from the
<emphasis>Transform</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Scale.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the segment or two points on it, right click and select
<emphasis>Scale Figure</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
A dialog will pop up. Fill in, if necessary, the points and a valid 
<link linkend="Expressions">expression</link>
for the factor. Click
<emphasis>OK</emphasis>.
Select a notepad
<link linkend="Notepad">record</link>
ahead of time to have it automatically copied to the factor input box.
</para>

<para>
As a result of scaling, the previously measured distances,
angles, areas and volumes will be recalculated and the assigned
variables updated. See
<link linkend="Variables">Variables</link>
for more details.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
The solver cannot scale a figure that is part of the problem. However,
the figures that have been created in the process of solving the problem
may be scaled.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="ShearFigure">
<title>Shear Figure</title>

<para>
Shearing refers to an affine transformation where planes
parallel to a fixed reference plane slide along a fixed line
contained in the reference plane. The term
<emphasis>affine</emphasis>
implies that the transformation preserves the collinearity
of points.
</para>

<para>
If XY is the fixed line in the reference plane, the shearing
transformation is uniquely identified by points X, Y and the image
of any point Z such that XZ is perpendicular to the reference plane.
</para>

<para>
To shear a figure, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Shear Figure</emphasis> from the
<emphasis>Transform</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Shear.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the reference segment XY and the image of point Z, right click and select
<emphasis>Shear Figure</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
A dialog will pop up. Fill in, if necessary, the
reference points (X, Y at the bottom and the image of point Z at the top).
Click
<emphasis>OK</emphasis>.
</para>

<para>
As a result of shearing, the previously measured distances and
angles will be recalculated and the assigned
variables updated. See
<link linkend="Variables">Variables</link>
for more details.
</para>

<para>
The solver cannot shear a figure that is part of the problem. However,
the figures that have been created in the process of solving the problem
may be sheared.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="Variables">Variables</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="CutFigure">
<title>Cut Figure</title>

<para>
To cut a figure with a plane, proceed, alternatively, as follows:
</para>

<itemizedlist>
<listitem>
Select <emphasis>Cut Figure</emphasis> from the
<emphasis>Transform</emphasis> menu, or
</listitem>

<listitem>
click the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Cut.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar, or
</listitem>

<listitem>
<link linkend="SelectElementsOneByOne">select</link>
the elements that reference the plane, such as 3 points, a point and a segment
or two segments, right click and select
<emphasis>Cut Figure</emphasis> from the popup menu.
</listitem>

</itemizedlist>

<para>
The selected elements must uniquely identify a plane. The plane must
pass through the figure's interior.
</para>

<para>
If a dialog pops up, fill in the points and click
<emphasis>OK</emphasis>.
</para>

<para>
The two resulting halves will be displayed in separate views. The original
figure will be kept intact in its own view.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="JoinFigures">Join Figures</link>
</listitem>
<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

<sect2 id="JoinFigures">
<title>Join Figures</title>

<para>
Two figures can be joined by either selecting
<emphasis>Join Figures</emphasis>
from the
<emphasis>Transform</emphasis>
menu or by clicking the

<inlinemediaobject> 
<imageobject role="html">
<imagedata fileref="../../images/24x24/Join.png"/>
</imageobject> 
</inlinemediaobject>

button on the tool bar.
</para>

<para>
A dialog will pop up. Select the figures to join and click
<emphasis>OK</emphasis>. A figure can be joined with a copy of
itself. Therefore the same figure can be selected in both lists.
</para>

<para>
If the figures can be joined in one way only,
a new view will appear with the combined figure in it. The two
original figures will be kept intact in their own views.
</para>

<para>
If, however, the figures can be joined in more than one way,
another dialog will be displayed asking if the figures should be joined
in any of the possible ways. Click
<emphasis>No</emphasis>
to proceed with a more accurate definition of the joining elements.
</para>

<para>
Click
<emphasis>Yes</emphasis>
to have the figures joined in one of the possible ways. A preview will be displayed
along with another dialog asking if the result should be kept. Click
<emphasis>Yes</emphasis>
to keep the result and conclude the action. Click
<emphasis>No</emphasis>
to get a preview of the next possible way of joining the figures.
</para>

<para>
It is recommended that, prior to joining the figures,
the corresponding points and/or faces be
<link linkend="SelectElementsOneByOne">selected</link>.
That will reduce to a minimum the subsequent dialog input. Note
that faces can only be selected in the
<link linkend="ToggleTransparency">opaque</link> view mode.
</para>

<para>
The joining faces must have the same shape, that is have equal angles 
and proportional sides at corresponding vertices. The joining faces
do not have to have the same size. If need be, one of the figures will be
automatically scaled to fit the other.
</para>

<para>
The action will be cancelled if the joint figure is not convex.
</para>

<para>
This action can be
<link linkend="UndoActions">undone</link>.
</para>

<para>
See also:
</para>

<itemizedlist mark="none">

<listitem>
<link linkend="CutFigure">Cut Figure</link>
</listitem>
<listitem>
<link linkend="SelectElements">Select Elements</link>
</listitem>
<listitem>
<link linkend="UndoActions">Undo Actions</link>
</listitem>

</itemizedlist>

</sect2>

</sect1>

</chapter>

</book>

