We now describe the various tools and options. Also, you will find here a description of all objects, which can be used in a construction.
If the mouse remains over an icon for a while, you will see a short description too. Have a look at the status line to see which steps
are expected by the tool.
Moreover, you can press the
I tool to get more information about a
selected tool.
The icon bar can be edited using the corresponding menu point. Note, that some tools are hidden by default, since they can be replaced by other tools.
You may also want to try the special mode for beginners. This mode reduces the icon bar and sets off preview options to enforce a more concentrated work.
The following textual properties are common to all objects.
The description is generated automatically, but can be changed by the user. Units are decorations for the output only. The following are other properties an object can have.
These properties can be set for new objects by default values, or by the properties dialog of an object. The properties dialog is opened by a click on the object with the right mouse button. An example for a settings dialog is here.
Note that names must be unique. If you need objects with the same name, include a ~ in the name. Names are only displayed up to this ~. Names and their value can be displayed combined, yielding "s = 4". If the name ends with "_", the equality sign will not be generated. Units are displayed after the value.
Breakpoints are used in the replay mode and the breakpoint animation.
See the replay tool for more information.
Properties can depend on conditions. To enter the dialog for conditional properties right click the object with the ctrl-key pressed. Each property in this dialog can have a condition. It will be enabled, when the condition evaluates to true (different from 0). This is a mighty feature for expert use.
Points can be fixed in their position, segments in their length, circles and angles in their size. To fix an object, one can use any expression. Of course, a simple example of an expression is a number.
If you want to create an object of fixed size or position, you can either create it and then call the settings dialog to fix it, or you can hold down the shif-key while creating the second end point. For fixed circles and angles, you should use the special tools for fixed objects, since they create different types of circles and angles.
Objects are stored in a row, and they do often depend on other objects. The chain of objects determines, which object is drawn first. To push an object to an earlier place, use the menu item "Push objects to the Background". The object cannot be move before any other object it depends on.
Filled polygons and other objects, can be drawn before the rest of the objects, if the background state is enabled in the settings dialog.
A point can be generated by various tools. The point tool
will normally generate a free (moveable) point.
However, if an intersection is clicked, an intersection is created after an
optional
confirmation (see the advanced settings). Intersection points are not free
(moveable), but depend on the two intersected objects of course.
Points will be bound to circles and lines, if a circle or line is selected.
Points can be fixed. Again, holding down the shift-key will open the dialog to fix
the point.
Like other objects, free points can be dragged immediately after generation.
During the drag, the size and name will display, unless this option is turned
off.
The settings dialog for points is explained on a separate page.
This is a point, which is bound to a line or a circle. It will move with the bound in a continuous way. A point can be released, and bound to a new object at any time using its properties dialog.
Points can be bound in two ways. Either the point is projected every time the object moves, or the point is kept in its relative position on the point. The second option is applied by holding the shift-key while the object is selected. Moreover, the relative fix can be removed or set in the object editor.
Bound points are not free. So segments with bound endpoints cannot be fixed (use a fixed circle instead). If however, a segment lies with both endpoints on a line, and one of them is a bounded point (to the line), the segment can be fixed (see above about fixed objects).
These objects depend on two points. So the user has to select two points. The differences between lines, segments and rays are not only restricted to the visual appearance. Intersections and perpendicular lines behave differently for these objects. E.g., intersections with segments become invalid, if the intersection point is not on the segment. Perpendicular lines to segments will be invalid, if the intersection with the line is not on the segment. For perpendicular lines, it is possible to switch this behavior off.
Note that the perpendicular line tool, the fixed angle tool, or the parallel tool generate lines too.
The length of a segment may be fixed, if it has one free endpoint. To generate such a segment, hold the shift-key while selecting the second point, or use the special icon. It is probably preferable to use the fixed circles instead.
Here is the settings dialog for lines.
The difference between the first two tools is that the first constructs circles with a center and a radius point, while the second can create circles with another center. Thus the latter tool will expect three points, two points A, B forming the radius AB, and a center M. This tool can be replaced by fixed circles with the expression d(A,B) for the radius.
The first kind of circles can be fixed in size, if the radius point is moveable. However, it is better to use a circle with fixed size instead.
The fixed circles are the third kind of circles. To generate such a circle, hold the shift-key when defining the radius point, or use the special tool. This will not create or select a point, but open the settings dialog, where you can enter any expression for the radius. If the circle is dragged immediately after the generation, the settings dialog will not open, but the current size will be used.
Drawing a circle can be restricted between two defining points. In this case, it is possible to keep the arc between 0 and 180 degrees (i.e., always the shortest arc will be drawn).
Fixed circles can be sized to the distance of two given points, the size of another circle, or a segment. To do this use the button "Set Size ..." in the settings dialog. Note that only previously constructed points can be used.
Circles can be filled. Moreover, they can be partially visible to improve the clarity of the construction-
Here you find the settings dialog for circles.
This tool generates intersections between lines, circles and between a line and a circle. In paper constructions, this might not be thought of as an extra step to do. But the computer cannot compute all possible intersections. Also it makes the necessary steps much clearer. As a shortcut, intersections are created, whenever the program expects a point, and the user clicks close to an intersection.
The intersection tool is hidden by default, since the point tool can be used instead in most cases. It is available in the menu never the less.
Note that circles intersect in two points. The program creates both intersections only if the two circles are selected as parameters one after the other. If you need only one, hide the other. For automatically created intersections, the other intersection will not be generated at all.
Furthermore, note that segments intersect only in their interior. Segments are no lines.
There is a subtle problem with the way the program orders the two intersects of circles (or a circle and a line). This is done in a predictable way. For circles, the order will change, if the circles are switched. The intersections between a line and a circle depend on the direction of the line (i.e. the order of its creating points). Try moving the line so that it does no longer intersect the circle, then move it back. The order of intersections will be the same.
Sometimes the order must be specified. This can be done by telling one of the intersection points to be different from a certain other point. The intersections will then be ordered such that the chosen intersection is furthest away from the other point. Alternatively, it is possible to choose the intersection closest to some point. The dialog for intersections contains a special input line to specify the other point, or it is possible to choose that point on the construction.
This type is intersection is created automatically, if the other intersection point is a point on the perimeter of both circles, and if this point is visible. The program then assumes that the user means to create a the new intersection point.
These are simply shortcuts for classical constructions. The tools create lines.
Another shortcut. It creates the point exactly in the middle between two other points.
This tool can be used to move points, as an alternative to using the right mouse button. It can also drag fixed circles and angles. The only difference to the right mouse button is that points will not snap on grid points if the grid is visible.
These important tools draw tracks of points, or generate a curve, which have a specific line as the tangent line.
The simple track works like this: The user moves one point, and the track of another points is drawn. Thus it expects a track point, then any other point can be moved with the left mouse button. More than one track point can be selected, yielding more than one track.
Alternatively, the tool can construct a curve, which has a given set of lines as tangents (a polar set). In this case, the first object to be selected must be a line or several lines, not a point.
The automatic track moves the point along a given object automatically. Thus it expects the point to be tracked, the point to be moved, and the object (circle, segment, line). This track is re-computed, if any other points is moved, showing the dependency of the track to parameters. The track is animated, until the user clicks somewhere into the construction. More than one line or point to be tracked can be chosen. However, the first object controls the track generation.
Automatic tracks try to run through all states of the construction avoiding invalid states. If the first tracked point or line becomes invalid, the moving point will turn, and invalid intersections will be switched.
The animation speed can be increased or decreased with the shift-key and the right or left cursor key. Click into the construction to give it the keyboard focus.
Tracks are saved to the construction file. If the track is animated it will be saved this way. When the construction is loaded the (animated) track will be displayed. Tracks are normally no construction objects, however. They are saved in the construction header. The track is deleted, when another tool is selected, or the track tool is re-selected.
Tracks in constructions have an own properties dialog. They can be filled too.
Automatic tracks can be added to the construction as normal objects using the corresponding menu entry "Keep Track" or shift-Return. This way, it is possible to create several independent automatic tracks in one construction. Note, that the tracks will slow down the redraw! It is possible to intersect these objects and to fix points to them, yielding very powerful constructions.
This will animate a single point, which walks along segments or circles. To start the animation, select a point, then a sequence of segments or circles. Finish by reselecting the point or any of the objects. To stop the animation, click on the construction.
Animations are saved to the construction file. In applets the animation will prevent user interaction completely.
Normal Angles are decoration and cannot be used to construct anything. The order of input is A, B, C (see the picture).
The second kind of angles have no point C, but a fixed size. It is generated by holding down the shift-key, while clicking for C, or with the special tool. This will not generate or select a point, but open the settings dialog, where the user can enter any expression for the size of the angle. If the angle is dragged immediately, the settings dialog will not open.
Angles can be displayed in three different sizes. The largest size will display a part of a circle, which starts in A.
Angles can have Greek letters in their name. To achieve an alpha, enter \a e.g. Angles, which are 90° or have a name starting with "." will be labeled with a dot, if either the name or the size display is switched on. Angles may be filled.
Angles can be prevented to become a reflex angle. In this case, the value will be between 0° and 180°. This is the default. Other angles observe the order of the points A and C.
Fixed angles can be sized by three given points, or by another angle. To do this select the button "set size ..." in the settings dialog an select three points A, B, C, or another angle. The angle will be the same size as the other angle. Note that only previously defined objects can be used.
Fixed angles can be inverted. Thus one does not have to use positive orientation. Furthermore, if a fixed angle is restricted to 180° by default, and if such an angle is constructed in a mathematical negative way, it will be inverted. There is an icon in the settings dialog, which controls the inversion.
One can display values of arithmetic expressions in the construction.
The expression can have an additional text, which
explains it and
may or may not display its value.
The syntax of expressions are explained on-line and here.
This fills the area between defined corners with a color. The fill should be set to light. In Java 1.3, it will be transparent. To define the area, select the corners. The definition is completed by re-selecting any of the previously selected corners.
Note, that areas can
be drawn in the background as other objects. By default, they are.
This displays a multi-line text in the construction. You can edit the text in an internal editor. This editor contains a button to reach the normal object editor. You can fix the position of the text using arithmetic expressions there. Note, that invalid positions make the text invisible, which may be useful sometimes.
Hidden texts does appear in replay mode. This allows local comments of constructions steps disappearing later.
This generates functions or curves. A variable runs in an interval with given step size. The interval name is "x" by default, but can be any string.
Simple functions have an empty X-value and an expression with the variable as Y-value. They will be drawn into the construction window. Invalid points are skipped.
Curves have expression both in the X-value and the Y-value. Usually, the variable is named "t" in this case.
Functions may be used in other expressions. In this case, the Y-value is evaluated. Probably, one wants to hide the function completely for this purpose. To edit the function, use the construction description.
Functions can intersect with other objects and can have gliding points on them, just like lines or circles. Functions can even intersect with automatic tracks.
Functions can be filled. For parametric curves, the fill center may be chosen. Open the properties dialog and exit with "Select Center".
Conic sections are sets of points equations formed by linear combinations of x^2, y^2, x, y, xy and 1 (quadratic functions in two variables) become zero. Conics are determined by 5 points. You simply need to select the 5 points.
To edit the properties of the curve, click on it and use the normal dialog. Conics will display the defining formula as their value. Currently, nothing can be constructed using these objects, but they are useful nevertheless.
If you just need a specific conic section type like an ellipse, it is probably better to use a parametric curve.
This is explained here.
This will hide objects. To make a hidden object visible, the option to show all hidden objects must be enabled. Hiding objects can also be
achieved by holding the ctrl-key and clicking on the object. In this case, circles and lines go to the partial
state and hide only on the second click.
If the shift-key is held, when an object is selected for hiding, the object will be completely hidden. In this case, one can make the object visible again with the construction description only, using the object properties.
There is a special feature that is sometimes useful. When this tool is selected with the ctrl-key all duplicate objects are hidden. So, if a segment is drawn on the same segment, only the first segment will be visible.
This tool deletes the most recent objects, and all hidden objects before it. Undo restores all these objects at once. The other tool deletes any object and all objects depending on it. Undo only restores one of these operations.
These are default values for new objects. Of course, all these properties can be set for existing objects in their properties dialog.
Some less common default values. Names are generated automatically using an object count for each object type and a prefix letter or a prefix string (long names).
Another default setting. If this button is enabled, new angles can become reflex angels, else they will be between 0° and 180°. It is probably better to use restricted angles only. These angles do not have an orientation, which makes them easier to handle.
Filled objects are transparent in Java 1.3. With this button, new objects will not become transparent.
Edits the properties of one more objects. To
select several objects, hold the shift-key until the last object. The edit dialog for more than one objects has fields in a special unknown
state. Only the changed fields will be used to update the objects.
If the edit tool is selected with the Ctrl-key, the most recent object will edited immediately.
One can use this tool to format an object with conditions. Select the object with the Ctrl-key then. In the dialog, enter conditions for colors, thickness etc. This can be used to create special effects in constructions under certain conditions. It can also be used to create 3D-constructions with changing colors for polygons depending on the side that is visible.
Toggle selective display of objects with certain colors. Black objects are always displayed.
Toggles the display of hidden objects. Completely hidden objects can only be accessed through the construction description.
Toggles the display of the grid. If the grid is on, new points and points moved by the right mouse button snap to grid points. Note that the grid can be reduced to the axis only.
If the grid is on while the construction is saved, it will be switched on, when the construction is loaded.
Show the comment, or, with the shift-key, the assignment text.
This switch fixes the current construction as a background picture, or releases the current background picture. It is possible to load background pictures from files.
This tool opens a small dialog with navigation buttons containing buttons for fast rewind etc.
Additionally, breakpoints can be set with this tool.
Breakpoints are important for HTML export in replay
style and for the breakpoint animation. Pressing the shift key generates a
hiding break point. Such a break point will hide the construction in front of it
until the previous break point or the start of the construction. Breakpoints can
be toggled in the object dialog as well.
Breakpoints
can be animated with this tool. While breakpoints are animated,
pressing the shift key plus left or right changed the animation speed.
Animations are saved with the construction.
You can paint with the mouse in the current color using this icon. To delete the painting, press escape or use the menu entry. The drawing will be saved. However, the construction file gets a lot bigger with paintings.