Tools

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  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 means.

On new installation, you are in a special mode for beginners. Turning of this mode will give you a richer icon bar.

Construction Objects

The following textual properties are common to all objects.

These are graphic properties:

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 value can be 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.

Fixed Objects

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 SHIFT 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.

Dependencies

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.

Point

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. The confirmation for this is optional.

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.

Point on Object

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).

Line - Segment - Ray - Segments of fixed length

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.

Here is the settings dialog for lines.

Circle - Circle from three points - Circles with fixed size

The difference between the first two tools is that the first constructs circles with center around the first 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.

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 to fix the radius.

The fixed circles are a third kind of circles. To generate such a circle, hold the SHIFT key when defining the radius point, or use the special icon. 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.

Here you find the settings dialog for circles.

Intersections

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 to have to construct intersections explicitly. As a shortcut, intersections are created, whenever the program expects a point, and the user clicks close to an intersection. Moreover, the user can click on the intersection point he wants, when the intersection tool is active, instead of selecting the two intersecting objects one after the other.

The intersection tool is hidden by default, since the point tool can be used instead in most cases.

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.

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). In contrast to other programs, 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. This is a continuous way to select the intersections. For an example see this construction. The dialog for intersections contains a special input line to specify the other point.

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.

Parallels - Perpendicular Lines

These are simply shortcuts for classical constructions. The tools create lines.

Middle point

Another shortcut. It creates the point exactly in the middle between two other points.

Move tool

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.

Track - Automatic Track and Tangent Curves

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. 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 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.

Automatic tracks can be added to the construction 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!

Animation

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.

Angle - Angles with fixed size

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 icon. 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 kept acute. In this case, the value will be between 0° and 180°.

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.

Settings dialog for angles.

Arithmetic Expressions

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 (depending on the button ). Expressions are explained on-line and here.

Filled Polygons

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.

Text

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 appear in replay mode. This allows local comments of constructions steps disappearing later.

Functions  

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 "x" as x-value and an expression of x 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.

Conic Sections

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 (Example).

Calling Macros and Defining Macros - -

This is explained here.

Hiding and Un-Hiding Objects

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 control 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.

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.

Delete last Object - Delete any Object - Undo

This tool deletes the most recent objects, and all hidden objects before it. Undo restores all these objects at once. The thrid tool deletes any object and all objects depending on it. Undo only restores one of these operations.

Color - Appearance - Style for Points - Partial Circles - Partial Lines - Arrows

These are default values for new objects.

Show Name - Show Values - Long Names

Other default values.

Obtuse Angles

If this button is enabled, new angles can be obtuse, else they will be acute. It is nice to use acute angles only. Acute angles do not have an orientation, which makes them easier to handle.

Non-transparent Objects

Filled objects are transparent in Java 1.3. With this button, new objects will not become transparent.

Edit Properties

Edits the properties of one more objects. To select several objects, hold the SHIFT key. 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 this tool is selected with the Ctrl-key, the most recent object will edited.

One can use this tool to format an object with conditions. Select the object with the Ctrl-key. 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.

Show Colors

Toggle selective display of objects with certain colors.

Show hidden Objects

Toggles the display of hidden objects.

Grid

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.

If the grid is on while the construction is saved, it will be switched on, when the construction is loaded.

Comment, Assignment

Show the comment, or, with SHIFT, the assignment text.

Background Picture

This switches fixes the current construction as a background picture, or releases the current background picture. It is possible to load background pictures from files.

Replay -

This tool opens a small dialog with navigation buttons containing the usual 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.

Breakpoint can be hiding breakpoints. Hiding breakpoints hide the construction before them up to the previous breakpoint. Thus one gets a sequence of constructions.

While breakpoints are animated, pressing the shift key plus left or right changed the animation speed. Animations are saved with the construction.

Paint with the Mouse

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.