1.4 Short reference
This section is for people who tend to understand programs quickly and do not want to read long
For a very first step I recommend working through the tutorials at ’Help - Tutorials’ in the
While the mouse is not pointing at an object you can navigate in the scene. By pressing ALT
(Linux: ctrl alt) you can navigate even if the mouse is pointing at something.
- Rotate the scene. By letting go of the mouse-button while still moving, you
canset the scene into continuous rotation.
Left + right drag:
- Translate the scene.
1.4.2 Selection of objects
In the scene:
- Clicking on an objects selects the objects and unselects the other
objects.Ctrl-Click or Shift-Click selects the object while keeping the old selection intact.
In the object tree / in the list:
- Clicking on a name selects the object and unselects
the other objects. Ctrl-click selects the object additionally, shift-click selects a range
(MacOS: select the range as usual on MacOS).
1.4.3 Deselecting objects
Click on an object:
- Deselects all other objects.
Ctrl-Click on a selected object:
- Deselects the object without changing the rest of the
So to unselect all objects you will have to click on an object and then unselect this object by
Ctrl-Clicking on this object again.
While this might seem a bit complicated at first, this makes sense in order to make the
navigation in the scene as easy as possible. If left-clicking into the scene had unselected all objects,
the construction of more complex objects (which requires rotating the scene inbetween) would have
Objects behind other objects can be selected using the TAB-key. The tooltip shows which
object the mouse is pointing at.
If you want a visual representation of which objects are selected, choose ”Extras - Make selected
1.4.4 Construction of free points
You can construct free points by
- Double-right-clicking into the scene (easiest way!).
- choosing Point - free point.
- the button ’free point’ in case you do not hide the button-list. (see extras - Settings -
View - Show buttons).
- in the command-line by entering ’P=(1,2,3)’
Attention: If a plane, sphere, line, segment or a circle is selected, the free point will be
constructed on these objects. If you do not want this, you can use Edit - detach to detach the point
from that object. See the section 4.2.9on arraching and detaching).
1.4.5 Object construction
Without selecting objects first:
- Click on the button for the object you want to
construct(for instance Plane - Plane by three points) and then click on the objects
(here: the three points) in the scene. The object you have to click on next is displayed
in the status-bar at the bottom right and on top of the OpenGL-screen. Press ESC to
quit this process.
With selecting objects first:
- Select suitable objects (three points, for instance) and then
press the plane- button (or use Alt-E).
1.4.6 Measure and calculate
Though there are not many commands in this menu you can get practically all measurements
you want by entering an expression. In expressions you can refer to points, vectors and other
expressions by their names.
More complex measurements are available through the menu ’Macros - Measure’.
Example: You want to measure the angle between two planes:
- Construct two planes PL1 and PL2.
- Construct the intersection line s
- Construct a point A on s
- Construct a plane PL3 through A perpendicular to s
- Construct the intersection lines s2 and s3 of the new plane with the two initial planes
- Construct points C and D on s2 and s3
- Construct the vectors V1 and V2 from A to C and from A to D
- Enter a new expression : acos(V1*V2/(abs(V1)*abs(V2)))
As the expression contains the well known formula for the angle between two vectors, now the angle
between the two planes (radian) is displayed.
The following operations, functions and variables are defined:
+ and - for number / number and vector / vector
for the addition / subtraction of two
numbers or vectors
- for number / number; number / vector
(multiplication with a scalar) and
vector / vekctor (inner product)
- for number / number and vector / number
(but not number / vector!)
- the symbol ĝives the power for
numbers, the cross-product for vectors.
sin, cos, tan:
- The trigonometric functions
for radian angles.
asin, acos, atan:
- The inverse functions of
the aforementioned functions. Be aware
of the restricted domain for those
- : Square-root of a nonnegative number.
- Absolute value of a number or length
of a vector. Note: The command
’length’in the menu for vectors is much
faster than using abs in an expression!
- This function expects
three comma-separated arguments and
will generate a vector from them.
x, y, or z:
- Those functions expect a point
or vector as argument and give the x-,
y- or z-co-ordinate of the given point or
- pi = 3.1415926535897932385
- e = 2.7182818284590452354
Using the menu ’Extras - Slider’ or entering ’s=SL(1,-5,5)’ will generate a slider. Sliders are useful
for adjusting parameters and for driving locus surfaces. The following example illustrates
- Enter: x=Slider(1,-6,6)
- Enter: y=Slider(1,-6,6)
- Enter: a=Slider(0.2,-1,1)
- Enter: X=(x,y,a*x*y)
- Select sliders x and y and point X, after that press Alt-O.
The resulting function-graph can be modified by changing the value of slider a.
In the sliders settings-dialogue the current value and the range of the slider can be
1.4.8 Defining functions
It is possible to create user-defined functions in the "enter expression"-dialogue. For instance you
can define an expression x*y with list of variables x,y . If you name this expression "‘f"’ you can
use it in another expression by entering f(1,2). You can even enter variables or more complex
expressions in the function.
All construcions can be used as macros.
Macros without given objects:
- If you use Macro - play and choose a ’normal’
construction where no objects are given, the construction will simply be merged with
the current one. Only the names of the inserted construction will be changed to avoid
Macros with given objects:
- Letīs assume that you have constructed a parallel plane to a
plane and want to reuse this construction. So you select the first plane and the point the
second plane goes through and use Macro - Mark as given. Then you save the macro,
for instance as ’Macro parallel plane by point and plane’. Now you can select a plane
and a point in a new construction and then choose Macro - Play and select the macro
just saved. You get the parallel plane, together with all the other objects you used to
construct it. You should hide all supplementary objects in the macro-construction if
you do not want them to be seen.
- If objects of the same kind as the given objects appear in the
construction again, you can select them and choose Macro - Recurse on. Note that
not all of the objects need to differ from the given objects, but at least one should,
otherwise the macro will just be doubled (resulting in lots of unnecessary objects). If
you play a macro with recursions, a dialogue appears that allows you to recursively
play the macro. See 12 the section on macros for details.