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Tutorial 2: Viewing Modes
This tutorial shows you the various ways in which you can view and manipulate equations.
- Create a new Osiris file from the System screen by choosing "New file" from the "File" menu whilst the highlight is over the "Osiris" icon.
- Complete the dialog with an appropriate name, "Example2" for instance, and press Enter
We shall now create a couple of graphs with which to experiment.
- Choose "Plot" from the "Graph" menu or press PSION-P.
- Use the arrow keys to select "Cartesian equation" and press "Enter"
- Complete the dialog as below
| Plot colour | Black |
| y= | 5*COS(2*#pi*x) |
- Choose "Plot" again from the "Graph" menu or press PSION-P.
- This time, use the arrow keys to select "Polar equation" and press "Enter"
We shall plot the line r=t from t=0 to t=4*PI in increments of PI/32. In polar co-ordinates, r represents the radius at an angle t. Here we shall use Radians to specify angles - they are indeed more useful to the mathematician - but if you prefer degrees you can set Osiris to use them from the "Set preferences" option in the "Special" menu. This is a global option as it affects every trigonometric function used.
- Complete the dialog as below
| Plot colour | Black |
| r= | t |
| Lower limit | 0 |
| Upper limit | 4*#pi |
| Interval | #pi/32 |
List View
There are two "views" in Osiris, "Graph" and "List". The current view is changed using the diamond key (to the left of te spacebar) in a similar way to the Agenda application and the current view is shown in the Status window on the right of the screen. Siena users: The status window is not shown by default on your machine, press Fn-Menu to it on and off.
- Press the diamond key to change to "List" view.
A small box appears in the middle of the screen. This is the "List" window which shows all equations entered. Have a go at using some of the keys described below.
- The up and down keys can be used to highlight an equation
- Pressing "Enter" opens the current equation for editing.
- "Delete" deleted the current (highlighted) equation after asking you to confirm this
- "Menu" opens the menu which has been changed for list view - the "Axes" and "Graph" menus have been replaced by a "List" menu.
- PSION-D or PSION-I differentiate or integrate the current equation respectively.
As List view is oriented towards managing your equations, it is often helpful to enter lots of equations whilst in this view.
- Change the polar equation r=t to r=t/2
- Press the diamond key to get back to "Graph" view.
Graph View
Graph view is used to view equations you have plotted. It provides two viewing tools which can be switched on on off independently. These are the "Navigus" to help with navigating the graph and "Trace" to help examine graphs in detail. You will often use the key shortcuts below (most of these have a corresponding menu option).
- The arrow keys move one grid line in each direction.
- Holding down PSION at the same time as pressing an arrow key moves one screen in each direction.
- The number keys 1-5 change between 5 levels of accuracy (1 is most accurate, 5 least accurate) - this replicates the "Plot speed" line in the "Set preferences" dialog from the "Special" menu (PSION-Q).
- PSION-/ ("Centre Axes") forces the axes to the centre of the screen, regardless of whether they are curently on-screen or not.
- PSION-* toggles the Navigus on and off.
- PSION-T launches Trace mode.
- Shift-PSION-R auto ranges the axes - the extent of the y-axes is changed so that the graph entirely fits on the screen.
The Navigus
The Navigus allows you to "preview" a graph before it is redrawn in detail. Because this takes place at a very high speed and in a small window, the Navigus is more responsive to use whilst moving around the graph. Also, as any changes made to the graph whilst in Navigus mode can easily be discarded, it is useful to reformat the graph and repeatedly zoom whilst in Navigus mode.
- Select "Navigus" from the "Tools" menu or press PSION-* to enter Navigus mode (ensure you are in "Graph" view).
Notice that the Navigus only shows an approximate view of the graph - notice that the COS function has the wrong period. It is for this reason that Navigus mode should be used with care - whilst it will show that something is in a particular region of a graph, it will not necessarily show precisely what is there.
Do have a go at moving about, changing the grid, ranges and labels etc. Also check that zooming works in the Navigus.
All your changes have been discarded! If you want to keep the changes you make whilst in Navigus mode, you should press "Enter" or PSION-* to leave rather than "Esc".
Trace mode
Trace mode is provided to allow you to determine accurately the co-ordinates of points on a particular graph. It is often used to find graphically points where two equations intersect, for example.
- From "Graph" view, press PSION-t to enter trace mode (or use "Trace" from the "Graph" menu.
You can now use the left and right arrow keys to move the cross along the equation and the up and down arrow keys to cycle through the available equations. The trace window shows the co-ordinates at a particular point in the graph which is shown by the flashing cross. If you move the cross near to this window, it will automatically jump to the other side of the screen. If you press any other key, you will leave trace mode.
- Use trace mode to find points where the equations y=5*COS(2*#pi*x) and r=t cross. [Hint: you may like to zoom in to get a more accurate result]
Now that you have completed this tutorial, you should know about the "Graph" and "List" views and how to move between them. You should be able to use "Navigus" mode and "Trace" mode in order to manipulate your graphs and you should also be able to control the speed/accuracy with which graphs are plotted.
A list of suggestions to experiment further is provided below, so do please have a go.
- Have a go at creating a pair of parametric equations (y and x given in terms of a common parameter t.
- Check that you can use the "Set preferences" dialog from the "Special" menu (PSION-Q) to alter a variety of global settings. Plot a graph of y=COS(x) where x is in degrees [Hint: You will need to set the x range from -360 to +360.
- Use the interactive help (launched by pressing the "Help" key) to explore additional Osiris features.
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