Locus
Another exclusive Foundation RISCWorld application
The main controls
In this section the main controls and their operation will be described. They are arranged at the top of the main window in three rows of icons, each dealing with a specific group of features.
- Top Row - Settings which control how the application behaves.
- Middle Row - Domain and range settings.
- Bottom Row - Formula input.
Each row will now be described, starting at the left hand side and dealing with each button in turn..
Top row.
Clear
This clears the screen and removes your work to date from memory. In the interest of speed you are not reminded to save work if you have not already done so. Clicking with SELECT will clear everything and clicking with ADJUST (the right hand mouse button) will clear everything except the Data Files.
Superimpose
This is primarily of interest to teachers for classroom demonstration and is only available when auto-scaling is on. Click on this icon before starting work and each time you plot a new graph Locus will redraw the window, rescaled appropriately for the latest graph plotted, and will then it each subsequent graph one in the newly scaled window.
Cartesian
Clicking on this icon changes Locus to cartesian mode and changes the graph type icon to 'y=' or ('xy=' if you are in parametric mode) and the formula menu will change to the cartesian set.
Polar
Clicking on this icon changes Locus to polar mode and the graph type icon to 'r=' (or 'rØ=' if you are in parametric mode) and the formula menu will change to the polar set.
Implicit
Clicking on this icon changes Locus to Implicit mode, empties the graph type icon and the formula menu will change to the implicit set.
Parametric Switch
This switch toggles between parametric and non-parametric modes. When the switch looks like this (see left) you are in non-parametric mode.
Coordinate Input
This opens the coordinates input window, which allows the user to input up to 20 coordinate points.
Internal dataset filer
This opens the Internal filer. I have included this in response to requests that Locus will allow data input without recourse to dragging files from a directory window. It is useful for teaching purposes and for demonstrations as you can set up the files you need beforehand.
Radians
Clicking on this changes the angle measurement between radians and degrees.
Step
This 'bump' icon set is used to define the plotting step. Locus works by plotting the number of points specified (in this case 512) and then joining them up with straight lines. There is obviously a trade-off between speed of plotting and accuracy. For most simple graphs (ones that don't oscillate too wildly) a step of 128 should suffice. For a complex formula like y=xsin(1/x). it would need to be considerably higher (>1000).
Zoom out
The effect of the Zoom Out icon is to double the domain. If auto-scaling is on, the range will be recalculated accordingly, if not the range will be doubled as well.
Zoom in
The Zoom In icon works differently from Zoom Out. When you click on it nothing will happen. However, if you then move the pointer over the main window and 'click and drag' from the top left hand corner of the area you want enlarged to the bottom right and release the mouse button, the area defined will be redrawn. If you use this feature with students who have difficulty with the mouse they may need to practice the 'click-drag' technique until they become familiar with it.
Move
When you click on this icon you can then click and drag the graph to a new position. When you release the mouse button the graph will be redrawn in the new location.
Constants
This opens the Constants dialogue box which lets the user store useful constants to be used in formulae and transformation expressions. Constants are also used in plotting families of graphs.
Families
This opens the Families dialogue box which lets the user plot families of related graphs by altering the values of any constants in use.
Coordinates
This opens the coordinates information window. Initially it will show just the the x and y coordinates of the last clicked mouse position. Clicking anywhere in the main window (ie. on the graph) will display the coordinates for that position and a pair of horizontal and vertical dotted lines will appear at the appropriate place on the graph.
Clicking with SELECT on a graph will change the coordinate values according to the position of the mouse. Click/Dragging on the graph will allow you to trace along the graph seeing the values change as you do so.
Clicking on the 'Toggle size' icon will enlarge the window so that you can see the polar coordinates and the derivative of the function at that point.
Clicking on the 'Coordinates' icon again will close the window.
Tangent
This can be used on its own or with the 'Coordinates' window. When this icon is selected you will see both the horizontal and vertical 'Coordinate' lines and the tangent to the curve at that point.
The dy/dx entry in the coordinates window will also display the gradient of the tangent at this point.
Derivative
When this is selected Locus will attempt to superimpose the derived function (wherever it is defined) on top of the original function. This is done numerically not algebraically, so the derived function is not found for you. However, you can then attempt to fit a function to the resulting curve manually, which is a useful way of acquiring an intuitive grasp of derivative functions.
Integral
This works in exactly the same way as the derivative icon but this time Locus will try to draw the integral function.
Middle row.
The five writable icons can be changed at any time (when they are not 'greyed out') to alter the extent of the graph. The 'max' number must obviously be higher than the 'min' number. You can also click drag the contents of one icon into another.
Auto scaling
When this icon is selected Locus will try to do some of the scaling for you. Precisely what it does depends on which mode you are in. This is explained in greater detail in the Tutorial.
Squaring up
When this icon is unselected it will show an ellipse and the graphs will be drawn in a rectangular format. When it is selected the ellipse will turn to a circle and the graphs will be drawn in a square on the left hand side of the main window.
Bottom row.
Formula input icon
This is where you place your formulae and it can be done in one of two ways. Either you can enter the formula directly by clicking on the icon with the mouse pointer and typing the appropriate formula for the mode you are currently in. For more details on this please see the Tutorial and Appendix A which gives full details on Locus' data input procedures.
Alternatively you can click on the menu icon which will open a menu displaying a number of functions. These are fully editable and you can create your own set if you wish. The menu will change automatically for the mode you are in. If, for example, you change to polar parametric mode the menu will contain this type of formulae.
Save to file
To the right of the formula menu icon is an icon which will add the current contents of the main formula icon to the formula menu and update the menu automatically.
x squared
Clicking on this icon will insert the squared symbol at the caret wherever that may be. This allows the user to type in such functions as "y=x²" or "y=sin²x".
x cubed
The same as the above except that this time it is the cubed ³ symbol that is inserted.
Plot
Clicking on this icon will plot the graph, assuming that there is a formula in the input icon and the scales are set correctly,
Locus will try to do this even if you have typed garbage into the formula icon although the results will then be useless.
If the plot takes too long or if nothing happens, pressing Escape will stop Locus from plotting and return control to the user.
Foundation RISCWorld