3D Grapher  -  three-dimensional graphs

by Andrew Benson

3D Grapher is an applications which can be used to produce three dimensional diagrams of various mathematical formulae. The results can be displayed on screen in a variety of ways and can also be saved in Draw file format for further editing, inclusion into DTP documents etc. 3D Grapher supports Acorn's Help.

Using the Program
3D Grapher is installed by double clicking on its icon in a Filer window, or running from the RISC User menu system. After a short delay the 3D Grapher icon will appear on the right hand side of the icon bar. Clicking Select on this icon will open the graph window which will be initially blank.

Clicking Menu over the icon displays a short menu. The entries Info and Quit perform the usual operations.

Save is initially unavailable from this menu, but once a graph has been produced it leads to a standard save box which allows the graph to be saved as a Draw file.

The other entry in the menu is Options. Selecting this option opens the main control window. This window has several sections. Each is described below.

On the left hand side of the window are icons which allow the formula to be plotted to be entered. The radio icons labelled Cartesian, Cylindrical and Spherical allow you to choose which coordinate system you wish to use. When one of these icons is selected the writable icons to the right of it will become available for entry. You will see that some example formulae have already been entered into the writable icons when you start up the program.

Each of the three systems has a large icon into which the formula may be entered. Any standard mathematical functions that the computer understands can be entered here. The variables to be used are given to the left of this icon (X and Y for Cartesian, P and Z for cylindrical and T and P for spherical).

Beneath these icons are four more icons which allow the range of the relevant variables to be specified. The graph will only be plotted over this range of values.

The Rotation section allows control over what angle the graph will be viewed from. The three icons allow you to enter the rotation about each axis in degrees. It can be quite difficult to visualise what various rotations will look like in 3D. Often the best idea is to just try various combinations of angles until a good one is found. The initial values give a good viewpoint for many graphs.

The Angles section allows a choice between degrees and radians for the angles in the cylindrical and spherical coordinate systems (360 degrees are equivalent to 2*PI radians).

The Display section allows control over various characteristics of the graph's appearance. Graphs can be plotted as just a wire frame image (i.e. a skeleton of lines) or as a filled solid-looking surface. Selecting Wire frame or Filled allows you to choose between these two effects. If Filled is selected you may also choose to have the surface drawn in colour or in a grey scale. If Colour is chosen then the plot on screen will be drawn in the desktop colours and the image in a saved Draw file will be created in shades of red and yellow. Backdrop if selected will cause a background to be displayed behind the graph. The background shows the values along the three axes.

Finally, when all the options are set as required, clicking on OK in the top right hand corner will cause the graph to be plotted. This is quite a lengthy process, taking a couple of minutes. The hourglass is displayed whilst this is done. Note that a wire frame graph will be drawn much more quickly than a filled graph so it often useful to plot the graph in wireframe until the correct rotations etc. are found, and only then plot the filled graph.

The graph will then be shown in the graph window, and can now be saved in Draw format. To do this simply use the save option from the icon bar menu. The save will also take a short while to complete as the graph is assembled in Draw format. The draw files created tend to be quite large because of the complexity of the graphs. Wire frame graphs will require smaller files in general. The Draw file of the graph can then be edited and manipulated in Draw, and then incorporated into a DTP program or indeed any other program which accepts Draw file input.

Further Information on 3D graphs
Some understanding of three dimensional graphs is necessary in order to make use of 3D Grapher. A normal two dimensional graph is usually drawn on a pair of axes labelled X and Y. A formula determines what the value of Y will be for any value of X. Such a formula might be Y=2X for example. Then for any value of X the corresponding value of Y can be found. To plot the graph we simply calculate Y for every value of X and draw the results on the axes. The result will be a line or curve.

For three dimensional graphs we have three axes, X, Y and Z. Now the value of Z is given by a formula which depends on both X and Y. For example, such a formula might be Z=X+Y. Now to plot the three dimensional graph we calculate the value of Z for every value of X and Y. The result is a surface. 3D Grapher will calculate and display such surfaces for any given formula.

3D Grapher is capable of working with other types of coordinates besides the usual X, Y, Z combination. These are a bit more difficult to use mathematically. Firstly there are cylindrical polar coordinates. In this system each point is specified by an angle, the distance from the Z axis and the distance along the Z axis.

The other type is called spherical polar coordinates. In this system each point is specified by two angles and the distance of the point from the origin. A good maths textbook will probably contain a better description of these two coordinate systems.


Copyright  RISC User 1994