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Insley/!FormuGrph/!Help/Instructs
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn User » AU 1995-02.adf » !StarInfo_StarInfo |
| Filename: | Insley/!FormuGrph/!Help/Instructs |
| Read OK: | ✔ |
| File size: | 30F7 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
Formugraph. By Steven Insley. Aged 15
�1994
Instructions
------------
Double-Click the !FormuGrph icon to run.
Load !Help for on-line interactive help.
The Icon
--------
Clicking Select opens the input window where the formulae are entered.
Clicking Adjust opens a similar window where the formulae are entered for animations
Clicking Menu will open a menu.
What the graphs are
-------------------
The 3D graph produced is just two ordinary 2D graphs displayed at the same time, over each other. Y is calculated from X and Z. The points for Y are plotted and neighbouring points are joined together to produce the curves. The curves in one direction are of X and Y axis, with Z as the constant. Thecurves in the other direction are of Y and Z with X as the constant. If these are plotted at right angles to each other isometrically, then the single 3D graph is produced, which appears to be a 3D form.
Getting a graph on screen / a crash course....
----------------------------------------------
To create a graph you first have to know which axis is which, for this, referto the draw file named 'Diagrams' and look at Fig 1.
Most people who have done maths to GCSE or 'O' Level know what a SINE Curve is. If you don't then Fig 2 shows one (more or less). The Sine of an angle plotted on a graph with the angle on the X axis and the Sine of the angle on the Y axis (See Fig 2) shows a curve. Any point on the curve can be plotted with the formula SIN(X).
So now if you click SELECT on the formugraph icon you should get an input window. Click in the Y= box and type :
SIN(X)/30
You must put the '/30' on or else the points will go off the top of the screen. Now click OK and wait for the graph to be calculated and drawn. A display window containing a graph should appear. The display, however, will not look like Fig 2, as it has taken into account the Z axis aswell. You should still be able to see the Sine Curve down the X axis. As the Z axis does not feature in the formula, the sine curve goes all the way along the Z axis. ie. take any point on the Z axis and move along the X axis and you should see the Y axis is the actual curve.
Now lets make it more interesting...
We are now going to introduce the Z axis to the formula. If we add the result of SIN(X) and SIN(Z) to get the position on the Y axis, we get a Sine Curve along both the X and Z axis plotted in relation to each other. ie type-
(SIN(X)+SIN(Z))/30
and click OK.
Now you can see Sine Curves along both the X and Z axis, but the interesting thing is that the Sine Curves on the X axis are plotted in relation to those on the Z axis. For each position on the Z axis, the the curve of the X axis starts at the the Y point. This may not be apparent to you, and if it isn't then nevermind. It isn't crucial. You are still able to produce interestinggraphs, even if you don't understand the maths and principles behind them. In other words, you don't have to be Van Gogh to be able to paint....
When entering a formula you may find the Y= icon becomes cluttered with
brackets etc. and is not easy to follow. The formula may be spread over
several lines. ie. the formula :
Y= (SIN(X)+COS(Z))/30
could become :
A= SIN(X)
B= COS(Z)
Y= (A+B)/30
which is a lot easier to understand and is also more easily modified. Note:
the Y= and C= are visible when the window is first opened, but to reveal the
A= and B= icons, you must click on the Toggle size icon in the top right
corner of the window. (to the right of the title bar)
Making your own graphs now is just a matter of experimentation. You can't
sit down and visualise a graph and then write a formula for it, unless you
are a Big Amazing Super Technical Arithmetic Reproduction Device!??
Remember, if the graph goes off the top and the bottom of the screen, then
divide the entire formula by a increasingly large number until it fits on.
If you don't get anything but a blank screen, then the formula produces a
value for Y that is larger or smaller than 0.8 or -0.8 for all points. In
other words.... that there formula don't work sonny Jim.... Try another one.
If you're one of the people who are by now thinking 'what the hell is he
going on about?', read this next bit.
Loading pre-saved formulae
--------------------------
If you Double-Click the !Formulae app. you should get a directory full of formulae files. There are several ways of loading them :
1) Drag one to the bar icon, which will load the file and open the input window.
2) Drag one to the input window which loads it in.
3) Double-Click one which loads it and opens the input window.
4) Drag one to the display window which loads it in, draws it, and opens the input window.
5) Drag one to the Sequence Input window. This loads the formulae in and
does not affect the loop extremes or the no. of frames.
Loading a file by any of these methods enters the full pathname of the file in the Formulae Save Box.
Saving formulae and displays
----------------------------
To save the formulae, click MENU in the input window and move the pointer through Save to open a Save Box. Enter the filename in the box and drag the icon to a directory viewer. Alternatively :
1) Enter the full pathname and click OK
2) If a full pathname is already in the box, click Save on the menu.
The same goes for saving displays, except Save is on the display menu.
The sequence input window / Animation
-------------------------------------
Making still images is very nice, but what makes these graphs more fun is
the creation of animations. You've probably already seen an animated wave
of some sort that came on some coverdisc or PD disc, but you never
considered making one. Well folks, now you can. And rather cleverly if I
may say so.
A number of frames must be produced, each slightly different, that all run
in sequence (Hence sequence input) to produce an animation. The way I
devised to do this is quite simple to understand. A variable is produced
that changes in a loop. Two extremes are set and depending on how many
frames you have, the number moves between the two extremes step by step,
each time a frame is produced. ie :
Extreme 1 : 20 Extreme 2 : 60 Frames : 11
Frame | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11
-----------|----|----|----|----|----|----|----|----|----|----|----
Variable V | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60
In other words, on frame 4, V will be 32. On frame 9, V will be 52 etc.
OK, you have made a formula that produces a nice graph that ya like. ie
(SIN(X)+COS(Z))/30
and you want to make it move. There two things that you could do that
spring to my mind :
1) Extreme 1 : 20 Extreme 2 : 60 Frames : 20
Y= (SIN(X)+COS(Z))/V
2) Extreme 1 : 0 Extreme 2 : 6 Frames : 20
Y= (SIN(X+V)+COS(Z))/45
Number 1 would produce a SIN/COS pattern that would appear to become flatter
as the number V increases each frame. This is because when you divide the
entire formula by a larger number it becomes flatter as explained earlier.
So V=60 will produce a flatter graph than V=20.
Number 2 would produce the same pattern but it would appear to move along
the X axis because it is displaced by V which is a different number each
frame. That is a little bit more difficult to understand but the same idea
can be applied to different formulae to produce a similar effect.
Again, experimentation is the only real way to learn what can be achieved so
have a go. Try different values out by replacing V with a number in the
input window and producing several still frames. Then go back to the
sequence input window and set the extremes, write the formula, and you're
away.....
Load in formulae already made by me and try altering them or animating them.
It is a good way to learn.
OK, to actually start the sequence rendering, you must drag one of two icons
to a directory viewer. If you drag the spritefile icon, a series of
spritefiles are saved, each having the name entered to the left + the frame
number. It it much better to drag the X� icon however, as this saves an
application which when run will show the animation. Within this application
the formula is also saved for future reference. To the left of the X� icon
there is a sort of circle like icon which is in fact the loop/yoyo icon.
When there are two arrow heads on the circle the animation goes from frames
1 to n and then n to 1 (n= number of frames). When there is only one arrow
head the animation goes from frame 1 to n and then 1 to n again etc.
Note: In either format, only up to 77 frames can be saved under ADFS, as
this is the maximum number of files allowed in a directory. I am not sure
about IDEFS or any SCSI filing systems though.
Loading pre-saved sequence formulae
-----------------------------------
If you Double-Click the !SeqForms app. you should get a directory full of
sequence formulae files. There are several ways of loading them :
1) Drag one to the bar icon, which will load the file and open the input window.
2) Drag one to the sequence input window which loads it in.
3) Double-Click one which loads it and opens the sequence input window.
4) Drag one to the Input window. This loads the formulae in but not the
loop or frames information, obviously.
Loading a file by any of these methods enters the full pathname of the file in the Formulae Save Box.
The grid/solid icons
--------------------
In both input windows there is another icon not yet explained. It is the
one which toggles whether a grid graph or a solid graph is produced. The
actual icon is a good representation of what a graph will look similar to so
I won't go into this. If you can't figure it out... tough luck, dummy.
Future versions of Formugraph will have other options defining how the graph
is drawn ie Light Sourcing or even texture mapping??
I may also incorporate a feature which would allow you to write your own
plotting routines and add them to a menu, but it depends whether or not this
version is a success.
Various other features
----------------------
On both input menus there is a Reset option, and believe it or not, clicking
on it clears all formulae and basically resets the input window to its
default state. Duh. Also there is a To ?????? icon. Clicking on this on
the input window menu sends all the formulae (A,B,C and Y) to the sequence
input window and puts them in the appropriate boxes. Clicking on it on the
Sequence menu sends the formulae but not the frames and extremes, obviously.
The grid/solid icons and the loop/yoyo icon are not affected by this
operation.
On both the input menus there is also the Commands option. Clicking this
opens a window containing every conceivable mathematical function (including
numbers) that you would ever need. Clicking on one of these enters the
command at the caret, so it even works in Edit or Ovation or, well,
anything. The functions are not explained so refer to a BASIC manual, the
old BBC B manual if you have one, or use the HELP command in BASIC to find
out what the functions do. If you have to look up what the numbers do,
Click MENU on the bar icon and SELECT Quit now....
AND THAT'S ABOUT IT! Use interactive !Help for on-line help.
� Notes on known Bugs
-------------------
While the sequence is rendering, do not attempt to do anything else. If you
try dragging a window or clicking an icon for example, you will cause BIG
errors. I think this is something to do with the way I arranged the
WimpPolling, which speeds up the plotting. Don't do it....
You may experience problems if you are using a high res monitor when
dragging save icons.
RISC PCs
--------
If you have a RISC PC and formugraph doesn't work for any reason. TOUGH.
It serves you right for having one and not buying me one! But seriously,
The RISC PC is far too expensive for me to get one, and I havn't had chance
to test FormuGraph on one, so write to me with problems, queries, money....
If I do ever have a chance to use one, I may write a version with real-time
rendering or near enough RTR. Well Maybe..... Or 24bit B/W
SILICON GRAPHICS WORK STATIONS
------------------------------
Ha Ha ! Yes... Yais! Ho Ho Ha Ha Hey. Whoopee..... I WANT ONE!!!!
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The Ic| 000000b0 6f 6e 0a 20 20 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 43 |on. --------..C| 000000c0 6c 69 63 6b 69 6e 67 20 53 65 6c 65 63 74 20 6f |licking Select o| 000000d0 70 65 6e 73 20 74 68 65 20 69 6e 70 75 74 20 77 |pens the input w| 000000e0 69 6e 64 6f 77 20 77 68 65 72 65 20 74 68 65 20 |indow where the | 000000f0 66 6f 72 6d 75 6c 61 65 20 61 72 65 20 65 6e 74 |formulae are ent| 00000100 65 72 65 64 2e 0a 43 6c 69 63 6b 69 6e 67 20 41 |ered..Clicking A| 00000110 64 6a 75 73 74 20 6f 70 65 6e 73 20 61 20 73 69 |djust opens a si| 00000120 6d 69 6c 61 72 20 77 69 6e 64 6f 77 20 77 68 65 |milar window whe| 00000130 72 65 20 74 68 65 20 66 6f 72 6d 75 6c 61 65 20 |re the formulae | 00000140 61 72 65 20 65 6e 74 65 72 65 64 20 66 6f 72 20 |are entered for | 00000150 20 20 20 61 6e 69 6d 61 74 69 6f 6e 73 0a 43 6c | animations.Cl| 00000160 69 63 6b 69 6e 67 20 4d 65 6e 75 20 77 69 6c 6c |icking Menu will| 00000170 20 6f 70 65 6e 20 61 20 6d 65 6e 75 2e 0a 0a 20 | open a menu... | 00000180 20 57 68 61 74 20 74 68 65 20 67 72 61 70 68 73 | What the graphs| 00000190 20 61 72 65 0a 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d | are. ---------| 000001a0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 54 68 65 20 |----------..The | 000001b0 33 44 20 67 72 61 70 68 20 70 72 6f 64 75 63 65 |3D graph produce| 000001c0 64 20 69 73 20 6a 75 73 74 20 74 77 6f 20 6f 72 |d is just two or| 000001d0 64 69 6e 61 72 79 20 32 44 20 67 72 61 70 68 73 |dinary 2D graphs| 000001e0 20 64 69 73 70 6c 61 79 65 64 20 61 74 20 74 68 | displayed at th| 000001f0 65 20 73 61 6d 65 20 20 20 74 69 6d 65 2c 20 6f |e same time, o| 00000200 76 65 72 20 65 61 63 68 20 6f 74 68 65 72 2e 20 |ver each other. | 00000210 20 59 20 69 73 20 63 61 6c 63 75 6c 61 74 65 64 | Y is calculated| 00000220 20 66 72 6f 6d 20 58 20 61 6e 64 20 5a 2e 20 20 | from X and Z. | 00000230 54 68 65 20 70 6f 69 6e 74 73 20 66 6f 72 20 59 |The points for Y| 00000240 20 61 72 65 20 20 70 6c 6f 74 74 65 64 20 61 6e | are plotted an| 00000250 64 20 6e 65 69 67 68 62 6f 75 72 69 6e 67 20 70 |d neighbouring p| 00000260 6f 69 6e 74 73 20 61 72 65 20 6a 6f 69 6e 65 64 |oints are joined| 00000270 20 74 6f 67 65 74 68 65 72 20 74 6f 20 70 72 6f | together to pro| 00000280 64 75 63 65 20 74 68 65 20 63 75 72 76 65 73 2e |duce the curves.| 00000290 20 20 20 54 68 65 20 63 75 72 76 65 73 20 69 6e | The curves in| 000002a0 20 6f 6e 65 20 64 69 72 65 63 74 69 6f 6e 20 61 | one direction a| 000002b0 72 65 20 6f 66 20 58 20 61 6e 64 20 59 20 61 78 |re of X and Y ax| 000002c0 69 73 2c 20 77 69 74 68 20 5a 20 61 73 20 74 68 |is, with Z as th| 000002d0 65 20 63 6f 6e 73 74 61 6e 74 2e 20 20 54 68 65 |e constant. The| 000002e0 63 75 72 76 65 73 20 69 6e 20 74 68 65 20 6f 74 |curves in the ot| 000002f0 68 65 72 20 64 69 72 65 63 74 69 6f 6e 20 61 72 |her direction ar| 00000300 65 20 6f 66 20 59 20 61 6e 64 20 5a 20 77 69 74 |e of Y and Z wit| 00000310 68 20 58 20 61 73 20 74 68 65 20 63 6f 6e 73 74 |h X as the const| 00000320 61 6e 74 2e 20 20 49 66 20 20 20 20 20 74 68 65 |ant. If the| 00000330 73 65 20 61 72 65 20 70 6c 6f 74 74 65 64 20 61 |se are plotted a| 00000340 74 20 72 69 67 68 74 20 61 6e 67 6c 65 73 20 74 |t right angles t| 00000350 6f 20 65 61 63 68 20 6f 74 68 65 72 20 69 73 6f |o each other iso| 00000360 6d 65 74 72 69 63 61 6c 6c 79 2c 20 74 68 65 6e |metrically, then| 00000370 20 74 68 65 20 20 20 20 20 20 73 69 6e 67 6c 65 | the single| 00000380 20 33 44 20 67 72 61 70 68 20 69 73 20 70 72 6f | 3D graph is pro| 00000390 64 75 63 65 64 2c 20 77 68 69 63 68 20 61 70 70 |duced, which app| 000003a0 65 61 72 73 20 74 6f 20 62 65 20 61 20 33 44 20 |ears to be a 3D | 000003b0 66 6f 72 6d 2e 0a 0a 20 20 47 65 74 74 69 6e 67 |form... Getting| 000003c0 20 61 20 67 72 61 70 68 20 6f 6e 20 73 63 72 65 | a graph on scre| 000003d0 65 6e 20 2f 20 61 20 63 72 61 73 68 20 63 6f 75 |en / a crash cou| 000003e0 72 73 65 2e 2e 2e 2e 0a 20 20 2d 2d 2d 2d 2d 2d |rse..... ------| 000003f0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| * 00000410 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 54 6f 20 63 72 65 |--------..To cre| 00000420 61 74 65 20 61 20 67 72 61 70 68 20 79 6f 75 20 |ate a graph you | 00000430 66 69 72 73 74 20 68 61 76 65 20 74 6f 20 6b 6e |first have to kn| 00000440 6f 77 20 77 68 69 63 68 20 61 78 69 73 20 69 73 |ow which axis is| 00000450 20 77 68 69 63 68 2c 20 66 6f 72 20 74 68 69 73 | which, for this| 00000460 2c 20 72 65 66 65 72 74 6f 20 74 68 65 20 64 72 |, referto the dr| 00000470 61 77 20 66 69 6c 65 20 6e 61 6d 65 64 20 27 44 |aw file named 'D| 00000480 69 61 67 72 61 6d 73 27 20 61 6e 64 20 6c 6f 6f |iagrams' and loo| 00000490 6b 20 61 74 20 46 69 67 20 31 2e 0a 0a 4d 6f 73 |k at Fig 1...Mos| 000004a0 74 20 70 65 6f 70 6c 65 20 77 68 6f 20 68 61 76 |t people who hav| 000004b0 65 20 64 6f 6e 65 20 6d 61 74 68 73 20 74 6f 20 |e done maths to | 000004c0 47 43 53 45 20 6f 72 20 27 4f 27 20 4c 65 76 65 |GCSE or 'O' Leve| 000004d0 6c 20 6b 6e 6f 77 20 77 68 61 74 20 61 20 53 49 |l know what a SI| 000004e0 4e 45 20 43 75 72 76 65 20 20 69 73 2e 20 49 66 |NE Curve is. If| 000004f0 20 79 6f 75 20 64 6f 6e 27 74 20 74 68 65 6e 20 | you don't then | 00000500 46 69 67 20 32 20 73 68 6f 77 73 20 6f 6e 65 20 |Fig 2 shows one | 00000510 28 6d 6f 72 65 20 6f 72 20 6c 65 73 73 29 2e 20 |(more or less). | 00000520 20 54 68 65 20 53 69 6e 65 20 6f 66 20 61 6e 20 | The Sine of an | 00000530 61 6e 67 6c 65 20 20 70 6c 6f 74 74 65 64 20 6f |angle plotted o| 00000540 6e 20 61 20 67 72 61 70 68 20 77 69 74 68 20 74 |n a graph with t| 00000550 68 65 20 61 6e 67 6c 65 20 6f 6e 20 74 68 65 20 |he angle on the | 00000560 58 20 61 78 69 73 20 61 6e 64 20 74 68 65 20 53 |X axis and the S| 00000570 69 6e 65 20 6f 66 20 74 68 65 20 61 6e 67 6c 65 |ine of the angle| 00000580 20 6f 6e 20 74 68 65 20 59 20 61 78 69 73 20 28 | on the Y axis (| 00000590 53 65 65 20 46 69 67 20 32 29 20 73 68 6f 77 73 |See Fig 2) shows| 000005a0 20 61 20 63 75 72 76 65 2e 20 20 41 6e 79 20 70 | a curve. Any p| 000005b0 6f 69 6e 74 20 6f 6e 20 74 68 65 20 63 75 72 76 |oint on the curv| 000005c0 65 20 63 61 6e 20 62 65 20 70 6c 6f 74 74 65 64 |e can be plotted| 000005d0 20 77 69 74 68 20 74 68 65 20 66 6f 72 6d 75 6c | with the formul| 000005e0 61 20 53 49 4e 28 58 29 2e 20 20 0a 0a 53 6f 20 |a SIN(X). ..So | 000005f0 6e 6f 77 20 69 66 20 79 6f 75 20 63 6c 69 63 6b |now if you click| 00000600 20 53 45 4c 45 43 54 20 6f 6e 20 74 68 65 20 66 | SELECT on the f| 00000610 6f 72 6d 75 67 72 61 70 68 20 69 63 6f 6e 20 79 |ormugraph icon y| 00000620 6f 75 20 73 68 6f 75 6c 64 20 67 65 74 20 61 6e |ou should get an| 00000630 20 69 6e 70 75 74 20 20 20 20 77 69 6e 64 6f 77 | input window| 00000640 2e 20 20 43 6c 69 63 6b 20 69 6e 20 74 68 65 20 |. Click in the | 00000650 59 3d 20 62 6f 78 20 61 6e 64 20 74 79 70 65 20 |Y= box and type | 00000660 3a 0a 0a 20 20 20 20 20 20 20 53 49 4e 28 58 29 |:.. SIN(X)| 00000670 2f 33 30 0a 0a 59 6f 75 20 6d 75 73 74 20 70 75 |/30..You must pu| 00000680 74 20 74 68 65 20 27 2f 33 30 27 20 6f 6e 20 6f |t the '/30' on o| 00000690 72 20 65 6c 73 65 20 74 68 65 20 70 6f 69 6e 74 |r else the point| 000006a0 73 20 77 69 6c 6c 20 67 6f 20 6f 66 66 20 74 68 |s will go off th| 000006b0 65 20 74 6f 70 20 6f 66 20 74 68 65 20 20 20 20 |e top of the | 000006c0 20 20 73 63 72 65 65 6e 2e 20 20 4e 6f 77 20 63 | screen. Now c| 000006d0 6c 69 63 6b 20 4f 4b 20 61 6e 64 20 77 61 69 74 |lick OK and wait| 000006e0 20 66 6f 72 20 74 68 65 20 67 72 61 70 68 20 74 | for the graph t| 000006f0 6f 20 62 65 20 63 61 6c 63 75 6c 61 74 65 64 20 |o be calculated | 00000700 61 6e 64 20 64 72 61 77 6e 2e 20 20 41 20 20 64 |and drawn. A d| 00000710 69 73 70 6c 61 79 20 77 69 6e 64 6f 77 20 63 6f |isplay window co| 00000720 6e 74 61 69 6e 69 6e 67 20 61 20 67 72 61 70 68 |ntaining a graph| 00000730 20 73 68 6f 75 6c 64 20 61 70 70 65 61 72 2e 20 | should appear. | 00000740 20 54 68 65 20 64 69 73 70 6c 61 79 2c 20 68 6f | The display, ho| 00000750 77 65 76 65 72 2c 20 77 69 6c 6c 20 6e 6f 74 20 |wever, will not | 00000760 6c 6f 6f 6b 20 6c 69 6b 65 20 46 69 67 20 32 2c |look like Fig 2,| 00000770 20 61 73 20 69 74 20 68 61 73 20 74 61 6b 65 6e | as it has taken| 00000780 20 69 6e 74 6f 20 61 63 63 6f 75 6e 74 20 74 68 | into account th| 00000790 65 20 5a 20 61 78 69 73 20 61 73 77 65 6c 6c 2e |e Z axis aswell.| 000007a0 20 20 59 6f 75 20 20 20 20 73 68 6f 75 6c 64 20 | You should | 000007b0 73 74 69 6c 6c 20 62 65 20 61 62 6c 65 20 74 6f |still be able to| 000007c0 20 73 65 65 20 74 68 65 20 53 69 6e 65 20 43 75 | see the Sine Cu| 000007d0 72 76 65 20 64 6f 77 6e 20 74 68 65 20 58 20 61 |rve down the X a| 000007e0 78 69 73 2e 20 20 41 73 20 74 68 65 20 5a 20 61 |xis. As the Z a| 000007f0 78 69 73 20 20 20 64 6f 65 73 20 6e 6f 74 20 66 |xis does not f| 00000800 65 61 74 75 72 65 20 69 6e 20 74 68 65 20 66 6f |eature in the fo| 00000810 72 6d 75 6c 61 2c 20 74 68 65 20 73 69 6e 65 20 |rmula, the sine | 00000820 63 75 72 76 65 20 67 6f 65 73 20 61 6c 6c 20 74 |curve goes all t| 00000830 68 65 20 77 61 79 20 61 6c 6f 6e 67 20 74 68 65 |he way along the| 00000840 20 5a 20 61 78 69 73 2e 20 20 69 65 2e 20 74 61 | Z axis. ie. ta| 00000850 6b 65 20 61 6e 79 20 70 6f 69 6e 74 20 6f 6e 20 |ke any point on | 00000860 74 68 65 20 5a 20 61 78 69 73 20 61 6e 64 20 6d |the Z axis and m| 00000870 6f 76 65 20 61 6c 6f 6e 67 20 74 68 65 20 58 20 |ove along the X | 00000880 61 78 69 73 20 61 6e 64 20 79 6f 75 20 20 20 20 |axis and you | 00000890 73 68 6f 75 6c 64 20 73 65 65 20 74 68 65 20 59 |should see the Y| 000008a0 20 61 78 69 73 20 69 73 20 74 68 65 20 61 63 74 | axis is the act| 000008b0 75 61 6c 20 63 75 72 76 65 2e 0a 0a 4e 6f 77 20 |ual curve...Now | 000008c0 6c 65 74 73 20 6d 61 6b 65 20 69 74 20 6d 6f 72 |lets make it mor| 000008d0 65 20 69 6e 74 65 72 65 73 74 69 6e 67 2e 2e 2e |e interesting...| 000008e0 0a 57 65 20 61 72 65 20 6e 6f 77 20 67 6f 69 6e |.We are now goin| 000008f0 67 20 74 6f 20 69 6e 74 72 6f 64 75 63 65 20 74 |g to introduce t| 00000900 68 65 20 5a 20 61 78 69 73 20 74 6f 20 74 68 65 |he Z axis to the| 00000910 20 66 6f 72 6d 75 6c 61 2e 20 20 49 66 20 77 65 | formula. 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If y| 000026e0 6f 75 20 63 61 6e 27 74 20 66 69 67 75 72 65 20 |ou can't figure | 000026f0 69 74 20 6f 75 74 2e 2e 2e 20 74 6f 75 67 68 20 |it out... tough | 00002700 6c 75 63 6b 2c 20 64 75 6d 6d 79 2e 0a 0a 46 75 |luck, dummy...Fu| 00002710 74 75 72 65 20 76 65 72 73 69 6f 6e 73 20 6f 66 |ture versions of| 00002720 20 46 6f 72 6d 75 67 72 61 70 68 20 77 69 6c 6c | Formugraph will| 00002730 20 68 61 76 65 20 6f 74 68 65 72 20 6f 70 74 69 | have other opti| 00002740 6f 6e 73 20 64 65 66 69 6e 69 6e 67 20 68 6f 77 |ons defining how| 00002750 20 74 68 65 20 67 72 61 70 68 0a 69 73 20 64 72 | the graph.is dr| 00002760 61 77 6e 20 69 65 20 4c 69 67 68 74 20 53 6f 75 |awn ie Light Sou| 00002770 72 63 69 6e 67 20 6f 72 20 65 76 65 6e 20 74 65 |rcing or even te| 00002780 78 74 75 72 65 20 6d 61 70 70 69 6e 67 3f 3f 0a |xture mapping??.| 00002790 0a 49 20 6d 61 79 20 61 6c 73 6f 20 69 6e 63 6f |.I may also inco| 000027a0 72 70 6f 72 61 74 65 20 61 20 66 65 61 74 75 72 |rporate a featur| 000027b0 65 20 77 68 69 63 68 20 77 6f 75 6c 64 20 61 6c |e which would al| 000027c0 6c 6f 77 20 79 6f 75 20 74 6f 20 77 72 69 74 65 |low you to write| 000027d0 20 79 6f 75 72 20 6f 77 6e 0a 70 6c 6f 74 74 69 | your own.plotti| 000027e0 6e 67 20 72 6f 75 74 69 6e 65 73 20 61 6e 64 20 |ng routines and | 000027f0 61 64 64 20 74 68 65 6d 20 74 6f 20 61 20 6d 65 |add them to a me| 00002800 6e 75 2c 20 62 75 74 20 69 74 20 64 65 70 65 6e |nu, but it depen| 00002810 64 73 20 77 68 65 74 68 65 72 20 6f 72 20 6e 6f |ds whether or no| 00002820 74 20 74 68 69 73 0a 76 65 72 73 69 6f 6e 20 69 |t this.version i| 00002830 73 20 61 20 73 75 63 63 65 73 73 2e 0a 0a 20 20 |s a success... | 00002840 56 61 72 69 6f 75 73 20 6f 74 68 65 72 20 66 65 |Various other fe| 00002850 61 74 75 72 65 73 0a 20 20 2d 2d 2d 2d 2d 2d 2d |atures. -------| 00002860 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a |---------------.| 00002870 0a 4f 6e 20 62 6f 74 68 20 69 6e 70 75 74 20 6d |.On both input m| 00002880 65 6e 75 73 20 74 68 65 72 65 20 69 73 20 61 20 |enus there is a | 00002890 52 65 73 65 74 20 6f 70 74 69 6f 6e 2c 20 61 6e |Reset option, an| 000028a0 64 20 62 65 6c 69 65 76 65 20 69 74 20 6f 72 20 |d believe it or | 000028b0 6e 6f 74 2c 20 63 6c 69 63 6b 69 6e 67 0a 6f 6e |not, clicking.on| 000028c0 20 69 74 20 63 6c 65 61 72 73 20 61 6c 6c 20 66 | it clears all f| 000028d0 6f 72 6d 75 6c 61 65 20 61 6e 64 20 62 61 73 69 |ormulae and basi| 000028e0 63 61 6c 6c 79 20 72 65 73 65 74 73 20 74 68 65 |cally resets the| 000028f0 20 69 6e 70 75 74 20 77 69 6e 64 6f 77 20 74 6f | input window to| 00002900 20 69 74 73 0a 64 65 66 61 75 6c 74 20 73 74 61 | its.default sta| 00002910 74 65 2e 20 20 44 75 68 2e 20 20 41 6c 73 6f 20 |te. Duh. Also | 00002920 74 68 65 72 65 20 69 73 20 61 20 54 6f 20 3f 3f |there is a To ??| 00002930 3f 3f 3f 3f 20 69 63 6f 6e 2e 20 20 43 6c 69 63 |???? icon. Clic| 00002940 6b 69 6e 67 20 6f 6e 20 74 68 69 73 20 6f 6e 0a |king on this on.| 00002950 74 68 65 20 69 6e 70 75 74 20 77 69 6e 64 6f 77 |the input window| 00002960 20 6d 65 6e 75 20 73 65 6e 64 73 20 61 6c 6c 20 | menu sends all | 00002970 74 68 65 20 66 6f 72 6d 75 6c 61 65 20 28 41 2c |the formulae (A,| 00002980 42 2c 43 20 61 6e 64 20 59 29 20 74 6f 20 74 68 |B,C and Y) to th| 00002990 65 20 73 65 71 75 65 6e 63 65 0a 69 6e 70 75 74 |e sequence.input| 000029a0 20 77 69 6e 64 6f 77 20 61 6e 64 20 70 75 74 73 | window and puts| 000029b0 20 74 68 65 6d 20 69 6e 20 74 68 65 20 61 70 70 | them in the app| 000029c0 72 6f 70 72 69 61 74 65 20 62 6f 78 65 73 2e 20 |ropriate boxes. | 000029d0 20 43 6c 69 63 6b 69 6e 67 20 6f 6e 20 69 74 20 | Clicking on it | 000029e0 6f 6e 20 74 68 65 0a 53 65 71 75 65 6e 63 65 20 |on the.Sequence | 000029f0 6d 65 6e 75 20 73 65 6e 64 73 20 74 68 65 20 66 |menu sends the f| 00002a00 6f 72 6d 75 6c 61 65 20 62 75 74 20 6e 6f 74 20 |ormulae but not | 00002a10 74 68 65 20 66 72 61 6d 65 73 20 61 6e 64 20 65 |the frames and e| 00002a20 78 74 72 65 6d 65 73 2c 20 6f 62 76 69 6f 75 73 |xtremes, obvious| 00002a30 6c 79 2e 20 0a 54 68 65 20 67 72 69 64 2f 73 6f |ly. .The grid/so| 00002a40 6c 69 64 20 69 63 6f 6e 73 20 61 6e 64 20 74 68 |lid icons and th| 00002a50 65 20 6c 6f 6f 70 2f 79 6f 79 6f 20 69 63 6f 6e |e loop/yoyo icon| 00002a60 20 61 72 65 20 6e 6f 74 20 61 66 66 65 63 74 65 | are not affecte| 00002a70 64 20 62 79 20 74 68 69 73 0a 6f 70 65 72 61 74 |d by this.operat| 00002a80 69 6f 6e 2e 0a 0a 4f 6e 20 62 6f 74 68 20 74 68 |ion...On both th| 00002a90 65 20 69 6e 70 75 74 20 6d 65 6e 75 73 20 74 68 |e input menus th| 00002aa0 65 72 65 20 69 73 20 61 6c 73 6f 20 74 68 65 20 |ere is also the | 00002ab0 43 6f 6d 6d 61 6e 64 73 20 6f 70 74 69 6f 6e 2e |Commands option.| 00002ac0 20 20 43 6c 69 63 6b 69 6e 67 20 74 68 69 73 0a | Clicking this.| 00002ad0 6f 70 65 6e 73 20 61 20 77 69 6e 64 6f 77 20 63 |opens a window c| 00002ae0 6f 6e 74 61 69 6e 69 6e 67 20 65 76 65 72 79 20 |ontaining every | 00002af0 63 6f 6e 63 65 69 76 61 62 6c 65 20 6d 61 74 68 |conceivable math| 00002b00 65 6d 61 74 69 63 61 6c 20 66 75 6e 63 74 69 6f |ematical functio| 00002b10 6e 20 28 69 6e 63 6c 75 64 69 6e 67 0a 6e 75 6d |n (including.num| 00002b20 62 65 72 73 29 20 74 68 61 74 20 79 6f 75 20 77 |bers) that you w| 00002b30 6f 75 6c 64 20 65 76 65 72 20 6e 65 65 64 2e 20 |ould ever need. | 00002b40 20 43 6c 69 63 6b 69 6e 67 20 6f 6e 20 6f 6e 65 | Clicking on one| 00002b50 20 6f 66 20 74 68 65 73 65 20 65 6e 74 65 72 73 | of these enters| 00002b60 20 74 68 65 0a 63 6f 6d 6d 61 6e 64 20 61 74 20 | the.command at | 00002b70 74 68 65 20 63 61 72 65 74 2c 20 73 6f 20 69 74 |the caret, so it| 00002b80 20 65 76 65 6e 20 77 6f 72 6b 73 20 69 6e 20 45 | even works in E| 00002b90 64 69 74 20 6f 72 20 4f 76 61 74 69 6f 6e 20 6f |dit or Ovation o| 00002ba0 72 2c 20 77 65 6c 6c 2c 0a 61 6e 79 74 68 69 6e |r, well,.anythin| 00002bb0 67 2e 20 20 54 68 65 20 66 75 6e 63 74 69 6f 6e |g. The function| 00002bc0 73 20 61 72 65 20 6e 6f 74 20 65 78 70 6c 61 69 |s are not explai| 00002bd0 6e 65 64 20 73 6f 20 72 65 66 65 72 20 74 6f 20 |ned so refer to | 00002be0 61 20 42 41 53 49 43 20 6d 61 6e 75 61 6c 2c 20 |a BASIC manual, | 00002bf0 74 68 65 0a 6f 6c 64 20 42 42 43 20 42 20 6d 61 |the.old BBC B ma| 00002c00 6e 75 61 6c 20 69 66 20 79 6f 75 20 68 61 76 65 |nual if you have| 00002c10 20 6f 6e 65 2c 20 6f 72 20 75 73 65 20 74 68 65 | one, or use the| 00002c20 20 48 45 4c 50 20 63 6f 6d 6d 61 6e 64 20 69 6e | HELP command in| 00002c30 20 42 41 53 49 43 20 74 6f 20 66 69 6e 64 0a 6f | BASIC to find.o| 00002c40 75 74 20 77 68 61 74 20 74 68 65 20 66 75 6e 63 |ut what the func| 00002c50 74 69 6f 6e 73 20 64 6f 2e 20 20 49 66 20 79 6f |tions do. If yo| 00002c60 75 20 68 61 76 65 20 74 6f 20 6c 6f 6f 6b 20 75 |u have to look u| 00002c70 70 20 77 68 61 74 20 74 68 65 20 6e 75 6d 62 65 |p what the numbe| 00002c80 72 73 20 64 6f 2c 0a 43 6c 69 63 6b 20 4d 45 4e |rs do,.Click MEN| 00002c90 55 20 6f 6e 20 74 68 65 20 62 61 72 20 69 63 6f |U on the bar ico| 00002ca0 6e 20 61 6e 64 20 53 45 4c 45 43 54 20 51 75 69 |n and SELECT Qui| 00002cb0 74 20 6e 6f 77 2e 2e 2e 2e 0a 0a 41 4e 44 20 54 |t now......AND T| 00002cc0 48 41 54 27 53 20 41 42 4f 55 54 20 49 54 21 20 |HAT'S ABOUT IT! | 00002cd0 20 55 73 65 20 69 6e 74 65 72 61 63 74 69 76 65 | Use interactive| 00002ce0 20 21 48 65 6c 70 20 66 6f 72 20 6f 6e 2d 6c 69 | !Help for on-li| 00002cf0 6e 65 20 68 65 6c 70 2e 0a 0a a0 20 4e 6f 74 65 |ne help.... Note| 00002d00 73 20 6f 6e 20 6b 6e 6f 77 6e 20 42 75 67 73 0a |s on known Bugs.| 00002d10 20 20 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d | --------------| 00002d20 2d 2d 2d 2d 2d 0a 0a 57 68 69 6c 65 20 74 68 65 |-----..While the| 00002d30 20 73 65 71 75 65 6e 63 65 20 69 73 20 72 65 6e | sequence is ren| 00002d40 64 65 72 69 6e 67 2c 20 64 6f 20 6e 6f 74 20 61 |dering, do not a| 00002d50 74 74 65 6d 70 74 20 74 6f 20 64 6f 20 61 6e 79 |ttempt to do any| 00002d60 74 68 69 6e 67 20 65 6c 73 65 2e 20 20 49 66 20 |thing else. If | 00002d70 79 6f 75 0a 74 72 79 20 64 72 61 67 67 69 6e 67 |you.try dragging| 00002d80 20 61 20 77 69 6e 64 6f 77 20 6f 72 20 63 6c 69 | a window or cli| 00002d90 63 6b 69 6e 67 20 61 6e 20 69 63 6f 6e 20 66 6f |cking an icon fo| 00002da0 72 20 65 78 61 6d 70 6c 65 2c 20 79 6f 75 20 77 |r example, you w| 00002db0 69 6c 6c 20 63 61 75 73 65 20 42 49 47 20 20 20 |ill cause BIG | 00002dc0 0a 65 72 72 6f 72 73 2e 20 20 49 20 74 68 69 6e |.errors. I thin| 00002dd0 6b 20 74 68 69 73 20 69 73 20 73 6f 6d 65 74 68 |k this is someth| 00002de0 69 6e 67 20 74 6f 20 64 6f 20 77 69 74 68 20 74 |ing to do with t| 00002df0 68 65 20 77 61 79 20 49 20 61 72 72 61 6e 67 65 |he way I arrange| 00002e00 64 20 74 68 65 0a 57 69 6d 70 50 6f 6c 6c 69 6e |d the.WimpPollin| 00002e10 67 2c 20 77 68 69 63 68 20 73 70 65 65 64 73 20 |g, which speeds | 00002e20 75 70 20 74 68 65 20 70 6c 6f 74 74 69 6e 67 2e |up the plotting.| 00002e30 20 20 44 6f 6e 27 74 20 64 6f 20 69 74 2e 2e 2e | Don't do it...| 00002e40 2e 0a 0a 59 6f 75 20 6d 61 79 20 65 78 70 65 72 |...You may exper| 00002e50 69 65 6e 63 65 20 70 72 6f 62 6c 65 6d 73 20 69 |ience problems i| 00002e60 66 20 79 6f 75 20 61 72 65 20 75 73 69 6e 67 20 |f you are using | 00002e70 61 20 68 69 67 68 20 72 65 73 20 6d 6f 6e 69 74 |a high res monit| 00002e80 6f 72 20 77 68 65 6e 0a 64 72 61 67 67 69 6e 67 |or when.dragging| 00002e90 20 73 61 76 65 20 69 63 6f 6e 73 2e 0a 0a 20 20 | save icons... | 00002ea0 52 49 53 43 20 50 43 73 0a 20 20 2d 2d 2d 2d 2d |RISC PCs. -----| 00002eb0 2d 2d 2d 0a 0a 49 66 20 79 6f 75 20 68 61 76 65 |---..If you have| 00002ec0 20 61 20 52 49 53 43 20 50 43 20 61 6e 64 20 66 | a RISC PC and f| 00002ed0 6f 72 6d 75 67 72 61 70 68 20 64 6f 65 73 6e 27 |ormugraph doesn'| 00002ee0 74 20 77 6f 72 6b 20 66 6f 72 20 61 6e 79 20 72 |t work for any r| 00002ef0 65 61 73 6f 6e 2e 20 20 54 4f 55 47 48 2e 20 0a |eason. TOUGH. .| 00002f00 49 74 20 73 65 72 76 65 73 20 79 6f 75 20 72 69 |It serves you ri| 00002f10 67 68 74 20 66 6f 72 20 68 61 76 69 6e 67 20 6f |ght for having o| 00002f20 6e 65 20 61 6e 64 20 6e 6f 74 20 62 75 79 69 6e |ne and not buyin| 00002f30 67 20 6d 65 20 6f 6e 65 21 20 20 42 75 74 20 73 |g me one! But s| 00002f40 65 72 69 6f 75 73 6c 79 2c 0a 54 68 65 20 52 49 |eriously,.The RI| 00002f50 53 43 20 50 43 20 69 73 20 66 61 72 20 74 6f 6f |SC PC is far too| 00002f60 20 65 78 70 65 6e 73 69 76 65 20 66 6f 72 20 6d | expensive for m| 00002f70 65 20 74 6f 20 67 65 74 20 6f 6e 65 2c 20 61 6e |e to get one, an| 00002f80 64 20 49 20 68 61 76 6e 27 74 20 68 61 64 20 63 |d I havn't had c| 00002f90 68 61 6e 63 65 0a 74 6f 20 74 65 73 74 20 46 6f |hance.to test Fo| 00002fa0 72 6d 75 47 72 61 70 68 20 6f 6e 20 6f 6e 65 2c |rmuGraph on one,| 00002fb0 20 73 6f 20 77 72 69 74 65 20 74 6f 20 6d 65 20 | so write to me | 00002fc0 77 69 74 68 20 70 72 6f 62 6c 65 6d 73 2c 20 71 |with problems, q| 00002fd0 75 65 72 69 65 73 2c 20 6d 6f 6e 65 79 2e 2e 2e |ueries, money...| 00002fe0 2e 20 0a 49 66 20 49 20 64 6f 20 65 76 65 72 20 |. .If I do ever | 00002ff0 68 61 76 65 20 61 20 63 68 61 6e 63 65 20 74 6f |have a chance to| 00003000 20 75 73 65 20 6f 6e 65 2c 20 49 20 6d 61 79 20 | use one, I may | 00003010 77 72 69 74 65 20 61 20 76 65 72 73 69 6f 6e 20 |write a version | 00003020 77 69 74 68 20 72 65 61 6c 2d 74 69 6d 65 0a 72 |with real-time.r| 00003030 65 6e 64 65 72 69 6e 67 20 6f 72 20 6e 65 61 72 |endering or near| 00003040 20 65 6e 6f 75 67 68 20 52 54 52 2e 20 20 57 65 | enough RTR. We| 00003050 6c 6c 20 4d 61 79 62 65 2e 2e 2e 2e 2e 20 4f 72 |ll Maybe..... Or| 00003060 20 32 34 62 69 74 20 42 2f 57 0a 0a 20 20 53 49 | 24bit B/W.. SI| 00003070 4c 49 43 4f 4e 20 47 52 41 50 48 49 43 53 20 57 |LICON GRAPHICS W| 00003080 4f 52 4b 20 53 54 41 54 49 4f 4e 53 0a 20 20 2d |ORK STATIONS. -| 00003090 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| 000030a0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 0a 0a 48 |-------------..H| 000030b0 61 20 48 61 20 21 20 20 59 65 73 2e 2e 2e 20 20 |a Ha ! Yes... | 000030c0 59 61 69 73 21 20 20 48 6f 20 48 6f 20 48 61 20 |Yais! Ho Ho Ha | 000030d0 48 61 20 48 65 79 2e 20 20 57 68 6f 6f 70 65 65 |Ha Hey. Whoopee| 000030e0 2e 2e 2e 2e 2e 20 20 49 20 57 41 4e 54 20 4f 4e |..... I WANT ON| 000030f0 45 21 21 21 21 0a 0a |E!!!!..| 000030f7
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