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1991-10-18
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These programs originally appeared in Hot CoCo magazine, June 1983,
pages 94 to 107. They were written for the Color Computer by Delmar E.
Searls (see end of this document) and I converted them to the PC with
some adjustments to the program. These versions do not save the images
created as the original programs did but the graphics drawn as pretty
much the same as the original. In CGA the graphics are slightly
stretched out in the vertical due to the shape of the CGA's pixel (dot
on the screen). In EGA the drawings are pretty much the same as the
photos that were contained within the article in Hot CoCo Magazine and
are pretty much what I obtained with the Color Computers 256x96
resolution at that time.
The basic versions are in CGA, 640x200 resolution. The size of
the graphic is controlled by the `(30*' or `(25*' values depending on
the program (option). The general location on the screen is at 320
horizontal and 100 vertical. I made some adjustments to 90 and 110 on
vertical to keep some displays in the center of the screen.
I took all the separate segments and assembled them into one
basic program titled GRAPHCGA. The program in both basic and compiled
basic using Microsoft's Quick Basic. I was a firm believer in
Borland's Turbo Basic but Quick Basic is much faster. I have included
BRUN30.EXE which is needed to run the compiled programs. Make sure it
is somewhere on your path. I keep my copy in my utility directory.
I also made an assembled version in EGA, 640x350 resolution and
is titled GRAPHEGA. I was able to use screen 9 to get the EGA mode.
There also is a VGA, 640x480 resolution and is titled GRAPHVGA.
At the completion of each graphic the computer makes a tone every
one and a half seconds without displaying anything on the screen. This
is to notify you that the graphic has been completed. If you plan to
do any screen dumps to a file or to the printer this is the time to do
it. If you press any key a prompt of `Press <R>epeat, <N>ext or
<E>xit' appears on line twenty five. Pressing <R> will repeat the
current graphic and you may change the inputs if so desired. Pressing
<N> proceeds to the next graphic and it's input statements. Pressing
<E> exits the program. Upper or lower case is acceptable.
In the EGA and VGA versions I made the displays as large as
possible changing most of the `30's to `60's/'70's and those options
using `30 and 25' to `50/60 and 42/52' (same ratio). Other than these
two changes the EGA, VGA, and CGA versions are the same.
I worked these out on an 80286 12 mhz turbo and the display speed
will vary depending on the machine. On the original Color Computer it
took several minutes to draw some of these and the time should be a
little faster on a 4.77 mhz PC since the .EXE programs are compiled
programs (run 10 to 100 times faster). So be prepared for a little
wait on some machines if you do not have an 80286 machine.
The programs prompt you for all or part of the following, (1)
LINE DENSITY. A MAX of 8 is suggested. (2) DOT DENSITY. 16, 32 and 64
are suggested. (3) VIEWING ANGLE. 65 to 75 degrees is suggested. In
all the segments and assembled programs the author's defaults are
built in. If you enter something like 100 degrees you start seeing the
bottom side of the graphic. On EGA and VGA color systems the bottom
side is yellow and if any yellow is showing this is the bottom side or
parts there of. This bottom color is not possible in CGA 2 color
640x200 screen. If you press <ENTER> on any or all of these prompts
you get a pretty good display.
I have also included the program CROSS-SE for Cross Section and
is only useful in basic so you can change line 1010. This is to let
you experiment with cross sections changing the values in line 1010 in
the basic version. If you change the assembled versions you will have
to find the appropriate line since these were renumbered as I added
the separate segments together.
You can run the Cross Section "and can eliminate many
possibilities by viewing these cross sections. Make note of those
functions that look promising and try them out in one of the display
programs. In the Basic exponential function is written EXP( ), where
some expression involving R is placed inside the parentheses. This
expression in the exponent of the number "e" (about 2.718). It would
be equally suitable, from a graphing standpoint, to use some other
base such as 2 or 3. The function would be written as 2^( ) or 3^( ),
where again an expression involving R goes in the parentheses.
If the base is a number greater than one, then the expressing
inside the parentheses (the exponent) should be negative or zero. If
the exponent is positive, the altitude will quickly become too large
to plot. Z=EXP(-R), Z=1.5*2^(-R*r), and Z=2*3^(-R*R/4)-1 are all
examples where the exponent is a negative or zero. Remember that R is
a distance and is always positive. The negative sign in each of the
exponents makes the exponent negative, or zero at most. Each of the
would produce a display resembling a mound.
The height of the mound is determined by the multiplies (if any)
in front. The first would have a height of 1, the second a height of
1.5, and the third a height of 2. In addition, if the display for the
third Z function would be lower on the screen because a 1 was
subtracted from the height calculation.
The trigonometric functions (sine and cosine) produce the graphs
that look like ripples in a pond. In Basic these functions are written
SIN( ) and COS( ), where once more they contain some expression
involving R. The values will range from -1 to 1, with the sine
function zero at the origin, and the cosine function equal to one at
the origin. The range can be adjusted by multiplying the trig function
by some number or by some other function (such as the exponential).
Most of the displays commonly seen are combinations of
trigonometric functions or of trigonometric and exponential functions.
This is where the trial and error process enters in; you enter a
function in line 1010 and see what you get. If you don't like it, try
again."
There are three different display programs in the basic and
assembled versions.
I hope you enjoy this as it is. The magazine article is pretty
complex and extensive. If you can get the above mentioned copy of the
magazine you can copy or read the original instructions. I have tried
to cover what is done to use the program CROSS-SE which is the
author's listing 5 in the article.
James Huckabey
3621-A Fraser Street
Bellingham, WA 98226
Original author is;
Delmar E. Searls
1825 S. Johnstone
Bartlesville, OK 74003
as of June 1983 when the article was published ...