A Couple Notes On 3DEXP2.BAS
                      By Rich Geldreich

     3DEXP2.BAS is made in QuickBASIC 4.5, and requires at
least a VGA adaptor to run properly(or at all, for that
matter). It demonstrates fast, integer math rotation &
perspective algorithms. It's really hard to believe that the
sample program is actually written in QuickBASIC. Of course,
if these routines were made in true assembly, the results
would be much faster, to say the least. (Please compile the
QB program for the best speed. DOS 5's QBASIC works fine
too[rather slowly though...] If you don't have QBASIC or QB
4.5, then run the already compiled 3DEXP2.EXE to get an
idea...)
ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ
   I am placing this program into the public domain, so use
and abuse this program as much as you want, I don't care. All
I ask is that you PLEASE keep my name on it! If you do change
     it a little, then put "modifications by so & so" or
 something. I have put a lot of work into making this program
 fast and I don't won't to be ripped off by some lame, code-
             stealing theif! Thank you very much.
ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

     The following is a short explanation of the perspective
routine that 3DEXP2.BAS uses(the rotating routines are
simple to understand once you understand the way sine and
cosine operate...)

     The perspective routine I used is (usually) very
realistic. It actually draws a line from the point that we
wish to put into perspective to the user- wherever this line
crosses the "viewing" plane (or the monitor) is where we
actually plot the point.  (make pretend that this line we
draw is actually a light ray... it's actually quite obvious
and easy to understand once you see it...)

     Here are the formulas:

Xnew = Xold + ( -Xold * Spos - Z )
                        --------
                        Mpos - Z

Ynew = Yold + ( -Yold * Spos - Z )
                        --------
                        Mpos - Z

Where Xold and Yold and Z are the original coordinates to be
put into perspective; Xpos is the Z coordinate of the
"viewing" plane and Mpos is the Z coordinate of the
user(which is usually 0).


For the most speed, I highly recommend that you avoid
floating point math whenever possible. It's great for
initialization routines, but it really sucks in tight loops
and high speed 3-D graphics.

For any questions, comments, or cool ideas, contact:

Rich Geldreich
410 Market St.
Gloucester City, NJ 08030
(609)-742-8752 between 4:30pm and 9:30pm Monday-Saturday


****Last Minute Additions

3DEXP2.BAS really flickers a lot... I didn't use page flipping
because I needed 64 colors.

I've also included some fast assembly code to rotate and display 
3-D points. It's called VECT.ASM. It's documented, but not
that much. It rotates 765 points at 12 frames per second on by 286-10.
This jem looks really cool in the dark! VECT.ASM is public domain too! 
Works only on VGA. The keys recognized are similar to the keys 
used by 3DEXP2.BAS.

Have fun and look both ways before crossing the street :-)


R. Geldreich 
June 4th, 1992A.D. 18:13:27