Nambafa
Graphics tutorials
Downloads: TUT08NEW.zip
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│ W E L C O M E │
│ To the VGA Trainer Program │ │
│ By │ │
│ DENTHOR of ASPHYXIA │ │ │
│ (updated by Snowman) │ │ │
╘═══════════════════════════════╛ │ │
────────────────────────────────┘ │
────────────────────────────────┘
--==[ PART 8 ]==--
[Note: things in brackets have been added by Snowman. The original text
has remained mostly unaltered except for the inclusion of C++ material]
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■ Contents
- Introduction
- Optimisation
- Defining a 3-D object
- Rotating a point with matrixes
- Drawing a 3D point to screen
- Possible improvements
- In closing
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■ Introduction
Hello everybody! Christmas is over, the last of the chocolates have been
eaten, so it's time to get on with this, the eighth part of the ASPHYXIA
Demo Trainer Series. This particular part is primarily about 3-D, but
also includes a bit on optimisation.
If you are already a 3-D guru, you may as well skip this text file, have
a quick look at the sample program then go back to sleep, because I am
going to explain in minute detail exactly how the routines work ;)
If you would like to contact me, or the team, there are many ways you
can do it : 1) Write a message to Grant Smith/Denthor/Asphyxia in private mail
on the ASPHYXIA BBS.
2) Write a message in the Programming conference on the
For Your Eyes Only BBS (of which I am the Moderator )
This is preferred if you have a general programming query
or problem others would benefit from.
4) Write to Denthor, EzE or Goth on Connectix.
5) Write to : Grant Smith
P.O.Box 270 Kloof
3640
Natal
6) Call me (Grant Smith) at (031) 73 2129 (leave a message if you
call during varsity)
7) Write to mcphail@beastie.cs.und.ac.za on InterNet, and
mention the word Denthor near the top of the letter.
NB : If you are a representative of a company or BBS, and want ASPHYXIA
to do you a demo, leave mail to me; we can discuss it.
NNB : If you have done/attempted a demo, SEND IT TO ME! We are feeling
quite lonely and want to meet/help out/exchange code with other demo
groups. What do you have to lose? Leave a message here and we can work
out how to transfer it. We really want to hear from you!
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■ Optimisation
Before I begin with the note on 3-D, I would like to stress that many of
these routines, and probably most of your own, could be sped up quite a
bit with a little optimisation. One must realise, however, that you must
take a look at WHAT to optimise ... converting a routine that is only
called once at startup into a tightly coded assembler routine may show
off your merits as a coder, but does absolutely nothing to speed up your
program. Something that is called often per frame is something that
needs to be as fast as possible. For some, a much used procedure is the
PutPixel procedure. Here is the putpixel procedure I gave you last week:
[Note: Snowman here! I consulted the official Intel documentation and
noticed that Denthor is basing the clock ticks on the 8088 processor and
not the 286, 386, or 486 processors. I have taken the time to include
the information for these other processors.]
Procedure Putpixel (X,Y : Integer; Col : Byte; where:word);
BEGIN -clock ticks-
Asm 8088 286 386 486
push ds 14 3 2 3
push es 14 3 2 3
mov ax,[where] 8 5 4 1
mov es,ax 2 2 2 3
mov bx,[X] 8 5 4 1
mov dx,[Y] 8 5 4 1
push bx 15 3 2 1
mov bx, dx 2 2 2 1
mov dh, dl 2 2 2 1
xor dl, dl 3 2 2 1
shl bx, 1 2 2 3 3
shl bx, 1 2 2 3 3
shl bx, 1 2 2 3 3
shl bx, 1 2 2 3 3
shl bx, 1 2 2 3 3
shl bx, 1 2 2 3 3
add dx, bx 3 2 2 1
pop bx 12 5 4 4
add bx, dx 3 2 2 1
mov di, bx 2 2 2 3
xor al,al 3 2 2 1
mov ah, [Col] 8 5 4 1
mov es:[di],ah 10 3 2 1
pop es 12 5 7 3
pop ds 12 5 7 3
End; ---------------
END; 153 75 76 52 Total ticks
NOTE : Don't take my clock ticks as gospel, I probably got one or two
wrong.
Right, now for some optimising. Firstly, if you have 286 instructions
turned on, you may replace the 6 shl,1 with shl,6. Secondly, the Pascal
compiler automatically pushes and pops ES, so those two lines may be
removed. DS:[SI] is not altered in this procedure, so we may remove
those too. Also, instead of moving COL into ah, we move it into AL and
call stosb (es:[di]:=al; inc di). Let's have a look at the routine now :
Procedure Putpixel (X,Y : Integer; Col : Byte; where:word);
BEGIN -clock ticks-
Asm 8088 286 386 486
mov ax,[where] 8 5 4 1
mov es,ax 2 2 2 3
mov bx,[X] 8 5 4 1
mov dx,[Y] 8 5 4 1
push bx 15 3 2 1
mov bx, dx 2 2 2 1
mov dh, dl 2 2 2 1
xor dl, dl 3 2 2 1
shl bx, 6 8 11 3 2
add dx, bx 3 2 2 1
pop bx 12 5 4 4
add bx, dx 3 2 2 1
mov di, bx 2 2 2 3
mov al, [Col] 8 5 4 1
stosb 11 3 4 5
End; ----------------
END; 95 56 43 27 Total ticks
Now, let us move the value of BX directly into DI, thereby removing a
costly push and pop. The MOV and the XOR of DX can be replaced by it's
equivalent, SHL DX,8
[Note: If you are running on a 286, this last set of optimizations
actually makes the routine slower! On a 286, an "SHL" takes 5 ticks
plus the number you are moving by. For example: an "SHL AX,6" would
take 11 clock ticks (5 ticks for SHL and 6 clock ticks for the "6"
part of the expression.]
Procedure Putpixel (X,Y : Integer; Col : Byte; where:word); assembler;
BEGIN -clock ticks-
asm 8088 286 386 486
mov ax,[where] 8 5 4 1
mov es,ax 2 2 2 3
mov bx,[X] 8 5 4 1
mov dx,[Y] 8 5 4 1
mov di,bx 2 2 2 3
mov bx, dx 2 2 2 1
shl dx, 8 8 13 3 2
shl bx, 6 8 11 3 2
add dx, bx 3 2 2 1
add di, dx 3 2 2 1
mov al, [Col] 8 5 4 1
stosb 11 3 4 5
end; ----------------
71 57 36 22 Total ticks
As you can see, we have brought the clock ticks down from 153-52 (8088-486)
ticks to 71-22 (8088-486) ticks ... quite an improvement. (The current
ASPHYXIA putpixel takes 48 clock ticks) . As you can see, by going through
your routines a few times, you can spot and remove unnecessary instructions,
thereby greatly increasing the speed of your program.
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■ Defining a 3-D object
Drawing an object in 3-D is not that easy. Sitting down and plotting a
list of X,Y and Z points can be a time consuming business. So, let us
first look at the three axes you are drawing them on :
Y Z
/|\ /
| /
X<-----|----->
|
\|/
X is the horisontal axis, from left to right. Y is the vertical axis,
from top to bottom. Z is the depth, going straight into the screen.
In this trainer, we are using lines, so we define 2 X,Y and Z
coordinates, one for each end of the line. A line from far away, in the
upper left of the X and Y axes, to close up in the bottom right of the
X and Y axes, would look like this :
{ x1 y1 z1 x2 y2 z2 }
( (-10,10,-10),(10,-10,10) )
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■ Rotating a point with matrixes
NOTE : I thought that more then one matix are matrisese (sp), but my
spellchecker insists it is matrixes, so I let it have it's way
;-)
Having a 3-D object is useless unless you can rotate it some way. For
demonstration purposes, I will begin by working in two dimensions, X and
Y.
Let us say you have a point, A,B, on a graph.
Y
| /O1 (Cos (a)*A-Sin (a)*B , Sin (a)*A+Cos (a)*B)
|/ (A,B)
X<-----|------O-->
|
|
Now, let us say we rotate this point by 45 degrees anti-clockwise. The
new A,B can be easily be calculated using sin and cos, by an adaption of
our circle algorithm, ie.
A2:=Cos (45)*A - Sin (45)*B
B2:=Sin (45)*A + Cos (45)*B
I recall that in standard 8 and 9, we went rather heavily into this in
maths. If you have troubles, fine a 8/9/10 maths book and have a look;
it will go through the proofs etc.
Anyway, we have now rotated an object in two dimensions, AROUND THE Z
AXIS. In matrix form, the equation looks like this :
[ Cos (a) -Sin (a) 0 0 ] [ x ]
[ Sin (a) Cos (a) 0 0 ] . [ y ]
[ 0 0 1 0 ] [ z ]
[ 0 0 0 1 ] [ 1 ]
I will not go to deeply into matrixes math at this stage, as there are
many books on the subject (it is not part of matric maths, however). To
multiply a matrix, to add the products of the row of the left matrix and
the column of the right matrix, and repeat this for all the columns of the
left matrix. I don't explain it as well as my first year maths lecturer,
but have a look at how I derived A2 and B2 above. Here are the other
matrixes :
Matrix for rotation around the Y axis :
[ Cos (a) 0 -Sin (a) 0 ] [ x ]
[ 0 1 0 0 ] . [ y ]
[ Sin (a) 0 Cos (a) 0 ] [ z ]
[ 0 0 0 1 ] [ 1 ]
Matrix for rotation around the X axis :
[ 1 0 0 ] [ x ]
[ 0 Cos (a) -Sin (a) 0 ] . [ y ]
[ 0 Sin (a) Cos (a) 0 ] [ z ]
[ 0 0 0 1 ] [ 1 ]
By putting all these matrixes together, we can translate out 3D points
around the origin of 0,0,0. See the sample program for how we put them
together.
In the sample program, we have a constant, never changing base object.
This is rotated into a second variable, which is then drawn. I am sure
many of you can thing of cool ways to change the base object, the
effects of which will appear while the object is rotating. One idea is
to "pulsate" a certain point of the object according to the beat of the
music being played in the background. Be creative. If you feel up to it,
you could make your own version of transformers ;)
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■ Drawing a 3D point to screen
Having a rotated 3D object is useless unless we can draw it to screen.
But how do we show a 3D point on a 2D screen? The answer needs a bit of
explaining. Examine the following diagram :
| ________-------------
____|___------ o Object at X,Y,Z o1 Object at X,Y,Z2
Eye -> O)____|___
| ------________
| -------------- Field of vision
Screen
Let us pretend that the centre of the screen is the horizon of our
little 3D world. If we draw a three dimensional line from object "o" to
the centre of the eye, and place a pixel on the X and Y coordinates
where it passes through the screen, we will notice that when we do the
same with object o1, the pixel is closer to the horizon, even though
their 3D X and Y coords are identical, but "o1"'s Z is larger then
"o"'s. This means that the further away a point is, the closer to the
horizon it is, or the smaller the object will appear. That sounds
right, doesent it? But, I hear you cry, how do we translate this into a
formula? The answer is quite simple. Divide your X and your Y by your Z.
Think about it. The larger the number you divide by, the closer to zero,
or the horizon, is the result! This means, the bigger the Z, the
further away is the object! Here it is in equation form :
[Pascal]
nx := 256*x div (z-Zoff)+Xoff
ny := 256*y div (z-Zoff)+Yoff
[C++]
nx = ((256*x) / (z-Zoff)) + Xoff;
nx = ((256*y) / (z-Zoff)) + Yoff;
NOTE : Zoff is how far away the entire object is, Xoff is the objects X
value, and Yoff is the objects Y value. In the sample program,
Xoff start off at 160 and Yoff starts off at 100, so that the
object is in the middle of the screen.
The 256 that you times by is the perspective with which you are viewing.
Changing this value gives you a "fish eye" effect when viewing the
object. Anyway, there you have it! Draw a pixel at nx,ny, and viola! you
are now doing 3D! Easy, wasn't it?
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■ Possible improvements
This program is not the most optimised routine you will ever encounter
(;-)) ... it uses 12 muls and 2 divs per point. (Asphyxia currently has
9 muls and 2 divs per point) Real math is used for all the calculations
in the sample program, which is slow, so fixed point math should be
implemented (I will cover fixed point math in a future trainer). The
line routine currently being used is very slow. Chain-4 could be used to
cut down on screen flipping times.
Color values per line should be added, base object morphing could be put
in, polygons could be used instead of lines, handling of more then one
object should be implemented, clipping should be added instead of not
drawing something if any part of it is out of bounds.
In other words, you have a lot of work ahead of you ;)
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■ In closing
There are a lot of books out there on 3D, and quite a few sample
programs too. Have a look at them, and use the best bits to create your
own, unique 3D engine, with which you can do anything you want. I am
very interested in 3D (though EzE and Goth wrote most of ASPHYXIA'S 3D
routines), and would like to see what you can do with it. Leave me a
message through one of the means described above.
I am delving into the murky world of texture mapping. If anyone out
there has some routines on the subject and are interested in swapping,
give me a buzz!
What to do in future trainers? Help me out on this one! Are there any
effects/areas you would like a bit of info on? Leave me a message!
I unfortunately did not get any messages regarding BBS's that carry this
series, so the list that follows is the same one from last time. Give
me your names, sysops!
Aaaaargh!!! Try as I might, I can't think of a new quote. Next time, I
promise! ;-)
Bye for now,
- Denthor
These fine BBS's carry the ASPHYXIA DEMO TRAINER SERIES : (alphabetical)
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║BBS Name ║Telephone No. ║Open ║Msg║File║Past║
╠══════════════════════════╬════════════════╬═════╬═══╬════╬════╣
║ASPHYXIA BBS #1 ║(031) 765-5312 ║ALL ║ * ║ * ║ * ║
║ASPHYXIA BBS #2 ║(031) 765-6293 ║ALL ║ * ║ * ║ * ║
║Connectix BBS ║(031) 266-9992 ║ALL ║ * ║ ║ ║
║For Your Eyes Only BBS ║(031) 285-318 ║A/H ║ * ║ * ║ * ║
╚══════════════════════════╩════════════════╩═════╩═══╩════╩════╝
Open = Open at all times or only A/H
Msg = Available in message base
File = Available in file base
Past = Previous Parts available
Downloads: TUT08NEW.zip