Tutorials: C++ Made Easy

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                            W E L C O M E         
                     To the VGA Trainer Program    
                                 By                
                         DENTHOR of ASPHYXIA        
                         (updated by Snowman)       
                   塒様様様様様様様様様様様様様様様  
                     陳陳陳陳陳陳陳陳陳陳陳陳陳陳陳陳 
                       陳陳陳陳陳陳陳陳陳陳陳陳陳陳陳陳

                           --==[ 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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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 120 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 MsgFilePast
麺様様様様様様様様様様様様洋様様様様様様様様陵様様陵様陵様洋様様
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   *  *   *  
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Open = Open at all times or only A/H
Msg  = Available in message base
File = Available in file base
Past = Previous Parts available