HPAVC/HPAVC CD-ROM.iso/pc/UGPRG.ZIP/DENTHOR/TUT20.DOC

Text File | 1996-07-27 | 39.2 KB | 1,482 lines

                   ╒═══════════════════════════════╕
                   │         W E L C O M E         │
                   │  To the VGA Trainer Program   │ │
                   │              By               │ │
                   │      DENTHOR of ASPHYXIA      │ │ │
                   ╘═══════════════════════════════╛ │ │
                     ────────────────────────────────┘ │
                       ────────────────────────────────┘

                           --==[ PART 20 ]==--



=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
■ Introduction

Hi all! It has been a _long_ time since my last trainer (as I am sure many
of you have noticed) A lot has happened between now and the last trainer...
but for once I won't bore you with the details ;) I do have a full time job
though, coding C++ applications.

I have taken over the production of the PCGPE from Mark Feldman. He is
mailing all the articles written so far, and as soon as I get them I will
get to work on releasing the PCGPE II. Mark is working on the Windows GPE.

This trainer is on 3d hidden face removal and face sorting. I was going to
add shading, but that can wait until a later trainer. For conveniance I
will build on the 3d code from tut 16(?). The maths for face removal is a
bit tricky, but just think back to your old High School trig classes.

I have noticed that in my absence, one or two people have started their own
trainer series. Read Hornet DemoNews for a great column by Trixter covering
some of the more tricky demo effects.

Well, on with the trainer!


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 to :  Grant Smith
                           P.O.Box 270 Kloof
                           3640
                           Natal
                           South Africa
            3) Call me (Grant Smith) at (031) 73 2129 (leave a message if you
                  call during varsity). Call [phone] if you call
                  from outside South Africa. (It's YOUR phone bill ;-))
            4) Write to [e-mail] in E-Mail.
            5) Write to [e-mail] to get to all of
               us at once.

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!

http://goth.vironix.co.za/~denthor                     (WWW)
ftp.eng.ufl.edu pub/msdos/demos/code/graph/tutor       (FTP)


=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
■  Face Sorting

There are many ways to sort faces in a 3d object. For now, I will show you
just about the easiest one of the lot.

Say you have to polygons....

                ------P1

           ------------------P2

                   Eye

As you can see, P1 has to be drawn before P2. The easiest way to do this is
as follows:

On startup, find the mid point of each of the polys, through the easy
equations,
        x = (P2.1.x + P2.2.x + P2.3.x + p2.4.x)/4
        y = (P2.1.y + P2.2.y + P2.3.y + p2.4.y)/4
        z = (P2.1.z + P2.2.z + P2.3.z + p2.4.z)/4

NOTE : For a triangle you would obviously only use three points and divide
by three.

Anyway, now you have the X,Y,Z of the midpoint of the polygon. You can then
rotate this point with the others. When it comes time to draw, you can
compare the resulting Z of the midpoint, sort all of the Z items, and then
draw them from back to front.

In the sample program I use a simple bubble sort... basically, I check the
first two values against each other, and swap them if the first is bigger
then the second. I continue doing this to all the numbers until I run
through the entire list without swapping once. Bubble sorts are standard
seven computer science topics... perhaps borrow a text book to find out
more about them and other (better) sorting methods.

The above isn't perfect, but it should work 90% of the time. But it still
means that when you are drawing a cube, you have to draw all 6 sides every
frame, even though only three or so are visible. That is where hidden face
removal comes in...

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
■  Hidden Face Removal

Pick up something square. A stiffy disk will do fine. Face it towards you,
and number all the corners from one to four in a clockwise direction.

                1 +-------------+ 2
                  |             |
                  |             |
                  |             |
                  |             |
                4 +-------------+ 3

Now rotate the stiffy disk on all three axese, making sure that you can
still see the front of the disk. You will notice that whenever you can see
the front of the disk, the four points are still in alphabetical order. Now
rotate it so that you can see the back of the stiffy. Your points will now
be :

                2 +-------------+ 1
                  |             |
                  |             |
                  |             |
                  |             |
                3 +-------------+ 4

The points are now anti-clockwise! This means, in it's simplest form, that
if you define all your poygon points in a clockwise order, when drawing you
ignore the polys that are anticlockwise. (Obviously when you define the 3d
object, you define the polygons facing away from you in an anticlockwise
order)

To find out weather a poly's points are clockwise or not, we need to find
it's normal. Here is where things start getting fun.

In school, you are told that a normal is perpendicular to the plane. In
ascii :
                      | Normal
                      |
                      |
        --------------------------- Polygon

As you can see, the normal is at 90 degrees to the surface of the poly. We
must extend this to three dimensions for our polygons. You'll have to trust
me on that, I can't draw it in ascii :)

To find a normal, you only need three points from your poly (ABC) :
A(x0,y0,z0), B(X1,Y1,Z1), C(X2,Y2,Z2)

then the vector normal = AB^AC = (Xn,Yn,Zn) with
        Xn=(y1-y0)(z0-z2)-(z1-z0)(y0-y2)
        Yn=(z1-z0)(x0-x2)-(x1-x0)(z0-z2)
        Zn=(x1-x0)(y0-y2)-(y1-y0)(x0-x2)

We are interested in the Z normal, so we will use the function :
  normal:=(x1-x0)(y0-y2)-(y1-y0)(x0-x2);

The result is something of a sine wave when you rotate the poly in three
dimensions. A negative value means that the poly is facing you, a posotive
value means that it is pointing away.

The above means that with a mere two muls you can discount an entire poly
and not draw it. This method is perfect for "closed" objects such as cubes
etc.

I am anything but a maths teacher, so go borrow someones math book to find
out more about surface normals. Trust me, there is a lot more written about
them then you think.

An extension of calculating your normal is finding out about light-sourcing
your polygons. Watch for more information in one of the next few tutors.


A combination of the above two routines should work quite nicely in
creating 3d objects with little or no overlapping. The example file will
show you the two methods and how well they work.


=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
■  In closing

As you can see, the above was quite easy. I have a few ideas for tut 21, so
keep watch for it. Also keep an eye open for PCGPE ][ (but don't mail me
asking when it's due! I already get too many of those! ;-)

My sister got married a few days ago. The worst part was that I was forced
to cut my hair. My hair was quite long (slightly longer then when the pic
on my web page was taken), and it is all quite depressing. Anyway, the
wedding was great, so it wasn't all for nothing.

I hope to get tut 21 and possibly 22 out before christmas, but I will be on
holiday from the 18th. I will be in Cape Town sometime after christmas day
for a week or two, so if you're there I'll meet you on the cable car :-)

I wrote a quote for this tut, but I have decided I didn't like it. I'll try
do better for tut 21 ;)

Byeeeee.....
  - Denthor
      14-12-95

PS. I seem to have lost my list of distribution sites... could you all
re-mail me your details? Thanks.
Unit GFX3;


INTERFACE

USES crt;
CONST VGA = $A000;

TYPE Virtual = Array [1..64000] of byte;  { The size of our Virtual Screen }
     VirtPtr = ^Virtual;                  { Pointer to the virtual screen }

VAR Virscr : VirtPtr;                     { Our first Virtual screen }
    Vaddr  : word;                        { The segment of our virtual screen}
    Scr_Ofs : Array[0..199] of Word;

Procedure SetMCGA;
   { This procedure gets you into 320x200x256 mode. }
Procedure SetText;
   { This procedure returns you to text mode.  }
Procedure Cls (Where:word;Col : Byte);
   { This clears the screen to the specified color }
Procedure SetUpVirtual;
   { This sets up the memory needed for the virtual screen }
Procedure ShutDown;
   { This frees the memory used by the virtual screen }
procedure flip(source,dest:Word);
   { This copies the entire screen at "source" to destination }
Procedure Pal(Col,R,G,B : Byte);
   { This sets the Red, Green and Blue values of a certain color }
Procedure GetPal(Col : Byte; Var R,G,B : Byte);
  { This gets the Red, Green and Blue values of a certain color }
procedure WaitRetrace;
   {  This waits for a vertical retrace to reduce snow on the screen }
Procedure Hline (x1,x2,y:word;col:byte;where:word);
   { This draws a horizontal line from x1 to x2 on line y in color col }
Procedure Line(a,b,c,d:integer;col:byte;where:word);
  { This draws a solid line from a,b to c,d in colour col }
Procedure DrawPoly(x1,y1,x2,y2,x3,y3,x4,y4:integer;color:byte;where:word);
   { This draw a polygon with 4 points at x1,y1 , x2,y2 , x3,y3 , x4,y4
     in color col }
Function rad (theta : real) : real;
   {  This calculates the degrees of an angle }
Procedure Putpixel (X,Y : Integer; Col : Byte; where:word);
   { This puts a pixel on the screen by writing directly to memory. }
Function Getpixel (X,Y : Integer; where:word) :Byte;
   { This gets the pixel on the screen by reading directly to memory. }
Procedure LoadCEL (FileName :  string; ScrPtr : pointer);
  { This loads the cel 'filename' into the pointer scrptr }
Procedure LoadPal (FileName : string);
  { This loads in an Autodesk Animator V1 pallette file }

IMPLEMENTATION

{──────────────────────────────────────────────────────────────────────────}
Procedure SetMCGA;  { This procedure gets you into 320x200x256 mode. }
BEGIN
  asm
     mov        ax,0013h
     int        10h
  end;
END;

{──────────────────────────────────────────────────────────────────────────}
Procedure SetText;  { This procedure returns you to text mode.  }
BEGIN
  asm
     mov        ax,0003h
     int        10h
  end;
END;

{──────────────────────────────────────────────────────────────────────────}
Procedure Cls (Where:word;Col : Byte); assembler;
   { This clears the screen to the specified color }
asm
   push    es
   mov     cx, 32000;
   mov     es,[where]
   xor     di,di
   mov     al,[col]
   mov     ah,al
   rep     stosw
   pop     es
End;

{──────────────────────────────────────────────────────────────────────────}
Procedure SetUpVirtual;
   { This sets up the memory needed for the virtual screen }
BEGIN
  GetMem (VirScr,64000);
  vaddr := seg (virscr^);
END;

{──────────────────────────────────────────────────────────────────────────}
Procedure ShutDown;
   { This frees the memory used by the virtual screen }
BEGIN
  FreeMem (VirScr,64000);
END;

{──────────────────────────────────────────────────────────────────────────}
procedure flip(source,dest:Word); assembler;
  { This copies the entire screen at "source" to destination }
asm
  push    ds
  mov     ax, [Dest]
  mov     es, ax
  mov     ax, [Source]
  mov     ds, ax
  xor     si, si
  xor     di, di
  mov     cx, 32000
  rep     movsw
  pop     ds
end;

{──────────────────────────────────────────────────────────────────────────}
Procedure Pal(Col,R,G,B : Byte); assembler;
  { This sets the Red, Green and Blue values of a certain color }
asm
   mov    dx,3c8h
   mov    al,[col]
   out    dx,al
   inc    dx
   mov    al,[r]
   out    dx,al
   mov    al,[g]
   out    dx,al
   mov    al,[b]
   out    dx,al
end;

{──────────────────────────────────────────────────────────────────────────}
Procedure GetPal(Col : Byte; Var R,G,B : Byte);
  { This gets the Red, Green and Blue values of a certain color }
Var
   rr,gg,bb : Byte;
Begin
   asm
      mov    dx,3c7h
      mov    al,col
      out    dx,al

      add    dx,2

      in     al,dx
      mov    [rr],al
      in     al,dx
      mov    [gg],al
      in     al,dx
      mov    [bb],al
   end;
   r := rr;
   g := gg;
   b := bb;
end;

{──────────────────────────────────────────────────────────────────────────}
procedure WaitRetrace; assembler;
  {  This waits for a vertical retrace to reduce snow on the screen }
label
  l1, l2;
asm
    mov dx,3DAh
l1:
    in al,dx
    and al,08h
    jnz l1
l2:
    in al,dx
    and al,08h
    jz  l2
end;

{──────────────────────────────────────────────────────────────────────────}
Procedure Hline (x1,x2,y:word;col:byte;where:word); assembler;
  { This draws a horizontal line from x1 to x2 on line y in color col }
asm
  mov   ax,where
  mov   es,ax
  mov   ax,y
  mov   di,ax
  shl   ax,8
  shl   di,6
  add   di,ax
  add   di,x1

  mov   al,col
  mov   ah,al
  mov   cx,x2
  sub   cx,x1
  shr   cx,1
  jnc   @start
  stosb
@Start :
  rep   stosw
end;

{──────────────────────────────────────────────────────────────────────────}
Procedure Line(a,b,c,d:integer;col:byte;where:word);
  { This draws a solid line from a,b to c,d in colour col }
  function sgn(a:real):integer;
  begin
       if a>0 then sgn:=+1;
       if a<0 then sgn:=-1;
       if a=0 then sgn:=0;
  end;
var i,s,d1x,d1y,d2x,d2y,u,v,m,n:integer;
begin
     u:= c - a;
     v:= d - b;
     d1x:= SGN(u);
     d1y:= SGN(v);
     d2x:= SGN(u);
     d2y:= 0;
     m:= ABS(u);
     n := ABS(v);
     IF NOT (M>N) then
     BEGIN
          d2x := 0 ;
          d2y := SGN(v);
          m := ABS(v);
          n := ABS(u);
     END;
     s := m shr 1;
     FOR i := 0 TO m DO
     BEGIN
          putpixel(a,b,col,where);
          s := s + n;
          IF not (s<m) THEN
          BEGIN
               s := s - m;
               a:= a + d1x;
               b := b + d1y;
          END
          ELSE
          BEGIN
               a := a + d2x;
               b := b + d2y;
          END;
     end;
END;


{──────────────────────────────────────────────────────────────────────────}
Procedure DrawPoly(x1,y1,x2,y2,x3,y3,x4,y4:integer;color:byte;where:word);
  { This draw a polygon with 4 points at x1,y1 , x2,y2 , x3,y3 , x4,y4
    in color col }
var
  x:integer;
  mny,mxy:integer;
  mnx,mxx,yc:integer;
  mul1,div1,
  mul2,div2,
  mul3,div3,
  mul4,div4:integer;

begin
  mny:=y1; mxy:=y1;
  if y2<mny then mny:=y2;
  if y2>mxy then mxy:=y2;
  if y3<mny then mny:=y3;
  if y3>mxy then mxy:=y3;    { Choose the min y mny and max y mxy }
  if y4<mny then mny:=y4;
  if y4>mxy then mxy:=y4;

  if mny<0 then mny:=0;
  if mxy>199 then mxy:=199;
  if mny>199 then exit;
  if mxy<0 then exit;        { Verticle range checking }

  mul1:=x1-x4; div1:=y1-y4;
  mul2:=x2-x1; div2:=y2-y1;
  mul3:=x3-x2; div3:=y3-y2;
  mul4:=x4-x3; div4:=y4-y3;  { Constansts needed for intersection calc }

  for yc:=mny to mxy do
    begin
      mnx:=320;
      mxx:=-1;
      if (y4>=yc) or (y1>=yc) then
        if (y4<=yc) or (y1<=yc) then   { Check that yc is between y1 and y4 }
          if not(y4=y1) then
            begin
              x:=(yc-y4)*mul1 div div1+x4; { Point of intersection on x axis }
              if x<mnx then
                mnx:=x;
              if x>mxx then
                mxx:=x;       { Set point as start or end of horiz line }
            end;
      if (y1>=yc) or (y2>=yc) then
        if (y1<=yc) or (y2<=yc) then   { Check that yc is between y1 and y2 }
          if not(y1=y2) then
            begin
              x:=(yc-y1)*mul2 div div2+x1; { Point of intersection on x axis }
              if x<mnx then
                mnx:=x;
              if x>mxx then
                mxx:=x;       { Set point as start or end of horiz line }
            end;
      if (y2>=yc) or (y3>=yc) then
        if (y2<=yc) or (y3<=yc) then   { Check that yc is between y2 and y3 }
          if not(y2=y3) then
            begin
              x:=(yc-y2)*mul3 div div3+x2; { Point of intersection on x axis }
              if x<mnx then
                mnx:=x;
              if x>mxx then
                mxx:=x;       { Set point as start or end of horiz line }
            end;
      if (y3>=yc) or (y4>=yc) then
        if (y3<=yc) or (y4<=yc) then   { Check that yc is between y3 and y4 }
          if not(y3=y4) then
            begin
              x:=(yc-y3)*mul4 div div4+x3; { Point of intersection on x axis }
              if x<mnx then
                mnx:=x;
              if x>mxx then
                mxx:=x;       { Set point as start or end of horiz line }
            end;
      if mnx<0 then
        mnx:=0;
      if mxx>319 then
        mxx:=319;          { Range checking on horizontal line }
      if mnx<=mxx then
        hline (mnx,mxx,yc,color,where);   { Draw the horizontal line }
    end;
  end;

{──────────────────────────────────────────────────────────────────────────}
Function rad (theta : real) : real;
  {  This calculates the degrees of an angle }
BEGIN
  rad := theta * pi / 180
END;

{──────────────────────────────────────────────────────────────────────────}
Procedure Putpixel (X,Y : Integer; Col : Byte; where:word); assembler;
  { This puts a pixel on the screen by writing directly to memory. }
asm
   mov  ax,where
   mov  es,ax
   mov  bx,[y]
   shl  bx,1
   mov  di,word ptr [Scr_Ofs + bx]
   add  di,[x]
   mov  al,[col]
   mov  es:[di],al
end;


{──────────────────────────────────────────────────────────────────────────}
Function Getpixel (X,Y : Integer; where:word):byte; assembler;
  { This puts a pixel on the screen by writing directly to memory. }
asm
   mov  ax,where
   mov  es,ax
   mov  bx,[y]
   shl  bx,1
   mov  di,word ptr [Scr_Ofs + bx]
   add  di,[x]
   mov  al,es:[di]
end;

{──────────────────────────────────────────────────────────────────────────}
Procedure LoadCEL (FileName :  string; ScrPtr : pointer);
  { This loads the cel 'filename' into the pointer scrptr }
var
  Fil : file;
  Buf : array [1..1024] of byte;
  BlocksRead, Count : word;
begin
  assign (Fil, FileName);
  reset (Fil, 1);
  BlockRead (Fil, Buf, 800);    { Read and ignore the 800 byte header }
  Count := 0;
  BlocksRead := $FFFF;
  while (not eof (Fil)) and (BlocksRead <> 0) do begin
    BlockRead (Fil, mem [seg (ScrPtr^): ofs (ScrPtr^) + Count], 1024, BlocksRead);
    Count := Count + 1024;
  end;
  close (Fil);
end;


procedure LoadPal (FileName : string);
var
  F:file;
  loop1:integer;
  pall:array[0..255,1..3] of byte;
begin
  assign (F, FileName);
  reset (F,1);
  blockread (F, pall,768);
  close (F);
  for loop1 := 0 to 255 do
    Pal(loop1,pall[loop1,1],pall[loop1,2],pall[loop1,3]);
end;


VAR Loop1:integer;

BEGIN
  For Loop1 := 0 to 199 do
    Scr_Ofs[Loop1] := Loop1 * 320;
END.{$X+}
USES Crt,GFX3;

CONST VGA = $A000;
      maxpolys = 18;

            A : Array [1..maxpolys,1..4,1..3] of integer =
        (
         ((-10, -10, 10 ),
          (10 , -10, 10 ),
          (10 , 10 , 10 ),
          (-10, 10 , 10 )),

         ((-10, 10 , -10),
          (10 , 10 , -10),
          (10 , -10, -10),
          (-10, -10, -10)),

         ((-10, 10 , 10 ),
          (-10, 10 , -10),
          (-10, -10, -10),
          (-10, -10, 10 )),

         ((10 , -10, 10 ),
          (10 , -10, -10),
          (10 , 10 , -10),
          (10 , 10 , 10 )),

         ((10 , 10 , 10 ),
          (10 , 10 , -10),
          (-10, 10 , -10),
          (-10, 10 , 10 )),

         ((-10, -10, 10 ),
          (-10, -10, -10),
          (10 , -10, -10),
          (10 , -10, 10 )),

(*********)

         ((-10, -10,-20 ),
          (10 , -10,-20 ),
          (10 , 10 ,-20 ),
          (-10, 10 ,-20 )),

         ((-10, 10 , -30),
          (10 , 10 , -30),
          (10 , -10, -30),
          (-10, -10, -30)),

         ((-10, 10 ,-20 ),
          (-10, 10 , -30),
          (-10, -10, -30),
          (-10, -10,-20 )),

         ((10 , -10,-20 ),
          (10 , -10, -30),
          (10 , 10 , -30),
          (10 , 10 ,-20 )),

         ((10 , 10 ,-20 ),
          (10 , 10 , -30),
          (-10, 10 , -30),
          (-10, 10 ,-20 )),

         ((-10, -10,-20 ),
          (-10, -10, -30),
          (10 , -10, -30),
          (10 , -10,-20 )),

(*********)

         ((-30, -10, 10 ),
          (-20, -10, 10 ),
          (-20, 10 , 10 ),
          (-30, 10 , 10 )),

         ((-30, 10 , -10),
          (-20, 10 , -10),
          (-20, -10, -10),
          (-30, -10, -10)),

         ((-30, 10 , 10 ),
          (-30, 10 , -10),
          (-30, -10, -10),
          (-30, -10, 10 )),

         ((-20, -10, 10 ),
          (-20, -10, -10),
          (-20, 10 , -10),
          (-20, 10 , 10 )),

         ((-20, 10 , 10 ),
          (-20, 10 , -10),
          (-30, 10 , -10),
          (-30, 10 , 10 )),

         ((-30, -10, 10 ),
          (-30, -10, -10),
          (-20, -10, -10),
          (-20, -10, 10 ))
        );  { The 3-D coordinates of our object ... stored as (X1,Y1,Z1), }
            { (X2,Y2,Z2) ... for the 4 points of a poly }

      XOfs = 100;
      YOfs = 160;


Type Point = Record
               x,y,z:integer;                { The data on every point we rotate}
             END;


VAR Lines : Array [1..maxpolys,1..4] of Point; { The base object to be rotated }
    Translated : Array [1..maxpolys,1..4] of Point; { The rotated object }
    centre, tcentre : Array [1..maxpolys] of Point;
    Order : Array[1..maxpolys] of integer;
    lookup : Array [0..360,1..2] of integer; { Our sin and cos lookup table }
    poly : array [0..199,1..2] of integer;
    ytopclip,ybotclip:integer;  {where to clip our polys to}
    xoff,yoff,zoff:integer;


{──────────────────────────────────────────────────────────────────────────}
Procedure SetMCGA;  { This procedure gets you into 320x200x256 mode. }
BEGIN
  asm
     mov        ax,0013h
     int        10h
  end;
END;


{──────────────────────────────────────────────────────────────────────────}
Procedure Hline (x1,x2,y:integer;col:byte;where:word); assembler;
  { This draws a horizontal line from x1 to x2 on line y in color col }
asm
  mov   ax,x1
  cmp   ax,0
  jge   @X1Okay
  mov   x1,0
@X1Okay :

  mov   ax,x2
  cmp   ax,319
  jle   @X2Okay
  mov   x2,319
@X2Okay :

  mov   ax,x1
  cmp   ax,x2
  jg    @Exit

  mov   ax,where
  mov   es,ax
  mov   ax,y
  mov   di,ax
  shl   ax,8
  shl   di,6
  add   di,ax
  add   di,x1

  mov   al,col
  mov   ah,al
  mov   cx,x2
  sub   cx,x1
  shr   cx,1
  jnc   @start
  stosb
@Start :
  rep   stosw
@Exit :
end;


{──────────────────────────────────────────────────────────────────────────}
Procedure DrawPoly(x1,y1,x2,y2,x3,y3,x4,y4:integer;color:byte;where:word);
  { This draw a polygon with 4 points at x1,y1 , x2,y2 , x3,y3 , x4,y4
    in color col }
var miny,maxy:integer;
    loop1:integer;

Procedure doside (x1,y1,x2,y2:integer);
  { This scans the side of a polygon and updates the poly variable }
VAR temp:integer;
    x,xinc:integer;
    loop1:integer;
BEGIN
  if y1=y2 then exit;
  if y2<y1 then BEGIN
    temp:=y2;
    y2:=y1;
    y1:=temp;
    temp:=x2;
    x2:=x1;
    x1:=temp;
  END;
  xinc:=((x2-x1) shl 7) div (y2-y1);
  x:=x1 shl 7;
  for loop1:=y1 to y2 do BEGIN
    if (loop1>(ytopclip)) and (loop1<(ybotclip)) then BEGIN
      if (x shr 7<poly[loop1,1]) then poly[loop1,1]:=x shr 7;
      if (x shr 7>poly[loop1,2]) then poly[loop1,2]:=x shr 7;
    END;
    x:=x+xinc;
  END;
END;

begin
  asm
    mov   si,offset poly
    mov   cx,200
@Loop1:
    mov   ax,32766
    mov   ds:[si],ax
    inc   si
    inc   si
    mov   ax,-32767
    mov   ds:[si],ax
    inc   si
    inc   si
    loop  @loop1
  end;     { Setting the minx and maxx values to extremes }
  miny:=y1;
  maxy:=y1;
  if y2<miny then miny:=y2;
  if y3<miny then miny:=y3;
  if y4<miny then miny:=y4;
  if y2>maxy then maxy:=y2;
  if y3>maxy then maxy:=y3;
  if y4>maxy then maxy:=y4;
  if miny<ytopclip then miny:=ytopclip;
  if maxy>ybotclip then maxy:=ybotclip;
  if (miny>199) or (maxy<0) then exit;

  Doside (x1,y1,x2,y2);
  Doside (x2,y2,x3,y3);
  Doside (x3,y3,x4,y4);
  Doside (x4,y4,x1,y1);

  for loop1:= miny to maxy do
    hline (poly[loop1,1],poly[loop1,2],loop1,color,where);
end;


{──────────────────────────────────────────────────────────────────────────}
Procedure SetUpPoints;
  { This creates the lookup table }
VAR loop1,loop2:integer;
BEGIN
  For loop1:=0 to 360 do BEGIN
    lookup [loop1,1]:=round(sin (rad (loop1))*16384);
    lookup [loop1,2]:=round(cos (rad (loop1))*16384);
  END;
  For loop1:=1 to maxpolys do BEGIN
    centre[loop1].x := (lines[loop1,1].x + lines[loop1,2].x +
                        lines[loop1,3].x + lines[loop1,4].x) div 4;
    centre[loop1].y := (lines[loop1,1].y + lines[loop1,2].y +
                        lines[loop1,3].y + lines[loop1,4].y) div 4;
    centre[loop1].z := (lines[loop1,1].z + lines[loop1,2].z +
                        lines[loop1,3].z + lines[loop1,4].z) div 4;
  END;
END;


{──────────────────────────────────────────────────────────────────────────}
Procedure RotatePoints (x,Y,z:Integer);
  { This rotates the objecct in lines to translated }
VAR loop1,loop2:integer;
    a,b,c:integer;
BEGIN
  For loop1:=1 to maxpolys do BEGIN
    for loop2:=1 to 4 do BEGIN
      b:=lookup[y,2];
      c:=lines[loop1,loop2].x;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        mov   a,dx
      end;
      b:=lookup[y,1];
      c:=lines[loop1,loop2].z;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        add   a,dx
      end;
      translated[loop1,loop2].x:=a;
      translated[loop1,loop2].y:=lines[loop1,loop2].y;
      b:=-lookup[y,1];
      c:=lines[loop1,loop2].x;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        mov   a,dx
      end;
      b:=lookup[y,2];
      c:=lines[loop1,loop2].z;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        add   a,dx
      end;
      translated[loop1,loop2].z:=a;


      if x<>0 then BEGIN
        b:=lookup[x,2];
        c:=translated[loop1,loop2].y;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          mov   a,dx
        end;
        b:=lookup[x,1];
        c:=translated[loop1,loop2].z;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          sub   a,dx
        end;
        b:=lookup[x,1];
        c:=translated[loop1,loop2].y;
        translated[loop1,loop2].y:=a;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          mov   a,dx
        end;
        b:=lookup[x,2];
        c:=translated[loop1,loop2].z;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          add   a,dx
        end;
        translated[loop1,loop2].z:=a;
      END;




      if z<>0 then BEGIN
        b:=lookup[z,2];
        c:=translated[loop1,loop2].x;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          mov   a,dx
        end;
        b:=lookup[z,1];
        c:=translated[loop1,loop2].y;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          sub   a,dx
        end;
        b:=lookup[z,1];
        c:=translated[loop1,loop2].x;
        translated[loop1,loop2].x:=a;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          mov   a,dx
        end;
        b:=lookup[z,2];
        c:=translated[loop1,loop2].y;
        asm
          mov   ax,b
          imul  c
          sal   ax,1
          rcl   dx,1
          sal   ax,1
          rcl   dx,1
          add   a,dx
        end;
        translated[loop1,loop2].y:=a;
      END;
    END;
  END;


{******************}
  For loop1:=1 to maxpolys do BEGIN
    b:=lookup[y,2];
    c:=centre[loop1].x;
    asm
      mov   ax,b
      imul  c
      sal   ax,1
      rcl   dx,1
      sal   ax,1
      rcl   dx,1
      mov   a,dx
    end;
    b:=lookup[y,1];
    c:=centre[loop1].z;
    asm
      mov   ax,b
      imul  c
      sal   ax,1
      rcl   dx,1
      sal   ax,1
      rcl   dx,1
      add   a,dx
    end;
    tcentre[loop1].x:=a;
    tcentre[loop1].y:=centre[loop1].y;
    b:=-lookup[y,1];
    c:=centre[loop1].x;
    asm
      mov   ax,b
      imul  c
      sal   ax,1
      rcl   dx,1
      sal   ax,1
      rcl   dx,1
      mov   a,dx
    end;
    b:=lookup[y,2];
    c:=centre[loop1].z;
    asm
      mov   ax,b
      imul  c
      sal   ax,1
      rcl   dx,1
      sal   ax,1
      rcl   dx,1
      add   a,dx
    end;
    tcentre[loop1].z:=a;


    if x<>0 then BEGIN
      b:=lookup[x,2];
      c:=tcentre[loop1].y;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        mov   a,dx
      end;
      b:=lookup[x,1];
      c:=tcentre[loop1].z;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        sub   a,dx
      end;
      b:=lookup[x,1];
      c:=tcentre[loop1].y;
      tcentre[loop1].y:=a;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        mov   a,dx
      end;
      b:=lookup[x,2];
      c:=tcentre[loop1].z;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        add   a,dx
      end;
      tcentre[loop1].z:=a;
    END;




    if z<>0 then BEGIN
      b:=lookup[z,2];
      c:=tcentre[loop1].x;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        mov   a,dx
      end;
      b:=lookup[z,1];
      c:=tcentre[loop1].y;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        sub   a,dx
      end;
      b:=lookup[z,1];
      c:=tcentre[loop1].x;
      tcentre[loop1].x:=a;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        mov   a,dx
      end;
      b:=lookup[z,2];
      c:=tcentre[loop1].y;
      asm
        mov   ax,b
        imul  c
        sal   ax,1
        rcl   dx,1
        sal   ax,1
        rcl   dx,1
        add   a,dx
      end;
      tcentre[loop1].y:=a;
    END;
  END;
END;



{──────────────────────────────────────────────────────────────────────────}
Procedure DrawPoints;
  { This draws the translated object to the virtual screen }
VAR loop1,loop2:Integer;
    temp, normal:integer;
    nx:integer;
    tx1,ty1,tx2,ty2,tx3,ty3,tx4,ty4:integer;
BEGIN
  For loop2:=1 to maxpolys do BEGIN
    loop1:=order[loop2];
    If (translated[loop1,1].z+zoff<0) and (translated[loop1,2].z+zoff<0)
       and (translated[loop1,3].z+zoff<0) and (translated[loop1,4].z+zoff<0)
       then BEGIN
      temp:=round (translated[loop1,1].z)+zoff;
      nx:=translated[loop1,1].X;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,YOfs
        mov   nx,ax
      end;
      tx1:=nx;
      nx:=translated[loop1,1].Y;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,XOfs
        mov   nx,ax
      end;
      ty1:=nx;


      temp:=round (translated[loop1,2].z)+zoff;
      nx:=translated[loop1,2].X;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,YOfs
        mov   nx,ax
      end;
      tx2:=nx;
      nx:=translated[loop1,2].Y;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,XOfs
        mov   nx,ax
      end;
      ty2:=nx;


      temp:=round (translated[loop1,3].z)+zoff;
      nx:=translated[loop1,3].X;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,YOfs
        mov   nx,ax
      end;
      tx3:=nx;
      nx:=translated[loop1,3].Y;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,XOfs
        mov   nx,ax
      end;
      ty3:=nx;


      temp:=round (translated[loop1,4].z)+zoff;
      nx:=translated[loop1,4].X;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,YOfs
        mov   nx,ax
      end;
      tx4:=nx;
      nx:=translated[loop1,4].Y;
      asm
        mov   ax,nx
        mov   dx,ax
        sal   ax,8
        sar   dx,8
        idiv  temp
        add   ax,XOfs
        mov   nx,ax
      end;
      ty4:=nx;

      normal:=(ty1-ty3)*(tx2-tx1)-(tx1-tx3)*(ty2-ty1);
      if normal<0 then
        drawpoly (tx1,ty1,tx2,ty2,tx3,ty3,tx4,ty4,loop1,vaddr);
    END;
  END;
END;



{──────────────────────────────────────────────────────────────────────────}
Procedure SortPoints;
VAR loop1,curpos, temp:integer;
BEGIN
  for loop1:=1 to maxpolys do BEGIN
    order[loop1]:=loop1;
  END;
  curpos := 1;
  while curpos<maxpolys do BEGIN
    if tcentre[curpos].z > tcentre[curpos+1].z then BEGIN
      temp := tcentre[curpos+1].x;
      tcentre[curpos+1].x := tcentre[curpos].x;
      tcentre[curpos].x := temp;

      temp := tcentre[curpos+1].y;
      tcentre[curpos+1].y := tcentre[curpos].y;
      tcentre[curpos].y := temp;

      temp := tcentre[curpos+1].z;
      tcentre[curpos+1].z := tcentre[curpos].z;
      tcentre[curpos].z := temp;

      temp := order[curpos+1];
      order[curpos+1] := order[curpos];
      order[curpos] := temp;

      curpos:=0;
    END;
    curpos:=curpos+1;
  END;
END;


{──────────────────────────────────────────────────────────────────────────}
Procedure MoveAround;
  { This is the main display procedure. }
VAR deg,deg2,loop1,loop2:integer;
    ch:char;

BEGIN
  pal (1,  0, 0,63);
  pal (2,  0,32,63);
  pal (3, 32, 0,63);
  pal (4, 32,32,63);
  pal (5,  0,63,63);
  pal (6, 32,63,63);

  pal ( 7,  0,63, 0);
  pal ( 8,  0,63,32);
  pal ( 9, 32,63, 0);
  pal (10, 32,63,32);
  pal (11,  0,63,63);
  pal (12, 32,63,63);

  pal (13, 63, 0, 0);
  pal (14, 63,32, 0);
  pal (15, 63, 0,32);
  pal (16, 63,32,32);
  pal (17, 63,63, 0);
  pal (18, 63,63,32);
{  for loop1:=1 to 15 do
    pal (loop1,0,loop1*4+3,63-(loop1*4+3));}
  pal (100,50,50,50);

  deg:=0;
  deg2:=0;
  ch:=#0;
  Cls (vaddr,0);
  For loop1:=1 to maxpolys do
    For loop2:=1 to 4 do BEGIN
      Lines [loop1,loop2].x:=a [loop1,loop2,1]*8;
      Lines [loop1,loop2].y:=a [loop1,loop2,2]*8;
      Lines [loop1,loop2].z:=a [loop1,loop2,3]*8;
    END;

  SetUpPoints;

  cls (vaddr,0);
  cls (vga,0);
  Xoff := 160;
  Yoff:=100;
  zoff:=-500;

  ytopclip:=101;
  ybotclip:=100;
  line (0,100,319,100,100,vga);
  delay (2000);
  for loop1:=1 to 25 do BEGIN
    RotatePoints (deg2,deg,deg2);
    SortPoints;
    DrawPoints;
    line (0,ytopclip,319,ytopclip,100,vaddr);
    line (0,ybotclip,319,ybotclip,100,vaddr);
    flip (vaddr,vga);
    cls (vaddr,0);
    deg:=(deg+5) mod 360;
    deg2:=(deg2+1) mod 360;
    ytopclip:=ytopclip-4;
    ybotclip:=ybotclip+4;
  END;
  Repeat
    if keypressed then ch:=upcase (Readkey);
    RotatePoints (deg2,deg,deg2);
    SortPoints;
    DrawPoints;
    line (0,0,319,0,100,vaddr);
    line (0,199,319,199,100,vaddr);
    flip (vaddr,vga);
    cls (vaddr,0);
    deg:=(deg+5) mod 360;
    deg2:=(deg2+3) mod 360;
  Until ch=#27;
  for loop1:=1 to 25 do BEGIN
    ytopclip:=ytopclip+4;
    ybotclip:=ybotclip-4;
    RotatePoints (deg2,deg,deg2);
    SortPoints;
    DrawPoints;
    line (0,ytopclip,319,ytopclip,100,vaddr);
    line (0,ybotclip,319,ybotclip,100,vaddr);
    flip (vaddr,vga);
    cls (vaddr,0);
    deg:=(deg+5) mod 360;
    deg2:=(deg2+1) mod 360;
  END;
END;


BEGIN
  clrscr;
  writeln ('Welcome to the twentieth(sp) trainer! This one is on face sorting');
  writeln ('and back face removal.');
  writeln;
  writeln ('Just hit a key to view the 3d shape. You will notice that you');
  writeln ('won''t see any of the faces you shouldn''t see :-)');
  writeln ('The code is based on that from the glenzing tut, so you should');
  writeln ('be able to understand it fairly quickly.');
  writeln;
  writeln;
  writeln;
  write ('Hit any key to continue ...');
  readkey;
  SetUpVirtual;
  SetMCGA;
  MoveAround;
  SetText;
  ShutDown;
  Writeln ('All done. This concludes the twentieth sample program in the ASPHYXIA');
  Writeln ('Training series. You may reach DENTHOR under the names of GRANT');
  Writeln ('SMITH/DENTHOR/ASPHYXIA on the ASPHYXIA BBS.I also occasinally');
  Writeln ('RSAProg, comp.lang.pascal and comp.sys.ibm.pc.demos. E-mail me at :');
  Writeln ('    [e-mail]');
  Writeln ('The numbers are available in the main text. You may also write to me at:');
  Writeln ('             Grant Smith');
  Writeln ('             P.O. Box 270');
  Writeln ('             Kloof');
  Writeln ('             3640');
  Writeln ('             Natal');
  Writeln ('             South Africa');
  Writeln ('I hope to hear from you soon!');
  Writeln; Writeln;
  Write   ('Hit any key to exit ...');
  readkey;
END.