# VGA Trainer Program: part 3

` Õ-------------------------------¸ `

| W E L C O M E |

| To the VGA Trainer Program | |

| By | |

| DENTHOR of ASPHYXIA | | |

Ô-------------------------------¾ | |

--------------------------------Ù |

--------------------------------Ù

--==[ PART 3 ]==--

## Introduction

Greetings! This is the third part of the VGA Trainer series! Sorry it took so long to get out, but I had a running battle with the traffic department for three days to get my car registered, and then the MailBox went down. Ahh, well, life stinks. Anyway, today will do some things vital to most programs : Lines and circles.

Watch out for next week's part : Virtual screens. The easy way to eliminate flicker, "doubled sprites", and subjecting the user to watch you building your screen. Almost every ASPHYXIA demo has used a virtual screen (with the exception of the SilkyDemo), so this is one to watch out for. I will also show you how to put all of these loose procedures into units.

If you would like to contact me, or the team, there are many ways you can do it :

- Write a message to Grant Smith in private mail here on the Mailbox BBS.
- Write a message here in the Programming conference here on the Mailbox (Preferred if you have a general programming query or problem others would benefit from)
- Write to ASPHYXIA on the ASPHYXIA BBS.
- Write to Denthor, Eze or Livewire on Connectix.
- Write to : Grant Smith P.O.Box 270 Kloof 3640
- Call me (Grant Smith) at 73 2129 (leave a message if you call during varsity)

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!

## Circle Algorithim

You all know what a circle looks like. But how do you draw one on the computer?

You probably know circles drawn with the degrees at these points :

` 0 `

ÜÛ|ÛÜ

ÛÛÛ|ÛÛÛ

270 ----+---- 90

ÛÛÛ|ÛÛÛ

ßÛ|Ûß

180

Sorry about my ASCI ;-) ... anyway, Pascal doesn't work that way ... it works with radians instead of degrees. (You can convert radians to degrees, but I'm not going to go into that now. Note though that in pascal, the circle goes like this :

` 270 `

ÜÛ|ÛÜ

ÛÛÛ|ÛÛÛ

180 ----+---- 0

ÛÛÛ|ÛÛÛ

ßÛ|Ûß

90

Even so, we can still use the famous equations to draw our circle ... (You derive the following by using the theorem of our good friend Pythagoras)

` Sin (deg) = Y/R `

Cos (deg) = X/R

(This is standard 8(?) maths ... if you haven't reached that level yet, take this to your dad, or if you get stuck leave me a message and I'll do a bit of basic Trig with you. I aim to please ;-))

Where

- Y = your Y-coord
- X = your X-coord
- R = your radius (the size of your circle)
- deg = the degree

To simplify matters, we rewrite the equation to get our X and Y values :

` Y = R*Sin(deg) `

X = R*Cos(deg)

This obviously is perfect for us, because it gives us our X and Y co-ords to put into our putpixel routine (see Part 1). Because the Sin and Cos functions return a Real value, we use a round function to transform it into an Integer.

` Procedure Circle (oX,oY,rad:integer;Col:Byte); `

VAR deg:real;

X,Y:integer;

BEGIN

deg:=0;

repeat

X:=round(rad*COS (deg));

Y:=round(rad*sin (deg));

putpixel (x+ox,y+oy,Col);

deg:=deg+0.005;

until (deg>6.4);

END;

In the above example, the smaller the amount that deg is increased by, the closer the pixels in the circle will be, but the slower the procedure. 0.005 seem to be best for the 320x200 screen. NOTE : ASPHYXIA does not use this particular circle algorithm, ours is in assembly language, but this one should be fast enough for most. If it isn't, give us the stuff you are using it for and we'll give you ours.

## Line algorithms

There are many ways to draw a line on the computer. I will describe one and give you two. (The second one you can figure out for yourselves; it is based on the first one but is faster)

The first thing you need to do is pass what you want the line to look like to your line procedure. What I have done is said that x1,y1 is the first point on the screen, and x2,y2 is the second point. We also pass the color to the procedure. (Remember the screens top left hand corner is (0,0); see Part 1)

`Ie. o (X1,Y1) `

ooooooooo

ooooooooo

oooooooo (X2,Y2)

Again, sorry about my drawings ;-)

To find the length of the line, we say the following :

` XLength = ABS (x1-x2) `

YLength = ABS (y1-y2)

The ABS function means that whatever the result, it will give you an absolute, or positive, answer. At this stage I set a variable stating wheter the difference between the two x's are negative, zero or positive. (I do the same for the y's) If the difference is zero, I just use a loop keeping the two with the zero difference positive, then exit.

If neither the x's or y's have a zero difference, I calculate the X and Y slopes, using the following two equations :

` Xslope = Xlength / Ylength `

Yslope = Ylength / Xlength

As you can see, the slopes are real numbers.

NOTE : XSlope = 1 / YSlope

Now, there are two ways of drawing the lines :

` X = XSlope * Y `

Y = YSlope * X

The question is, which one to use? if you use the wrong one, your line will look like this :

` o `

o

o

Instead of this :

` ooo `

ooo

ooo

Well, the solution is as follows :

` *\``|``/* `

***\|/***

----+----

***/|\***

*/``|``\*

If the slope angle is in the area of the stars (*) then use the first equation, if it is in the other section (`) then use the second one. What you do is you calculate the variable on the left hand side by putting the variable on the right hand side in a loop and solving. Below is our finished line routine :

`Procedure Line (x1,y1,x2,y2:integer;col:byte); `

VAR x,y,xlength,ylength,dx,dy:integer;

xslope,yslope:real;

BEGIN

xlength:=abs (x1-x2);

if (x1-x2)<0 then dx:=-1;

if (x1-x2)=0 then dx:=0;

if (x1-x2)>0 then dx:=+1;

ylength:=abs (y1-y2);

if (y1-y2)<0 then dy:=-1;

if (y1-y2)=0 then dy:=0;

if (y1-y2)>0 then dy:=+1;

if (dy=0) then BEGIN

if dx<0 then for x:=x1 to x2 do

putpixel (x,y1,col);

if dx>0 then for x:=x2 to x1 do

putpixel (x,y1,col);

exit;

END;

if (dx=0) then BEGIN

if dy<0 then for y:=y1 to y2 do

putpixel (x1,y,col);

if dy>0 then for y:=y2 to y1 do

putpixel (x1,y,col);

exit;

END;

xslope:=xlength/ylength;

yslope:=ylength/xlength;

if (yslope/xslope<1) and (yslope/xslope>-1) then BEGIN

if dx<0 then for x:=x1 to x2 do BEGIN

y:= round (yslope*x);

putpixel (x,y,col);

END;

if dx>0 then for x:=x2 to x1 do BEGIN

y:= round (yslope*x);

putpixel (x,y,col);

END;

END

ELSE

BEGIN

if dy<0 then for y:=y1 to y2 do BEGIN

x:= round (xslope*y);

putpixel (x,y,col);

END;

if dy>0 then for y:=y2 to y1 do BEGIN

x:= round (xslope*y);

putpixel (x,y,col);

END;

END;

END;

Quite big, isn't it? Here is a much shorter way of doing much the same thing :

`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;

procedure line(a,b,c,d,col:integer);

var u,s,v,d1x,d1y,d2x,d2y,m,n:real;

i: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 := INT(m / 2);

FOR i := 0 TO round(m) DO

BEGIN

putpixel(a,b,col);

s := s + n;

IF not (s<m) THEN

BEGIN

s := s - m;

a:= a +round(d1x);

b := b + round(d1y);

END

ELSE

BEGIN

a := a + round(d2x);

b := b + round(d2y);

END;

end;

END;

This routine is very fast, and should meet almost all of your requirements (ASPHYXIA used it for quite a while before we made our new one.) In the end program, both the new line routine and the circle routine are tested. A few of the procedures of the first parts are also used.

Line and circle routines may seem like fairly trivial things, but they are a vital component of many programs, and you may like to look up other methods of drawing them in books in the library (I know that here at the varsity they have books for doing this kind of stuff all over the place) A good line routine to look out for is the Bressenhams line routine ... there is a Bressenhams circle routine too ... I have documentation for them if anybody is interested, they are by far some of the fastest routines you will use.

## In closing

Varsity has started again, so I am (shock) going to bed before three in the morning, so my quote this week wasn't written in the same wasted way my last weeks one was (For last week's one, I had gotten 8 hours sleep in 3 days, and thought up and wrote the quote at 2:23 am before I fell asleep.)

[ "What does it do?" she asks.

"It's a computer," he replies.

"Yes, dear, but what does it do?"

"It ..er.. computes! It's a computer."

"What does it compute?"

"What? Er? Um. Numbers! Yes, numbers!" He smiles worriedly.

"Why?"

"Why? Well ..um.. why?" He starts to sweat.

"I mean, is it just something to dust around, or does it actually do something useful?"

"Um...you can call other computers with it!" Hope lights up his eyes. "So you can get programs from other computers!"

"I see. Tell me, what do these programs do?"

"Do? I don't think I fol..."

"I see. They compute. Numbers. For no particular reason." He withers under her gaze.

"Yes, but..."

She smiles, and he trails off, defeated. She takes another look at the thing. "Although," she says, with a strange look in her eyes. He looks up, an insane look of hope on his face. "Does it come in pink?" she asks. ]- Grant Smith

Tue 27 July, 1993

9:35 pm.

See you next time,

- Denthor

## TUTPROG3.PAS

`{$X+} `

USES crt;

CONST VGA = $a000;

VAR loop1:integer;

Pall : Array [1..199,1..3] of byte;

{ This is our temporary pallette. We ony use colors 1 to 199, so we

only have variables for those ones. }

{--------------------------------------------------------------------------}

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 Putpixel (X,Y : Integer; Col : Byte);

{ This puts a pixel on the screen by writing directly to memory. }

BEGIN

Mem [VGA:X+(Y*320)]:=Col;

END;

{--------------------------------------------------------------------------}

procedure WaitRetrace; assembler;

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 Pal(ColorNo : Byte; R,G,B : Byte);

{ This sets the Red, Green and Blue values of a certain color }

Begin

Port[$3c8] := ColorNo;

Port[$3c9] := R;

Port[$3c9] := G;

Port[$3c9] := B;

End;

{--------------------------------------------------------------------------}

Procedure Circle (X,Y,rad:integer;Col:Byte);

{ This draws a circle with centre X,Y, with Rad as it's radius }

VAR deg:real;

BEGIN

deg:=0;

repeat

X:=round(rad*COS (deg));

Y:=round(rad*sin (deg));

putpixel (x+160,y+100,col);

deg:=deg+0.005;

until (deg>6.4);

END;

{--------------------------------------------------------------------------}

Procedure Line2 (x1,y1,x2,y2:integer;col:byte);

{ This draws a line from x1,y1 to x2,y2 using the first method }

VAR x,y,xlength,ylength,dx,dy:integer;

xslope,yslope:real;

BEGIN

xlength:=abs (x1-x2);

if (x1-x2)<0 then dx:=-1;

if (x1-x2)=0 then dx:=0;

if (x1-x2)>0 then dx:=+1;

ylength:=abs (y1-y2);

if (y1-y2)<0 then dy:=-1;

if (y1-y2)=0 then dy:=0;

if (y1-y2)>0 then dy:=+1;

if (dy=0) then BEGIN

if dx<0 then for x:=x1 to x2 do

putpixel (x,y1,col);

if dx>0 then for x:=x2 to x1 do

putpixel (x,y1,col);

exit;

END;

if (dx=0) then BEGIN

if dy<0 then for y:=y1 to y2 do

putpixel (x1,y,col);

if dy>0 then for y:=y2 to y1 do

putpixel (x1,y,col);

exit;

END;

xslope:=xlength/ylength;

yslope:=ylength/xlength;

if (yslope/xslope<1) and (yslope/xslope>-1) then BEGIN

if dx<0 then for x:=x1 to x2 do BEGIN

y:= round (yslope*x);

putpixel (x,y,col);

END;

if dx>0 then for x:=x2 to x1 do BEGIN

y:= round (yslope*x);

putpixel (x,y,col);

END;

END

ELSE

BEGIN

if dy<0 then for y:=y1 to y2 do BEGIN

x:= round (xslope*y);

putpixel (x,y,col);

END;

if dy>0 then for y:=y2 to y1 do BEGIN

x:= round (xslope*y);

putpixel (x,y,col);

END;

END;

END;

{--------------------------------------------------------------------------}

procedure line(a,b,c,d,col:integer);

{ This draws a line from x1,y1 to x2,y2 using the first method }

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 u,s,v,d1x,d1y,d2x,d2y,m,n:real;

i: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 := INT(m / 2);

FOR i := 0 TO round(m) DO

BEGIN

putpixel(a,b,col);

s := s + n;

IF not (s<m) THEN

BEGIN

s := s - m;

a:= a +round(d1x);

b := b + round(d1y);

END

ELSE

BEGIN

a := a + round(d2x);

b := b + round(d2y);

END;

end;

END;

{--------------------------------------------------------------------------}

Procedure PalPlay;

{ This procedure mucks about with our "virtual pallette", then shoves it

to screen. }

Var Tmp : Array[1..3] of Byte;

{ This is used as a "temporary color" in our pallette }

loop1 : Integer;

BEGIN

Move(Pall[199],Tmp,3);

{ This copies color 199 from our virtual pallette to the Tmp variable }

Move(Pall[1],Pall[2],198*3);

{ This moves the entire virtual pallette up one color }

Move(Tmp,Pall[1],3);

{ This copies the Tmp variable to the bottom of the virtual pallette }

WaitRetrace;

For loop1:=1 to 199 do

pal (loop1,pall[loop1,1],pall[loop1,2],pall[loop1,3]);

END;

BEGIN

ClrScr;

Writeln ('This sample program will test out our line and circle algorithms.');

Writeln ('In the first part, many circles will be draw creating (hopefully)');

Writeln ('a "tunnel" effect. I will the rotate the pallete to make it look');

Writeln ('nice. I will then draw some lines and rotate the pallette on them');

Writeln ('too. Note : I am using the slower (first) line algorithm (in');

Writeln ('procedure line2). Change it to Procedure Line and it will be using');

Writeln ('the second line routine. NB : For descriptions on how pallette works');

Writeln ('have a look at part two of this series; I won''t re-explain it here.');

Writeln;

Writeln ('Remember to send me any work you have done, I am most eager to help.');

Writeln; Writeln;

Writeln ('Hit any key to continue ...');

Readkey;

setmcga;

For Loop1 := 1 to 199 do BEGIN

Pall[Loop1,1] := Loop1 mod 30+33;

Pall[Loop1,2] := 0;

Pall[Loop1,3] := 0;

END;

{ This sets colors 1 to 199 to values between 33 to 63. The MOD

function gives you the remainder of a division, ie. 105 mod 10 = 5 }

WaitRetrace;

For loop1:=1 to 199 do

pal (loop1,pall[loop1,1],pall[loop1,2],pall[loop1,3]);

{ This sets the true pallette to variable Pall }

for loop1:=1 to 90 do

circle (160,100,loop1,loop1);

{ This draws 90 circles all with centres at 160,100; with increasing

radii and colors. }

Repeat

PalPlay;

Until keypressed;

Readkey;

for loop1:=1 to 199 do

line2 (0,1,319,loop1,loop1); { *** Replace Line2 with Line to use the

second line algorithm *** }

{ This draws 199 lines, all starting at 0,1 }

Repeat

PalPlay;

Until keypressed;

readkey;

SetText;

Writeln ('All done. Okay, so maybe it wasn''t a tunnel effect, but you get the');

Writeln ('general idea ;-) This concludes the third sample program in the ASPHYXIA');

Writeln ('Training series. You may reach DENTHOR under the name of GRANT SMITH');

Writeln ('on the MailBox BBS, or leave a message to ASPHYXIA on the ASPHYXIA BBS.');

Writeln ('Get the numbers from Roblist, or write to :');

Writeln (' Grant Smith');

Writeln (' P.O. Box 270');

Writeln (' Kloof');

Writeln (' 3640');

Writeln ('I hope to hear from you soon!');

Writeln; Writeln;

Write ('Hit any key to exit ...');

Readkey;

END.