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back2root:archives:denthor:part-03

Ceci est une ancienne révision du document !


PART 03 : Lines and circles

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 :

  1. Write a message to Grant Smith in private mail here on the Mailbox BBS.
  2. 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)
  3. Write to ASPHYXIA on the ASPHYXIA BBS.
  4. Write to Denthor, Eze or Livewire on Connectix.
  5. Write to :
Grant Smith
P.O.Box 270 Kloof
3640
  1. 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
                              ▄█|█▄
                             ███|███
                        270 ----+---- 90
                             ███|███
                              ▀█|█▀
                               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
                              ▄█|█▄
                             ███|███
                        180 ----+---- 0
                             ███|███
                              ▀█|█▀
                                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 obviousy 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 320×200 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 posotive, answer. At this stage I set a variable stating wheter the difference between the two x's are negative, zero or posotive. (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 posotive, 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 :

  • \``|``/*
  • \|/*
  1. —+—-
  • /|\*
  • /``|``\*

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 documentaiton 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.

back2root/archives/denthor/part-03.1630007943.txt.gz · Dernière modification: 2021/08/26 21:59 de frater