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³ W E L C O M E ³
³ To the VGA Trainer Program ³ ³
³ By ³ ³
³ DENTHOR of ASPHYXIA ³ ³ ³
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--==[ PART 3 ]==--
þ 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 : 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
6) 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!
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
þ 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 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 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.
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
þ 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 :
*\``|``/*
***\|/***
----+----
***/|\***
*/``|``\*
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 (s6.4);
END;
{ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ}
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;
{ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ}
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