GameDev.netCircles and Lines

Circles and Lines ÕÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¸ 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 ÔÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ¾ ³ ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ --==[ 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 [BACK] Back
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