Hidden Surface Removal ีอออออออออออออออออออออออออออออออธ ณ W E L C O M E ณ ณ To the VGA Trainer Program ณ ณ ณ By ณ ณ ณ DENTHOR of ASPHYXIA ณ ณ ณ ิอออออออออออออออออออออออออออออออพ ณ ณ ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤู ณ ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤู --==[ 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 +27-31-73-2129 if you call from outside South Africa. (It's YOUR phone bill ;-)) 4) Write to denthor@beastie.cs.und.ac.za in E-Mail. 5) Write to asphyxia@beastie.cs.und.ac.za 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 {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} Procedure SetMCGA; { This procedure gets you into 320x200x256 mode. } BEGIN asm mov ax,0013h int 10h end; END; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} Procedure SetText; { This procedure returns you to text mode. } BEGIN asm mov ax,0003h int 10h end; END; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} Procedure SetUpVirtual; { This sets up the memory needed for the virtual screen } BEGIN GetMem (VirScr,64000); vaddr := seg (virscr^); END; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} Procedure ShutDown; { This frees the memory used by the virtual screen } BEGIN FreeMem (VirScr,64000); END; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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 (smxy then mxy:=y2; if y3mxy then mxy:=y3; { Choose the min y mny and max y mxy } if y4mxy 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 xmxx 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 xmxx 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 xmxx 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 xmxx 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} Function rad (theta : real) : real; { This calculates the degrees of an angle } BEGIN rad := theta * pi / 180 END; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} Procedure SetMCGA; { This procedure gets you into 320x200x256 mode. } BEGIN asm mov ax,0013h int 10h end; END; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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(ytopclip)) and (loop1<(ybotclip)) then BEGIN if (x shr 7poly[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 y2maxy then maxy:=y2; if y3>maxy then maxy:=y3; if y4>maxy then maxy:=y4; if minyybotclip 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} Procedure SortPoints; VAR loop1,curpos, temp:integer; BEGIN for loop1:=1 to maxpolys do BEGIN order[loop1]:=loop1; END; curpos := 1; while curpos 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; {ฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤฤ} 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 (' denthor@goth.vironix.co.za'); 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.