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Text File | 1993-09-04 | 28.5 KB | 1,224 lines

;math.inc - general math functions. ; point rotation is 16 bit and uses vmatrix ; camera rotation is 32 bit and uses ematrix ; frotate uses rotation along a plane and uses ematrix with precal147 ; point rotation ; bx = x cx = y bp = z 16 bit! ; clobbers dx,si,ax ; remember , matrix offsets are: ; ; 0 1 2 multiply those by 4 four the doublewords ; 3 4 5 ; 6 7 8 ; align 4 public rotate rotate: movsx ebx,bx ; x movsx ecx,cx ; y movsx ebp,bp ; z mov eax,vmatrix+8 ; solve x = bx(0)+cx(1)+bp(2) imul ebp shr eax,14 movsx edi,ax mov eax,vmatrix+4 imul ecx shr eax,14 movsx eax,ax add edi,eax mov eax,vmatrix+0 imul ebx shr eax,14 movsx eax,ax add edi,eax ; di = new x mov eax,vmatrix+20 ; solve y = bx(3)+cx(4)+bp(5) imul ebp shr eax,14 movsx esi,ax mov eax,vmatrix+16 imul ecx shr eax,14 movsx eax,ax add esi,eax mov eax,vmatrix+12 imul ebx shr eax,14 movsx eax,ax add esi,eax ; si = new y mov eax,vmatrix+32 ; solve z = bx(6)+cx(7)+bp(8) imul ebp shr eax,14 movsx ebp,ax mov eax,vmatrix+28 imul ecx shr eax,14 movsx eax,ax add ebp,eax mov eax,vmatrix+24 imul ebx shr eax,14 movsx eax,ax add ebp,eax ; bp = new z mov ecx,esi mov ebx,edi ret align 4 ; fast ratiox and ratioy are 320x and 464y ; multiplication has been substituted with fast lea ; trashes eax,edx,edi public make3d public make3dx public make3dy make3d: ; bp must always be positive if ratiox eq 320 lea eax,[ebx*4+ebx] ; 320 = %1 0100 0000 shl eax,6 cdq elseif not ratiox eq 320 imul eax,ratiox display "Note: Slow X multiplication used in make3d routine" endif idiv ebp mov ebx,eax make3dy: if ratioy eq 464 lea eax,[ecx*8+ecx] ; 464 = %1 1101 0000 shl ecx,2 lea ecx,[ecx*4+ecx] add eax,ecx shl eax,4 cdq elseif not ratioy eq 464 mov eax,ecx mov ecx,ratioy imul ecx display "Note: Slow Y multiplication used in make3dy routine" endif idiv ebp mov ecx,eax ret make3dx: ; bp must always be positive if ratiox eq 320 lea eax,[edi*4+edi] ; 320 = %1 0100 0000, eax=320*edi shl eax,6 cdq elseif not ratiox eq 320 mov eax,edi mov edi,ratiox imul edi display "Note: Slow X multiplication used in make3dx routine" endif idiv esi mov edi,eax ret ; checks if a side is visible. ; DI, SI, DX = x's ; BP, DS, ES = y's ; return: cx register... ; cx > 0: side visible...else not...routine courtesy of "RAZOR" ; eg: ; call checkfront ; cmp cx,0 ; jng dontdraw align 4 checkfront: cmp di,si jng s cfc mov ax,di mov di,si mov si,dx mov dx,ax mov ax,bp mov bp,dsq mov bx,esq mov dsq,bx mov esq,ax cfc: cmp di,si jng s cfc2 mov ax,di mov di,si mov si,dx mov dx,ax mov ax,bp mov bp,dsq mov bx,esq mov dsq,bx mov esq,ax cfc2: mov ax,dx ; ax = x3 sub ax,di ; ax = x3 - x1 mov bx,dsq ; bx = y2 sub bx,bp ; bx = y2 - y1 movsx eax,ax ; modification to allow large checks movsx ebx,bx imul ebx ; ax = (x3-x1)*(y2-y1) mov ecx,eax ; save it... mov ax,si ; ax = x2 sub ax,di ; ax = x2 - x1 mov bx,esq ; bx = y3 sub bx,bp ; bx = y3 - y1 movsx eax,ax movsx ebx,bx imul ebx ; ax = (x2-x1)*(y3-y1) sub ecx,eax ; cx = (x3-x1)*(y2-y1)-(x2-x1)*(y3-y1) ret ; point rotation for eye - solves all x,y,z parameters ; ebx = x ecx = y ebp = z 32 bit rotation! ; clobbers dx,si,di,ax align 4 public erotate erotate: mov eax,ematrix+8 imul ebp shrd eax,edx,14 mov edi,eax if usez eq yes mov eax,ematrix+4 imul ecx shrd eax,edx,14 add edi,eax endif mov eax,ematrix+0 imul ebx shrd eax,edx,14 add edi,eax ; di = new x mov eax,ematrix+20 imul ebp shrd eax,edx,14 mov esi,eax mov eax,ematrix+16 imul ecx shrd eax,edx,14 add esi,eax mov eax,ematrix+12 imul ebx shrd eax,edx,14 add esi,eax ; si = new y mov eax,ematrix+32 imul ebp shrd eax,edx,14 mov ebp,eax mov eax,ematrix+28 imul ecx shrd eax,edx,14 add ebp,eax mov eax,ematrix+24 imul ebx shrd eax,edx,14 add ebp,eax ; bp = new z mov ecx,esi mov ebx,edi ret ; solve z from ematrix - same as above erotate but only solves z for fast ; test of where object is - result is in esi align 4 public zsolve public ysolve public xsolve zsolve: mov eax,ematrix+32 imul ebp shrd eax,edx,14 mov esi,eax mov eax,ematrix+28 imul ecx shrd eax,edx,14 add esi,eax mov eax,ematrix+24 imul ebx shrd eax,edx,14 add esi,eax ; si = new z ret ; if object z test from above routine is positive, this routine will solve ; the rest of the rotation matrix. this is so we don't waste time solving ; for x and y locations if the object is not within screen parameters. ; saves imuls align 4 xsolve: mov eax,ematrix+8 imul ebp shrd eax,edx,14 mov edi,eax if usez eq yes mov eax,ematrix+4 imul ecx shrd eax,edx,14 add edi,eax endif mov eax,ematrix+0 imul ebx shrd eax,edx,14 add edi,eax ; di = new x ret align 4 ysolve: mov eax,ematrix+16 imul ecx shrd eax,edx,14 mov ecx,eax mov eax,ematrix+12 imul ebx shrd eax,edx,14 add ecx,eax mov eax,ematrix+20 imul ebp shrd eax,edx,14 add ecx,eax ; cx = new y mov ebx,edi ; final test, move into appropriate regs mov ebp,esi ret ; calculate sign into eax, from ax, smashes bx ; after imul by sign, shr eax,14 to compensate for decimal factor! align 4 public cosign public sign cosign: add ax,4000h sign: shr ax,2 cmp ax,2000h jge s q3o4 ; quadrant 3 or 4 cmp ax,1000h jl s q0 ; quad 1 mov bx,1fffh sub bx,ax jmp s halfsign ; quad 2 q0: mov bx,ax jmp s halfsign q3o4: cmp ax,3000h jl s q3 mov bx,3fffh sub bx,ax call halfsign ; quad 4 neg eax ret q3: and ax,0fffh mov bx,ax ; quad 3 call halfsign neg eax ret halfsign: shl bx,1 movsx eax,w sinus[bx] ret ; arctan, cx=rise,ax=run, returns ax as angle of triangle ; smashes cx,ax,dx,si align 4 public arctan arctan: cmp ax,0 jl s qd2or3 cmp cx,0 jge s halftax ; quadrant 1 neg cx ; quadrant 4, ax=-ax call halftan neg ax shl ax,2 ret qd2or3: neg ax cmp cx,0 jge s qd2 neg cx ; quad 3, ax=ax+8192 call halftan add ax,8192 shl ax,2 ret qd2: call halftan neg ax add ax,8192 shl ax,2 ret halftax: call halftan shl ax,2 ret align 4 halftan: movsx eax,ax movsx ecx,cx mov edx,0 ; cx=rise positive ; ax=run positive cmp eax,ecx jl s opptan ; greater than 45 degrees, other side... xchg ecx,eax ; ax<cx shl eax,10 ; *2048 div ecx mov si,ax shl si,2 mov ax,w negtan[si] ; resulting angle (0-512 is 0-45) in ax ret align 4 opptan: shl eax,10 ; *2048 div ecx mov si,ax ; ax remainder shl si,2 mov cx,w negtan[si] mov ax,1000h sub ax,cx ; resulting angle (2048-4096 is 45-90) in ax ret align 4 ; generate object matrix, 12 imul's first ; x y z ; ;x= cz * cy - sx * sy * sz - sz * cy - sx * sy * cz - cx * sy ; ;y= sz * cx cx * cz - sx ; ;z= cz * sy + sx * sz * cy - sy * sz + sx * cy * cz cx * cy ; ;then perform matrix multiply by negative x and z matricies ; ; -x matrix -z matrix ; x y z x y z ; ;x 1 0 0 cz sz 0 ; ;y 0 cx sx -sz cz 0 ; ;z 0 -sx cx 0 0 1 ; ; notice original object matrix takes 12 imuls, camera modify takes 24, can ; you do this faster? (less imuls) public compound compound: push esi mov ax,vxs[esi] neg ax push ax call cosign mov vcosx,eax pop ax call sign mov vsinx,eax mov ebp,eax ; bp = sx neg eax mov [vmatrix+20],eax mov ax,vzs[esi] neg ax push ax call cosign mov vcosz,eax mov edi,eax ; di = cz pop ax call sign mov vsinz,eax mov edx,eax ; dx = sz mov ax,vys[esi] neg ax add ax,eyeay push ax call cosign mov vcosy,eax pop ax call sign mov vsiny,eax ; ax = sy mov ebx,edx ; save sz mov ecx,eax ; save sy imul ebx ; bx = - sy * sz shr eax,14 movsx ebx,ax neg ebx mov [vmatrix+28],ebx mov eax,ecx ; si = cz * sy imul edi shr eax,14 movsx esi,ax mov [vmatrix+24],esi mov eax,vcosy imul edi ; di = cy * cz shr eax,14 movsx edi,ax mov [vmatrix+0],edi mov eax,vsinz mov ecx,vcosy imul ecx ; cx = - sz * cy shr eax,14 movsx ecx,ax neg ecx mov [vmatrix+4],ecx mov eax,ebp imul esi shr eax,14 movsx esi,ax neg esi add [vmatrix+4],esi mov eax,ebp imul edi shr eax,14 movsx edi,ax add [vmatrix+28],edi mov eax,ebp imul ebx shr eax,14 movsx ebx,ax add [vmatrix+0],ebx mov eax,ebp imul ecx shr eax,14 movsx ecx,ax neg ecx add [vmatrix+24],ecx mov esi,vcosx mov eax,vcosy imul esi ; cx * cy shr eax,14 movsx eax,ax mov [vmatrix+32],eax mov eax,vsiny imul esi ;-cx * sy shr eax,14 movsx eax,ax neg eax mov [vmatrix+8],eax mov eax,vsinz imul esi ; cx * sz shr eax,14 movsx eax,ax mov [vmatrix+12],eax mov eax,vcosz imul esi ; cx * cz shr eax,14 movsx eax,ax mov [vmatrix+16],eax mov edi,ecosx ; now perform camera x rotation,12 imuls mov esi,esinx mov ebp,esi neg ebp mov eax,[vmatrix+12] imul edi shr eax,14 movsx ecx,ax mov eax,[vmatrix+24] imul esi shr eax,14 movsx eax,ax add ecx,eax ; ecx = new vmatrix+12 mov eax,[vmatrix+12] imul ebp shr eax,14 movsx ebx,ax mov eax,[vmatrix+24] imul edi shr eax,14 movsx eax,ax add ebx,eax ; ebx = new vmatrix+24 mov [vmatrix+12],ecx mov [vmatrix+24],ebx mov eax,[vmatrix+16] imul edi shr eax,14 movsx ecx,ax mov eax,[vmatrix+28] imul esi shr eax,14 movsx eax,ax add ecx,eax ; ecx = new vmatrix+16 mov eax,[vmatrix+16] imul ebp shr eax,14 movsx ebx,ax mov eax,[vmatrix+28] imul edi shr eax,14 movsx eax,ax add ebx,eax ; ebx = new vmatrix+28 mov [vmatrix+16],ecx mov [vmatrix+28],ebx mov eax,[vmatrix+20] imul edi shr eax,14 movsx ecx,ax mov eax,[vmatrix+32] imul esi shr eax,14 movsx eax,ax add ecx,eax ; ecx = new vmatrix+20 mov eax,[vmatrix+20] imul ebp shr eax,14 movsx ebx,ax mov eax,[vmatrix+32] imul edi shr eax,14 movsx eax,ax add ebx,eax ; ebx = new vmatrix+32 mov [vmatrix+20],ecx mov [vmatrix+32],ebx if usez eq yes mov edi,ecosz ; now perform camera z rotation,12 imuls mov esi,esinz mov ebp,esi neg esi mov eax,[vmatrix+0] imul edi shr eax,14 movsx ecx,ax mov eax,[vmatrix+12] imul esi shr eax,14 movsx eax,ax add ecx,eax mov eax,[vmatrix+0] imul ebp shr eax,14 movsx ebx,ax mov eax,[vmatrix+12] imul edi shr eax,14 movsx eax,ax add ebx,eax mov [vmatrix+0],ecx mov [vmatrix+12],ebx mov eax,[vmatrix+4] imul edi shr eax,14 movsx ecx,ax mov eax,[vmatrix+16] imul esi shr eax,14 movsx eax,ax add ecx,eax mov eax,[vmatrix+4] imul ebp shr eax,14 movsx ebx,ax mov eax,[vmatrix+16] imul edi shr eax,14 movsx eax,ax add ebx,eax mov [vmatrix+4],ecx mov [vmatrix+16],ebx mov eax,[vmatrix+8] imul edi shr eax,14 movsx ecx,ax mov eax,[vmatrix+20] imul esi shr eax,14 movsx eax,ax add ecx,eax mov eax,[vmatrix+8] imul ebp shr eax,14 movsx ebx,ax mov eax,[vmatrix+20] imul edi shr eax,14 movsx eax,ax add ebx,eax mov [vmatrix+8],ecx mov [vmatrix+20],ebx endif pop esi ret ; generate rotation matrix for y,x,z camera rotation ; called only once every frame. completed in 12 multiplys ; matrix is also used for objects with no rotation (always angle 0,0,0) ; ; where is my postcard! see readme.doc for info. ; ; x y z ; ;x= cz * cy + sx * sy * sz -cx * sz - sy * cz + sx * cy * sz ; ;y= sz * cy - sx * sy * cz cx * cz - sy * sz - sz * cy * cz ; ;z= cx * sy sx cx * cy ; ; matrix offsets: ; ; x y z ; ;x 0 4 8 ;y 12 16 20 ;z 24 28 32 align 4 public setsincose setsincose: mov ax,eyeax call cosign mov ecosx,eax ; ecosx and such are used by object rotation mov ax,eyeax ; ematrix is used to find where object is call sign mov esinx,eax mov [ematrix+28],eax mov ebp,eax ; bp = sx if usez eq yes mov ax,eyeaz call cosign mov ecosz,eax mov edi,eax ; di = cz mov ax,eyeaz call sign mov esinz,eax mov edx,eax ; dx = sz endif if usez eq no mov edi,4000h ; di = cos 0 mov ecosz,4000h xor edx,edx ; dx = sin 0 mov esinz,0 endif mov ax,eyeay call cosign mov ecosy,eax mov ax,eyeay call sign mov esiny,eax ; ax = sy mov ebx,edx ; save sz mov ecx,eax ; save sy imul ebx ; bx = sy * sz shr eax,14 movsx ebx,ax neg ebx mov [ematrix+20],ebx neg ebx mov eax,ecx ; si = - (cz * sy) imul edi shr eax,14 movsx esi,ax neg esi mov [ematrix+8],esi mov eax,ecosy imul edi ; di = cy * cz shr eax,14 movsx edi,ax mov [ematrix+0],edi mov eax,esinz mov ecx,ecosy imul ecx ; cx = sz * cy shr eax,14 movsx ecx,ax mov [ematrix+12],ecx mov eax,ebp imul esi shr eax,14 movsx esi,ax add [ematrix+12],esi mov eax,ebp imul edi shr eax,14 movsx edi,ax neg edi add [ematrix+20],edi mov eax,ebp imul ebx shr eax,14 movsx ebx,ax add [ematrix+0],ebx mov eax,ebp imul ecx shr eax,14 movsx ecx,ax add [ematrix+8],ecx mov esi,ecosx mov eax,ecosy imul esi ; cx * cy shr eax,14 movsx eax,ax mov [ematrix+32],eax mov eax,esiny imul esi ; cx * sy shr eax,14 movsx eax,ax mov [ematrix+24],eax mov eax,esinz imul esi ;-cx * sz shr eax,14 movsx eax,ax neg eax mov [ematrix+4],eax mov eax,ecosz imul esi ; cx * cz shr eax,14 movsx eax,ax mov [ematrix+16],eax neg esinx ; reverse angles for object rotation neg esiny ret ;getroot: ; get square root of ax, where ax = 0-65535 ; cmp ax,0fe01h ; since ax cannot be negative anyway! ; jae sqr255 ; routine requires squares tables. ; mov si,offset squares ; mov cx,ax ; inc cx ; cld ;nextroot: ; lodsw ; cmp ax,cx ; jbe nextroot ; jb is exact but jbe is better approximation ; mov ax,si ; sub ax,offset squares+3 ; sar ax,1 ; ret ;sqr255: ; mov ax,255 ; ret ; routine courtesy TRAN ; ; square root ; in: ; eax - number to take root of ; out: ; eax - root ; sqrtbasetbl db 0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225 public sqrt align 4 sqrt: pushad mov ebp,eax bsr ebx,eax jnz short sqrtf0 xor ebx,ebx sqrtf0: shr ebx,3 lea eax,[ebx*8] mov cl,32 sub cl,al rol ebp,cl mov eax,ebp movzx eax,al mov edi,offset sqrtbasetbl mov ecx,10h sqrtl0: scasb je short sqrtl0d jb short sqrtl0d2 loop sqrtl0 inc edi sqrtl0d2: dec edi inc cl sqrtl0d: movzx edx,byte ptr [edi-1] dec cl xor cl,0fh mov edi,ecx mov ecx,ebx jecxz short sqrtdone sub eax,edx sqrtml: shld eax,ebp,8 rol ebp,8 mov ebx,edi shl ebx,5 xor edx,edx mov esi,eax div ebx rol edi,4 add edi,eax add ebx,eax sqrtf2: imul eax,ebx mov edx,eax mov eax,esi sub eax,edx jc short sqrtf1 loop sqrtml sqrtdone: mov [esp+28],edi popad ret sqrtf1: dec ebx dec edi movzx eax,bl and al,1fh jmp sqrtf2 ; solve for z when x = bx (takes a point/object on a y plane and figures ; where it would be if z = 16, y = precal7, only good for square translations) ; uses ematrix as rotation matrix ; cs set if not possible ; formula is inverse of z = bx6+cx7+bp8. where precal7 is y*7 ; (16-bx(6)-precal7)/(8)=z public set_precal7 public set_precal147 public frotate public z16x public z16z public precal1 public precal4 public precal7 align 4 precal1 dd 0 precal4 dd 0 precal7 dd 0 z16x: cmp ematrix+32,0 je abort_attempt mov eax,ematrix+24 imul ebx shrd eax,edx,14 neg eax add eax,16 sub eax,precal7 cdq shld edx,eax,14 mov ebx,ematrix+32 idiv ebx stc ret abort_attempt: clc ret ; solve for x when z = bp (takes a point/object on a y plane and figures ; where it would be if z = 16, y = precal7, only good for square translations) ; uses ematrix as rotation matrix. output solves for z = 16 ; cs set if not possible ; formula is inverse of z = bx6+cx7+bp8. where precal7 is y*7 ; (16-bp(8)-precal7)/(6)=x align 4 z16z: cmp ematrix+24,0 je abort_attempt mov eax,ematrix+32 imul ebp shrd eax,edx,14 neg eax add eax,16 sub eax,precal7 cdq shld edx,eax,14 mov ebx,ematrix+24 idiv ebx stc ret ; set precal7 for plane transformation - plane is ecx and allows above formulas ; to determine where a point/object would be along that plane if z is negative ; good for runway translations or super huge background polygons - not used ; by regular 3d.asm routines ; how to use: lets say you've got a million background objects that are ; on the ground (or all on the same y plane). you call set_precal147 ; with that y plane location and use frotate instead of erotate to ; determine where points rotated along that plane will end up. this ; speeds the routine up by 33% by cutting out 3 imuls. align 4 set_precal147: if usez eq yes mov eax,ecx sub eax,eyey imul ematrix+4 shr eax,14 mov precal1,eax endif mov eax,ecx sub eax,eyey imul ematrix+16 shr eax,14 mov precal4,eax set_precal7: sub ecx,eyey mov eax,ecx imul ematrix+28 shr eax,14 mov precal7,eax ret align 4 ; fast object/point rotation along pre-calculated y plane frotate: mov eax,ematrix+8 imul ebp shrd eax,edx,14 mov edi,eax if usez eq yes add edi,precal1 endif mov eax,ematrix+0 imul ebx shrd eax,edx,14 add edi,eax ; di = new x mov eax,ematrix+20 imul ebp shrd eax,edx,14 mov esi,eax add esi,precal4 mov eax,ematrix+12 imul ebx shrd eax,edx,14 add esi,eax ; si = new y mov eax,ematrix+32 imul ebp shrd eax,edx,14 mov ebp,eax add ebp,precal7 mov eax,ematrix+24 imul ebx shrd eax,edx,14 add ebp,eax ; bp = new z mov ecx,esi mov ebx,edi ret ; fast solve for single matrix variable similar to erotate but uses frotate ; plane matrix with precal147 ; ; remember , matrix offsets are: ; ; 0 1 2 multiply those by 4 four the doublewords ; 3 4 5 ; 6 7 8 ; public fzsolve public fxsolve public fysolve align 4 fzsolve: mov eax,ematrix+32 ; solve z = bx(6)+cx(7)+bp(8) imul ebp shrd eax,edx,14 mov esi,eax add esi,precal7 mov eax,ematrix+24 imul ebx shrd eax,edx,14 add esi,eax ; si = new z ret align 4 fxsolve: mov eax,ematrix+8 ; solve x = bx(0)+cx(1)+bp(2) imul ebp shrd eax,edx,14 mov edi,eax if usez eq yes add edi,precal1 endif mov eax,ematrix+0 imul ebx shrd eax,edx,14 add edi,eax ; di = new x ret align 4 fysolve: mov eax,ematrix+20 ; solve y = bx(3)+cx(4)+bp(5) imul ebp shrd eax,edx,14 mov ecx,eax add ecx,precal4 mov eax,ematrix+12 imul ebx shrd eax,edx,14 add ecx,eax ; cx = new y mov ebx,edi mov ebp,esi ret