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Text File | 1995-11-01 | 14.8 KB | 532 lines

;------------------------------------------------------------------- ; BEZ.ASM -- Logic to quickly compute the points along a bezier curve. ; ; Assembly : TASM BEZ; ; ; Should be linked with Turbo-C V2.0 small memory model. ; ; Author : Bob Zigon ; Date : July 23, 1989 ;------------------------------------------------------------------- ; ; NOTE : This code is assembled with the .287 directive to avoid the ; generation of the unnecessary FWAITS on an AT or '386 class ; machine. If this code is to be executed on an 8087, the ; .287 directive must be commented out. ; .287 dosseg .model small ;------------------------------------------------------------------- ; EQUATES ;------------------------------------------------------------------- MaxControl equ 10 ; Max number of control points MaxDivisions equ 151 ; Max number of divisions for t ;------------------------------------------------------------------- ; VARIABLE DECLARATIONS ;------------------------------------------------------------------- .data extrn _XvpMin:word,_XvpMax:word,_YvpMin:word,_YvpMax:word extrn _XCpMin:qword,_XCpMax:qword,_YCpMin:qword,_YCpMax:qword extrn _XCpScr:word,_YCpScr:word,_XCp:qword,_YCp:qword extrn _XCurve:qword,_YCurve:qword K1 dq ? ; Coefficient for transforming X Q1 dq ? K2 dq ? ; Coefficient for transforming Y Q2 dq ? T dq MaxControl dup (?) BCoef dq MaxControl dup (?) ; Double Prec array of Binomial Coefficients OneMinusT dq MaxControl dup (?) NumTerms dw ? ; Number of terms in the summations .code public _Binomial, _BezierToScreen, _WToVConst public XformWXtoScr, XformWYtoScr ; ------------------------------------------------------------------- ; Binomial -- This routine precomputes the table of binomial coefficients ; for a given number of control points. ; ; The table of N coefficients is computed according to the ; following recursive formula : ; ; N N-1 N-1 ; C = C + C ; i i i-1 ; ; C Prototype : ; ; void Binomial(short int NumControl) ; ; Input : 4[BP] -- Number of control points > 1 ; Output : The BCoef array is filled with the coefficients. ; ------------------------------------------------------------------- NumControl equ 4[bp] _Binomial proc near push bp mov bp,sp push si push di ; Save in case Register Variables = ON mov ax,NumControl mov NumTerms,ax ; ; Begin by initializing the BCoef array to ; ; 1.0 0 0 0 .... 0 ; <--- N-1 ----> ; fld1 fstp qword ptr BCoef ; Store the 1.0 fwait lea di,BCoef+8 mov cx,ax dec cx shl cx,1 shl cx,1 cld xor ax,ax push ds pop es ; Init ES for the STOSW rep stosw ; Now store lots of Zeros mov ax,NumTerms cmp ax,MaxControl ; Number of control points > Number allocated? jle Bi10 xor ax,ax mov NumTerms,ax jmp short Bi80 ; ; Now begin the recursive generation of the BCoef array in situ. ; ; The equivalent C code is : ; ; for (j = 1; j < NumTerms; j++) ; { ; Last = 0.0 ; for (k = 0; k<=j; k++) ; { ; Temp = BCoef[k]+Last ; Last = BCoef[k] ; BCoef[k] = Temp ; } ; } ; Bi10: mov ax,1 ; AX is j Bi20: cmp ax,NumTerms je Bi80 fldz ; Last is on the stack xor bx,bx ; BX is k lea di,BCoef Bi30: cmp bx,ax ja Bi40 fld qword ptr [di] ; Load BCoef[k] fld st ; Duplicate top of stack fadd st,st(2) ; Temp = BCoef[k]+Last fxch ; Temp <-> BCoef[k] fstp st(2) ; Store BCoef[k] to Last and pop fstp qword ptr [di] ; Store Temp out to BCoef[k] add di,8 ; Adv to next BCeof inc bx jmp Bi30 Bi40: fstp st ; Clean up the coprocessor stack fwait inc ax jmp Bi20 Bi80: pop di pop si mov sp,bp ; Pop of the local variables pop bp ; Reset BP ret _Binomial endp ; ------------------------------------------------------------------- ; _BezierToScreen -- Compute the points along the Bezier curve and ; transform them to screen coordinates. ; ; C Prototype : ; ; void BezierToScreen(short int, short int, short int *, short int *) ; ; Input : 4[BP] -- Number of divisions of the parameter ; 6[BP] -- Number of Control Points ; 8[bp] -- Ptr to X Screen Coordinates ; 10[bp] -- Ptr to Y Screen Coordinates ; ; Output : The array of X and Y screen coordinates. ; ------------------------------------------------------------------- TDivisions equ 4[bp] NP equ 6[bp] XV equ 8[bp] YV equ 10[bp] _BezierToScreen proc near local u:qword,du:qword local XCurvePtr:word,YCurvePtr:word local NumCurvePts:word=AutoSize push bp mov bp,sp sub sp,AutoSize ; Allocate some local variables push si push di ; Save in case Register Variables = ON mov ax,NP lea si,_XCp lea di,_XCpScr call XformWXtoScr ; Convert XCp to screen coordinates mov ax,NP lea si,_YCp lea di,_YCpScr call XformWYtoScr ; Convert YCp to screen coordinates ; ; Now, compute the coordinates of the curve. ; mov ax,word ptr TDivisions inc ax mov NumCurvePts,ax ; Number of points on the curve fld1 fidiv word ptr TDivisions fstp du ; du = 1/TDivisions fldz fstp u ; u = 0.0 fwait lea ax,_XCurve mov XCurvePtr,ax lea ax,_YCurve mov YCurvePtr,ax ; ; Since the address of _XCp and _YCp doesn't change, why push them ; on the stack every time you need to call Bezier. Push them ; once here, and clean up on exit. ; lea ax,_YCp push ax lea ax,_XCp push ax BS10: mov ax,NumCurvePts or ax,ax ; EXIT when no more points to compute jz BS20 mov ax, word ptr u+6 push ax mov ax, word ptr u+4 push ax mov ax, word ptr u+2 push ax mov ax, word ptr u push ax call Bezier ; Compute X(t) and Y(t) add sp,2*4 ; Pop the t parameter mov si,YCurvePtr fstp qword ptr [si] ; Save and pop Y(t) add si,8 mov YCurvePtr,si mov si,XCurvePtr fstp qword ptr [si] ; Save and pop X(t) add si,8 mov XCurvePtr,si fld u fadd du fstp u ; Increment u by du fwait dec NumCurvePts ; 1 less point to consider jmp short BS10 BS20: add sp,2*2 ; Pop address of _XCp and _YCp mov ax,TDivisions inc ax lea si,_XCurve mov di,XV call XformWXtoScr ; Convert X curve values to screen coordinates mov ax,TDivisions inc ax lea si,_YCurve mov di,YV call XformWYtoScr ; Convert Y curve values to screen coordinates pop di pop si mov sp,bp ; Pop of the local variables pop bp ; Reset BP ret _BezierToScreen endp ; ------------------------------------------------------------------- ; XformWXtoScr -- transform world X coordinates to X screen coordinates. ; ; Input : AX -- Number of points ; SI -- Ptr to Double Precision World X values ; DI -- Ptr to Word Screen X values ; ; Transform is : ; ; X' = Q1 + K1*X ; ; K1 = (XvpMax-XvpMin)/(XCpMax-XCpMin) ; Q1 = XvpMin - K1*XCpMin ; ; ------------------------------------------------------------------- XformWXtoScr proc near fld Q1 fld K1 XFX10: or ax,ax jz XFX20 ; Exit when AX = 0 fld st ; Dup the top of stack fmul qword ptr [si] ; X*K add si,8 fadd st,st(2) ; X*K+Q fistp word ptr [di] ; Store the Screen coordinate add di,2 dec ax ; 1 less point to consider jmp short XFX10 XFX20: fstp st fstp st ; Clean up the stack ret XformWXtoScr endp ; ------------------------------------------------------------------- ; XformWYtoScr -- transform world Y coordinates to Y screen coordinates. ; ; Input : AX -- Number of points ; SI -- Ptr to Double Precision World Y values ; DI -- Ptr to Word Screen Y values ; ; Transform is : ; ; Y' = Q2 - K2*Y ; ; K2 = (YvpMax-YvpMin)/(YCpMax-YCpMin) ; Q2 = K2*YCpMax + YsMin ; ; Note : Since the screen values for Y start in the upper left hand ; corner instead of the lower left hand corner, this routine ; inverts the Y coordinate. ; ------------------------------------------------------------------- XformWYtoScr proc near fld Q2 fld K2 XFY10: or ax,ax jz XFY20 ; Exit when AX = 0 fld st ; Dup the top of stack fmul qword ptr [si] ; Y*K add si,8 fsubr st,st(2) ; Q-Y*K fistp word ptr [di] add di,2 dec ax ; 1 less point to consider jmp short XFY10 XFY20: fstp st fstp st ; Clean up the stack ret XformWYtoScr endp ; ------------------------------------------------------------------- ; WToVConst -- Calculate the constants used to perform the window ; to viewport transformations in XformWXtoScr and ; XformWYtoScr. ; ; C Prototype : ; ; void WToVConst(void); ; ; ------------------------------------------------------------------- _WToVConst proc near fild _XvpMax fisub _XvpMin fld _XCpMax fsub _XCpMin fdiv fst K1 ; K1 = (XvpMax-XvpMin)/(XCpMax-XCpMin) fmul _XCpMin fisubr _XvpMin fstp Q1 ; Q1 = XvpMin - K1*XCpMin fild _YvpMax fisub _YvpMin fld _YCpMax fsub _YCpMin fdiv fst K2 ; K2 = (YvpMax-YvpMin)/(YCpMax-YCpMin) fmul _YCpMax fiadd _YvpMin fstp Q2 ; Q2 = K2*YcpMax + YvpMin ret _WToVConst endp ; ------------------------------------------------------------------- ; Bezier -- local subroutine used to compute the actual value of ; X(t) and Y(t). ; ; Input : 4[BP] -- Double Precision value of t, the parameter ; : 12[BP] -- Ptr to X Control Points. ; 14[bp] -- Ptr to Y Control Points. ; ; Output : ST(1) -- Double Precision X when the polynomial is ; evaluated at t and the X Control Points. ; ST(0) -- Double Precision Y when the polynomial is ; evaluated at t and the Y Control Points. ; ------------------------------------------------------------------- ParamT equ qword ptr 4[bp] XCp equ 12[bp] YCp equ 14[bp] Bezier proc near push bp mov bp,sp lea di,T mov ax,NumTerms mov bx,ax ; ; Compute the T array. ; ; 1 T T**2 T**3 T**4 T**5 .... ; fld ParamT fld1 B10: fst qword ptr [di] dec ax or ax,ax jz B50 ; EXIT when AX = 0 fmul st,st(1) add di,8 jmp B10 B50: fstp st ; Clean up the stack fstp st lea di,OneMinusT ; ; Compute the OneMinusT array. ; ; 1 1-T (1-T)**2 (1-T)**3 (1-T)**4 (1-T)**5 .... ; fld1 fld ParamT fsub fld1 B60: fst qword ptr [di] dec bx or bx,bx jz B70 ; EXIT when BX = 0 fmul st,st(1) add di,8 jmp B60 B70: lea di,T fst qword ptr [di] ; Copy (1-T)**N to T**0 fstp st fstp st ; ; Now multiply the T array by the OneMinusT array. ; add di,8 mov ax,NumTerms sub ax,2 mov bl,8 mul bl lea si,OneMinusT add si,ax ; SI points to (1-T)**(N-1) mov ax,NumTerms sub ax,2 B80: or ax,ax jz B90 fld qword ptr [si] ; Get element from 1-T fmul qword ptr [di] ; Multiply by T**i fstp qword ptr [di] ; Save product back to T sub si,8 add di,8 dec ax jmp B80 ; ; Now form the term by term product of the T array and the BCoef array. ; B90: lea si,T lea di,BCoef mov ax,NumTerms B100: or ax,ax jz B120 fld qword ptr [si] ; Get a T element fmul qword ptr [di] ; Multiply by a binomial coefficient fstp qword ptr [si] add si,8 add di,8 dec ax jmp B100 ; ; Now that the T array has the product of the T array, the OneMinusT array, ; and the Binomial coefficients, form the dot product of the T array ; with the XCp array to produce X(t). ; B120: lea si,T mov di,XCp mov ax,NumTerms fldz B200: or ax,ax jz B210 fld qword ptr [si] ; Load a term from T fmul qword ptr [di] ; Multiply by an XCp faddp ; Accumulate in stack top add si,8 add di,8 dec ax jmp B200 B210: ; ; Now form the dot product of the T array with the YCp array to ; produce Y(t). ; lea si,T mov di,YCp mov ax,NumTerms fldz B220: or ax,ax jz B230 fld qword ptr [si] ; Load a term from T fmul qword ptr [di] ; Multiply by an YCp faddp ; Accumulate in stack top add si,8 add di,8 dec ax jmp B220 B230: mov sp,bp ; Pop of the local variables pop bp ; Reset BP ret Bezier endp end