Coding - In this article I will try to tell you how to calculate three-dimensional space as quickly as possible. Printing dots. Line construction. Multiplication/division. SIN(x), COS(x). Rotate x, y, z axes.

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|               Coding...               | 
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                       Emloyer/Alliance   
                       2:5O8O/141.16      
                       Dmitry Krylov      
                       subj: то Employer  
                                          
             Вступление                   
             ----------                   
 На сегодня создано достаточно программ,  
а в частности демух, с использованием     
3D renderinga в реальном времени. В этой  
статье я попытаюсь рассказать, о том      
как максимально (!?) быстро обсчитать     
трехмерное пространство. Я буду считать,  
что вы знаете как представляется в прос-  
транстве 3D обьекты, линии, грани, точки  
и т.д. Расскажу лишь о том какquickly     
perform these calculations with examples on as-  
assembler.                                 
                                          
 First, a few procedures on Asme:   
 Print dots   
            ------------    
 To construct a point, you need a procedure    
converting coordinates to screen address  
The INFORCOM procedure is too slow.    
My procedure requires 1kb to work   
memory. I will also note that the procedure          
INFORCOM eats xxx cycles, and mine      
76-8O cycles. Here are 2 (two)   
procedures (76.8O cycles).                 
For a procedure of 8O clock cycles in register B, C  
X,Y coordinates must be specified, and      
for 76 bars in C,L.                      
 The installer for both procedures is the same  
therefore, he comes first, and then, PLOT.  
                                          
: Install                                 
INST                                      
        LD HL,#62OO: Table address   
        LD В,4                       
LO1I PUSH Sun                        
        XOR A                         
        LD V,8LO2I PUSH Sun                        
        LD V,8                       
LOЗI LD (HL),A                    
        INC HL                        
        DJNZ LOЗI                      
        ADD A,#2O                     
        POP sun                        
        DJNZ LO2I                      
 POP BC                        
        DJNZ LO1I                      
        LD A,#4O : Segment address  
        LD B,3: for printing       
LOCHI PUSH Sun                        
        LD V,8                       
LOSI PUSH VS,AF                     
        LD V,8                       
LObI LD (HL),A                    
        INC HL                        
        INC A                         
        DJNZ LObI                      
        POP AF,SUN                     
        DJNZ LOSI                      
        ADD A,8                       
        POP sun                        
        DJNZ LOCHI                      
        LD D,H                       
        LD E,L                       
        INC DE                        
 LD BC,63                     
        XOR A                         
        LD(HL),ALDIR                              
        INC     HL                        
        LD      В,#2O                     
LO7I    PUSH    ВС                        
        LD      В,8                       
LO8I    LD      (HL),A                    
        INC     HL                        
        DJNZ    LO8I                      
        INC     A                         
        POP     ВС                        
        DJNZ    LO7I                      
        LD      A,#8O                     
        LD      В,#2O                     
LO9I    PUSH    ВС,AF                     
        LD      В,8                       
LOAI    LD      (HL),A                    
        SRL     A                         
        INC     HL                        
        DJNZ    LOAI                      
        POP     AF,ВС                     
        DJNZ    LO9I                      
        RET                               
                                          
: FAST PLOT 8O takts                      
        LD      ВС,#OOOO                  
        CALL    PLOT                      
        RET                               
PLOT    LD      H,#62:  7                 
        LD      L,В:    4                 
        LD      A,(HL): 7                 
        INC     H:      4                 
        LD      D,(HL): 7INC     H:      4                 
        LD      L,C:    4                 
        ADD     A,(HL): 7                 
        LD      E,A:    4                 
        INC     H:      4                 
        LD      A,(DE): 7                 
        OR      (HL):   7                 
        LD      (DE),A: 7                 
        RET                               
                                          
: FAST PLOT 76 takts                      
        LD      C,O:          OR      (HL):   7                 
        LD      (DE),A: 7                 
        RET                               
                                          
           Построение линии ----------------               
 bc x1y1                                  
 of x2y2                                  
                                          
                                          
LINE LD A,H                       
        SUB D                         
        JR NC,LINE1                  
        EX DE,HL                     
        NEG                               
LINE1 LD H,A                       
        LD A,L                       
        SUB E                         
        JR NC,LINER                  
        NEG                               
 СР H                         
        LD L,A                       
        JR C,LINELU                  
        PUSH HL                        
        CALL GET_ADR                   
        POP OF                        
        LD В,E                       
        LD A,E                       
        INC D                         
        INC В                         
        EX AF,AF                     
LINELD1 LD A,(HL)                    
        OR C                         
        LD (HL),A                    
        RLC C                         
        JP NC,LINELD2                
        DEC L                         
LINELD2EX      AF,AF                     
        SUB     D                         
        JR      NC,LINELDЧ                
        ADD     A,E                       
        EX      AF,AF                     
        LD      A,H                       
        DEC     H                         
        AND     7                         
        JP      NZ,LINELDЗ                
        LD      A,L                       
        SUB     #2O                       
        LD      L,A                       
        JR      C,LINELDЗ                 
        LD      A,H                       
        ADD     A,8                       
        LD      H,A                       
LINELDЗ DJNZ    LINELD1                   
        RET                               
LINELDЧ EX      AF,AF                     
        DJNZ    LINELD1                   
        RET                               
LINELU  PUSH    HL                        
        CALL    GET_ADR                   
        POP     DE                        
        LD      В,D                       
        LD      A,D                       
        INC     E                         
        INC     В                         
        EX      AF,AF                     
LINELU1 LD      A,(HL)                    
        OR      C                         
        LD      (HL),ALD A,H                       
        DEC H                         
        AND 7                         
        JP NZ,LINELU2                
        LD A,L                       
        SUB #2O                       
        LD L,A                       
        JR C,LINELU2                 
        LD A,H                       
        ADD A,8                       
        LD H,A                       
LINELU2 EX AF,AF                     
        SUB E                         
        JR NC,LINELUZ                
        ADD A,D                       
        RLC C                         
        JP NC,LINELUZ                
        DEC L                         
LINELUZ EX AF,AF                     
        DJNZ LINELU1                   
        RET                               
LINER SR H                         
        LD L,A                       
        JR C,LINERU                  
        PUSH HL                        
        CALL GET_ADR                   
        POP DE                        
        LD B,E                       
        LD A,E                       
        INC D                         
        INC B                         
        EX      AF,AF                     
LINERD1 LD      A,(HL)                    
        OR      C                         
        LD      (HL),A                    
        RRC     C                         
        JP      NC,LINERD2                
        INC     L                         
LINERD2 EX      AF,AF                     
        SUB     D                         
        JR      NC,LINERDЧ                
        ADD     A,E                       
        EX      AF,AF                     
        LD      A,H                       
        DEC     H                         
        AND     7                         
        JP      NZ,LINERDЗ                
        LD      A,L                       
        SUB     #2O                       
        LD      L,A                       
        JR      C,LINERDЗ                 
        LD      A,H                       
        ADD     A,8                       
        LD      H,A                       
LINERDЗ DJNZ    LINERD1                   
        RET                               
LINERDЧ EX      AF,AF                     
        DJNZ    LINERD1                   
        RET                               
LINERU  PUSH    HL                        
        CALL    GET_ADR                   
        POP     DE                        
        LD      В,DLD      A,D                       
        INC     E                         
        INC     В                         
        EX      AF,AF                     
LINERU1 LD      A,(HL)                    
        OR      C                         
        LD      (HL),A                    
        LD      A,H                       
        DEC     H                         
        AND     7                         
        JP      NZ,LINERU2                
        LD      A,L                       
        SUB     #2O                       
        LD      L,A                       
        JR      C,LINERU2                 
        LD      A,H                       
        ADD     A,8                       
        LD      H,A                       
LINERU2 EX      AF,AF                     
        SUB     E                         
        JR      NC,LINERUЗ                
        ADD     A,D                       
        RRC     C                         
        JP      NC,LINERUЗ                
        INC     L                         
LINERUЗ EX      AF,AF                     
        DJNZ    LINERU1                   
        RET                               
GET_ADR LD      A,#BF                     
        SUB     D                         
        LD      D,ASRL     A                         
        SCF                               
        RRA                               
        SRL     A                         
        XOR     D                         
        AND     #F8                       
        XOR     D                         
        LD      H,A                       
        LD      A,E                       
        RLCA                              
        RLCA                              
        RLCA                              
        XOR     D                         
        AND     #C7                       
        XOR     D                         
        RLCA                              
        RLCA                              
        LD      L,A                       
        LD      A,E                       
        AND     7                         
        INC     A                         
        LD      C,В                       
        LD      В,A                       
        LD      A,1                       
GETADR1 RRCA                              
        DJNZ    GETADR1                   
        LD      В,C                       
        LD      C,A                       
        RET Multiplication/division             
           -----------------              
 You will have to multiply at every step because   
3D graphics are, as you know, solid    
mathematics.                                
In registers A,B there are multipliers                 
You will receive the result in the A/HL register        
                                          
MUL_AB PUSH DE,HL                     
        LD C,A                       
        LD A,127                     
        SR C                         
        JR NC,N2                     
        SR B                         
        JR NC,N21                    
        PUSH Sun                        
        LD A,B                       
        N.E.G.                               
        LD B,A                       
        LD A,C                       
        N.E.G.                               
        CALL MUL                       
        POP sun                        
        ADD HL,HL                     
        LD A,H                       
 JP OK                        
N21 LD A,C                       
        N.E.G.                               
        CALL MUL                       
        ADD HL,HLXOR     A                         
        SUB     L                         
        LD      L,A                       
        LD      A,O                       
        SBC     A,H                       
        LD      H,A                       
        JP      OK                        
N2      СР      В                         
        JR      NC,N22                    
        PUSH    ВС                        
        LD      A,В                       
        NEG                               
        LD      В,A                       
        LD      A,C                       
        CALL    MUL                       
        POP     ВС                        
        ADD     HL,HL                     
        XOR     A                         
        SUB     L                         
        LD      L,A                       
        LD      A,O                       
        SBC     A,H                       
        LD      H,A                       
        JP      OK                        
N22     LD      A,C                       
        CALL    MUL                       
        ADD     HL,HL                     
        LD      A,H                       
OK      POP     HL,DE                     
        RET                               
MUL     LD      D,O                       
        LD      E,ВLD      HL,O                      
        RLA                               
        JP      NC,М1                     
        ADD     HL,DE                     
М1      ADD     HL,HL                     
        RLA                               
        JP      NC,М2                     
        ADD     HL,DE                     
М2      ADD     HL,HL                     
        RLA                               
        JP      NC,М3                     
        ADD     HL,DE                     
М3      ADD     HL,HL                     
        RLA                               
        JP      NC,М4                     
        ADD     HL,DE                     
М4      ADD     HL,HL                     
        RLA                               
        JP      NC,М5                     
        ADD     HL,DE                     
М5      ADD     HL,HL                     
        RLA                               
        JP      NC,М6                     
        ADD     HL,DE                     
М6      ADD     HL,HL                     
        RLA                               
        JP      NC,М7                     
        ADD     HL,DE                     
М7      ADD     HL,HL                     
        RLA                               
        RET     NC                        
        ADDHL,DE                     
        RET                               
                                          
 This program works quite quickly  
because it was written not by anyone but by himself       
Sergey Kovinov, but it’s still possible       
faster. And in a faster way I will   
I'll tell you later.                              
Speaking of division:                         
According to the author of this procedure, she   
can only multiply, but I noticed    
one feature. If you multiply the coordinates   
natu on numbers from 128 to 255, then they       
will be divisible by numbers from 1 to 127        
 Using this, for example, you can scale  
capture a 3D object.                       
                                          
         SIN (x), COS (x)               
           ----------------               
 Because SPECCY has no math     
coprocessor to implement these functions      
It is possible only programmatically, i.e. on Asm'e      
And this can be implemented in three ways.  
 1. expansion of functions in Fourier series.       
 2. use the built-in calculator.  
 3. calculate the table in advance.            
The first method will lead to a fatal accident.     
capabilities comparable to BASIC.            
Method 2 will not improve performance     
because the built-in calculator is also laid out  
puts these functions into a Fourier series.By the way, BASIC actively uses this     
the most calculator.                        
The last method is preferable because     
You won’t have to count SIN and COS.     
Values ​​are already ready for all angles.          
Because SIN and COS values are in the range  
not from O to 1 they will have to be multiplied by     
the amplitude you need.                
 I give a program for calculating the table using  
cabbage soup built-in calculator. She is enough    
call exactly 1 time at the beginning of the program, and  
then use the resulting table.   
 The program was pulled from 3D_LAME4k (personally   
I always uploaded a ready-made table, but 4k..)  
                                          
        LD HL,#61OO: Address where  
DESIN1 PUSH HL: builds a table   
        LD A,255 : faces           
        CALL 1156O                     
        LD A,128                     
        CALL 1156O                     
 POP HL                        
        PUSH HL                        
        LD A,L                       
        CALL 1156O                     
        RST #28: Calling the calculator   
        DEFB #A3,4,1,5,#1F,4,#38       
        CALL 898O:^^^^^^^^^^^^^^       
        POP HL: Calculator codes.  
        LD(HL),A                    
        INC L                         
        J.P.P,DESIN1                  
        LD D,H                       
        LD E,L                       
SNS DEC HL                        
        LD A,(HL)                    
        LD(DE),A                    
        INC E                         
        JR NZ,SNS                    
        RET                               
Attention!                                 
a table will be built with 256 corners, not 36O  
To improve performance and convenience  
256 is specially taken, not 36O.      
                                          
The calculation itself is carried out like this:                   
                                          
LD H,#61: Let's say there is a table here         
LD L,N : N-Angle                         
LD A,(HL): Take the value of the sine          
                                          
 For cosine, a table is not needed because this is   
shifted sine by 96 degrees. Just    
add #6O to the angle and everything will be OK.       
                                          
                                          
         Rotate x,y,z axes               
         ------------------               
                                          
Let me remind you of Euler's formulas for those who have forgotten  
                                          
around the x-axis:x'=x                                     
y'= y*cos(fi) - z*sin(fi)                 
z'= y*sin(fi) + z*cos(fi)                 
                                          
around the y axis:                             
x'= x*cos(fi) + z*sin(fi)                 
y'=y                                     
z'=-x*sin(fi) + z*cos(fi)                 
                                          
around the z axis:                             
x'= x*cos(fi) - y*sin(fi)                 
y'= x*sin(fi) + y*cos(fi)                 
z'=z                                     
                                          
fi - angle                                 
                                          
If you're not going to shortchange        
perspective projection, then the calculation of z' can-  
Feel free to discard it.                   
 Well, now everything seems to be... :)