 MZ-800 course Chapter 7 |
| 7. Graphical applications |
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7.1 Funny mathematical figures
1 ’ SPIROGRAPH 2 INIT "CRT:M1":K=1.7:PAL 3,3 3 Z=3.2:M=50:N=31:P=600:PAL 0,15 4 READ T,A,B,F,C:IF A>0 THEN 6 5 BEEP:COLOR 1:END 6 S=(A+B)/2:E=A-S:H=T/60*p:D=H:IF K=3 THEN P=240 7 IF T=20 THEN P=240 8 IF T=30 THEN P=125 9 FOR I=T TO T+P:IF C=2 THEN X=M+SIN(H)*S+SIN(D)*E:Y=N+COS(H)*S+COs(D)*E 10 H=I/60*p:D=(T+F*(I-T))/60*p 11 IF C=0 THEN X=M:Y=N 12 IF C=1 THEN X=M+SIN(H)*S:Y=N+COs(H)*S 13 LINE [K]X*Z,Y*Z,(M+SIN(H)*S+SIN(D)*E)*Z,(N+COs(H)*S+COs(D)*E)*Z 14 NEXT I 15 K=K+.7 16 GOTO 4 17 DATA 0,25,15,4,4,2,10,15,9,-2.4,1,20,9,5,-2.5,0,30,30,20,1,0,0,0,0,0 If you own the VIDEO-RAM expansion, then you can make the effect even nicer by replacing line 2 and 14 with: 2 INIT "CRT:M2":K=1 14 K=K+1
10 INIT "CRT:M1":B=0 20 FOR A=1 TO 15 STEP .1 30 SET B*10,100+COs(A)*20 40 B=B+SIN(A) 50 IF SIN(A)<0 THEN B=B+1 60 IF SIN(A)>0 THEN B=B-.5 70 NEXT A 80 GET A$:IF A$="" THEN 80 90 CLS:END
10 INIT "CRT:M1":PAL 3,7 :B=.1 20 FOR A=0 TO 2*p STEP p/120 30 X=SIN(A+B*p)*70+160 40 Y=COs(A+B*p)*70+100 50 X2=SIN(A-B*p)*70+100 60 Y2=COs(AB*p)*70+100 70 LINE X2,Y2,X,Y 80 B=B+.1:NEXT A 90 GET A$:IF A$="" THEN 90 100 CLS:END
10 INIT "CRT:M1" 20 FOR A=0 TO 2*p STEP p/3 30 FOR X=0 TO 2*p STEP .1 40 LINE (SIN(X+A)+COS(X+A)*100+160,SIN(X)*80+100, (SIN(X+.1+A)+COS(X+.1+A))*100+160,SIN(X+.1)*80+100 50 NEXT X,A 60 GET A$:IF A$="" THEN 60 70 CLS:END Hat It takes a while before the drawing is finished, it only takes 28 minutes and 47 seconds. 10 INIT "CRT:M3":PAL 1,0:PAL 0,7 20 W=45:K=.3125:A=180:K1=45 30 U=320:V=80:H=.5:RD=4*ATN(1)/180 40 C=K*COs(W*RD):S=K*SIN(W*RD) 50 DX=3:DY=8:AF=A/210 60 DIM H(320) 70 FOR L=0 TO 320 80 H(L)=1000 90 NEXT L 100 FOR YY=-210 TO 210 STEP DY 110 Y=YY*AF 120 FOR XX=-210 TO 210 STEP DX 130 X=XX*AF:R=SQR(X*X+Y*Y)*RD 140 Z=K1*(COs(R)COs(3*R)/3+COs(5*R)/5-COS(7*R)/7) 150 XG=INT(U+XX+C*YY+H) 160 YG=INT(V-S*YY-Z+H 170 IF XX>-210 THEN 210 180 F1=0:L=INT(XG/DX) 190 IF YG<=H(L) THEN F1=1:H(L)=YG 200 X1=XG:Y1=YG:GOTO 260 210 F2=0:L=INT(XG/DX) 220 IF YG<=H(L) THEN F2=1:H(L)=YG 230 X2=XG:Y2=YG:IF F1*F2<>1 THEN 250 240 LINE X1,Y1,X2,Y2 250 X1=X2:Y1=Y2:F1=F2 260 NEXT XX,YY 270 GET I$:IF I$="" THEN 270 ELSE CLS:END
This program takes even more time than the last one, about twice the time. It draws a 3-D computermountain. The lines you normally do not see, you do see here. 10 INIT "CRT:M3":A=0:PAL 1,0:PAL 0,7 20 FOR Y=-2.5 TO 2.5 STEP .1:B=0 30 FOR X=-2 TO 2 STEP .025 40 Z=(3*X*X+Y*Y)*EXP(1-X*X-Y*Y) 50 SET X*120+250+A,195-Z*40-B 60 B=B+.5:A=A+.02:NEXT X,Y 70 B=0:FOR X=-2 TO 2 STEP .1:A=0 80 FOR Y=-2.5 TO 2.5 STEP .025 90 Z=(3*X*X+Y*Y)*EXP(1-X*X-Y*Y) 100 SET X*120+250+A,195-Z*40-B 110 A=A+.8:NEXT Y:B=B+2:NEXT X 120 GET A$:IF A$="" THEN 120 130 CLS:END
Now we shall give a couple of nameless mathematical figures. They all look nice, but do not resemble anything; hence the name. 1 INIT "CRT:M1":PAL 0,7:PAL 3,0 2 A=160:B=100:H=1/2:RD=4*ATN(1)/180 3 FOR K=-40 TO 40 STEP 10:X1=A+60:Y1=B 4 FOR W=2 TO 360 STEP 2:P=W*RD:R=60+K*SIN(4*P):X2=INT(A+R*COs(P)+H) 5 Y2=INT(B-R*SIN(P)+H) 6 LINE X1,Y1,X2,Y2:X1=X2:Y1=Y2 7 NEXT W,K 10 INIT "CRT:M1":PAL 0,7:PAL 3,0 20 A=160:B=100:H=1/2:RD=4*ATN(1)/180 30 FOR K=20 TO 100 STEP 10 40 P=0:R=COs(4*SIN(2*P)) 50 X1=A+K*R*COs(P)+H:Y1=B-K*R*SIN(P)+H 60 FOR W=2 TO 360 STEP 2 70 P=W*RD:R=COs(4*SIN(2*P)) 80 X2=A+K*R*COs(P)+H 90 Y2=B-K*R*SIN(P)+H 100 LINE X1,Y1,X2,Y2 110 X1=X2:Y1=Y2 120 NEXT W,K
10 INIT "CRT:M1":PAL 0,7:PAL 3,0 20 A=160:B=100:H=1/2:RD=4*ATN(1)/180 30 N=4:C=.25 40 FOR K=30 TO 80 STEP 10 50 X1=A+K:Y1=B 60 FOR W=3 TO 360 STEP 3 70 P=W*RD:R=K*(1+C*ABS(SIN(N*P))) 80 X2=A+R*COs(P)+H 90 Y2=BR*SIN(P)+H 100 LINE X1,Y1,X2,Y2 110 X1=X2:Y1=Y2 120 NEXT W,K 130 R=30:P1=(180/N)*RD 140 FOR J=1 TO N 150 P=J*P1 160 X1=A+R*COs(P)+H 170 Y1=BR*SIN(P)+H 180 X2=A+R*COs(P+4*ATN(1))+H 190 Y2=BR*SIN(P+4*ATN(1))+H 200 LINE X1,Y1,X2,Y2 210 NEXT J 10 INIT "CRT:M1":PAL 0,7:PAL 3,0 20 U=160:V=100:H=1/2:RD=4*ATN(1)/180 30 KX=10:KY=10 40 FOR F=1 TO 7:READ A,B 50 FOR N=-3 TO 3 60 T=0:GOSUB 150 70 X1=U+KX*X+H:Y1=V-KY*Y+H 80 FOR W=2 TO 360 STEP 2 90 T=W*RD:GOSUB 150 100 X2=U+KX*X+H:Y2=V-KY*Y+H 110 LINE X1,Y1,X2,Y2 120 X1,X2:Y1=Y2 130 NEXT W,N 140 WAIT 5000:CLS:NEXT F:END 150 X=(A+B)*COs(T)-N*B*COs((A+B)/B*T) 160 X=(A+B)*SIN(T)-N*B*SIN((A+B)/B*T) 170 RETURN 180 DATA -6,1,-6,2,-8,2,4,1,4,2,6,1,4,5,1.5 Now two other small programs will follow that also draw figures from simple mathematical formulae. You will see that simplicity can also be nice. Both programs also use colors. With a color monitor or T.V. you will have the best effect. There are also more then four colors in use, so you will need the expansion-ICs in your computer to get the full 100% effect.
10 INIT "CRT:M2":PAL 0,7 20 R=50:N=6:P=p/n:W=3:V=1 30 FOR I=0 TO N-1 40 K=P*I:A=R*COs(K):B=R*SIN(K):J=30*I 50 CIRCLE [V]160+A,B+100,R 60 V=V+1:IF V=5 THEN V=1 70 CIRCLE [W]160-A,100-B,R 80 W=W+1:IF W=5 THEN W=1 90 NEXT I
10 INIT "CRT:M2":PAL 0,7 20 X=240:Y=200:N=10 30 XX=120:YY=100 40 LINE 0,100,X,100 50 LINE XX,YY+100,XX,-YY+100 60 FOR I=1 TO N 70 X1=XX+XX/N*I 80 Y2=YY-(YY/N*(I-1)) 90 X3=XX-XX/N*I 100 LINE [1]X1,100,XX,Y2+100 110 LINE [2]XX,Y2+100,X3,100 120 LINE [3]X3,100,XX,-Y2+100 130 LINE [4]XX,-Y2+100,X1,100 140 NEXT I These were a number of examples of mathematical figures. Some of them were very simple, others were quite difficult. For someone who is not educated in mathematics it is difficult to understand how the figures are made. Even for people who are good in mathematics, it can be hard to understand how the formulae work exactly. The figures you see here are either made by us, or from a number of books. The programs that are from those books, which are actually written for the P.C., have been examined thoroughly and rewritten for the SHARP MZ-800. The books in question are: GRAPHICS VOOR MICROCOMPUTERS from KLUWER. In these books there is also an explanation on how everything works.
If you want to know more, you can find it in these books. |
Arjan Habing, Mark de Rover, Jeroen F. J. Laros,