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À4:�¦11000:€X³1¥2:Æ"C0BM"«ÿˆ(111«X)«",93;UER3FD2GLRFD2GL3HU":Æ"BM123,95R6UL6":Æ"BM"«ÿˆ(136¬X)«",91;D8R3E2U4H2L3":‹&©€X³1¥1000:‹'—ž:‡"    A  3-D  GRAPHICS  PRIMER.":‡"==>  NO SPECIAL MATH NEEDED  <==":‡"   THIS PROGRAM WILL PRESENT    AND EXPLAIN HOW TO USE A VERY   SIMPLE 3-D GRAPHICS SUBROUTINE. WE WILL ALSO, WITH EXAMPLES,    SHOW YOU HOW TO USE THIS SIMPLE"(]‡"ROUTINE TO DRAW 3-D FIGURES AND SURFACES.":‡"DEF'N === 3-D GRAPHICS SUB-         ROUTINE. - ONE THAT CONVERTS    3-D COORDINATES INTO 2-D        GRAPHABLE FORM.":‡"PRESS <SPACE> TO CONTINUE";(sA$³ÿ’:…A$´²" "§30(³ ž:‡@256,"FIRST, THE SUBROUTINE ...":€X³1¥1000:‹:ž:�¦35:�¥50)p#‡"10000 IF (Z<=0) OR (VD=0) THEN        EF=2 : RETURN":‡"10001 YL=191 : YC=95 : XL=255 :       XC=127 : REM FOR PMODE 4  10002 Y1 = YC - Y / ( VD * Z ) :      X1 = X / ( VD * Z ) + XC")Þ(‡"10003 IF (Y1>YL) OR (Y1<0) OR            (X1>XL) OR (X1<0) THEN       EF=1 : ELSE EF=0":‡"10004 RETURN")ä-�*”2‡"EF => ERROR FLAG":‡"X,Y,Z => INPUT 3-D CO-ORD.":‡"X1,Y1 => RESULTANT 2-D CO-ORD.  XL,XC,YL,YC => LIMIT AND CENTER     OF GRAPHICS SCREEN.":‡"PRESS <SPACE> TO CONTINUE.";*ª7A$³ÿ’:…A$´²" "§55+…<ž:‡"WE'LL SHOW YOU THE SUBROUTINE   AGAIN LATER, BUT FIRST, SOME    EXPLANATION.":‡"THE BASIC FORMULA STATES THAT   THE RESULTANT X OR Y COORDINATE IS PROPORTIONAL TO THE X OR Y   COORDINATE IN 3-D DIVIDED BY THE";,wA‡"Z COORDINATE, OR DISTANCE AWAY. THIS CAN BE SHOWN BY COMMON     SENSE, WHEN WE CONSIDER PERSPEC-TIVE, WHERE OBJECTS THAT ARE    FARTHER AWAY APPEAR SMALLER.    THIS ALSO PLACES THE LIMITATION THAT THE Z VALUE MUST BE GREATERTHAN ZERO.",žF‡"PRESS <SPACE> TO CONTINUE.";:�¦5-uPž:‡"THE OTHER SIGNIFICANT VARIABLE  IN THE ROUTINE IS VD, WHICH REP-RESENTS THE VIEWING DISTANCE.":‡:‡"THIS IS ESSENTIALLY THE DISTANCEFROM YOUR EYE TO THE ORIGIN     (0,0,0).":‡:‡"VALUES OF THIS VARIABLE WILL".U‡"TYPICALLY RANGE FROM  .1 TO .001NOTE THAT SHRINKING THIS DIST-  ANCE WILL RESULT IN THE PICTURE BECOMING LARGER.":‡:‡"PRESS <SPACE> TO CONTINUE.";:�¦5:ž.ðZ‡"THE VARIABLE EF, WHICH STANDS   FOR ERROR FLAG, HOLDS ONE OF    THREE VALUES ON EXIT.":‡"0 => NO ERROR, X1 AND Y1 ARE         VALID.":‡"1 => OVERFLOW. X1 AND Y1 ARE         VALID, BUT BEYOND SCREEN        LIMITS."/«_‡"2 => INPUT ERROR. EITHER Z IS        LESS THAN OR EQUAL TO ZERO,     OR THE VIEWING DISTANCE IS      ZERO. X1 AND Y1 ARE             INVALID.":‡:‡"PRESS <SPACE> TO CONTINUE.":�¦5:ž0�d‡"THE LAST FOUR VARIABLES WHICH   NEED EXPLAINING ARE XL, YL, XC, AND YC.":‡:‡"XL AND YL ARE THE LIMITS OF THE GRAPHICS SCREEN, AND ARE USED   TO DETERMINE IF X1 AND Y1 ARE   VALID. FOR EXAMPLE, FOR PMODE 4,";0Ài‡"XL=255 AND YL=191.":‡:‡"XC AND YC ARE SIMPLY THE COORD-"1@n‡"INATES OF THE CENTER OF THE     SCREEN, AGAIN, FOR THAT PARTIC- ULAR GRAPHICS MODE.":‡:‡"PRESS <SPACE> TO CONTINUE.";:�¦52sž:‡@128,"WITH THIS EXPLANATION, WE'LL    GIVE YOU ANOTHER LOOK AT OUR    ROUTINE, WITH THE HOPE THAT     ALL OF YOU CAN UNDERSTAND IT,   AND BE ABLE TO USE THESE IDEAS.":‡:‡"PRESS <SPACE> TO CONTINUE.":�¦5:ž:�¦35:‡2Cx‡"PRESS <SPACE> TO CONTINUE.":�¦5:ž3}‡"USES OF THE HANDY-DANDY 3-D         SUPER SUB.":‡"AN OBVIOUS USE, AND VERY SIMPLE,IS TO DRAW 3-D SHAPES.   THE    SIMPLEST, AND RECOMMENDED IN    MOST CASES,IS TO USE DATA STATE-MENTS  TO  HOLD A LIST OF POINTS";4‚‡"IN 3-D COORDINATE FORM, AND USE THE SUBROUTINE TO CONVERT THEM. ADMITTEDLY, IN MANY CASES,  IT  WOULD BE EASIER TO CONVERT  THE POINTS, AND THEN PUT THEM INTO  DATA STATEMENTS, BUT THERE  ARE USES.  THIS IS HOW THE OPENING"4K‡‡"OF THIS PROGRAM WAS DRAWN.":‡"PRESS <SPACE> TO CONTINUE.";:�¦5:ž4|Œ‡"ANOTHER USE IS TO DRAW COMPLEX  SURFACES."5U‘‡:‡" A TYPICAL ROUTINE FOR PLOTTING A SURFACE MIGHT LOOK LIKE THE   FOLLOWING ...":‡:‡"100 VD=.002":‡"110 FOR X = -1 TO 1 STEP .2":‡"120 FOR ZZ = -1 TO 1 STEP .2":‡"130 Y = X^2 - ZZ^2 : Z=ZZ+10    140 GOSUB10000"5±–‡"150 IF EF=0 THEN PSET(X1,Y1,1)  160 NEXT ZZ,X":‡:‡"PRESS <SPACE> TO CONTINUE.";:�¦5:ž6›‡@128,"IF YOU WISH TO SEE THIS ONE,    PRESS <G> , OTHERWISE, PRESS    <SPACE>."61 A$³ÿ’:…A$³"G"§�¥170::„…A$³" "§190:„1606üªž:‡@128,"PRESS <SPACE> TO EXIT THE DEMO.":‡"PRESS <SPACE> TO SEE DEMO.":�¦5:�¦20000:�¦5:ž:‡"NOT VERY MUCH, HUH?":‡:‡"BUT WE'LL HAVE A LITTLE BETTER  IN A MINUTE.":‡:‡"PRESS <SPACE> TO CONTINUE.":�¦57㾞:‡"NEXT, WE'LL DISCUSS AN EASY WAY OF ADDING LINES,SO THAT OUR SUR-FACES ARE EASIER TO SEE.":‡:‡"THE WAY WE DID IT WAS TO FIGURE THE POINTS AT EACH END OF EACH  LINE SEGMENT, AND IN THAT WAY TODRAW EACH SEGMENT OF THE 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WAY MIGHT BE TO KEEP  AN ARRAY OF X,Y COORDINATES AS  EACH ROW IS PLOTTED,  THEN  TO  PLOT ACROSS THE ROWS FROM  THE  ARRAY.":‡:‡"PRESS <SPACE> TO CONTINUE.";:�¦5:ž8üȇ@128,"TO SEE OUR PLOT (WITH LINES),   PRESS <G>, OTHERWISE,   PRESS   <SPACE>."9$ÍA$³ÿ’:…A$³"G"§210:„…A$³" "§225:„2059ÐÒž:‡@128,"PRESS <SPACE> TO EXIT THE DEMO.":‡"PRESS <SPACE> TO SEE THE DEMO.":�¦5:�¦25000:�¦5:ž:‡@128,"QUITE A BIT BETTER . . .":‡@320,"PRESS <SPACE> TO CONTINUE.":�¦5:ž:¹áž:‡"THE ONLY THING OUR GRAPH NEEDS  NOW IS A HIDDEN LINE ROUTINE.   A HIDDEN LINE ROUTINE IS, HOW-  EVER, EASIER SAID THAN DONE,    ALTHOUGH THERE ARE WAYS OF FAK- ING A HIDDEN LINE ROUTINE.":‡:‡"  ONE SUCH WAY IS TO GRAPH ONLY";wæ‡"THOSE PARTS OF THE GRAPH WHICH  ARE ASCENDING ( GOING FROM FRONTTO BACK ).  THAT'S THE WAY WE'VEUSED IN THE LAST OF OUR GRAPHICSDEMONSTRATIONS.":‡:‡"PRESS <SPACE> TO CONTINUE.";:�¦5:ž<7ë‡@64,"PRESS <G> TO SEE THE DEMO.      PRESS <R> TO REVIEW             PRESS <ENTER> TO END THE PROGRAM":‡@224,"FOR THOSE WHO WISH TO LIST THEM,OUR ROUTINES ARE LOCATED AS     FOLLOWS ..."<üí‡"11000-11030 => OPENING PICTURE  15000  => DATA FOR ABOVE.       20000-20170 => SURFACE WITH DOTS25000-25500 => SURFACE W/ LINES 30000-30500 => SURFACE WITHE                   HIDDEN LINES.";=8ðA$³ÿ’:…A$³"G"§�¥250::„…A$³"R"§20::„…A$³ÿ‹(13)§ž:Š::„240=›úž:‡@128,"AFTER THE DEMO., PRESS <SPACE>.":‡:‡:‡"PRESS <SPACE> FOR DEMO.":�¦5:�¦30000:�¦5:�¥235=µ'…(Z´³0)±(VD³0)§EF³2:�=ã'YL³191:YC³95:XL³255:XC³127:‚  FOR PMODE 4>'Y1³YC¬Y®(VD­Z):X1³X®(VD­Z)«XC>4'…(Y1²YL)±(Y1´0)±(X1²XL)±(X1´0)§EF³1::„EF³0>:'�>L*ø:ƒTETRAHEDRON>U*ùVD³5>p*ýÈ 4,1:¼1:¿ 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