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MA8 =( OPTIONB&6-F:B2y,&"@A&a}L AV--7,50, MAISON en Šśll10,6,0,-10,6,0,-10,-6,0,10,-6,0,10,6,4,-10,6,4,-10&b},-6,4,10,-6,4,10,0,7,-10,0,7,8,6,1.5,4,6,1.5,4,6,3.5qq8,6,3.5,1,6,0.5,-1,6,0.5,-1,6,3.5,1,6,3.5,-4,6,1.5,-8,6,1.5,-8,6,3.&c}5,-4,6,3.5,10,-4,1.5,10,-2,1.5,10,-2,3.5ll10,-4,3.5,10,-1,0.5,10,1,0.5,10,1,3.5,10,-1,3.5,10,2,1.5,10,4,1.5,10,4,3.5,10,2&d},3.5,-3,-6,2.5,3,-6,2.5rr3,-6,3.5,-3,-6,3.5,-10,3,2,-10,3,3.5,-10,-3,3.5,-10,-3,2,-4,-0.5,6.75,-5,-0.5,6.75,-5,-1.5,6.25,&e}-4,-1.5,6.25//-10,3,0.5,-10,-3,0.5,-10,-3,1.0,-10,3,1.0 1,0,0,5,1,1,4,3,2,1TT2,0,3,6,0,4,1,5,9,8,4,5,1,23,24,25,&f}26,23,5,1,27,28,29,30,27,5,1,31,32,33,34,31 RR3,0,3,5,0,1,2,6,5,1,5,1,11,12,13,14,11,5,1,15,16,17,18,15,5,1,19,20,21,22,19&g}*BB4,0,2,6,1,2,3,7,10,6,2,5,0,39,40,41,42,39,5,1,47,48,49,50,474,,5,0,1,5,0,3,4,8,7,3,5,1,35,36,37,38,35>6,0,0,5,1&h},5,6,10,9,5H--7,0,1,5,1,7,8,9,10,7,5,0,43,44,45,46,43R!!4.1,+00,+50,+00,-10,+10,+00\""3.5,+10,+150,+25,-10,+10,+30f&i}""3.1,+20,+250,+50,-10,+10,+60p""2.5,+30,+350,+75,-10,+10,+90z$$2.1,+40,+450,+100,-10,+10,+120$$1.5,+50,+550,+300&j},-10,+10,+150$$1.1,+60,+650,+300,-10,+10,+180$$1.1,+70,+750,+300,-10,+10,+210$$1.1,+80,+800,+300,-10,+10,+240$&k}$1.1,+90,+850,+300,-10,+10,+270%%1.1,+100,+950,+300,-10,+10,+300$$1.1,+110,+950,+300,10,+10,+330&&1.1,+120,+1050&l},+200,-10,+10,+360%%1.1,+130,+1150,+100,-10,+10,+15$$1.1,+140,+1250,+50,-10,+10,+45$$1.1,+150,+1300,+00,-10,+10,+&m}75$$1.1,+160,+1350,+00,-55,+10,+75%%1.1,+170,+1400,+00,-100,+10,+75 %%1.1,+180,+1450,+00,-145,+10,+75 %%1.1,+19&n}0,+1500,+00,-190,+10,+75 %%1.1,+200,+1550,+00,-235,+10,+75$ %%1.1,+210,+1600,+00,-280,+10,+75. %%1.1,+220,+1650,+00,-3&o}25,+10,+758 %%1.1,+230,+1700,+00,-370,+00,+75B $$1.1,+240,+1750,+00,-10,+00,+75L $$1.1,+250,+1800,+00,-10,+10,+75V $$&p}1.1,+260,+1850,+00,-10,+55,+75` %%1.1,+270,+1900,+00,-10,+100,+75j %%1.1,+280,+1950,+00,-10,+145,+75t %%1.1,+290,+2000,&q}+00,-10,+190,+75~ %%1.1,+300,+2050,+00,-10,+235,+75 %%1.1,+310,+2100,+00,-10,+280,+75 %%1.1,+320,+2150,+00,-10,+325,+&r}75 $$1.1,+330,+2250,+00,-10,+10,+75D1:PERSPEC5.BAS,+310,+2100,+00,-10,+280,+75 %%1.1,+320,+2150,+00,-10,+325,+$>2000 DATA 7,38,2010 DATA 10,6,0,-10,6,0,-10,-6,0,10,-6,0,10,6,4,-10,6,4,-10,-6,4,10,-6,4,10,0,7,-10,0,7,8,6,1.5,4,6,1.5,4,*t}6,3.52020 DATA 8,6,3.5,1,6,.5,-1,6,.5,-1,6,3.5,1,6,3.5,-4,6,1.5,-8,6,1.5,-8,6,3.5,-4,6,3.5,10,-4,1.5,10,-2,1.5,10,-2,3.5203*u}0 DATA 10,-4,3.5,10,-1,.5,10,1,.5,10,1,3.5,10,-1,3.5,10,2,1.5,10,4,1.5,10,4,3.5,10,2,3.5,-3,-6,2.5,3,-6,2.5,3,-6,3.52040 DAT*v}A -3,-6,3.52050 DATA 1,0,0,5,1,1,4,3,2,12060 DATA 2,0,3,6,0,4,1,5,9,8,4,5,1,23,24,25,26,23,5,1,27,28,29,30,27,5,1,31,32,33,*w}34,312070 DATA 3,0,3,5,0,1,2,6,5,1,5,1,11,12,13,14,11,5,1,15,16,17,18,15,5,1,19,20,21,22,192080 DATA 4,0,0,6,1,2,3,7,10,6,2*x}2090 DATA 5,0,1,5,0,3,4,8,7,3,5,1,35,36,37,38,352100 DATA 6,0,0,5,0,5,6,10,9,52110 DATA 7,0,0,5,1,7,8,9,10,72120 DATA 3,+*y}800,+1200,+400,-10,+10,+002130 DATA 3,+800,+1200,+400,-10,+10,+302140 DATA 3,+800,+1200,+400,-10,+10,+602150 DATA 3,+800,+*z}1200,+400,-10,+10,+902160 DATA 3,+800,+1200,+400,-10,+10,+1202170 DATA 3,+800,+1200,+400,-10,+10,+1502180 DATA 3,+800,+120*{}0,+400,-10,+10,+1802190 DATA 3,+800,+1200,+400,-10,+10,+2102200 DATA 3,+800,+1200,+400,-10,+10,+2402210 DATA 3,+800,+1200,*|}+400,-10,+10,+2702220 DATA 3,+800,+1200,+400,-10,+10,+3002230 DATA 3,+800,+1200,+400,-10,+10,+3302240 DATA 3,+800,+1200,+4*}}00,-10,+10,+3602250 DATA 3,+800,+1200,+400,-10,+10,+152260 DATA 3,+800,+1200,+400,-10,+10,+452270 DATA 3,+800,+1200,+400,-*~}10,+10,+75+3602250 DATA 3,+800,+1200,+400,-10,+10,+152260 DATA 3,+800,+1200,+400,-10,+10,+452270 DATA 3,+800,+1200,+400,-( 2000 DATA 9,9,2010 DATA 6,4,0,6,20,0,-6,20,0,-6,4,0,6,4,6,6,20,6,-6,20,6,-6,4,6,0,12,142020 DATA 1,0,0,5,1,1,4,3,2,12030.} DATA 2,0,0,5,0,1,2,6,5,12040 DATA 3,0,0,5,1,2,3,7,6,22050 DATA 4,0,0,5,0,3,4,8,7,32060 DATA 5,0,0,5,1,4,1,5,8,42070 DATA.} 6,0,0,4,1,5,6,9,52080 DATA 7,0,0,4,0,6,7,9,62090 DATA 8,0,0,4,1,7,8,9,72100 DATA 9,0,0,4,0,8,5,9,82110 DATA 3,+800,+1200.},+400,-10,+10,+002120 DATA 3,+800,+1200,+400,-10,+10,+302130 DATA 3,+800,+1200,+400,-10,+10,+602140 DATA 3,+800,+1200,+400.},-10,+10,+902150 DATA 3,+800,+1200,+400,-10,+10,+1202160 DATA 3,+800,+1200,+400,-10,+10,+1502170 DATA 3,+800,+1200,+400,-1.}0,+10,+1802180 DATA 3,+800,+1200,+400,-10,+10,+2102190 DATA 3,+800,+1200,+400,-10,+10,+2402200 DATA 3,+800,+1200,+400,-10,.}+10,+2702210 DATA 3,+800,+1200,+400,-10,+10,+3002220 DATA 3,+800,+1200,+400,-10,+10,+3302230 DATA 3,+800,+1200,+400,-10,+1.}0,+3602240 DATA 3,+800,+1200,+400,-10,+10,+152250 DATA 3,+800,+1200,+400,-10,+10,+452260 DATA 3,+800,+1200,+400,-10,+10,+7.}5+3602240 DATA 3,+800,+1200,+400,-10,+10,+152250 DATA 3,+800,+1200,+400,-10,+10,+452260 DATA 3,+800,+1200,+400,-10,+10,+7,******DESCRIPTIVE & PERSPECTIVE****** *************************:Numrisation d'un dessin  3 dimensions----2}----------------------------------- Les points sont reprs d'aprs l'ordre dans lequel ils sont enregistrs; ils sont r2}eprs, dans l'espace  3 dimensions par leurs coordonnes x,y,z.Reprsentation en 2 dimensions x',z'---------------------2}---------------La gomtrie descriptive donne les vues dans les plans xoy yoz zox en utilisant seulement 2 coordonnes xy yz2} zx.La gomtrie perspective donne le relief de l'objet en rduisant  2 dimensions x'z' qui sont foncions de xyz......et d2}e la position de l'observateur !Dessin des lignes et des surfaces--------------------------------- Chaque ligne est consi2}dre comme tant un segment de droite dfinie par deux points. Chaque surface est dtermine par une succession de points2}  joindre dans un ordre bien prcis : il faut donner les points dans le sens des aiguilles d'une montre en regardant le c2}ot que l'on veut voir. On utilise la gomtrie vectorielle qui fait intervenir les notions de:vecteurs, projections, p2}roduit vectoriel et produit scalaire de 2 vecteurs. Les produits vectoriel et scalaire permettent de savoir si une surface2} est vue de l'observateur.Dplacement de l'objet dans l'espace------------------------------------ Il peut rsulter de t2}ranslations et/ou de rotations. Toute rotation peut se dcomposer en rotations successives de l'objet autour des 3 axes o2}x,oy,oz; elle peut aussi rsulter du fait que l'observateur tourne autour de l'objet qui alors est fixe. La2} translation rsulte de l'loignement ...ou du rapprochement de l'observateur par rapport  l'objet.Mais elle peut aussi r2}sulter d'un effet de "zoom" par modifiction de l'chelle de reprsentation de l'objet ! Les programmes permettent l'utilisa2}tion de toutes les mthodes.󠙠 C'est le TURBO-BASIC qui a t choisi parce qu'il permet PAINT ,2}TEXT etest plus rapide. Le TURBO-BASIC compil acclre la vitesse ! (programmes --------.CTB ) L' cran GR.8 fo2}urnit la dfinition la plus prcise(320*192). Mais l'cran GR.15 (160*192) a l'avantage d'une meilleure reprsentation des2} surfaces partiellement caches. En effet, il existe un problme li aux objets avec parties "rentrantes".La coloratio2}n des surfaces intervient en empchant de tirer des traits dessus !PERSPECT.BAS(ou .CTB)est en GR.8 pour un objet "convexe" 2}sans problme.PERSPEC5.BAS(ou .CTB)est une variante :toute surface "principale",colore,peut comporter des surfaces "second2}aires" non colores...ou inversement !PERSPE15.BAS(ou .CTB) est en GR.15.PERSVRAI.BAS(ou .CTB)est encore plus volue: un t2}rait peut tre vu en partie .PERSPE01.DAT, PERSPE02.DAT ,etc ... sont des exemples de fichiers DATA destins  remplacer les2} autres DATA.PERSPECT.EXP est le texte explicatif qui peut tre lu et imprim avec FRAPPE.LST ou seulement lu avec LIT.BAS.2}Ĕ四lecture du nombre de surfaces NSlecture du nombre de points NPdimensionnement des tables:X(NP)2},Y(NP),Z(NP),XTT(NP),YTT(NP),ZTT(NP),S(NS,NP), X4(NP),Y4(NP),T(NS)lecture du reprage du fichier en DATAconstitution de l2}a table des points : X(I) Y(I) Z(I)constitution de la table des surfaces : S(J,..)calcul des minima et maxi2}ma des x y zcalcul de ECH chelle de reprsentationpour chaque position observateur-objet:-------------------------------2}---------lecture de R,EX,EY,EZ,AX,AY,AZ soit: coefficient de rduction "zoom" R position de l'observateur EX EY EZ 2} angles de rotation AX AY AZ-rduction: 0 <= angles <= 360 degrs-calcul des sinus et cosinus des angles AX AY AZ-ca2}lcul du coefficient W=ECH/R-calcul des coordonnes 3-D xtt ytt ztt aprs dplacement-dtermination des surfaces vues2} +pour chaque surface, vue ou cache: ----------------------------------- +calcul de MYTT(J) moyennes des coordonn2}es des segments de droites-contour de chaque surface +tri dee surfaces suivant les valeurs dcroissantes des moyennes MYTT(2}J) +pour chaque surface vue: ------------------------- ( et dans l'ordre du tri, c'est--dire depuis la surface la plus2} en avant )-conversion en coordonnes 2-D X4 Y4-dessin en perspective avec X4 Y4 : -des surfaces "principales" vues 2} (avec coloration s'il y a lieu) -des surfaces "secondaires" sur ces surfaces principales le cas chant 2} ( slection suivant la couleur COLP de la surface principale ) Il est possible de re2}mplacer lesDATA des exemples donns par un fichier D1:PERSPE--.DAT . Il suffit de: -charger le programme avec 2}LOAD -supprimer les lignes  partir de 2000, -faire ENTER"D1:PERSPE01.DAT" par exemple, -et de faire RU2}NNS,NP,coordonnes des pointsdlimitation des surfaces: "principales 2} et "secondaires" s'il y a lieupositions  reprsenter(se reporter au LISTING des programmes)2}Coordonnes rapportes  un centre:----------------------------------- choix d'un point pour le zro des coordonnespar 2}exemple: XC4=79 YC4=95 en GR.15Coordonnes d'un vecteur:-------------------------(segment de droite orient)coordonnes 2}d'un vecteur=extrmit moins origine: x2-x1 y2-y1 z2-z1Paramtrage d'une droite:------------------------- param2}tre k tel que 0<=k<= +1 x=x1+k*(x2-x1) y=y1+k*(y2-y1) z=z1+k*(z2-z1)C'est la faon la plus commode2} de reprsenter une droite en gomtrie analytiqueProduit vectoriel de 2 vecteurs:-------------------------------- sens de2} rotation: aiguille d'une montre pour prendre 2 vecteurs dfinissant chaque surface  examiner Le produit vectoriel est 2}un vecteur perpandiculaire  ces 2 vecteurs. Son sens dpend de l'ordre dans lequel ont t pris les 2 vecteurs de la2} surface  examiner.Produit scalaire de 2 vecteurs:-------------------------------l'un des 2 vecteurs est le prcdentl'2}autre est celui qui joint l'oeil de l'observateur au pied duc vecteur-produit vectoriel.si le produit est >0, la surface es2}t vueHomothtie:-----------La perspective rsulte d'une homothtie: le centre est l'oeil de l'observateur.(x'-xe)/(x-xe)=2}(ye-0)/(ye-y)(z'-ze)/(z-ze)=(ye-0)/(ye-y)on peut poser (ye-0)/(ye-y)=net l'on a: x'=xe+n*(x-xe) z'=ze+n*(z2}-ze)NB: Dans les programmes: X4=x' Y4=y' EX=xe EY=ye EZ=ze XTT=x YTT=y ZTT=ze) z'=ze+n*(z0h******DESCRIPTIVE & PERSPECTIVE****** *************************:Numrisation d'un dessin  3 dimensions----6}----------------------------------- Les points sont reprs d'aprs l'ordre dans lequel ils sont enregistrs; ils sont r6}eprs, dans l'espace  3 dimensions par leurs coordonnes x,y,z.Reprsentation en 2 dimensions x',z'---------------------6}---------------La gomtrie descriptive donne les vues dans les plans xoy yoz zox en utilisant seulement 2 coordonnes xy yz6} zx.La gomtrie perspective donne le relief de l'objet en rduisant  2 dimensions x'z' qui sont foncions de xyz......et d6}e la position de l'observateur !Dessin des lignes et des surfaces--------------------------------- Chaque ligne est consi6}dre comme tant un segment de droite dfinie par deux points. Chaque surface est dtermine par une succession de points6}  joindre dans un ordre bien prcis : il faut donner les points dans le sens des aiguilles d'une montre en regardant le c6}ot que l'on veut voir. On utilise la gomtrie vectorielle qui fait intervenir les notions de:vecteurs, projections, p6}roduit vectoriel et produit scalaire de 2 vecteurs. Les produits vectoriel et scalaire permettent de savoir si une surface6} est vue de l'observateur.Dplacement de l'objet dans l'espace------------------------------------ Il peut rsulter de t6}ranslations et/ou de rotations. Toute rotation peut se dcomposer en rotations successives de l'objet autour des 3 axes o6}x,oy,oz; elle peut aussi rsulter du fait que l'observateur tourne autour de l'objet qui alors est fixe. La6} translation rsulte de l'loignement ...ou du rapprochement de l'observateur par rapport  l'objet.Mais elle peut aussi r6}sulter d'un effet de "zoom" par modifiction de l'chelle de reprsentation de l'objet ! Les programmes permettent l'utilisa6}tion de toutes les mthodes.󠙠 C'est le TURBO-BASIC qui a t choisi parce qu'il permet PAINT ,6}TEXT etest plus rapide. Le TURBO-BASIC compil acclre la vitesse ! (programmes --------.CTB ) L' cran GR.8 fo6}urnit la dfinition la plus prcise(320*192). Mais l'cran GR.15 (160*192) a l'avantage d'une meilleure reprsentation des6} surfaces partiellement caches. En effet, il existe un problme li aux objets avec parties "rentrantes".La coloratio6}n des surfaces intervient en empchant de tirer des traits dessus !PERSPECT.BAS(ou .CTB)est en GR.8 pour un objet "convexe" 6}sans problme.PERSPEC5.BAS(ou .CTB)est une variante :toute surface "principale",colore,peut comporter des surfaces "second6}aires" non colores...ou inversement !PERSPE15.BAS(ou .CTB) est en GR.15.PERSVRAI.BAS(ou .CTB)est encore plus volue: un t6}rait peut tre vu en partie .PERSPE01.DAT, PERSPE02.DAT ,etc ... sont des exemples de fichiers DATA destins  remplacer les6} autres DATA.PERSPECT.EXP est le texte explicatif qui peut tre lu et imprim avec FRAPPE.LST ou seulement lu avec LIT.BAS.6}Ĕ四lecture du nombre de surfaces NSlecture du nombre de points NPdimensionnement des tables:X(NP)6},Y(NP),Z(NP),XTT(NP),YTT(NP),ZTT(NP),S(NS,NP), X4(NP),Y4(NP),T(NS)lecture du reprage du fichier en DATAconstitution de l6}a table des points : X(I) Y(I) Z(I)constitution de la table des surfaces : S(J,..)calcul des minima et maxi6}ma des x y zcalcul de ECH chelle de reprsentationpour chaque position observateur-objet:-------------------------------6}---------lecture de R,EX,EY,EZ,AX,AY,AZ soit: coefficient de rduction "zoom" R position de l'observateur EX EY EZ 6} angles de rotation AX AY AZ-rduction: 0 <= angles <= 360 degrs-calcul des sinus et cosinus des angles AX AY AZ-ca6}lcul du coefficient W=ECH/R-calcul des coordonnes 3-D xtt ytt ztt aprs dplacement-dtermination des surfaces vues6} +pour chaque surface, vue ou cache: ----------------------------------- +calcul de MYTT(J) moyennes des coordonn6}es des segments de droites-contour de chaque surface +tri dee surfaces suivant les valeurs dcroissantes des moyennes MYTT(6}J) +pour chaque surface vue: ------------------------- ( et dans l'ordre du tri, c'est--dire depuis la surface la plus6} en avant )-conversion en coordonnes 2-D X4 Y4-dessin en perspective avec X4 Y4 : -des surfaces "principales" vues 7}DEUNNSFXTXTTYTYTTZTZTTEXEYETXTYXCYCMXNPMYCOFINSCXMIXMAYMIYMANXYDDSBAXECYEC:}ECNZMNRVNSNRAAACSCSCSYZXKNP1P1P1P2P2P2P3P3P3VVVWWWPPPXPISINSKKRKRCCO:}LCOLCOLKZARKFTYTMYTTYYMYTTRNUKMTTYADRTTTMPMYTMPSSIKCXCY@@A @@:}AHA A   A (q@1 %4@:}@%@(@(u@2q@@@ @!@A"(A#:}$@%@@&'@(@)@*@`+@A,-.@/@01@23:}45@6789@:;@?@@@A@B:}C@D@E@F@GH@I@JKL@MNOPQR@:}ST@BU@VVB(WXY@Z[\]^_`ab:}c@defghi(j@k@lAmh n@o@p@q:}rsAt uvw@x@yz{|@}@~@@U@):}e#8((DESCRI15.BAS : AVA-@:;@@, 6."44:}9,9,9,9,9,9,9,9,9<,( A`2V6-8<%,6-8,"6-8,+6-8,36-&C6-&$+&,':}S6-&$+&,'V$< 6-%6-%$F3 6-'6-'6-%$)6-&$31G"H_:} @vI@J @vKAL$P,%$&$$Z/%$&$$dA6-@@# @P- @:}A"A n%6-6-% @`x-@+ @P @+"AP @`:} "Ap @p 6-%$A6-@# @P- @A"@A:}%6-6-% @`-@+ @P @+"@A@ @` "@:}A` @p 6-%$""짔ҽ36-6-'6-36-:}"-@, O:8,,6-O:8,,6 !8,6-8,@ O:8,,6-O:8,,J !8,6-8,T ^:}6-P:O:&,,6-P:O:&,,hK6-P:@r'+%@,,96-P:@@'+%@,,?6-E K6-r$|:}囆1 +@AA1AVA.-@@.(@ DESSIN .-@:}@.(@ en .-@@.(@ .-@@.(@ :}00((Ĕ par $$( par Jacques $ AMA:}-@& "68,-68,-&68,-  A-@p" 68<,-:}168<@,-B68<@,-S68<@,-d68<@,-p6-@-@&"68<%,-0 :}"A@: 6-%D-@N= "68<%@,-/68<%@,-=6-%@X-@:}b"68<%,-l 6-%v  h +@@)AAH;AAMA :}h6-@y6-@-@-@/6-@%@@:}$/6-@(%@V$! @!Y" @6-@/ 6-N:,O:, +:}$@,/6-$@$O:,!A`6-O:,!A`6-O:,!A`6- 6-';}g/('Ҡ/ؠ٠ڠ/ؠ٠ڠ/g(      9 6-E:,6-G:,;}6-E:,'6-G:,06-E:,96-G:,󠳭ě-@ 6-8,6-8,6-8,6-$&;}$6-$%$6-$&$6-$%$6-$%$6-6$%$  68,-68,-68,-  %%;}*-@4/6-8<@,6-8,&6-8,/6-8,>/6-8<@,6-8,&6-8,/6;}-8,H/6-8<@,6-8,&6-8,/6-8,R 6-&6-&6-&\ 6-&6-&6-&f 6-&6-&;}6-&p'6-$&$6-$&$'6-$&$z6-$%$%$&&68<@,-&!&68;}<@,-@""Ԩʩ,6-6-@,6-8<@,-@+&@,;}6-8<%,6-%8, 6-'+&@,68,- ((Ԩʩ 1-@;}68,- $$-+&@,@6@6-6@-@ 6-8,6-8%@,8, 8; },G 6-8, 68,-8%@,168%@,-=6-G A 1@ A 1A 6"6@6-; }@& A 3)@3 A 36A -@ 6-8,j6-8<@,%6-; }8<@,66-8<@,G6-8<@,M6-j(8,-8<@, "A`6-@ ; }A"A`-@76-8<%@,)6-8<%@,76-%@" A; }"@ A $ )( . 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Q. w:  / w9  @ Q- w=  ? w>  A QCP}- w>  ? w=   QA w;  @ w<   QA w W<  @ w;  Q >CQ} w  > w  > w   + w (L1 > C QC  D QC  E QCCR} F Q > C QC  G QC  H QC I Q > C QC  J QC  CS}K QC L QG wD M QH wE N QI wF O QJ wD P QK wE Q QL wF CT}R Q wD : Q wE < Q wF > QN wR  O wQ  S QO wP  M wR CU} T QM wQ  N wP  U QS w:  T w<  U w>  V QV w\8 gL1 CV} > >  3V w\8 LI1 > > â 3\8j   >  Qn  w n (L1CW} > wn  o Qj w o   j Qn j w  w k Q >k wm  n CX}+ wn (L,2n >n wt n + w v Q t8 v 2L?3t8f w v ww (L3w t | Qw wCY} t } Q| m  } m  L3w t  Qw >w w t t w w > wt CZ}\8f L3L3L3w f wt8 L73v L:3L:3L:3v n + wn (L4n t  Q > 2 Q C[} > 3 Q >  Q >  Q wc Q n t  -  > 2 w\C\}8 L4  L%3 w\8 L4[ 3 w[ (L4 > w   Q > w   QC]} +c w\8 L4 L%c wb8 L4 L%[ n 49 Р z8 L4L4 ʢ^ _ C^}` J` wz8 L5L4 11,15, /14,-4,0,14,4,0,4,4,0,4,10,0,-4,10,0,-4,-4,0/14,-4,4,14,4,4C_},4,4,4,4,10,4,-4,10,4,-4,-4,414,0,7,0,0,7,0,10,71,0,0,7,1,1,6,5,4,3,2,12,0,0,6,2,1,2,8,13,7,1 3,0,0,5,3,2,3,9,C`}8,24,0,0,5,2,3,4,10,9,3 5,0,0,6,3,4,5,11,15,10,4*6,0,0,5,2,5,6,12,11,547,0,0,5,3,6,1,7,12,6>8,0,0,5,1,12,7,13Ca},14,12H9,0,0,5,3,8,9,14,13,8R10,0,0,5,1,9,10,15,14,9\11,0,0,5,3,11,12,14,15,11f"1.6,+00,+1800,-400,+00,+00,-90p!Cb}1.6,+00,+1800,+00,+90,+00,+00z"1.6,+00,+1800,-600,+00,+00,+90#1.6,+00,+1800,-600,+00,+00,+180!1.6,+00,+1800,+00,+00,+Cc}00,-90!1.6,+00,+1800,+00,+00,+00,+00!1.6,+00,+1800,+00,+00,+00,+90"1.6,+00,+1800,+00,+00,+00,+180"1.6,+00,+1800,+Cd}600,+00,+00,-90!1.6,+00,+1800,+00,-90,+00,+00"1.6,+00,+1800,+600,+00,+00,+90#1.6,+00,+1800,+600,+00,+00,+180Ce}@@A`@ DESSIN en (Ĕ par  Cf} par Jacques 'Ҡ/ؠ٠ڠ/ؠ٠ڠ/      o" o"""(#2#Cg}<#F#Gd$Hw$I$J$K$L$P$Z$d%nE%x]%s%%%%%%%% &#&B&H&`&f&x&{&{&"&,Ch}&6&@'JT'T'^'h'r(|((*(B(Z(r(((((((()))0))&)0 *:%*D7*NM*XCi}*b*l*v**++'+?+W+++++2,Q,p,,, -n-n----E. .. .*.4.>&Cj}/Hi/R/\/f0pN0z001I1I1o1111111,2R2[2q222 33333:3?3?3Ck}U3d33444'4=4444$4)4.4/48494=4B4L5V5555555 55 5*54Cl}5>5H5R5\5f5p5z555555555554B4L5V5555555 55 5*54@GŸ058 R̍+ ! ! " ! # ! , !  !  ! + >!  a Uf5Gn} a ta L' > w   Q   Q   Q  Q w  Q w wGo}  w   Q w w w    Q  w  Q w  Q Gp} w  Q w  Q w  w  텈 w  w  T  w w  Gq} UV w  w   w w  UV w  w    L" LC$Gr} wH5 L$ L#  w (L/% L" L$ wH5 L*% L#  wH5 LH% L# w Gs} Q H5 H5 H5 H5  ! w (Ll& w "  ` L% "  ` Q wGt} "  L% "  Q w #  ` L6& #  ` Q w #  Gu}Lg& #  Q  w  ` $ Q w  ` % QN5 $ w ' Q멀  % w Gv} ( Q' w) Q( w' L&( w) Q    g5   s5   Gw}5   5 5 H5\ T5 \ (L'\ 5 L&  ! w (L (- Gx}. /  >- w"  >. w#  >/ w,  L]% + w (L)1 2 3    Gy} > >1 w 3 > >2 w 3 > >3 w 3 > > w 3 > > w 3Gz} 5  w5 (L )  > w5 > w 35 3 wH5 L) w  Q4 3 w4 G{}(L)   > w > w 3 > w > w 3 +5  w5 (L)  >G|} w5 > w 35  w  Q4    ȩča w ǩH5G}}_  _ (L^0H5^  ^ (LY09  ꩀ ^   Q#  H _   Q*    6 G~}7 8 6 w 9 Q6 w : Q7 w ; Q7 w < Q8 w = Q8 w > Q  ! w (Lm, " - G}Q # . Q , / Q. w9  / w:  ? Q. w:  / w9  @ Q- w=  ? G}w>  A Q- w>  ? w=   QA w;  @ w<   QA w W<  @ w;  G} Q > w  > w  > w   + w (L. > C QC  D QG}C  E QC F Q > C QC  G QC  H QC I Q > C QC G} J QC  K QC L QG wD M QH wE N QI wF O QJ wD P QK wE G}Q QL wF R Q wD : Q wE < Q wF > QN wR  O wQ  S QO wP G} M wR  T QM wQ  N wP  U QS w:  T w<  U w>  V QV wHG}5 gL. > >  3V wH5 L. > > â 3 ) w*  Q + w (LT0 G} > 2 Q >  Q >  Q >  Q2 wH5 LO0 wZ5 L/HG}5 H5   L$ wH5 LO0[  w[ (LO0 > w   Q > w  G} Q wZ5 L=0H5 H5  + L$[  ^ _ ݠ5 ǭР` J` w`5 G}L0Lx0  7,38,j10,6,0,-10,6,0,-10,-6,0,10,-6,0,10,6,4,-10,6,4,-10,-6,4,10,-6,4,10,0,7,-10,0,7,8,6,1.5,4,6,1.5,4G},6,3.5m8,6,3.5,1,6,.5,-1,6,.5,-1,6,3.5,1,6,3.5,-4,6,1.5,-8,6,1.5,-8,6,3.5,-4,6,3.5,10,-4,1.5,10,-2,1.5,10,-2,3.5q10,-4,G}3.5,10,-1,.5,10,1,.5,10,1,3.5,10,-1,3.5,10,2,1.5,10,4,1.5,10,4,3.5,10,2,3.5,-3,-6,2.5,3,-6,2.5,3,-6,3.5 -3,-6,3.51,0,0G},5,1,1,4,3,2,1 R2,0,3,6,0,4,1,5,9,8,4,5,1,23,24,25,26,23,5,1,27,28,29,30,27,5,1,31,32,33,34,31P3,0,3,5,0,1,2,6,5,1,5,1,1G}1,12,13,14,11,5,1,15,16,17,18,15,5,1,19,20,21,22,19 4,0,0,6,1,2,3,7,10,6,2**5,0,1,5,0,3,4,8,7,3,5,1,35,36,37,38,3546,G}0,0,5,0,5,6,10,9,5>7,0,0,5,1,7,8,9,10,7H!3,+800,+1200,+400,-10,+10,+00R!3,+800,+1200,+400,-10,+10,+30\!3,+800,+1200,G}+400,-10,+10,+60f!3,+800,+1200,+400,-10,+10,+90p"3,+800,+1200,+400,-10,+10,+120z"3,+800,+1200,+400,-10,+10,+150"3,+8G}00,+1200,+400,-10,+10,+180"3,+800,+1200,+400,-10,+10,+210"3,+800,+1200,+400,-10,+10,+240"3,+800,+1200,+400,-10,+10,+G}270"3,+800,+1200,+400,-10,+10,+300"3,+800,+1200,+400,-10,+10,+330"3,+800,+1200,+400,-10,+10,+360!3,+800,+1200,+40G}0,-10,+10,+15!3,+800,+1200,+400,-10,+10,+45!3,+800,+1200,+400,-10,+10,+75ADA @@ DESSIN G} en (DEPLACEMENTS par  par Jacques  OPTIONG}o"o"" " " # # C$$d$f$g$h%j$%k*%mB%nH%oZ%]%%%%%6&g&l&&&&& 'G}!'9'Q'i''''' ' ' ( (('( (!(")$)&.)(D)*)+),).)/)X)\3*]K*^c*b*d*gG}+h+i$+jQ+k+l+m2,nh,m,m,,, -L----].... .!."/#/$n/%/&/'/(/*/+G}/,0-=0.D0/J03O04T05Y06^0zx0{00000000 00 0*040>0H0R0\0f0p0z000G}0000000000{00000000 00 0*040>0H0R0\0f0p0z000D$•1:/= ̍R(i U9 i t+ ! i ! " ! # ! , !  !  ! + K} >!  LX( > w   Q   Q   Q  Q w  Q w wK}  w   Q w w w    Q  w  Q w  Q K} w  Q w  Q Ȣ w  w  텈 w  w  T  w w K}  UV w  w   w w  UV w  w    K}L" LJ$ w멕9 L %9 멕9 L#  w (LL% L" L$ w멕9 LG% L#  w멕9K} Le% L# w  Q   L" LJ$ w멛9 L%9 멕9 L#  w (L%K} L" L$ w멛9 L% L#  w멛9 L& L# w  Q 9 멕9 멕9 멕9 K}  ! w (L9' w "  ` L& "  ` Q w "  L& "  QK} w #  ` L' #  ` Q w #  L4' #  Q  w  `K} $ Q w  ` % Q멡9 $ w ' Q멀  % w ( Q' w) Q( w' L'( w)K} Q  ̍  9   9   ̠9   ؠ9 9 K} : L'd ;  ! w (L(- . /  >- w"  >. w#  >/ w, K} L*& + w (L*1 2 3    > >1 w 3 > >2 w 3 > >3K} w 3 > > w 3 > > w 3 5  w5 (L)  > w5 > wK} 35 3 w멕9 L* w  Q4 3 w4 (L*   > w > w 3 > wK} > w 3 +5  w5 (L*  > w5 > w 35  w  Q4  K}9  쩕9_ 3 _ (La1 ȩ i w Ǣ*    6 7 8 ) wK}*  Q *: * w 쩯  w R: w U:  w Y: 6 w \: 7 w `: 8 w K}d: _ w g: 6 w 9 Q6 w : Q7 w ; Q7 w < Q8 w = Q8 w > Q  ! w (K}Lx- " - Q # . Q , / Q. w9  / w:  ? Q. w:  / w9  @ Q-K} w=  ? w>  A Q- w>  ? w=   QA w;  @ w<   QA w W< K} @ w;  Q > w  > w  > w   + w (L/ > C K}QC  D QC  E QC F Q > C QC  G QC  H QC I Q >K} C QC  J QC  K QC L QG wD M QH wE N QI wF O QJ wD PK} QK wE Q QL wF R Q wD : Q wE < Q wF > QN wR  O wQ  K}S QO wP  M wR  T QM wQ  N wP  U QS w:  T w<  U w> K} V QV w멕9 gL/ > >  3V w멕9 L/ > > â 3  + w (LU1 K} > 2 Q > 3 Q >  Q >  Q wc Q  > 2 K}w멕9 LP1  L$3 w멕9 LP1[ 3 w[ (LP1 > w   Q > w  K} Q +c w멕9 L21 L$c w멛9 LK1 Lz%[  Ƞ ;_ : Р` J` w멭9 LK}1Ln1 +7,50, MAISON en Šśj10,6,0,-10,6,0,-10,-6,0,10,-6,0,10,6,4,-10,6,4,-10,-6,4,10,-6,4,10,0K},7,-10,0,7,8,6,1.5,4,6,1.5,4,6,3.5o8,6,3.5,1,6,0.5,-1,6,0.5,-1,6,3.5,1,6,3.5,-4,6,1.5,-8,6,1.5,-8,6,3.5,-4,6,3.5,10,-4,1.5K},10,-2,1.5,10,-2,3.5j10,-4,3.5,10,-1,0.5,10,1,0.5,10,1,3.5,10,-1,3.5,10,2,1.5,10,4,1.5,10,4,3.5,10,2,3.5,-3,-6,2.5,3,-6,2.K}5p3,-6,3.5,-3,-6,3.5,-10,3,2,-10,3,3.5,-10,-3,3.5,-10,-3,2,-4,-0.5,6.75,-5,-0.5,6.75,-5,-1.5,6.25,-4,-1.5,6.25--10,3,0.K}5,-10,-3,0.5,-10,-3,1.0,-10,3,1.0 1,0,0,5,1,1,4,3,2,1R2,0,3,6,0,4,1,5,9,8,4,5,1,23,24,25,26,23,5,1,27,28,29,30,27,5,1,3K}1,32,33,34,31 P3,0,3,5,0,1,2,6,5,1,5,1,11,12,13,14,11,5,1,15,16,17,18,15,5,1,19,20,21,22,19*@4,0,2,6,1,2,3,7,10,6,2,5,0,3K}9,40,41,42,39,5,1,47,48,49,50,474*5,0,1,5,0,3,4,8,7,3,5,1,35,36,37,38,35>6,0,0,5,1,5,6,10,9,5H+7,0,1,5,1,7,8,9,10,7,5,K}0,43,44,45,46,43R4.1,+00,+50,+00,-10,+10,+00\ 3.5,+10,+150,+25,-10,+10,+30f 3.1,+20,+250,+50,-10,+10,+60p 2.5,+30,+3K}50,+75,-10,+10,+90z"2.1,+40,+450,+100,-10,+10,+120"1.5,+50,+550,+300,-10,+10,+150"1.1,+60,+650,+300,-10,+10,+180"1K}.1,+70,+750,+300,-10,+10,+210"1.1,+80,+800,+300,-10,+10,+240"1.1,+90,+850,+300,-10,+10,+270#1.1,+100,+950,+300,-10,+K}10,+300"1.1,+110,+950,+300,10,+10,+330$1.1,+120,+1050,+200,-10,+10,+360#1.1,+130,+1150,+100,-10,+10,+15"1.1,+140,K}+1250,+50,-10,+10,+45"1.1,+150,+1300,+00,-10,+10,+75"1.1,+160,+1350,+00,-55,+10,+75#1.1,+170,+1400,+00,-100,+10,+75K} #1.1,+180,+1450,+00,-145,+10,+75 #1.1,+190,+1500,+00,-190,+10,+75 #1.1,+200,+1550,+00,-235,+10,+75$ #1.1,+210,+1600,+0K}0,-280,+10,+75. #1.1,+220,+1650,+00,-325,+10,+758 #1.1,+230,+1700,+00,-370,+00,+75B "1.1,+240,+1750,+00,-10,+00,+75L "1.1K},+250,+1800,+00,-10,+10,+75V "1.1,+260,+1850,+00,-10,+55,+75` #1.1,+270,+1900,+00,-10,+100,+75j #1.1,+280,+1950,+00,-10,+1K}45,+75t #1.1,+290,+2000,+00,-10,+190,+75~ #1.1,+300,+2050,+00,-10,+235,+75 #1.1,+310,+2100,+00,-10,+280,+75 #1.1,+320,+K}2150,+00,-10,+325,+75 "1.1,+330,+2250,+00,-10,+10,+75@ADAY@ DESSIN en K} (Ĕ par  par Jacques 'Ҡ/ؠ٠ڠ/ؠ٠ڠ/ K}      -123456789101112131415  OPTIONo" o"""("2"<#F#PJ$Z$dK}$n$x %"%A%G%_%e%w%z%%%%%%&&'&*&"N&,d&6&@&J'T4'^9'hi'r'|'''K}' (#(;(H(U(X(X(e({(((((~)&)0):)D)N)XQ*bg*l*v****** +?++K}+,,/,\,,, =-s- x-*x-4->-H.RW.\.f.p.zh//////0000000K}121K1$P1.U18\1=a1Bn1L1V1111111 11 1*141>1H1R1\1f1p1z1111K}1111111111 1 1 1$ 1. 18 1B 1L 1V 1` 1j 1t 1~ 1 1 1 111z1111Hj (avec coloration s'il y a lieu) -des surfaces "secondaires" sur ces surfaces principales le cas chant 7} ( slection suivant la couleur COLP de la surface principale ) Il est possible de re7}mplacer lesDATA des exemples donns par un fichier D1:PERSPE--.DAT . Il suffit de: -charger le programme avec 7}LOAD -supprimer les lignes  partir de 2000, -faire ENTER"D1:PERSPE01.DAT" par exemple, -et de faire RU7}NNS,NP,coordonnes des pointsdlimitation des surfaces: "principales 7} et "secondaires" s'il y a lieupositions  reprsenter(se reporter au LISTING des programmes)7}Coordonnes rapportes  un centre:----------------------------------- choix d'un point pour le zro des coordonnespar 7}exemple: XC4=79 YC4=95 en GR.15Coordonnes d'un vecteur:-------------------------(segment de droite orient)coordonnes 7}d'un vecteur=extrmit moins origine: x2-x1 y2-y1 z2-z1Paramtrage d'une droite:------------------------- param7}tre k tel que 0<=k<= +1 x=x1+k*(x2-x1) y=y1+k*(y2-y1) z=z1+k*(z2-z1)C'est la faon la plus commode7} de reprsenter une droite en gomtrie analytiqueProduit vectoriel de 2 vecteurs:-------------------------------- sens de7} rotation: aiguille d'une montre pour prendre 2 vecteurs dfinissant chaque surface  examiner Le produit vectoriel est 7}un vecteur perpandiculaire  ces 2 vecteurs. Son sens dpend de l'ordre dans lequel ont t pris les 2 vecteurs de la7} surface  examiner.Produit scalaire de 2 vecteurs:-------------------------------l'un des 2 vecteurs est le prcdentl'7}autre est celui qui joint l'oeil de l'observateur au pied duc vecteur-produit vectoriel.si le produit est >0, la surface es7}t vueHomothtie:-----------La perspective rsulte d'une homothtie: le centre est l'oeil de l'observateur.(x'-xe)/(x-xe)=7}(ye-0)/(ye-y)(z'-ze)/(z-ze)=(ye-0)/(ye-y)on peut poser (ye-0)/(ye-y)=net l'on a: x'=xe+n*(x-xe) z'=ze+n*(z7}-ze)NB: Dans les programmes: X4=x' Y4=y' EX=xe EY=ye EZ=ze XTT=x YTT=y ZTT=ze) z'=ze+n*(z4h,Y(NP),Z(NP),XTT(NP),YTT(NP),ZTT(NP),S(NS,NP), X4(NP),Y4(NP),T(NS)lecture du reprage du fichier en DATAconstitution de l6}a table des points : X(I) Y(I) Z(I)constitution de la table des surfaces : S(J,..)calcul des minima et maxi6}ma des x y zcalcul de ECH chelle de reprsentationpour chaque position observateur-objet:-------------------------------6}