Présentation de 006.jps

/syracuse/bbgraf/albums/coniques_03/006.jpg
%% PhS %% 35 setxunit -8 12 setxrange -6.5 6.5 setyrange %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% procÚdures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /bddroite { 8 dict begin /kd exch def /kg exch def /By exch def /Bx exch def /B {Bx By} def /Ay exch def /Ax exch def /A {Ax Ay} def gsave [A A B vecteur kg mulv addv A A B vecteur kd mulv addv] ligne grestore end } def /Fleche_sur_C { 2 dict begin %% t long /long exch def /t exch def [t xdet t ydet dupp dupp t 0.01 add dup xdet exch ydet vecteur %% 0.01 1 exch div mulv 0.01 -1 exch div mulv %% ici, il faut tricher...j'ai honte! dupp norme long exch div mulv addv] (->) ligne end } def /Fleche_sur_Cp { 2 dict begin %% t long /long exch def /t exch def [t xdet neg t ydet dupp dupp t 0.01 add dup xdet neg exch ydet vecteur %% 0.01 1 exch div mulv 0.01 -1 exch div mulv %% ici, il faut tricher...j'ai honte! dupp norme long exch div mulv addv] (->) ligne end } def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% definition des points %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /a {3} def /c {3.8} def /b {c c mul a a mul sub sqrt} def /e {c a div} def /Kx {a e div} def /K {Kx neg 0} def /K+ {K 0 6 addv} def /K- {K 0 -6 addv} def /Kp {Kx 0} def /Kp+ {Kp 0 6 addv} def /Kp- {Kp 0 -6 addv} def /O {0 0} def /F {c neg 0} def /Fp {c 0} def /S1 {a neg 0} def /S2 {a 0} def /B {0 b} def /R11 {a neg b} def /R12 {a b} def /R21 {a neg b neg} def /R22 {a b neg} def /omeg {F O milieu} def /Ry {1 e e mul 1 exch div sub sqrt a mul} def /R {Kx neg Ry} def /xdet {settvar t t mul b b mul div 1 add sqrt a mul} def /ydet {settvar t} def /Mx {b 1.3 mul xdet} def /My {b 1.3 mul ydet} def /M {Mx My} def /H {M Kp Kp+ orthoproj} def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% definition d'une couleur %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /coul1 {120 255 div 70 255 div 9 255 div setrgbcolor} def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% tracÚs %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 1.1 setlinewidth [O F Fp S1 S2 B K Kp M] points F Fp -0.6 2 bddroite [O 0 -6.5 addv O 0 6.5 addv] ligne coul1 2 setlinewidth b -2.7 mul b 2.7 mul settrange {xdet} {ydet} courbeparam b -2.2 mul b 2.2 mul settrange {xdet neg} {ydet} courbeparam /arrowscale {2.5 dup} def 5 0.2 Fleche_sur_C 4 0.2 Fleche_sur_Cp -5 0.2 Fleche_sur_C -4 0.2 Fleche_sur_Cp 1.1 setlinewidth vert [K+ K-] ligne [Kp+ Kp-] ligne rouge [Fp M] ligne /arrowangle -9 def Fp 1 0 addv Fp M 1.3 (->) tripointarc /arrowangle 0 def bleu pointilles [R11 R12 R22 R21] polygone noir mixte 0.6 setlinewidth R11 R22 -1 2 bddroite R12 R21 -1 2 bddroite orange pointilles Fp Fp a b addv -0.2 2.5 bddroite Fp Fp a neg b addv -2 0.2 bddroite %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% texte %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% setTimesItalic noir (O) O [1.8 dup] dltext (F) Fp [1.8 dup] drtext (B) B [1.5 dup] ultext (M) M [1.5 dup] crtext vert (K) Kp [1.5 dup] dltext <latex> $ \mathcal{D}' $ </latex> K 0 -5 addv [2 dup] cltexlabel <latex> $ \mathcal{D} $ </latex> Kp 0 -5 addv[2 dup] crtexlabel rouge <latex> $ \theta $ </latex> Fp 1.6 0.5 addv [2 dup] cctexlabel <latex> $ \theta=0 $ </latex> b neg 0 -0.7 0 addv [1.5 dup] dltexlabel orange <latex> $ \theta=\mathrm{Arccos}(\frac{1}{e}) $ </latex> 9.4 2.8 [1.5 dup] cctexlabel <latex> $ \theta=-\mathrm{Arccos}(\frac{1}{e}) $ </latex> 10.5 -5 [1.5 dup] cctexlabel noir <latex> \fbox{$ \rho(\theta)=\displaystyle\frac{p}{1-e\cos(\theta)} $} </latex> 9 -1.2 [1.8 dup] cctexlabel