input geometriesyr16;
input dlf_tex.mp;
u:=1cm;
%----------------------------------- Définition du cadre
path cadre;
numeric xmin,xmax,ymin,ymax;
xmin:=-4u;
xmax:=15u;
ymin:=-6u;
ymax:=7u;
cadre:=(xmin,ymin)--(xmax,ymin)--(xmax,ymax)--(xmin,ymax)--cycle;
%---------------------------------- Définitions générales utilisées
% sur toutes les figures
pair A,B,O,AA,BB,OO,I;
numeric rb;
rb:=2.5; % rayon de base
pair V;
V:=(5u,3u); % vecteur
O:=(0,0);
OO:= O shifted V;
numeric h;
h:=6; %hauteur
pair W;
W:=(11u,-u);
pair T,TT;
T:=(3u,-4u);
TT:=(11u,-4u);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%beginfig(1)
figure (xmin,ymin,xmax,ymax);
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
fin;
%endfig;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=-9 upto -1:
beginfig(i+11)
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d:=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
numeric cr,rr;
cr:=0.1*i; %coefficient servant à placer OO
rr:=rb*sqrt(1-cr*cr);
pair I,J,K,L;
I:=(-rr*u,cr*rb*u);
J:=(rr*u,cr*rb*u);
K:=J shifted V;
L:=I shifted V;
path section;
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw I--J--K;
draw K--L--I dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
I:=(-rr*u,0) shifted W;
J:=(rr*u,0) shifted W;
K:= J shifted (0,h*u);
L:= I shifted (0,h*u);
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw section;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
endfig;
endfor
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
beginfig(11)
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d:=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
pair I,J,K,L;
I:=(-rb*u,0);
J:=(rb*u,0);
K:=J shifted V;
L:=I shifted V;
path section;
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw I--J--K;
draw K--L--I dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
I:=(-rb*u,0) shifted W;
J:=(rb*u,0) shifted W;
K:= J shifted (0,h*u);
L:= I shifted (0,h*u);
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw section;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
endfig;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1 upto 9:
beginfig(i+11)
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d:=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
numeric cr,rr;
cr:=0.1*i; %coefficient servant à placer OO
rr:=rb*sqrt(1-cr*cr);
pair I,J,K,L;
I:=(-rr*u,cr*rb*u);
J:=(rr*u,cr*rb*u);
K:=J shifted V;
L:=I shifted V;
path section;
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw I--J--K;
draw K--L--I dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
I:=(-rr*u,0) shifted W;
J:=(rr*u,0) shifted W;
K:= J shifted (0,h*u);
L:= I shifted (0,h*u);
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw section;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
endfig;
endfor
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
beginfig(21)
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d:=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
endfig;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1 upto 9:
beginfig(i+21)
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d:=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
numeric cr,rr;
cr:=1-0.1*i; %coefficient servant à placer OO
rr:=rb*sqrt(1-cr*cr);
pair I,J,K,L;
I:=(-rr*u,cr*rb*u);
J:=(rr*u,cr*rb*u);
K:=J shifted V;
L:=I shifted V;
path section;
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw I--J--K;
draw K--L--I dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
I:=(-rr*u,0) shifted W;
J:=(rr*u,0) shifted W;
K:= J shifted (0,h*u);
L:= I shifted (0,h*u);
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw section;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
endfig;
endfor
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
beginfig(31)
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d:=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
pair I,J,K,L;
I:=(-rb*u,0);
J:=(rb*u,0);
K:=J shifted V;
L:=I shifted V;
path section;
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw I--J--K;
draw K--L--I dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
I:=(-rb*u,0) shifted W;
J:=(rb*u,0) shifted W;
K:= J shifted (0,h*u);
L:= I shifted (0,h*u);
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw section;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
endfig;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=-9 upto -1:
beginfig(i+41)
path cc;
cc= cercles(O,rb*u);
draw cc;
path d;
d:=demidroite(O,OO);
I := d intersectionpoint cc;
A:= rotation(I,O,270);
AA:= A shifted V;
B= symetrie(A,O);
BB:= B shifted V;
trace arccercle(BB,AA,OO) dashed evenly;
trace arccercle(AA,BB,OO);
draw A--AA;
draw B--BB;
draw O--OO dashed evenly;
numeric cr,rr;
cr:=-1-0.1*i; %coefficient servant à placer OO
rr:=rb*sqrt(1-cr*cr);
pair I,J,K,L;
I:=(-rr*u,cr*rb*u);
J:=(rr*u,cr*rb*u);
K:=J shifted V;
L:=I shifted V;
path section;
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw I--J--K;
draw K--L--I dashed evenly;
%------- vue de dessus ;
pair E,F,G,H;
E:=(-rb*u,0) shifted W;
F:=(rb*u,0) shifted W;
G:= F shifted (0,h*u);
H:= E shifted (0,h*u);
draw E--F--G--H--cycle;
draw W--W shifted (0,h*u) dashed evenly;
I:=(-rr*u,0) shifted W;
J:=(rr*u,0) shifted W;
K:= J shifted (0,h*u);
L:= I shifted (0,h*u);
section := I--J--K--L--cycle;
fillcolor:=1.3orange;
transparence section;
draw section;
label(TEX("\uline{Vue en perspective}"),T);
label(TEX("\uline{Vue de dessus}"),TT);
draw cadre withcolor black withpen pencircle scaled 2pt;
clip currentpicture to cadre;
endfig;
endfor
end
Section d’un cylindre couché
cylincouche