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Quadriques
\302\251 Alain Le Stang - "Apprendre Maple" - 2006
S\303\251lectionner Edit/Execute/Worksheet ou cliquer le bouton !!! pour ex\303\251cuter ce Maplet.
restart;
with(Maplets[Elements]): with(Maplets[Tools]): with(plots):
-------------------------------------------------------------- ELLIPSOIDE --------------------------------------------------------------
ellipsoide := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Ellipsoide" end proc;
type := proc() ELLIPSOIDE end proc;
equation := proc() x^2/a^2 + y^2/b^2 +z^2/c^2=1 end proc;
param := proc(a,b,c) [a*cos(u)*cos(v), b*sin(u)*cos(v), c*sin(v)], u=0..2*Pi, v=-Pi/2..Pi/2 end proc;
traceX := proc(a,b,c,k) [k, cos(u)*sqrt(a^2-k^2)*b/a, sin(u)*sqrt(a^2-k^2)*c/a],u=0..2*Pi end proc;
traceY := proc(a,b,c,k) [a*sqrt(b^2-k^2)*cos(u)/b, k, c*sqrt(b^2-k^2)*sin(u)/b], u=0..2*Pi end proc;
traceZ := proc(a,b,c,k) [a*sqrt(c^2-k^2)*sin(u)/c, b*sqrt(c^2-k^2)*cos(u)/c, k], u=0..2*Pi end proc;
info := proc()
["Quadrique \303\240 centre unique.","Surface non r\303\251gl\303\251e.",x=a*cos(phi)*cos(theta), y=b*cos(phi)*sin(theta), z=c*sin(phi), theta = 0..2*Pi, phi = -Pi/2..Pi/2, x*x[0]/a^2+y*y[0]/b^2+z*z[0]/c^2 = 1," " ]
end proc;
end module;
ellipsoide:-equation();
X:=spacecurve(ellipsoide:-traceX(3,4,5,2), thickness=3, color=cyan):
Y:=spacecurve(ellipsoide:-traceY(3,4,5,2), thickness=3, color=yellow):
Z:=spacecurve(ellipsoide:-traceZ(3,4,5,2), thickness=3, color=red):
Q:=plot3d(ellipsoide:-param(3,4,5)):
display([Q,X,Y,Z],orientation=[45,60], scaling=constrained, axes = boxed);
--------------------------------------------- HYPERBOLOIDE A UNE NAPPE -----------------------------------------------------------
hyp1 := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Hyperboloide a une nappe" end proc;
type := proc() HYP1 end proc;
equation := proc() x^2/a^2 + y^2/b^2 - z^2/c^2 = 1 end proc;
param := proc(a,b,c)
[a*cos(u)*cosh(v),b*sin(u)*cosh(v),c*sinh(v)],u=0..2*Pi,v=-arcsinh(10/c)..arcsinh(10/c)
end proc;
traceX := proc(a,b,c,k)
if abs(k)<a then
[[k,cosh(u)*sqrt(a^2-k^2)*b/a,sinh(u)*sqrt(a^2-k^2)*c/a],u=-arcsinh(10*a/(c*sqrt(a^2-k^2)))..arcsinh(10*a/(c*sqrt(a^2-k^2))),
[k,-cosh(u)*sqrt(a^2-k^2)*b/a,sinh(u)*sqrt(a^2-k^2)*c/a],u=-arcsinh(10*a/(c*sqrt(a^2-k^2)))..arcsinh(10*a/(c*sqrt(a^2-k^2)))]
elif abs(k)>a then
[[k,sinh(u)*sqrt(k^2-a^2)*b/a,cosh(u)*sqrt(k^2-a^2)*c/a],u=-arccosh(10*a/(c*sqrt(k^2-a^2)))..arccosh(10*a/(c*sqrt(k^2-a^2))),
[k,sinh(u)*sqrt(k^2-a^2)*b/a,-cosh(u)*sqrt(k^2-a^2)*c/a],u=-arccosh(10*a/(c*sqrt(k^2-a^2)))..arccosh(10*a/(c*sqrt(k^2-a^2)))]
else
[[k,b*u,c*u],u=-10/c..10/c,[k,-b*u,c*u],u=-10/c..10/c]
end if;
end proc;
traceY := proc(a,b,c,k)
if abs(k)<b then
[[cosh(u)*sqrt(b^2-k^2)*a/b,k,sinh(u)*sqrt(b^2-k^2)*c/b],u=-arcsinh(10*b/(c*sqrt(b^2-k^2)))..arcsinh(10*b/(c*sqrt(b^2-k^2))),
[-cosh(u)*sqrt(b^2-k^2)*a/b,k,sinh(u)*sqrt(b^2-k^2)*c/b],u=-arcsinh(10*b/(c*sqrt(b^2-k^2)))..arcsinh(10*b/(c*sqrt(b^2-k^2)))]
elif abs(k)>b then
[[sinh(u)*sqrt(k^2-b^2)*a/b,k,cosh(u)*sqrt(k^2-b^2)*c/b],u=-arccosh(10*b/(c*sqrt(k^2-b^2)))..arccosh(10*b/(c*sqrt(k^2-b^2))),
[sinh(u)*sqrt(k^2-b^2)*a/b,k,-cosh(u)*sqrt(k^2-b^2)*c/b],u=-arccosh(10*b/(c*sqrt(k^2-b^2)))..arccosh(10*b/(c*sqrt(k^2-b^2)))]
else
[[a*u,k,c*u],u=-10/c..10/c,[-a*u,k,c*u],u=-10/c..10/c]
end if;
end proc;
traceZ := proc(a,b,c,k) [ a*sqrt(k^2+c^2)*sin(u)/c, b*sqrt(k^2+c^2)*cos(u)/c, k], u=0..2*Pi end proc;
info := proc()
["Quadrique \303\240 centre unique.","Surface r\303\251gl\303\251e.",x=a*cosh(phi)*cos(theta), y=b*cosh(phi)*sin(theta), z=c*sinh(phi), theta = 0..2*Pi, phi = -infinity..infinity, x*x[0]/a^2+y*y[0]/b^2-z*z[0]/c^2 = 1," " ]
end proc;
end module;
hyp1:-equation();
X:=spacecurve(op(hyp1:-traceX(3,4,5,2)[1..2]),thickness=3,color=cyan),spacecurve(op(hyp1:-traceX(3,4,5,2)[3..4]), thickness=3, color=cyan):
Y:=spacecurve(op(hyp1:-traceY(3,4,5,2)[1..2]),thickness=3,color=yellow),spacecurve(op(hyp1:-traceY(3,4,5,2)[3..4]), thickness=3, color=yellow):
Z:=spacecurve(hyp1:-traceZ(3,4,5,2), thickness=3, color=red):
Q:=plot3d(hyp1:-param(3,4,5)):
display([Q,X,Y,Z],orientation=[45,60], scaling=constrained, axes = boxed);
--------------------------------------------- HYPERBOLOIDE A DEUX NAPPES -----------------------------------------------------------
hyp2 := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Hyperboloide a deux nappes" end proc;
type := proc() HYP2 end proc;
equation := proc() x^2/a^2 + y^2/b^2 - z^2/c^2 = -1 end proc;
param := proc(a,b,c)
[[a*cos(u)*sinh(v), b*sin(u)*sinh(v), c*cosh(v)], u=0..2*Pi,v=-arccosh(10/c)..arccosh(10/c),
[a*cos(u)*sinh(v), b*sin(u)*sinh(v), -c*cosh(v)], u=0..2*Pi,v=-arccosh(10/c)..arccosh(10/c)]
end proc;
traceX := proc(a,b,c,k) [[k,sinh(u)*sqrt(k^2+a^2)*b/a,cosh(u)*sqrt(k^2+a^2)*c/a],u=-arccosh(10*a/(c*sqrt(k^2+a^2)))..arccosh(10*a/(c*sqrt(k^2+a^2))),
[k,sinh(u)*sqrt(k^2+a^2)*b/a,-cosh(u)*sqrt(k^2+a^2)*c/a],u=-arccosh(10*a/(c*sqrt(k^2+a^2)))..arccosh(10*a/(c*sqrt(k^2+a^2)))]
end proc;
traceY := proc(a,b,c,k)
[[sinh(u)*sqrt(k^2+b^2)*a/b,k,cosh(u)*sqrt(k^2+b^2)*c/b],u=-arccosh(10*b/(c*sqrt(k^2+b^2)))..arccosh(10*b/(c*sqrt(k^2+b^2))),
[sinh(u)*sqrt(k^2+b^2)*a/b,k,-cosh(u)*sqrt(k^2+b^2)*c/b],u=-arccosh(10*b/(c*sqrt(k^2+b^2)))..arccosh(10*b/(c*sqrt(k^2+b^2)))]
end proc;
traceZ := proc(a,b,c,k) [ a*sqrt(k^2-c^2)*sin(u)/c, b*sqrt(k^2-c^2)*cos(u)/c, k], u=0..2*Pi end proc;
info := proc()
["Quadrique \303\240 centre unique.","Surface non r\303\251gl\303\251e.",x=a*sinh(phi)*cos(theta), y=b*sinh(phi)*sin(theta), z=\302\261*c*cosh(phi), theta = 0..2*Pi, phi = -infinity..infinity, x*x[0]/a^2+y*y[0]/b^2-z*z[0]/c^2 = -1," " ]
end proc;
end module;
X:=spacecurve(op(hyp2:-traceX(3,5,2,6)[1..2]),thickness=3,color=cyan),spacecurve(op(hyp2:-traceX(3,5,2,6)[3..4]), thickness=3, color=cyan):
Y:=spacecurve(op(hyp2:-traceY(3,5,2,6)[1..2]),thickness=3,color=yellow),spacecurve(op(hyp2:-traceY(3,5,2,6)[3..4]), thickness=3, color=yellow):
Z:=spacecurve(hyp2:-traceZ(3,5,2,6), thickness=3, color=red):
Q:=plot3d(op(hyp2:-param(3,5,2)[1..3])),plot3d(op(hyp2:-param(3,5,2)[4..6])):
display([Q,X,Y,Z],orientation=[45,60], scaling=unconstrained, axes = boxed);
--------------------------------------------- CONE ELLIPTIQUE (OU DU SECOND DEGRE) ------------------------------------------------
cone := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Cone elliptique" end proc;
type := proc() CONE end proc;
equation := proc() x^2/a^2 + y^2/b^2 - z^2/c^2 = 0 end proc;
param := proc(a,b,c) [a*cos(u)*v, b*sin(u)*v, c*v], u=0..2*Pi,v=-10/c..10/c end proc;
traceX := proc(a,b,c,k)
if k<>0 then
[[k, k*b/a*sinh(u), k*c/a*cosh(u)], u=-arccosh(10*a/(abs(k)*c))..arccosh(10*a/(abs(k)*c)),
[k, k*b/a*sinh(u), -k*c/a*cosh(u)], u=-arccosh(10*a/(abs(k)*c))..arccosh(10*a/(abs(k)*c))]:
else
[[k,b*u,c*u], u=-10/c..10/c, [k,b*u,-c*u], u=-10/c..10/c ]:
end if;
end proc;
traceY := proc(a,b,c,k)
if k<>0 then
[[k*a/b*sinh(u),k, k*c/b*cosh(u)], u=-arccosh(10*b/(abs(k)*c))..arccosh(10*b/(abs(k)*c)),
[k*a/b*sinh(u),k, -k*c/b*cosh(u)], u=-arccosh(10*b/(abs(k)*c))..arccosh(10*b/(abs(k)*c))]
else
[[a*u,k,c*u], u=-10/c..10/c, [a*u,k,-c*u], u=-10/c..10/c ]
end if;
end proc;
traceZ := proc(a,b,c,k) [k*a*cos(u)/c, k*b*sin(u)/c, k], u=0..2*Pi end proc;
info := proc()
["Quadrique \303\240 centre unique.","Surface r\303\251gl\303\251e.",x=a*lambda*cos(theta), y=b*lambda*sin(theta), z=c*lambda, theta = 0..2*Pi, lambda = -infinity..infinity, x*x[0]/a^2+y*y[0]/b^2-z*z[0]/c^2 = 0," " ]
end proc;
end module;
X:=spacecurve(op(cone:-traceX(3,4,5,2)[1..2]),thickness=3,color=cyan),spacecurve(op(cone:-traceX(3
,4,5,2)[3..4]), thickness=3, color=cyan):
Y:=spacecurve(op(cone:-traceY(3,4,5,2)[1..2]),thickness=3,color=yellow),spacecurve(op(cone:-traceY(3,4,5,2)[3..4]),thickness=3,color=yellow):
Z:=spacecurve(cone:-traceZ(3,4,5,2), thickness=3, color=red):
Q:=plot3d(cone:-param(3,4,5)):
display([Q,X,Y,Z],orientation=[45,60], scaling=constrained, axes = boxed);
--------------------------------------------- PARABOLOIDE ELLIPTIQUE -----------------------------------------------------------
parabell := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Paraboloide elliptique" end proc;
type := proc() PARABELL end proc;
equation := proc() x^2/a^2 + y^2/b^2 - z/c = 0 end proc;
param := proc(a,b,c) [a*cos(u)*v, b*sin(u)*v, c*v^2], u=0..2*Pi, v=0..sqrt(10/c) end proc;
traceX := proc(a,b,c,k)
if k^2/a^2<=10/c then
[[k,b*sqrt(u-k^2/a^2),c*u], u=k^2/a^2..10/c,
[k,-b*sqrt(u-k^2/a^2),c*u], u=k^2/a^2..10/c]
else
[[0,0,0], u=-a..a, [0,0,0], u=-a..a ]
end if;
end proc;
traceY := proc(a,b,c,k)
if k^2/b^2<=10/c then
[[a*sqrt(u-k^2/b^2),k,c*u], u=k^2/b^2..10/c ,
[-a*sqrt(u-k^2/b^2),k,c*u], u=k^2/b^2..10/c ]
else
[ [0,0,0], u=-a..a, [0,0,0], u=-a..a ]
end if;
end proc;
traceZ := proc(a,b,c,k)
if k>0 then
[a*cos(u)*sqrt(k/c),b*sin(u)*sqrt(k/c),k], u=0..2*Pi
else [0,0,0], u=-a..a;
end if;
end proc;
info := proc()
["Quadrique sans centre.","Surface non r\303\251gl\303\251e.",x=a*lambda*cos(theta), y=b*lambda*sin(theta), z=c*lambda^2, theta = 0..2*Pi, lambda = 0..infinity, x*x[0]/a^2+y*y[0]/b^2-(z+z[0])/(2*c) = 0," " ]
end proc;
end module;
X:=spacecurve(op(parabell:-traceX(3,5,4,2)[1..2]),thickness=3,color=cyan),spacecurve(op(parabell:-traceX(3,4,5,2)[3..4]), thickness=3, color=cyan):
Y:=spacecurve(op(parabell:-traceY(3,5,4,2)[1..2]),thickness=3,color=yellow),spacecurve(op(parabell:-traceY(3,4,5,2)[3..4]),thickness=3,color=yellow):
Z:=spacecurve(parabell:-traceZ(3,5,4,2), thickness=3, color=red):
Q:=plot3d(parabell:-param(3,5,4)):
display([Q,X,Y,Z],orientation=[45,60], scaling=unconstrained, axes = boxed);
--------------------------------------------- PARABOLOIDE HYPERBOLIQUE -----------------------------------------------------------
parabhyp := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Paraboloide hyperbolique" end proc;
type := proc() PARABHYP end proc;
equation := proc() x^2/a^2 - y^2/b^2 - z/c = 0 end proc;
param := proc(a,b,c) [u,v, c*(u^2/a^2-v^2/b^2)], u=-10..10, v=-10..10 end proc;
traceX := proc(a,b,c,k) [k,u,c*(k^2/a^2-u^2/b^2)], u=-10..10 end proc;
traceY := proc(a,b,c,k) [u,k,c*(u^2/a^2-k^2/b^2)], u=-10..10 end proc;
traceZ := proc(a,b,c,k)
[[a*sqrt(u^2/b^2+k/c), u, k], u=-10..10 , [-a*sqrt(u^2/b^2+k/c), u, k], u=-10..10 ]
end proc;
info := proc()
["Quadrique sans centre.","Surface r\303\251gl\303\251e.",x=theta, y=lambda, z=c*(theta^2/a^2-lambda^2/b^2), theta = -infinity..infinity, lambda = -infinity..infinity, x*x[0]/a^2-y*y[0]/b^2-(z+z[0])/(2*c) = 0,"Dans un rep\303\250re convenable, une \303\251quation est: xy=z." ]
end proc;
end module;
X:=spacecurve(parabhyp:-traceX(3,4,5,2),thickness=3,color=cyan):
Y:=spacecurve(parabhyp:-traceY(3,4,5,2),thickness=3,color=yellow):
Z:=spacecurve(op(parabhyp:-traceZ(3,4,5,2)[1..2]),thickness=3,color=red,view=[-10..10,-10..10,-10..10]),spacecurve(op(parabhyp:-traceZ(3,4,5,2)[3..4]),thickness=3,color=red,view=[-10..10,-10..10,-10..10]):
Q:=plot3d(parabhyp:-param(3,4,5)):
display([Q,X,Y,Z],orientation=[45,60],scaling=unconstrained,axes=boxed);
--------------------------------------------- CYLINDRE ELLIPTIQUE -----------------------------------------------------------
cylell := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Cylindre elliptique" end proc;
type := proc() CYLELL end proc;
equation := proc() x^2/a^2 + y^2/b^2 = 1 end proc;
param := proc(a,b,c) [a*cos(u), b*sin(u), v] ,u=0..2*Pi, v=-10..10 end proc;
traceX := proc(a,b,c,k)
[[k,b*sqrt(1-k^2/a^2),c*u],u=-10/c..10/c,
[k,-b*sqrt(1-k^2/a^2),c*u],u=-10/c..10/c ]
end proc;
traceY := proc(a,b,c,k)
[[a*sqrt(1-k^2/b^2),k,c*u],u=-10/c..10/c,
[-a*sqrt(1-k^2/b^2),k,c*u],u=-10/c..10/c ]
end proc;
traceZ := proc(a,b,c,k) [a*cos(u),b*sin(u),k],u=0..2*Pi end proc;
info := proc()
["Quadrique admettant une droite des centres (l'axe du cylindre).","Surface r\303\251gl\303\251e.",x=a*cos(theta), y=b*sin(theta), z=lambda, theta = 0..2*Pi, lambda = -infinity..infinity, x*x[0]/a^2+y*y[0]/b^2 = 1," " ]
end proc;
end module;
X:=spacecurve(op(cylell:-traceX(3,4,5,2)[1..2]),thickness=3,color=cyan),spacecurve(op(cylell:-traceX(3,4,5,2)[3..4]),thickness=3,color=cyan):
Y:=spacecurve(op(cylell:-traceY(3,4,5,2)[1..2]),thickness=3,color=yellow),spacecurve(op(cylell:-traceY(3,4,5,2)[3..4]),thickness=3,color=yellow):
Z:=spacecurve(cylell:-traceZ(3,4,5,2),thickness=3,color=red):
Q:=plot3d(cylell:-param(3,4,5)):
display([Q,X,Y,Z],orientation=[45,60],scaling=unconstrained,axes=boxed);
--------------------------------------------- CYLINDRE HYPERBOLIQUE -----------------------------------------------------------
cylhyp := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Cylindre hyperbolique" end proc;
type := proc() CYLHYP end proc;
equation := proc() x^2/a^2 - y^2/b^2 = 1 end proc;
param := proc(a,b,c)
[[a*cosh(u), b*sinh(u), v], u=-arcsinh(10/b)..arcsinh(10/b), v=-10..10,
[-a*cosh(u), b*sinh(u), v], u=-arcsinh(10/b)..arcsinh(10/b), v=-10..10 ]
end proc;
traceX := proc(a,b,c,k)
[[k,b*sqrt(-1+k^2/a^2),c*u],u=-10/c..10/c,
[k,-b*sqrt(-1+k^2/a^2),c*u],u=-10/c..10/c ]
end proc;
traceY := proc(a,b,c,k)
[[a*sqrt(1+k^2/b^2),k,c*u],u=-10/c..10/c,
[-a*sqrt(1+k^2/b^2),k,c*u],u=-10/c..10/c ]
end proc;
traceZ := proc(a,b,c,k)
[[a*cosh(u),b*sinh(u),k],u=-10..10,
[-a*cosh(u),b*sinh(u),k],u=-10..10 ]
end proc;
info := proc()
["Quadrique admettant une droite des centres (l'axe du cylindre).","Surface r\303\251gl\303\251e.",x=\302\261*a*cosh(theta), y=b*sinh(theta), z=lambda, theta = -infinity..infinity, lambda = -infinity..infinity, x*x[0]/a^2-y*y[0]/b^2 = 1," " ]
end proc;
end module;
X:=spacecurve(op(cylhyp:-traceX(3,4,5,6)[1..2]),thickness=3,color=cyan),spacecurve(op(cylhyp:-traceX(3,4,5,6)[3..4]),thickness=3,color=cyan):
Y:=spacecurve(op(cylhyp:-traceY(3,4,5,6)[1..2]),thickness=3,color=yellow),spacecurve(op(cylhyp:-traceY(3,4,5,6)[3..4]),thickness=3,color=yellow):
Z:=spacecurve(op(cylhyp:-traceZ(3,4,5,6)[1..2]),thickness=3,color=red),spacecurve(op(cylhyp:-traceZ(3,4,5,6)[3..4]),thickness=3,color=red):
Q:=plot3d(op(cylhyp:-param(3,4,5)[1..3])),plot3d(op(cylhyp:-param(3,4,5)[4..6])):
display([Q,X,Y,Z],orientation=[45,60],scaling=unconstrained,axes=boxed,view=[-10..10,-10..10,-10..10]);
--------------------------------------------- CYLINDRE PARABOLIQUE -----------------------------------------------------------
cylparab := module()
export nom,type,equation,param,traceX,traceY,traceZ,info;
nom := proc() "Cylindre parabolique" end proc;
type := proc() CYLPARAB end proc;
equation := proc() x^2 = 2*a*y end proc;
param := proc(a,b,c) [u, u^2/(2*a), v], u=-10..10, v=-10..10 end proc;
traceX := proc(a,b,c,k) [k,k^2/(2*a),u],u=-10..10 end proc;
traceY := proc(a,b,c,k)
[[sqrt(2*a*k),k,u],u=-10..10,
[-sqrt(2*a*k),k,u],u=-10..10 ]
end proc;
traceZ := proc(a,b,c,k) [u,u^2/(2*a),k],u=-10..10 end proc;
info := proc()
["Quadrique sans centre.","Surface r\303\251gl\303\251e.",x=theta, y=theta^2/(2*a), z=lambda, theta = -infinity..infinity, lambda = -infinity..infinity, x*x[0]-a*(y+y[0]) = 0," " ]
end proc;
end module;
X:=spacecurve(cylparab:-traceX(3,4,5,8),thickness=3,color=cyan):
Y:=spacecurve(op(cylparab:-traceY(3,4,5,8)[1..2]),thickness=3,color=yellow),spacecurve(op(cylparab:-traceY(3,4,5,8)[3..4]),thickness=3,color=yellow):
Z:=spacecurve(cylparab:-traceZ(3,4,5,8),thickness=3,color=red):
Q:=plot3d(cylparab:-param(3,4,5)):
display([Q,X,Y,Z],orientation=[45,60],scaling=unconstrained,axes=boxed);
------------------------------------------------------ GESTION DES OPTIONS -------------------------------------------------------------------------------------
optionAxes:=proc()
MesOptions[1]
end proc:
optionRepere:=proc()
MesOptions[2]
end proc:
optionProj:=proc()
MesOptions[3]
end proc:
optionOmbre:=proc()
MesOptions[4]
end proc:
optionLumiere:=proc()
MesOptions[5]
end proc:
optionStyle:=proc()
MesOptions[6]
end proc:
optionType:=proc()
MesOptions[7]
end proc:
MiseAJourOptions:=proc()
global MesOptions;
local opt,equation,visibleSliders;
opt:=NULL:visibleSliders:=[true,true]:
# option Axes
if Maplets:-Tools:-Get('MenuAxes1'('value')) then opt:=opt,NORMAL end if:
if Maplets:-Tools:-Get('MenuAxes2'('value')) then opt:=opt,BOXED end if:
if Maplets:-Tools:-Get('MenuAxes3'('value')) then opt:=opt,FRAMED end if:
if Maplets:-Tools:-Get('MenuAxes4'('value')) then opt:=opt,NONE end if:
# option Rep\303\250re
if Maplets:-Tools:-Get('MenuRepere1'('value')) then opt:=opt,CONSTRAINED end if:
if Maplets:-Tools:-Get('MenuRepere2'('value')) then opt:=opt,UNCONSTRAINED end if:
# option Projection
if Maplets:-Tools:-Get('MenuProj1'('value')) then opt:=opt,NORMAL end if:
if Maplets:-Tools:-Get('MenuProj2'('value')) then opt:=opt,ORTHOGONAL end if:
if Maplets:-Tools:-Get('MenuProj3'('value')) then opt:=opt,FISHEYE end if:
# option Ombre
if Maplets:-Tools:-Get('MenuOmbre1'('value')) then opt:=opt,XYZ end if:
if Maplets:-Tools:-Get('MenuOmbre2'('value')) then opt:=opt,XY end if:
if Maplets:-Tools:-Get('MenuOmbre3'('value')) then opt:=opt,Z end if:
if Maplets:-Tools:-Get('MenuOmbre4'('value')) then opt:=opt,ZGRAYSCALE end if:
if Maplets:-Tools:-Get('MenuOmbre5'('value')) then opt:=opt,ZHUE end if:
if Maplets:-Tools:-Get('MenuOmbre6'('value')) then opt:=opt,NONE end if:
# option Lumi\303\250re
if Maplets:-Tools:-Get('MenuLumiere1'('value')) then opt:=opt,light1 end if:
if Maplets:-Tools:-Get('MenuLumiere2'('value')) then opt:=opt,light2 end if:
if Maplets:-Tools:-Get('MenuLumiere3'('value')) then opt:=opt,light3 end if:
if Maplets:-Tools:-Get('MenuLumiere4'('value')) then opt:=opt,light4 end if:
if Maplets:-Tools:-Get('MenuLumiere5'('value')) then opt:=opt,NONE end if:
# option Style
if Maplets:-Tools:-Get('MenuStyle1'('value')) then opt:=opt,PATCH end if:
if Maplets:-Tools:-Get('MenuStyle2'('value')) then opt:=opt,HIDDEN end if:
if Maplets:-Tools:-Get('MenuStyle3'('value')) then opt:=opt,WIREFRAME end if:
if Maplets:-Tools:-Get('MenuStyle4'('value')) then opt:=opt,CONTOUR end if:
if Maplets:-Tools:-Get('MenuStyle5'('value')) then opt:=opt,PATCHNOGRID end if:
if Maplets:-Tools:-Get('MenuStyle6'('value')) then opt:=opt,PATCHCONTOUR end if:
if Maplets:-Tools:-Get('MenuStyle7'('value')) then opt:=opt,LINE end if:
if Maplets:-Tools:-Get('MenuStyle8'('value')) then opt:=opt,POINT end if:
# option Type de Quadrique et fenetre Information
if Maplets:-Tools:-Get('MenuType1'('value')) then
opt:=opt,ellipsoide:-type(): equation:=ellipsoide:-equation():
end if:
if Maplets:-Tools:-Get('MenuType2'('value')) then
opt:=opt,hyp1:-type(): equation:=hyp1:-equation():
end if:
if Maplets:-Tools:-Get('MenuType3'('value')) then
opt:=opt,hyp2:-type(): equation:=hyp2:-equation():
end if:
if Maplets:-Tools:-Get('MenuType4'('value')) then
opt:=opt,cone:-type(): equation:=cone:-equation():
end if:
if Maplets:-Tools:-Get('MenuType5'('value')) then
opt:=opt,parabell:-type(): equation:=parabell:-equation():
end if:
if Maplets:-Tools:-Get('MenuType6'('value')) then
opt:=opt,parabhyp:-type(): equation:=parabhyp:-equation():
end if:
if Maplets:-Tools:-Get('MenuType7'('value')) then
opt:=opt,cylell:-type(): equation:=cylell:-equation(): visibleSliders:=[true,false]:
end if:
if Maplets:-Tools:-Get('MenuType8'('value')) then
opt:=opt,cylhyp:-type(): equation:=cylhyp:-equation(): visibleSliders:=[true,false]:
end if:
if Maplets:-Tools:-Get('MenuType9'('value')) then
opt:=opt,cylparab:-type(): equation:=cylparab:-equation(): visibleSliders:=[false,false]:
end if:
# mise \303\240 jour de l'\303\251quation et des Sliders:
Maplets:-Tools:-Set('MMLV'('value')=MathML[Export](equation) ):
Maplets:-Tools:-Set('bLabel'('visible')= visibleSliders[1]):
Maplets:-Tools:-Set('cLabel'('visible')= visibleSliders[2]):
Maplets:-Tools:-Set('b'('visible')= visibleSliders[1]):
Maplets:-Tools:-Set('c'('visible')= visibleSliders[2]):
MesOptions:=[opt]:
end proc:
MiseAJourInfo:=proc()
# option Type de Quadrique et fenetre Information
if Maplets:-Tools:-Get('MenuType1'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=ellipsoide:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](ellipsoide:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](ellipsoide:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](ellipsoide:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](ellipsoide:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](ellipsoide:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](ellipsoide:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](ellipsoide:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=ellipsoide:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=ellipsoide:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=ellipsoide:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType2'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=hyp1:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](hyp1:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](hyp1:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](hyp1:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](hyp1:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](hyp1:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](hyp1:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](hyp1:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=hyp1:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=hyp1:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=hyp1:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType3'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=hyp2:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](hyp2:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](hyp2:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](hyp2:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](hyp2:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](hyp2:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](hyp2:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](hyp2:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=hyp2:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=hyp2:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=hyp2:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType4'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=cone:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](cone:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](cone:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](cone:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](cone:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](cone:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](cone:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](cone:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=cone:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=cone:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=cone:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType5'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=parabell:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](parabell:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](parabell:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](parabell:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](parabell:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](parabell:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](parabell:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](parabell:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=parabell:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=parabell:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=parabell:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType6'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=parabhyp:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](parabhyp:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](parabhyp:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](parabhyp:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](parabhyp:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](parabhyp:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](parabhyp:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](parabhyp:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=parabhyp:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=parabhyp:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=parabhyp:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType7'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=cylell:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](cylell:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](cylell:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](cylell:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](cylell:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](cylell:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](cylell:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](cylell:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=cylell:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=cylell:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=cylell:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType8'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=cylhyp:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](cylhyp:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](cylhyp:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](cylhyp:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](cylhyp:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](cylhyp:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](cylhyp:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](cylhyp:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=cylhyp:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=cylhyp:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=cylhyp:-info()[9]):
end if:
if Maplets:-Tools:-Get('MenuType9'('value')) then
Maplets:-Tools:-Set('Titre'('caption')=cylparab:-nom()):
Maplets:-Tools:-Set('MMLV1'('value')=MathML[Export](cylparab:-equation())):
Maplets:-Tools:-Set('MMLV2'('value')=MathML[Export](cylparab:-info()[3])):
Maplets:-Tools:-Set('MMLV3'('value')=MathML[Export](cylparab:-info()[4])):
Maplets:-Tools:-Set('MMLV4'('value')=MathML[Export](cylparab:-info()[5])):
Maplets:-Tools:-Set('MMLV5'('value')=MathML[Export](cylparab:-info()[6])):
Maplets:-Tools:-Set('MMLV6'('value')=MathML[Export](cylparab:-info()[7])):
Maplets:-Tools:-Set('MMLV7'('value')=MathML[Export](cylparab:-info()[8])):
Maplets:-Tools:-Set('Centre'('caption')=cylparab:-info()[1]):
Maplets:-Tools:-Set('Reglee'('caption')=cylparab:-info()[2]):
Maplets:-Tools:-Set('Rem'('caption')=cylparab:-info()[9]):
end if
end proc:
-------------------------------------------- GRAPHE DE LA QUADRIQUE ET DES SECTIONS ---------------------------------------------------------
Quadrique:= proc(a, b, c, vView, hView)
local type,opt;
type:=optionType();
opt:=axes=optionAxes(), orientation=[hView, vView],scaling=optionRepere() , projection=optionProj(), shading=optionOmbre(), lightmodel=optionLumiere(), style=optionStyle(), titlefont = [TIMES, BOLD, 14]:
if type=ELLIPSOIDE then
plot3d(ellipsoide:-param(a,b,c), opt, title=ellipsoide:-nom())
elif type=HYP1 then
plot3d(hyp1:-param(a,b,c), opt, title=hyp1:-nom())
elif type=HYP2 then
display( [plot3d(op(hyp2:-param(a,b,c)[1..3])),plot3d(op(hyp2:-param(a,b,c)[4..6]))], opt, title=hyp2:-nom())
elif type=CONE then
plot3d(cone:-param(a,b,c), opt, title=cone:-nom())
elif type=PARABELL then
plot3d(parabell:-param(a,b,c), opt, title=parabell:-nom())
elif type=PARABHYP then
plot3d(parabhyp:-param(a,b,c), opt, title=parabhyp:-nom())
elif type=CYLELL then
plot3d(cylell:-param(a,b,c), opt, title=cylell:-nom())
elif type=CYLHYP then
display( [plot3d(op(cylhyp:-param(a,b,c)[1..3])),plot3d(op(cylhyp:-param(a,b,c)[4..6]))], opt, title=cylhyp:-nom())
else # CYLPARAB
plot3d(cylparab:-param(a,b,c), opt, title=cylparab:-nom())
end if;
end proc:
QuadSectionX := proc(k, a, b, c, hV, vV)
global GrapheX;
local x,type;
type:=optionType();
if type=ELLIPSOIDE then
x:=spacecurve(ellipsoide:-traceX(a,b,c,k), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=HYP1 then
x:=spacecurve(op(hyp1:-traceX(a,b,c,k)[1..2]),thickness=3,color=cyan),spacecurve(op(hyp1:-traceX(a,b,c,k)[3..4]), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a, color=white);
elif type=HYP2 then
x:=spacecurve(op(hyp2:-traceX(a,b,c,k)[1..2]),thickness=3,color=cyan),spacecurve(op(hyp2:-traceX(a,b,c,k)[3..4]), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a, color=white);
elif type=CONE then
x:=spacecurve(op(cone:-traceX(a,b,c,k)[1..2]),thickness=3,color=cyan),spacecurve(op(cone:-traceX(a,b,c,k)[3..4]), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a, color=white);
elif type=PARABELL then
x:=spacecurve(op(parabell:-traceX(a,b,c,k)[1..2]),thickness=3,color=cyan),spacecurve(op(parabell:-traceX(a,b,c,k)[3..4]), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a, color=white);
elif type=PARABHYP then
x:=spacecurve(parabhyp:-traceX(a,b,c,k), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=CYLELL then
x:=spacecurve(op(cylell:-traceX(a,b,c,k)[1..2]),thickness=3,color=cyan),spacecurve(op(cylell:-traceX(a,b,c,k)[3..4]), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a, color=white);
elif type=CYLHYP then
x:=spacecurve(op(cylhyp:-traceX(a,b,c,k)[1..2]),thickness=3,color=cyan),spacecurve(op(cylhyp:-traceX(a,b,c,k)[3..4]), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a, color=white);
else # CYLPARAB
x:=spacecurve(cylparab:-traceX(a,b,c,k), thickness=3, color=cyan), spacecurve([t,0,0], t=-a..a,
color=white);
end if;
GrapheX:=display ([x], axes=optionAxes() , orientation=[hV,vV],scaling=optionRepere() , projection=optionProj(), shading=optionOmbre(), lightmodel=optionLumiere(), style=optionStyle()):
end proc:
QuadSectionY := proc (k, a, b, c, hV,vV)
global GrapheY;
local y,type;
type:=optionType();
if type=ELLIPSOIDE then
y:=spacecurve(ellipsoide:-traceY(a,b,c,k), thickness=3, color=yellow), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=HYP1 then
y:=spacecurve(op(hyp1:-traceY(a,b,c,k)[1..2]),thickness=3,color=yellow),spacecurve(op(hyp1:-traceY(a,b,c,k)[3..4]), thickness=3, color=yellow), spacecurve([t,0,0], t=-a..a, color=white);
elif type=HYP2 then
y:=spacecurve(op(hyp2:-traceY(a,b,c,k)[1..2]),thickness=3,color=yellow),spacecurve(op(hyp2:-traceY(a,b,c,k)[3..4]), thickness=3, color=yellow), spacecurve([t,0,0], t=-a..a, color=white);
elif type=CONE then
y:=spacecurve(op(cone:-traceY(a,b,c,k)[1..2]),thickness=3,color=yellow),spacecurve(op(cone:-traceY(a,b,c,k)[3..4]),thickness=3,color=yellow), spacecurve([t,0,0], t=-a..a, color=white);
elif type=PARABELL then
y:=spacecurve(op(parabell:-traceY(a,b,c,k)[1..2]),thickness=3,color=yellow),spacecurve(op(parabell:-traceY(a,b,c,k)[3..4]),thickness=3,color=yellow), spacecurve([t,0,0], t=-a..a, color=white);
elif type=PARABHYP then
y:=spacecurve(parabhyp:-traceY(a,b,c,k), thickness=3, color=yellow), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=CYLELL then
y:=spacecurve(op(cylell:-traceY(a,b,c,k)[1..2]),thickness=3,color=yellow),spacecurve(op(cylell:-traceY(a,b,c,k)[3..4]), thickness=3, color=yellow), spacecurve([t,0,0], t=-a..a, color=white);
elif type=CYLHYP then
y:=spacecurve(op(cylhyp:-traceY(a,b,c,k)[1..2]),thickness=3,color=yellow),spacecurve(op(cylhyp:-traceY(a,b,c,k)[3..4]), thickness=3, color=yellow), spacecurve([t,0,0], t=-a..a, color=white);
else #CYLPARAB
y:=spacecurve(op(cylparab:-traceY(a,b,c,k)[1..2]),thickness=3,color=yellow),spacecurve(op(cylparab:-traceY(a,b,c,k)[3..4]), thickness=3, color=yellow), spacecurve([t,0,0], t=-a..a, color=white);
end if;
GrapheY:=display ([y], axes=optionAxes() , orientation=[hV,vV],scaling=optionRepere() , projection=optionProj(),shading=optionOmbre(), lightmodel=optionLumiere(), style=optionStyle()):
end proc:
QuadSectionZ := proc (k, a, b, c, hV,vV)
global GrapheZ;
local z,type,vw;
type:=optionType();
vw:=view=[-10..10,-10..10,-10..10];
if type=ELLIPSOIDE then
z:=spacecurve(ellipsoide:-traceZ(a,b,c,k), thickness=3, color=red), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=HYP1 then
z:=spacecurve(hyp1:-traceZ(a,b,c,k), thickness=3, color=red), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=HYP2 then
z:=spacecurve(hyp2:-traceZ(a,b,c,k), thickness=3, color=red), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=CONE then
z:=spacecurve(cone:-traceZ(a,b,c,k), thickness=3, color=red), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=PARABELL then
z:=spacecurve(parabell:-traceZ(a,b,c,k), thickness=3, color=red), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=PARABHYP then
z:=spacecurve(op(parabhyp:-traceZ(a,b,c,k)[1..2]),thickness=3,color=red,vw),spacecurve(op(parabhyp:-traceZ(a,b,c,k)[3..4]),thickness=3,color=red,vw), spacecurve([t,0,0], t=-a..a, color=white);
elif type=CYLELL then
z:=spacecurve(cylell:-traceZ(a,b,c,k), thickness=3, color=red), spacecurve([t,0,0], t=-a..a,
color=white);
elif type=CYLHYP then
z:=spacecurve(op(cylhyp:-traceZ(a,b,c,k)[1..2]),thickness=3,color=red,vw),spacecurve(op(cylhyp:-traceZ(a,b,c,k)[3..4]),thickness=3,color=red,vw), spacecurve([t,0,0], t=-a..a, color=white);
else # CYLPARAB
z:=spacecurve(cylparab:-traceZ(a,b,c,k), thickness=3, color=red), spacecurve([t,0,0], t=-a..a,
color=white);
end if;
GrapheZ:=display ([z], axes=optionAxes() , orientation=[hV,vV],scaling=optionRepere() , projection=optionProj(),shading=optionOmbre(), lightmodel=optionLumiere(), style=optionStyle()):
end proc:
Vide:= proc(a,hV,vV)
display([spacecurve([t,0,0], t=-a..a, color = white)],axes=optionAxes() , orientation=[hV,vV],scaling=optionRepere() , projection=optionProj(), shading=optionOmbre(), lightmodel=optionLumiere(), style=optionStyle())
end proc:
TraceQuadSectionX:=proc(xsect,valX,a,b,c, hV,vV)
if xsect then
QuadSectionX(valX,a,b,c, hV,vV)
else
Vide(a, hV,vV)
end if;
end proc:
TraceQuadSectionY:=proc(ysect,valY,a,b,c, hV,vV)
if ysect then
QuadSectionY(valY,a,b,c, hV,vV)
else
Vide(a, hV,vV):
end if;
end proc:
TraceQuadSectionZ:=proc(zsect,valZ,a,b,c, hV,vV)
if zsect then
QuadSectionZ(valZ,a,b,c, hV,vV)
else
Vide(a, hV,vV)
end if;
end proc:
-------------------------------------------- GESTIONNAIRE D'ERREURS --------------------------------------------------------
TraceQuadrique := proc(a, b, c,vView, hView, xsection, ysection, zsection)
global GrapheQ;
try
GrapheQ:=display(Quadrique(a, b, c, vView, hView),xsection,ysection,zsection):
catch:
display(textplot3d([5,5,5,"Erreur dans les param\303\250tres."]), axes=NONE, view=[-10..10, -10..10, -10..10], color=RED, titlefont = [TIMES, BOLD, 14]):
end try;
end proc:
---------------------------------------------------------- ENREGISTRER AU FORMAT .GIF ---------------------------------
Enregistrer := proc()
global nomFichier,nouvGraphe,GrapheQ,GrapheX,GrapheY,GrapheZ;
if Maplets:-Tools:-Get('RB1'('value')) then nouvGraphe:=GrapheQ end if:
if Maplets:-Tools:-Get('RB2'('value')) then nouvGraphe:=GrapheX end if:
if Maplets:-Tools:-Get('RB3'('value')) then nouvGraphe:=GrapheY end if:
if Maplets:-Tools:-Get('RB4'('value')) then nouvGraphe:=GrapheZ end if:
if assigned( nomFichier ) then
plotsetup( 'gif', 'plotoutput' = nomFichier );
print( nouvGraphe );
plotsetup( 'default' );
nomFichier:='nomFichier';
else
EnregSous();
end if;
end proc:
EnregSous := proc()
global nomFichier;
local nnomFichier;
try
nnomFichier := Maplets:-Examples:-GetFile(
'title' = "Enregistrer sous",
'filefilter' = "gif",
'approvecaption' = "Enregistrer"
);
catch:
return;
end try;
if nnomFichier[-4..-1] = ".gif" then
nomFichier := nnomFichier;
else
nomFichier := cat( nnomFichier, ".gif" );
end if;
Enregistrer();
end proc:
-------------------------------------------- MAPLET QUADRIQUES --------------------------------------------------------------
MesOptions := [NORMAL, CONSTRAINED, NORMAL, XYZ, light1, PATCH, ELLIPSOIDE]:
nomFichier:='nomFichier': nouvGraphe:=NULL: GrapheQ:=NULL:
GrapheX:=NULL: GrapheY:=NULL: GrapheZ:=NULL:
QuadriquesMaplet := Maplet(
'onstartup' = RunWindow('FenPrincipale'),
Font['F1']('family'="TIMES", 'bold'='false', 'italic'='false', size=12),
Font['F2']('family'="TIMES", 'bold'='true', 'italic'='false', size=18),
Font['F3']('family'="TIMES", 'bold'='true', 'italic'='false', size=12),
ButtonGroup['Groupe0'](), ButtonGroup['Groupe1'](), ButtonGroup['Groupe2'](),
ButtonGroup['Groupe3'](), ButtonGroup['Groupe4'](), ButtonGroup['Groupe5'](),
ButtonGroup['Groupe6'](), ButtonGroup['Groupe7'](),
Window['FenPrincipale']('title' = "Quadriques", 'menubar'='Menu', 'layout' = 'PrincipalLayout' ),
Window['FenInfo']('title' = "Information", 'layout' = 'InfoLayout', width=500, height=650),
Window['FenDesc']('title' = "Description", 'layout' = 'DescLayout', width=400, height=500),
Window['FenAideEnreg']('title' = "Aide sur Enregistrer", 'layout' = 'AideEnregLayout', width=400, height=500),
Window['FenEnregistrer']('title' = "Enregistrer", 'layout' = 'EnregistrerLayout', width=400, height=250),
Window['FenApropos']('title' = "A propos", 'layout' = 'AproposLayout', width=400, height=300),
MenuBar['Menu'](
Menu("Type",
RadioButtonMenuItem['MenuType1']("Ellipso\303\257de",'value'=true,'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType2']("Hyperbolo\303\257de \303\240 une nappe",'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType3']("Hyperbolo\303\257de \303\240 deux nappes",'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType4']("C\303\264ne elliptique",'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType5']("Parabolo\303\257de elliptique",'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType6']("Parabolo\303\257de hyperbolique",'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType7']("Cylindre elliptique",'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType8']("Cylindre hyperbolique",'group'='Groupe0','onclick'='maj'),
RadioButtonMenuItem['MenuType9']("Cylindre parabolique",'group'='Groupe0','onclick'='maj'),
MenuSeparator(),
MenuItem("Information sur cette quadrique", onclick='inform')
),
Menu("Axes",
RadioButtonMenuItem['MenuAxes1']("Normal",'value'=true,'group'='Groupe1','onclick'='maj'),
RadioButtonMenuItem['MenuAxes2']("Boxed",'group'='Groupe1','onclick'='maj'),
RadioButtonMenuItem['MenuAxes3']("Framed",'group'='Groupe1','onclick'='maj'),
RadioButtonMenuItem['MenuAxes4']("None",'group'='Groupe1','onclick'='maj')
),
Menu("Rep\303\250re",
RadioButtonMenuItem['MenuRepere1']("Constrained",'value'=true,'group'='Groupe2','onclick'='maj') ,
RadioButtonMenuItem['MenuRepere2']("Unconstrained",'group'='Groupe2','onclick'='maj')
),
Menu("Projection", RadioButtonMenuItem['MenuProj1']("Normal",'value'=true,'group'='Groupe3','onclick'='maj'),
RadioButtonMenuItem['MenuProj2']("Orthogonal",'group'='Groupe3','onclick'='maj'),
RadioButtonMenuItem['MenuProj3']("Fisheye",'group'='Groupe3','onclick'='maj')
),
Menu("Ombre",
RadioButtonMenuItem['MenuOmbre1']("XYZ",'value'=true,'group'='Groupe4','onclick'='maj'),
RadioButtonMenuItem['MenuOmbre2']("XY",'group'='Groupe4','onclick'='maj'),
RadioButtonMenuItem['MenuOmbre3']("Z",'group'='Groupe4','onclick'='maj'),
RadioButtonMenuItem['MenuOmbre4']("ZGRAYSCALE ",'group'='Groupe4','onclick'='maj'),
RadioButtonMenuItem['MenuOmbre5']("ZHUE",'group'='Groupe4','onclick'='maj'),
RadioButtonMenuItem['MenuOmbre6']("None",'group'='Groupe4','onclick'='maj')
),
Menu("Lumi\303\250re",
RadioButtonMenuItem['MenuLumiere1']("Light1",'value'=true,'group'='Groupe5','onclick'='maj'),
RadioButtonMenuItem['MenuLumiere2']("Light2", 'group'='Groupe5','onclick'='maj'),
RadioButtonMenuItem['MenuLumiere3']("Light3",'group'='Groupe5','onclick'='maj'),
RadioButtonMenuItem['MenuLumiere4']("Light4",'group'='Groupe5','onclick'='maj'),
RadioButtonMenuItem['MenuLumiere5']("None",'group'='Groupe5','onclick'='maj')
),
Menu("Style",
RadioButtonMenuItem['MenuStyle1']("Patch",value=true,'group'='Groupe6','onclick'='maj'),
RadioButtonMenuItem['MenuStyle2']("Hidden",'group'='Groupe6','onclick'='maj'),
RadioButtonMenuItem['MenuStyle3']("WireFrame",'group'='Groupe6','onclick'='maj'),
RadioButtonMenuItem['MenuStyle4']("Contour",'group'='Groupe6','onclick'='maj'),
RadioButtonMenuItem['MenuStyle5']("PatchNoGrid",'group'='Groupe6','onclick'='maj'),
RadioButtonMenuItem['MenuStyle6']("PatchContour",'group'='Groupe6','onclick'='maj'),
RadioButtonMenuItem['MenuStyle7']("Line",'group'='Groupe6','onclick'='maj'),
RadioButtonMenuItem['MenuStyle8']("Point",'group'='Groupe6','onclick'='maj')
),
Menu("Aide",
MenuItem("Description", onclick=RunWindow('FenDesc')),
MenuItem("Enregistrer", onclick=RunWindow('FenAideEnreg')),
MenuItem("A propos", onclick=RunWindow('FenApropos'))
)
), # fin MenuBar['Menu']
Action['maj'](
Evaluate('function' = "MiseAJourOptions"),
Evaluate('PlotterQ'='TraceQuadrique(
'a','b','c','phi','theta' ,
TraceQuadSectionX('boolX','valX','a','b','c','phi','theta'),
TraceQuadSectionY('boolY','valY','a','b','c','phi','theta'),
TraceQuadSectionZ('boolZ','valZ','a','b','c','phi','theta')
)') ,
Evaluate('PlotterX'='display(QuadSectionX('valX','a','b','c',0,90))') ,
Evaluate('PlotterY'='display(QuadSectionY('valY','a','b','c',90,90))'),
Evaluate('PlotterZ'='display(QuadSectionZ('valZ','a','b','c',90,0))')
),
Action['inform'](
Evaluate('function' = "MiseAJourInfo"),RunWindow('FenInfo')
),
BoxLayout['InfoLayout'](
BoxColumn('border'=true, 'inset'=0, 'spacing'=0,
Label['Titre']('font'='F2', 'caption'=ellipsoide:-nom() ),
BoxRow('inset'=0, 'spacing'=0, 'border'=false,
MathMLViewer['MMLV1']('height' = 70, 'width' = 200,'value'=MathML[Export](ellipsoide:-equation()))
),
Label['Centre']( 'caption'=ellipsoide:-info()[1]),
Label['Reglee']( 'caption'=ellipsoide:-info()[2]),
Label['Rem'](),
VerticalGlue(),
Label('font'='F3', 'caption'="Param\303\251trage:"),
BoxLayout(
BoxColumn(
MathMLViewer['MMLV2']('height' = 70, 'width' = 200,'value'=MathML[Export](ellipsoide:-info()[3])),
MathMLViewer['MMLV3']('height' = 70, 'width' = 200,'value'=MathML[Export](ellipsoide:-info()[4])),
MathMLViewer['MMLV4']('height' = 70, 'width' = 200,'value'=MathML[Export](ellipsoide:-info()[5]))
),
BoxColumn(
MathMLViewer['MMLV5']('height' = 70, 'width' = 200,'value'=MathML[Export](ellipsoide:-info()[6])),
MathMLViewer['MMLV6']('height' = 70, 'width' = 200,'value'=MathML[Export](ellipsoide:-info()[7]))
)
),
Label('font'='F3', 'caption'="Equation du plan tangent au point M0 (x0, y0, z0):"),
BoxRow('inset'=0, 'spacing'=0, 'border'=false,
MathMLViewer['MMLV7']('height' = 70, 'width' = 200,'value'=MathML[Export](ellipsoide:-info()[8]))
),
BoxColumn(VerticalGlue(),VerticalGlue()),
Button("Fermer", CloseWindow('FenInfo'))
) ),
BoxLayout['DescLayout'](
BoxColumn('border'=true, 'inset'=0, 'spacing'=4,
BoxRow('inset'=0, 'spacing'=0,
TextBox('wrapped'=true, 'width'=80, 'height'=20, ck,
'editable'='false', 'value'=
"Ce maplet donne la repr\303\251sentation graphique des 9 types de quadriques.\134nPour cela, cliquer le bouton ""Dessiner"" ou changer les options graphiques \303\240 partir des diff\303\251rents menus:\134nType, Axes, Rep\303\250re, Projection, Ombre, Lumi\303\250re, Style.\134n\134nCe maplet permet \303\251galement de visualiser les sections de la quadrique choisie par des plans d'\303\251quation X=k, Y=k ou Z=k.\134nPour cela, cliquer les options ""Section X"",""Section Y"", ""Section Z"" et saisissez la valeur de k.\n\nPour sauvegarder les graphiques cr\303\251\303\251s au format .gif, cliquer le bouton ""Enregistrer"".\134n\134nPour obtenir des informations compl\303\251mentaires sur la quadrique choisie, cliquer le bouton ""Infos"".\134n\134nPour quitter la fen\303\252tre de Maplet, cliquer le bouton ""Fermer""."
)
),
BoxRow('inset'=0, 'spacing'=0,
Button("Fermer", CloseWindow('FenDesc') )
)
)
),
BoxLayout['EnregistrerLayout'](
BoxColumn(
BoxColumn('border'=true, 'inset'=0, 'spacing'=0,
[RadioButton['RB1']("Quadrique",'value'=true,'group'='Groupe7'),
RadioButton['RB2']("Section X",'group'='Groupe7'),
RadioButton['RB3']("Section Y",'group'='Groupe7'),
RadioButton['RB4']("Section Z",'group'='Groupe7')],
Button("Enregistrer", Evaluate('function' = "Enregistrer"))
),
Button("Fermer", CloseWindow('FenEnregistrer'))
)
),
BoxLayout['AideEnregLayout'](
BoxColumn('border'=true, 'inset'=0, 'spacing'=4,
BoxRow('inset'=0, 'spacing'=0,
TextBox('wrapped'=true, 'width'=80, 'height'=18, ck,
'editable'='false', 'value'=
"Pour enregistrer les graphiques cr\303\251\303\251s au format .gif, cliquer le bouton ""Enregistrer"" de la fen\303\252tre principale.\134n\134nEnsuite, s\303\251lectionner l'une des 4 options:\134nQuadrique(sauvegarde du graphique de la quadrique avec \303\251ventuellement ses sections)\134nSection X (sauvegarde du graphique de la section de la quadrique par le plan X=k)\134nSection Y (sauvegarde du graphique de la section de la quadrique par le plan Y=k)\134nSection Z (sauvegarde du graphique de la section de la quadrique par le plan Z=k)\134n\134nCliquer ensuite le bouton ""Enregistrer"".\134nEntrer alors un nom de fichier pour le graphique s\303\251lectionn\303\251.\134n\134nPour quitter la fen\303\252tre ""Enregistrer"", cliquer le bouton ""Fermer""."
)
),
BoxRow('inset'=0, 'spacing'=0,
Button("Fermer", CloseWindow('FenAideEnreg') )
)
)
),
BoxLayout['AproposLayout'](
BoxColumn('border'=true, 'inset'=0, 'spacing'=0,
Label(font=F2,"Quadriques"),
Label("\302\251 Alain Le Stang - ""Apprendre Maple"" - 2004"),
Button("Fermer", CloseWindow('FenApropos'))
)), # fin BoxLayout['AproposLayout']
BoxLayout['PrincipalLayout'](
BoxColumn(
BoxColumn('inset'=0, 'spacing'=0, 'border'=true, 'caption'="Param\303\250tres",
BoxRow('inset'=0, 'spacing'=0,
Label['aLabel'](" a: "), Slider['a'](lower=1,filled=true,majorticks=1,orientation=horizontal,snapticks=false,upper=10,value=3,'onchange'='maj')
),
BoxRow('inset'=0, 'spacing'=0,
Label['bLabel'](" b: "), Slider['b'](lower=1,filled=true,majorticks=1,orientation=horizontal,snapticks=false,upper=10,value=5,'onchange'='maj')
),
BoxRow('inset'=0, 'spacing'=0,
Label['cLabel'](" c: "), Slider['c'](lower=1,filled=true,majorticks=1,orientation=horizontal,snapticks=false,upper=10,value=4,'onchange'='maj')
)
),
BoxRow('inset'=0, 'spacing'=0, 'border'=true, 'caption'="Equation",
MathMLViewer['MMLV'](height = 70, width = 200)
),
BoxRow('inset'=0, 'spacing'=0,
Button(" Dessiner ", 'tooltip'="Dessiner", 'onclick'='maj'),
Button(" Infos ", 'tooltip'="Informations", 'onclick'='inform')
),
BoxRow('inset'=0, 'spacing'=0,
Button("Enregistrer", 'tooltip'="Enregistrer", RunWindow('FenEnregistrer') ),
Button("Fermer", 'tooltip'="Fermer", Shutdown())
)
),
BoxRow('inset'=0, 'spacing'=0,
BoxColumn('inset'=0, 'spacing'=0, 'border'=true, 'caption'="Quadrique",
BoxRow('inset'=0, 'spacing'=0,
Plotter['PlotterQ']()
),
BoxColumn('inset'=0, 'spacing'=0, 'border'=true, 'caption'="Orientation: theta, phi", Slider['theta'](lower=0,filled=true,majorticks=30,minorticks=10,orientation=horizontal,snapticks=false,upper=360,value=45,'onchange'='maj'),
Slider['phi'](lower=0,filled=true,majorticks=30,minorticks=10,orientation=horizontal,snapticks=false,upper=360,value=60,'onchange'='maj')
),
BoxRow('inset'=0, 'spacing'=0,
[CheckBox['boolX'](caption="Section X", 'onchange'='maj')],
[CheckBox['boolY'](caption="Section Y", 'onchange'='maj')],
[CheckBox['boolZ'](caption="Section Z", 'onchange'='maj')])
),
BoxColumn('inset'=0, 'spacing'=0, 'border'=true, 'caption'="Sections",
Plotter['PlotterX'](width=150, height=150),
BoxRow('inset'=0, 'spacing'=0, 'border'=true,
Label("Section X = "),
TextField['valX'](3,'value'=2)
),
Plotter['PlotterY'](width=150, height=150),
BoxRow('inset'=0, 'spacing'=0, 'border'=true,
Label("Section Y = "),
TextField['valY'](3,'value'=2)
),
Plotter['PlotterZ'](width=150, height=150),
BoxRow('inset'=0, 'spacing'=0, 'border'=true,
Label("Section Z = "),
TextField['valZ'](3,'value'=2)
)
)
) # fin BoxLayout['PrincipalLayout']
)
):
Maplets[Display] (QuadriquesMaplet);