Cône circonscrit à une sphère

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Cône circonscrit à une sphère

Messagepar G.J.M » Jeudi 20 Mars 2014, 22:36

Bonjour,
Est-ce quelqu'un a déjà réalisé un cône circonscrit à une sphère, ou une un cylindre inscrit dans une sphère ?
Voilà deux dessins que j'aimerais réaliser en Asymptote, j'ai bien regarder les galeries d'images asymptote mais je n'ai pas réussi à sortir quelque chose.
Merci pour les pistes et les conseils.
GJM.
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Re: Cône circonscrit à une sphère

Messagepar OG » Jeudi 20 Mars 2014, 22:45

Bonsoir

Je ne vois pas les deux dessins ?

O.G.
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Re: Cône circonscrit à une sphère

Messagepar G.J.M » Jeudi 20 Mars 2014, 22:50

Pour un problème d'optimisation (1° S), je fais chercher les dimension d'un cylindre de volume maximal, inscrit dans une sphère de rayon donné (R).
Donc je dois réaliser un cylindre à l'intérieur d'une sphère.
GJM.
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Re: Cône circonscrit à une sphère

Messagepar OG » Vendredi 21 Mars 2014, 13:57

Bonjour

Avec les dessins, cela pourrait être mieux.
Voici un début de code qui j'espère aidera. Le paramètre est $\theta$ variant de 0 à pi/2,
l'angle du cône/2.

Code: Tout sélectionner
import three;

size(200);
currentprojection=orthographic(5,4,3);
real theta=pi/3;
real a=1-2*sin(theta)*sin(theta);
real b=sin(2*theta);
draw(unitsphere,green+opacity(.5),render(compression=Zero,merge=true));
dot((0,0,0));
draw(shift(0,0,-a)*
     zscale3((1+a)/b)*
     scale3(b)*
     unitcone,blue+opacity(.5));




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Re: Cône circonscrit à une sphère

Messagepar G.J.M » Vendredi 21 Mars 2014, 18:34

Bonjour,
Je n'ai pas pu compiler ton fichier, je l'ai pourtant inséré dans un document vide, voici mon source et mon fichier log:
Code: Tout sélectionner
    \documentclass{article}
    \usepackage[utf8]{inputenc}
    \usepackage[T1]{fontenc}
    \usepackage{fourier}

   \usepackage{asymptote}
   
   \begin{document}
   
   
   \begin{asy}
        import three;

          size(200);
          currentprojection=orthographic(5,4,3);
          real theta=pi/3;
          real a=1-2*sin(theta)*sin(theta);
          real b=sin(2*theta);           
          draw(unitsphere,green+opacity(.5),render(compression=Zero,merge=true));
          dot((0,0,0));
          draw(shift(0,0,-a)*
         zscale3((1+a)/b)*
         scale3(b)*
         unitcone,blue+opacity(.5));


    \end{asy}


   \end{document}

l
Code: Tout sélectionner
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GJM.
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Re: Cône circonscrit à une sphère

Messagepar G.J.M » Vendredi 21 Mars 2014, 20:35

Bonjour
J'ai réussi à compiler ton code, mais je voulais juste des figures comme dans http://asy.gmaths.net/forum/geometrie-espace-f9/cylindres-et-cones-de-revolution-t60.html, mais pas des figures "pleines".
Merci.
GJM.
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Re: Cône circonscrit à une sphère

Messagepar OG » Vendredi 21 Mars 2014, 21:56

Bonsoir

Déjà il y a du mieux si tu as réussi à compiler, je ne pouvais pas répondre avant.
Question pointillés, tout est certainement possible avec un peu (ou beaucoup) de travail.
Voici une figure qui n'est pas satisfaisante.

f9948129c356b624f0cc2e46518cb133.png

Code: Tout sélectionner
import solids;
settings.render=0;
settings.prc=false;

size(200);

revolution r=sphere(O,1);
real theta=pi/3;
real a=1-2*sin(theta)*sin(theta);
real b=sin(2*theta);
triple c=(0,0,a);

revolution c1=cone(c, b, 1-a,1);
draw(c1);

draw(r,1,longitudinalpen=nullpen);
draw(r.silhouette());


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Re: Cône circonscrit à une sphère

Messagepar G.J.M » Vendredi 21 Mars 2014, 22:52

Bonsoir et merci pour ta réponse,
C'est presque ce que je veux obtenir, sauf que c'est la sphère qui est dans le cône (le cône sert de chapeau à la sphère).
La compilation ne passe pas chez moi, je ne sais pas où je fais l'erreur, j'ai passé du temps à regarder le fichier log, je n'ai pas pu comprendre d'où venait l'erreur. Peut-être dans les options de compilation : je fais une compilation rapide, en choisissant :PdfLatex+Asymptote+PdfLatex+VoirPdr

Code: Tout sélectionner
    \documentclass{article}
    \usepackage[utf8]{inputenc}
    \usepackage[T1]{fontenc}
    \usepackage{fourier}
   \usepackage[inline]{asymptote}
   
   \begin{document}

      \begin{asy}

          import solids;
          settings.render=0;
          settings.prc=false;

          size(200);

          revolution r=sphere(O,1);
          real theta=pi/3;
          real a=1-2*sin(theta)*sin(theta);
          real b=sin(2*theta);
          triple c=(0,0,a);

          revolution c1=cone(c, b, 1-a,1);
          draw(c1);

          draw(r,1,longitudinalpen=nullpen);
          draw(r.silhouette());
      \end{asy}
   \end{document}
G.J.M
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Re: Cône circonscrit à une sphère

Messagepar G.J.M » Vendredi 21 Mars 2014, 22:54

Désolé pour l'erreur de copier-coller
voici le log :
Code: Tout sélectionner
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Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO)
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(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty
Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO)
(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty
Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO)
Package ifluatex Info: LuaTeX not detected.
)
Package etexcmds Info: Could not find \expanded.
(etexcmds) That can mean that you are not using pdfTeX 1.50 or
(etexcmds) that some package has redefined \expanded.
(etexcmds) In the latter case, load this package earlier.
))
\openout4 = `montest6.pre'.
)
(./montest6.aux)
\openout1 = `montest6.aux'.
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 7.
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 7.
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 7.
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 7.
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 7.
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 7.
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for FML/futm/m/it on input line 7.
LaTeX Font Info: Try loading font information for FML+futm on input line 7.
(/usr/share/texlive/texmf-dist/tex/latex/fourier/fmlfutm.fd
File: fmlfutm.fd 2004/10/30 Fontinst v1.926 font definitions for FML/futm.
)
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for FMS/futm/m/n on input line 7.
LaTeX Font Info: Try loading font information for FMS+futm on input line 7.
(/usr/share/texlive/texmf-dist/tex/latex/fourier/fmsfutm.fd
File: fmsfutm.fd 2004/10/30 Fontinst v1.926 font definitions for FMS/futm.
)
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for FMX/futm/m/n on input line 7.
LaTeX Font Info: Try loading font information for FMX+futm on input line 7.
(/usr/share/texlive/texmf-dist/tex/latex/fourier/fmxfutm.fd
File: fmxfutm.fd futm-extension
)
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 7.
LaTeX Font Info: Try loading font information for TS1+cmr on input line 7.
(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmr.fd
File: ts1cmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions
)
LaTeX Font Info: ... okay on input line 7.
LaTeX Font Info: Try loading font information for T1+futs on input line 7.
(/usr/share/texlive/texmf-dist/tex/latex/fourier/t1futs.fd
File: t1futs.fd 2004/03/02 Fontinst v1.926 font definitions for T1/futs.
)
\openout3 = `montest6-1.asy'.
Runaway argument?
! Paragraph ended before \ProcessAsymptoteLine was complete.
<to be read again>
\par
l.10
I suspect you've forgotten a `}', causing me to apply this
control sequence to too much text. How can we recover?
My plan is to forget the whole thing and hope for the best.
)
! Emergency stop.
<*> montest6.tex
*** (job aborted, no legal \end found)
Here is how much of TeX's memory you used:
2356 strings out of 493308
31318 string characters out of 6139931
70746 words of memory out of 5000000
5776 multiletter control sequences out of 15000+600000
8625 words of font info for 16 fonts, out of 8000000 for 9000
957 hyphenation exceptions out of 8191
32i,0n,21p,223b,101s stack positions out of 5000i,500n,10000p,200000b,80000s
No pages of output.
G.J.M
Hecto-utilisateur
 
Messages: 90
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Re: Cône circonscrit à une sphère

Messagepar OG » Vendredi 21 Mars 2014, 23:08

Re

Pour la sphère dans le cône ou la réciproque, c'est juste des calculs...

Pour la compilation, l'environnement {asy} est très chatouilleux car basé sur {comments}.
\begin{asy} et \end{asy} ne doivent pas être indentés.
Je suppose que c'est cela, si la figure toute seule compile avec asy.

O.G.
OG
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Re: Cône circonscrit à une sphère

Messagepar G.J.M » Vendredi 21 Mars 2014, 23:41

C'est bizarre, car même avec le code suivant j'ai le même message f'erreur :
Code: Tout sélectionner
    \documentclass{article}
    \usepackage[utf8]{inputenc}
    \usepackage[T1]{fontenc}
    \usepackage{fourier}
   \usepackage[inline]{asymptote}
   
\begin{document}
\begin{asy}


\end{asy}
\end{document}

GJM.
G.J.M
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Re: Cône circonscrit à une sphère

Messagepar G.J.M » Samedi 22 Mars 2014, 00:30

En modifiant les options de compilation je suis arrivé à compiler et générer un fichier Pdf.
Il ne me reste qu'à déchiffrer ton code, comprendre les commande et l'adapter à mon cas, car je veux dessiner un cylindre inscrit dans une sphère.
Merci beaucoup.
GJM.
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