{"id":5774,"date":"2021-02-09T16:51:38","date_gmt":"2021-02-09T15:51:38","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?p=5774"},"modified":"2021-02-10T12:46:43","modified_gmt":"2021-02-10T11:46:43","slug":"latex-et-courbe-parametree-ou-polaire","status":"publish","type":"post","link":"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/","title":{"rendered":"LaTeX et courbe param\u00e9tr\u00e9e ou polaire"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">LaTeX et courbe param\u00e9tr\u00e9e ou polaire: comment la tracer? Quand on souhaite tracer une courbe param\u00e9tr\u00e9e en \\(\\LaTeX\\), on doit s&rsquo;orienter vers une solution graphique, bien s\u00fbr. TiKZ \u00e0 le vent en poupe par sa simplicit\u00e9 d&rsquo;utilisation. En effet, les autres solutions graphiques, telles PSTricks ou Asymptote par exemple, peuvent sembler plus difficiles \u00e0 appr\u00e9hender.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p class=\"wp-block-paragraph\">Me concernant, j&rsquo;utilise toujours TiKZ car je compile toujours via PdfLaTeX, et ce depuis toujours. Or, il y a quelques ann\u00e9es, PSTricks n&rsquo;offrait pas l&rsquo;opportunit\u00e9 de compiler via PdfLaTeX (ce qui n&rsquo;est plus le cas).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Je vais donc commencer par TiKZ, puis m&rsquo;aventurerai en terre inconnue&#8230;<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Au menu sur cette page...<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/#Courbe_parametree_ou_polaire_et_LaTeX_avec_TiKZ\" >Courbe param\u00e9tr\u00e9e ou polaire et LaTeX avec TiKZ<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/#Exemple_dune_courbe_parametree_en_LaTeX_avec_TiKZ\" >Exemple d&rsquo;une courbe param\u00e9tr\u00e9e en LaTeX avec TiKZ<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/#Autre_exemple_courbe_polaire_en_LaTeX_avec_TiKZ\" >Autre exemple : courbe polaire en LaTeX avec TiKZ<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/#Courbe_parametree_ou_polaire_et_LaTeX_avec_PSTricks\" >Courbe param\u00e9tr\u00e9e ou polaire et LaTeX avec PSTricks<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/#Exemple_dune_courbe_parametree_en_LaTeX_avec_PSTricks\" >Exemple d&rsquo;une courbe param\u00e9tr\u00e9e en LaTeX avec PSTricks<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/#Autre_exemple_avec_PSTricks\" >Autre exemple : avec PSTricks<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.mathweb.fr\/euclide\/2021\/02\/09\/latex-et-courbe-parametree-ou-polaire\/#Et_les_autres_methodes\" >Et les autres m\u00e9thodes ?<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Courbe_parametree_ou_polaire_et_LaTeX_avec_TiKZ\"><\/span>Courbe param\u00e9tr\u00e9e ou polaire et LaTeX avec TiKZ<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Quand on regarde le manuel de PGF, les courbes param\u00e9tr\u00e9es sont syst\u00e9matiquement trac\u00e9es \u00e0 l&rsquo;aide de GNUPlot&#8230; Or, moi, je n&rsquo;aime pas GNUPlot. Et puis, pourquoi installer un logiciel tiers alors que l&rsquo;on peut tr\u00e8s bien tracer la plupart des courbes souhait\u00e9es ?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Il faut comprendre que nativement, PGF ne calcule pas super bien (je veux dire par l\u00e0 que les m\u00e9thodes de calculs ne sont pas aussi pr\u00e9cises que GNUPlot) et que c&rsquo;est sans doute pour cela que l&rsquo;auteur passe par un logiciel tiers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mais pour tracer une courbe \u00ab\u00a0lambda\u00a0\u00bb, nous n&rsquo;avons pas besoin de calculs ultra-pr\u00e9cis !<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Exemple_dune_courbe_parametree_en_LaTeX_avec_TiKZ\"><\/span>Exemple d&rsquo;une courbe param\u00e9tr\u00e9e en LaTeX avec TiKZ<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Je souhaite tracer la courbe $$\\begin{cases}x(t)=4\\cos(t)\\sin(t)\\\\y(t)=3\\sin(t)+\\cos(t)\\end{cases}$$Pour cela, j&rsquo;utilise le code suivant:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\\documentclass{standalone}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[dashed, gray] (-5,-5) grid (5,5);\n\\draw[very thick, ->, >=latex] (-5,0) -- (5,0);\n\\draw[very thick, ->, >=latex] (0,-5) -- (0,5);\n\\draw[very thick, red] plot[domain=0:360,samples=100] ({4*cos(\\x)*sin(\\x)},{3*sin(\\x)+cos(\\x)});\n\\end{tikzpicture}\n\n\\end{document}<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">qui produit le document suivant:<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"745\" height=\"745\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-01.png\" alt=\"Courbe param\u00e9tr\u00e9e ou polaire en LaTeX avec TiKZ\" class=\"wp-image-5775\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-01.png 745w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-01-100x100.png 100w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-01-600x600.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-01-300x300.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-01-150x150.png 150w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Comme vous pouvez le constater, je n&rsquo;utilise que TiKZ. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La courbe param\u00e9tr\u00e9e est d\u00e9finie ligne 10: pas d&rsquo;appel \u00e0 GNUPlot.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Autre_exemple_courbe_polaire_en_LaTeX_avec_TiKZ\"><\/span>Autre exemple : courbe polaire en LaTeX avec TiKZ<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Pour les courbes polaires, c&rsquo;est aussi simple! En effet, TiKZ permet de sp\u00e9cifier des coordonn\u00e9es polaires autant que des coordonn\u00e9es cart\u00e9siennes. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">J&rsquo;ai envie de tracer la spirale d&rsquo;\u00e9quation:$$\\rho(\\theta)=0,005\\theta.$$Pour cela, je vais utiliser le code suivant:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\\documentclass{standalone}\n\\usepackage{tikz}\n\n\\begin{document}\n\n\\begin{tikzpicture}\n\\draw[dashed, gray] (-5,-5) grid (5,5);\n\\draw[very thick, ->, >=latex] (-5,0) -- (5,0);\n\\draw[very thick, ->, >=latex] (0,-5) -- (0,5);\n\\draw[very thick, blue] plot[domain=0:720, samples=100] ({\\x}:{0.005*\\x});\n\\end{tikzpicture}\n\n\\end{document}<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">J&rsquo;obtiens alors:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"745\" height=\"745\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-01.png\" alt=\"courbe param\u00e9tr\u00e9e ou polaire en LaTeX avec TiKZ\" class=\"wp-image-5776\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-01.png 745w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-01-300x300.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-01-100x100.png 100w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-01-600x600.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-01-150x150.png 150w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Courbe_parametree_ou_polaire_et_LaTeX_avec_PSTricks\"><\/span>Courbe param\u00e9tr\u00e9e ou polaire et LaTeX avec PSTricks<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Exemple_dune_courbe_parametree_en_LaTeX_avec_PSTricks\"><\/span>Exemple d&rsquo;une courbe param\u00e9tr\u00e9e en LaTeX avec PSTricks<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Je souhaite compiler toujours avec PdfLaTeX, donc j&rsquo;ai besoin de faire appel \u00e0 l&rsquo;extension <em>auto-pst-pdf<\/em>, en passant une option :<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\\documentclass{standalone}\n\\usepackage[crop=off]{auto-pst-pdf}\n\\usepackage{pstricks-add}\n\\begin{document}\n\n\\psframebox{ %\n\\begin{pspicture*}(-4, -4)(4,4)\n\\psgrid[subgriddiv=0,griddots=10,gridlabels=7pt,gridcolor=gray]\n\\parametricplot[plotstyle=curve,algebraic,linecolor=red]{0}{6.28}{4*sin(t)*cos(t) | 3*sin(t)+cos(t) }\n\\psaxes[ticks=none]{->}(0,0)(-4,-4)(4,4)\n\\end{pspicture*}}\n\n\\end{document}<\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"753\" height=\"745\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-02.png\" alt=\"Courbe param\u00e9tr\u00e9e ou polaire en LaTeX avec PSTricks\" class=\"wp-image-5778\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-02.png 753w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-02-300x297.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-02-100x100.png 100w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-parametree-02-600x594.png 600w\" sizes=\"auto, (max-width: 753px) 100vw, 753px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Autre_exemple_avec_PSTricks\"><\/span>Autre exemple : avec PSTricks<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"latex\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\\documentclass{standalone}\n\\usepackage[crop=off]{auto-pst-pdf}\n\\usepackage{pstricks-add}\n\\begin{document}\n\n\\begin{pspicture}(-3,-4)(4,3)\n\\psgrid[subgriddiv=0,griddots=10,gridlabels=7pt,gridcolor=gray]\n\\psaxes[ticks=none,labels=none]{->}(0,0)(-3,-4)(4,3)\\psplot[polarplot,linecolor=blue,plotpoints=500]{0}{720}{x 0.005 mul}\n\\end{pspicture}\n\n\\end{document}<\/pre>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"746\" height=\"746\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-02.png\" alt=\"Courbe param\u00e9tr\u00e9e ou polaire en LaTeX avec PSTricks\" class=\"wp-image-5779\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-02.png 746w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-02-300x300.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-02-100x100.png 100w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-02-600x600.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2021\/02\/courbe-polaire-02-150x150.png 150w\" sizes=\"auto, (max-width: 746px) 100vw, 746px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Honn\u00eatement, je pr\u00e9f\u00e8re de loin TiKZ car la syntaxe est \u00e0 mes yeux plus naturelle. Mais chacun ses go\u00fbts !<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Et_les_autres_methodes\"><\/span>Et les autres m\u00e9thodes ?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Dans la mesure o\u00f9 je n&rsquo;utilise pas Asymptote, ni m\u00eame MetaPost, je ne peux pas vous en parler (bien s\u00fbr).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mais il y a aussi la m\u00e9thode consistant \u00e0 tout faire sur GeoGebra et de l&rsquo;exporter (soit en code TiKZ ou PSTRicks, pour l&rsquo;ins\u00e9rer directement dans le code \\(\\LaTeX\\), soit au format image et \u00e0 l&rsquo;ins\u00e9rer au format image dans le code avec la commande <tt>\\includegraphics<\/tt> du package <strong>graphicx<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>LaTeX et courbe param\u00e9tr\u00e9e ou polaire: comment la tracer? Quand on souhaite tracer une courbe param\u00e9tr\u00e9e en \\(\\LaTeX\\), on doit s&rsquo;orienter vers une solution graphique, bien s\u00fbr. TiKZ \u00e0 le vent en poupe par sa simplicit\u00e9 d&rsquo;utilisation. En effet, les autres solutions graphiques, telles PSTricks ou Asymptote par exemple, peuvent [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":5775,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[258,224],"class_list":["post-5774","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-latex","tag-pstricks","tag-tikz"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>LaTeX et courbe param\u00e9tr\u00e9e ou polaire - Mathweb.fr<\/title>\n<meta name=\"description\" content=\"Comment dessiner une courbe param\u00e9tr\u00e9e ou polaire en LaTeX ? 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