{"id":59,"date":"2007-05-20T02:02:00","date_gmt":"2007-05-20T00:02:00","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/les-transformations\/"},"modified":"2023-10-14T20:12:40","modified_gmt":"2023-10-14T18:12:40","slug":"les-transformations","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/edition-mathematique\/metapost\/figures-geometriques\/les-transformations\/","title":{"rendered":"Les transformations"},"content":{"rendered":"<h2>Rotation<\/h2>\n<hr>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">image := objet rotatedaround(centre,angle);<\/pre>\n<p>ou<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">image := rotation(objet,centre,angle);<\/pre>\n<h2>Sym\u00e9trie centrale<\/h2>\n<hr>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">image := objet rotatedaround(centre,180);<\/pre>\n<p>ou<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">image := symetrie(objet,centre);<\/pre>\n<h2>Sym\u00e9trie axiale d&rsquo;axe (AB)<\/h2>\n<hr>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">image := objet reflectedabout(point_A,point_B);<\/pre>\n<p>ou<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">image := symetrie(objet,point_A,point_B);<\/pre>\n<h2>Translation de vecteur <span class=\"katex-eq\" data-katex-display=\"false\">\\overrightarrow{AB}<\/span><\/h2>\n<hr>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">image := objet shifted (point_B-point_A);<\/pre>\n<h2>Exemples<\/h2>\n<hr>\n<p>Voici une figure r\u00e9sumant les utilisations possibles. On y trouve des images du drapeau gris :<br \/>\n&#8211; par la rotation de centre O, de 90\u00ba dans le sens inverse des aiguilles d&rsquo;une montre (figure rouge) ;<br \/>\n&#8211; par la sym\u00e9trie de centre G (figure verte) ;<br \/>\n&#8211; par la sym\u00e9trie d&rsquo;axe (EF) (figure bleue) ;<br \/>\n&#8211; par la translation de vecteur <span class=\"katex-eq\" data-katex-display=\"false\">\\overrightarrow{EF}<\/span> (figure orange).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" aligncenter size-full wp-image-551\" src=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2007\/05\/jpg_transf1.jpg\" alt=\"transf1.jpg\" width=\"299\" height=\"277\" align=\"center\"><\/p>\n<p>Voici son code dans lequel on peut noter l&rsquo;utilisation du type <em>picture<\/em> :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">u:=1cm;\nfigure (0,0,8u,8u);\npair O,E,F,G;\n\nO=(3.5u,3.5u);\nE=(4u,3u);\nF=(6.5u,5.5u);\nG=(2.5u,5.5u);\n\npicture figd,figi;\ncurrentpicture:=nullpicture;\n\npath tri,piquet;\ntri:=(3.5u,5u)--(4.5u,5u)--(3.5u,4.5u)--cycle ;\nfill tri withcolor 0.5[black,white];\ntrace tri withpen pencircle scaled 1.5bp;\npiquet:=O--(3.5u,4.5u);\ntrace piquet withpen pencircle scaled 1.5bp;\n\nfigd:=currentpicture;\n\n\ntrace grille(0.5) withcolor 0.5[black,white];\n\nmarque_p:=\"croix\";\nnomme.urt(O);\nnomme.lrt(E);\nnomme.lrt(F);\nnomme.ulft(G);\n\nlabel.rt(btex  $d_1$ etex,(3.5u,4.85u));\n\n\nfigi := rotation(figd,O,90);  %rotation\n%figi := figd rotatedaround(O,90);\ndraw figi withcolor red;\n\n\nfigi := symetrie(figd,G);   %symetrie centrale\n%figi :=figd rotatedaround(G,180);\ndraw figi withcolor green;\n\n\nfigi := symetrie(figd,E,F);   %symetrie axiale\n%figi := figd reflectedabout(E,F);\ndraw figi withcolor blue;\n\n\nfigi := figd shifted (F-E);  %translation de vecteur EF\ndraw figi withcolor orange;\n\n\nfin;<\/pre>\n<hr>\n","protected":false},"excerpt":{"rendered":"<p>Rotation image := objet rotatedaround(centre,angle); ou image := rotation(objet,centre,angle); Sym\u00e9trie centrale image := objet rotatedaround(centre,180); ou image := symetrie(objet,centre); Sym\u00e9trie axiale d&rsquo;axe (AB) image := objet reflectedabout(point_A,point_B); ou image :=&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2412,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-59","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Les transformations - Maths &amp; 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