{"id":7671,"date":"2021-10-20T19:08:00","date_gmt":"2021-10-20T23:08:00","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=7671"},"modified":"2021-10-20T19:08:00","modified_gmt":"2021-10-20T23:08:00","slug":"roll-yaw-pitch-taxi-and-more","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/20\/roll-yaw-pitch-taxi-and-more\/","title":{"rendered":"Roll, Yaw, Pitch, Taxi and More"},"content":{"rendered":"<div class=\"content\"><!--introduction--><p>See <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/03\/the-computer-graphics-matrix-and-a-cube\">Cube<\/a> and <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/03\/the-matrix-at-the-heart-of-computer-graphics\/\">Teapot<\/a>.<\/p><!--\/introduction--><h3>Contents<\/h3><div><ul><li><a href=\"#9bc8b3c7-4da5-4b5d-a142-527e7d71a591\">Plane<\/a><\/li><li><a href=\"#69067bad-c2e8-48cd-ac08-6bad04f65df7\">Cube<\/a><\/li><li><a href=\"#cf6ca207-3484-4c6b-9ede-51372a46c013\">Teapot<\/a><\/li><li><a href=\"#b2225016-f774-4e1c-8eed-ad3b5d17cb9d\">Earth<\/a><\/li><\/ul><\/div><h4>Plane<a name=\"9bc8b3c7-4da5-4b5d-a142-527e7d71a591\"><\/a><\/h4><p><tt>R_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/plane_roll.gif\" alt=\"\"> <\/p><p><tt>R_y<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/plane_yaw.gif\" alt=\"\"> <\/p><p><tt>R_z<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/plane_pitch.gif\" alt=\"\"> <\/p><p><tt>T_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/plane_taxi.gif\" alt=\"\"> <\/p><p>ReLU?<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/plane_ReLU.gif\" alt=\"\"> <\/p><h4>Cube<a name=\"69067bad-c2e8-48cd-ac08-6bad04f65df7\"><\/a><\/h4><p><tt>R_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/cube_roll.gif\" alt=\"\"> <\/p><p><tt>R_y<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/cube_yaw.gif\" alt=\"\"> <\/p><p><tt>R_z<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/cube_pitch.gif\" alt=\"\"> <\/p><p><tt>T_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/cube_taxi.gif\" alt=\"\"> <\/p><p>ReLU?<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/cube_ReLU.gif\" alt=\"\"> <\/p><h4>Teapot<a name=\"cf6ca207-3484-4c6b-9ede-51372a46c013\"><\/a><\/h4><p><tt>R_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/teapot_roll.gif\" alt=\"\"> <\/p><p><tt>R_y<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/teapot_yaw.gif\" alt=\"\"> <\/p><p><tt>R_z<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/teapot_pitch.gif\" alt=\"\"> <\/p><p><tt>T_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/teapot_taxi.gif\" alt=\"\"> <\/p><p>ReLU?<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/teapot_ReLU.gif\" alt=\"\"> <\/p><h4>Earth<a name=\"b2225016-f774-4e1c-8eed-ad3b5d17cb9d\"><\/a><\/h4><p><tt>R_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/earth_roll.gif\" alt=\"\"> <\/p><p><tt>R_y<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/earth_yaw.gif\" alt=\"\"> <\/p><p><tt>R_z<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/earth_pitch.gif\" alt=\"\"> <\/p><p><tt>T_x<\/tt><\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/earth_taxi.gif\" alt=\"\"> <\/p><p>ReLU?<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"http:\/\/blogs.mathworks.com\/cleve\/files\/earth_ReLU.gif\" alt=\"\"> <\/p><script language=\"JavaScript\"> <!-- \r\n    function grabCode_f9d51d39af4a445b89827fcd4fb7c596() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='f9d51d39af4a445b89827fcd4fb7c596 ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' f9d51d39af4a445b89827fcd4fb7c596';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2021 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_f9d51d39af4a445b89827fcd4fb7c596()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; R2021b<br><\/p><\/div><!--\r\nf9d51d39af4a445b89827fcd4fb7c596 ##### SOURCE BEGIN #####\r\n%% Roll, Yaw, Pitch, Taxi and More\r\n%\r\n% See\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/03\/the-computer-graphics-matrix-and-a-cube\r\n% Cube> and\r\n% <https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/03\/the-matrix-at-the-heart-of-computer-graphics\/\r\n% Teapot>.\r\n\r\n%% Plane\r\n%\r\n% |R_x|\r\n%\r\n% <<plane_roll.gif>>\r\n%\r\n% |R_y|\r\n%\r\n% <<plane_yaw.gif>>\r\n%\r\n% |R_z|\r\n%\r\n% <<plane_pitch.gif>>\r\n%\r\n%\r\n% |T_x|\r\n%\r\n% <<plane_taxi.gif>>\r\n%\r\n% ReLU?\r\n%\r\n% <<plane_ReLU.gif>>\r\n%\r\n\r\n%% Cube\r\n%\r\n% |R_x|\r\n%\r\n% <<cube_roll.gif>>\r\n%\r\n% |R_y|\r\n%\r\n% <<cube_yaw.gif>>\r\n%\r\n% |R_z|\r\n%\r\n% <<cube_pitch.gif>>\r\n%\r\n%\r\n% |T_x|\r\n%\r\n% <<cube_taxi.gif>>\r\n%\r\n% ReLU?\r\n%\r\n% <<cube_ReLU.gif>>\r\n%\r\n\r\n%% Teapot\r\n%\r\n% |R_x|\r\n%\r\n% <<teapot_roll.gif>>\r\n%\r\n% |R_y|\r\n%\r\n% <<teapot_yaw.gif>>\r\n%\r\n% |R_z|\r\n%\r\n% <<teapot_pitch.gif>>\r\n%\r\n%\r\n% |T_x|\r\n%\r\n% <<teapot_taxi.gif>>\r\n%\r\n% ReLU?\r\n%\r\n% <<teapot_ReLU.gif>>\r\n%\r\n\r\n%% Earth\r\n%\r\n% |R_x|\r\n%\r\n% <<earth_roll.gif>>\r\n%\r\n% |R_y|\r\n%\r\n% <<earth_yaw.gif>>\r\n%\r\n% |R_z|\r\n%\r\n% <<earth_pitch.gif>>\r\n%\r\n%\r\n% |T_x|\r\n%\r\n% <<earth_taxi.gif>>\r\n%\r\n% ReLU?\r\n%\r\n% <<earth_ReLU.gif>>\r\n%\r\n\r\n##### SOURCE END ##### f9d51d39af4a445b89827fcd4fb7c596\r\n-->","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/takeoff.png\" class=\"img-responsive attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/div><!--introduction--><p>See <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/03\/the-computer-graphics-matrix-and-a-cube\">Cube<\/a> and <a href=\"https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/03\/the-matrix-at-the-heart-of-computer-graphics\/\">Teapot<\/a>.... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2021\/10\/20\/roll-yaw-pitch-taxi-and-more\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":7677,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[32,23,6],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/7671"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=7671"}],"version-history":[{"count":1,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/7671\/revisions"}],"predecessor-version":[{"id":7674,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/7671\/revisions\/7674"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media\/7677"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=7671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=7671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=7671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}