{"id":16007,"date":"2024-01-19T18:12:25","date_gmt":"2024-01-19T14:42:25","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2024-01-19T18:12:25","modified_gmt":"2024-01-19T14:42:25","slug":"%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"\u062f\u0631\u06a9 OpenGL \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u0627\u06cc\u062a\u0648\u0646"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><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:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\u0645\u0639\u0631\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%b9%d9%85%d9%84%db%8c%d8%a7%d8%aa_%d9%85%d8%a7%d8%aa%d8%b1%db%8c%d8%b3_%d9%be%d8%a7%db%8c%d9%87\" >\u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0627\u062a\u0631\u06cc\u0633 \u067e\u0627\u06cc\u0647<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%aa%d8%b1%d8%ac%d9%85%d9%87\" >\u062a\u0631\u062c\u0645\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%da%86%d8%b1%d8%ae%d8%b4\" >\u0686\u0631\u062e\u0634<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d9%82%db%8c%d8%a7%d8%b3_%d8%a8%d9%86%d8%af%db%8c\" >\u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%aa%d8%a8%d8%af%db%8c%d9%84_%d9%87%d8%a7%db%8c_%d9%85%d8%b1%da%a9%d8%a8\" >\u062a\u0628\u062f\u06cc\u0644 \u0647\u0627\u06cc \u0645\u0631\u06a9\u0628<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%af%da%af%d8%b1%da%af%d9%88%d9%86%db%8c_%d9%87%d8%a7%db%8c%db%8c_%da%a9%d9%87_%d8%b4%d8%a7%d9%85%d9%84_%db%8c%da%a9_%d9%86%d9%82%d8%b7%d9%87_%d8%a7%d8%b1%d8%ac%d8%a7%d8%b9_%d9%87%d8%b3%d8%aa%d9%86%d8%af\" >\u062f\u06af\u0631\u06af\u0648\u0646\u06cc \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0634\u0627\u0645\u0644 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0627\u0631\u062c\u0627\u0639 \u0647\u0633\u062a\u0646\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%86%d9%85%d8%a7%db%8c%d8%b4_%d9%85%d8%af%d9%84%db%8c%d9%86%da%af\" >\u0646\u0645\u0627\u06cc\u0634 \u0645\u062f\u0644\u06cc\u0646\u06af<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%af%d8%b1%da%a9-opengl-%d8%a7%d8%b2-%d8%b7%d8%b1%db%8c%d9%82-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 10<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h2 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u067e\u06cc\u0631\u0648 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u0648\u0633\u0637 \u0645\u062d\u0645\u062f \u062c\u0646\u06cc\u062f \u062e\u0627\u0644\u062f\u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u067e\u0627\u06cc\u0647 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.opengl.org\/\" class=\"broken_link\">OpenGL<\/a> \u0645\u0641\u0627\u0647\u06cc\u0645 \u0648 \u062a\u0646\u0638\u06cc\u0645\u0627\u062a \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u060c \u0627\u06a9\u0646\u0648\u0646 \u0645\u0627 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u0686\u06af\u0648\u0646\u06af\u06cc \u0633\u0627\u062e\u062a \u0628\u06cc\u0634\u062a\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u0628\u0648\u062f <em>\u0645\u062c\u062a\u0645\u0639<\/em> \u0627\u0634\u06cc\u0627\u0621 \u0648 \u0686\u06af\u0648\u0646\u06af\u06cc <em>\u062c\u0627\u0646 \u062f\u0627\u062f\u0646<\/em> \u0622\u0646\u0647\u0627 \u0631\u0627<\/p>\n<p>OpenGL \u0628\u0633\u06cc\u0627\u0631 \u0642\u062f\u06cc\u0645\u06cc \u0627\u0633\u062a \u0648 \u0622\u0645\u0648\u0632\u0634 \u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0622\u0646\u0644\u0627\u06cc\u0646 \u067e\u06cc\u062f\u0627 \u0646\u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f \u0631\u0648\u06cc \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0622\u0646 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f \u0648 \u0622\u0646 \u0631\u0627 \u062f\u0631\u06a9 \u06a9\u0631\u062f \u0632\u06cc\u0631\u0627 \u062a\u0645\u0627\u0645 \u0633\u06af \u0647\u0627\u06cc \u0628\u0631\u062a\u0631 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u062f\u0631 \u0641\u0646 \u0622\u0648\u0631\u06cc \u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u062a\u0627 \u0632\u0627\u0646\u0648 \u0639\u0645\u06cc\u0642 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u06a9\u062f OpenGL \u0645\u062f\u0631\u0646\u060c \u0627\u0628\u062a\u062f\u0627 \u0628\u0627\u06cc\u062f \u0622\u0646 \u0631\u0627 \u062f\u0631\u06a9 \u06a9\u0646\u06cc\u062f <em>\u06a9\u0647\u0646<\/em> \u0645\u0641\u0627\u0647\u06cc\u0645\u06cc \u06a9\u0647 \u0646\u0648\u0634\u062a\u0647 \u0634\u062f \u0631\u0648\u06cc \u062a\u0628\u0644\u062a \u0647\u0627\u06cc \u0633\u0646\u06af\u06cc \u062a\u0648\u0633\u0637 \u0628\u0627\u0632\u06cc \u0633\u0627\u0632\u0627\u0646 \u062f\u0627\u0646\u0627 \u0645\u0627\u06cc\u0627\u0646.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0686\u0646\u062f \u0645\u0648\u0636\u0648\u0639 \u0627\u0633\u0627\u0633\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u062f\u0627\u0646\u06cc\u062f \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u06cc\u0645:<\/p>\n<p>\u062f\u0631 \u0628\u062e\u0634 \u0622\u062e\u0631\u060c \u0631\u0648\u0634 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0648\u0627\u0642\u0639\u06cc \u0627\u0632 OpenGL \u0628\u0627 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0647\u0627\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.pygame.org\">PyGame<\/a> \u0648 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"http:\/\/pyopengl.sourceforge.net\/\">PyOpenGL<\/a>.<\/p>\n<p>\u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0628\u0639\u062f\u06cc \u0646\u06af\u0627\u0647\u06cc \u0639\u0645\u06cc\u0642 \u062a\u0631 \u0628\u0647 \u0631\u0648\u0634 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 OpenGL \u0628\u0627 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0648 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0647\u0627\u06cc \u0630\u06a9\u0631 \u0634\u062f\u0647 \u062f\u0631 \u0628\u0627\u0644\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a.<\/p>\n<h2 id=\"basicmatrixoperations\"><span class=\"ez-toc-section\" id=\"%d8%b9%d9%85%d9%84%db%8c%d8%a7%d8%aa_%d9%85%d8%a7%d8%aa%d8%b1%db%8c%d8%b3_%d9%be%d8%a7%db%8c%d9%87\"><\/span>\u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0627\u062a\u0631\u06cc\u0633 \u067e\u0627\u06cc\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u0627\u0632 \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u062f\u0631 OpenGL \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0647 \u0645\u0642\u062f\u0627\u0631\u06cc \u0647\u0646\u062f\u0633\u0647 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645.<\/p>\n<p>\u062a\u06a9 \u062a\u06a9 <em>\u0646\u0642\u0637\u0647 \u062f\u0631 \u0641\u0636\u0627<\/em> \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 <strong>\u0645\u062e\u062a\u0635\u0627\u062a \u06a9\u0627\u0631\u062a\u0632\u06cc\u0646<\/strong>.  \u0645\u062e\u062a\u0635\u0627\u062a \u0645\u06a9\u0627\u0646 \u0647\u0631 \u0646\u0642\u0637\u0647 \u0645\u0639\u06cc\u0646 \u0631\u0627 \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0622\u0646 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f <em>\u0627\u06cc\u06a9\u0633<\/em>\u060c <em>Y<\/em> \u0648 <em>\u0632<\/em> \u0627\u0631\u0632\u0634 \u0647\u0627\u06cc.<\/p>\n<p>\u0645\u0627 \u0639\u0645\u0644\u0627\u064b \u0627\u0632 \u0622\u0646\u0647\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <em>\u0645\u0627\u062a\u0631\u06cc\u0633 1&#215;3<\/em>\u060c \u06cc\u0627 \u0628\u0647\u062a\u0631 \u0627\u0633\u062a \u0628\u06af\u0648\u06cc\u06cc\u0645 3 \u0628\u0639\u062f\u06cc <em>\u0628\u0631\u062f\u0627\u0631\u0647\u0627<\/em> (\u0628\u06cc\u0634\u062a\u0631 \u0631\u0648\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0639\u062f \u0631\u0648\u06cc).<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc\u06cc \u0627\u0632 \u0645\u062e\u062a\u0635\u0627\u062a \u0622\u0648\u0631\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0622<\/mi>\n  <mo>=<\/mo>\n  <mo stretchy=\"false\">(<\/mo>\n  <mn>5<\/mn>\n  <mo>\u060c<\/mo>\n  <mn>3<\/mn>\n  <mo>\u060c<\/mo>\n  <mn>4<\/mn>\n  <mo stretchy=\"false\">)<\/mo>\n  <mtext> <\/mtext>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mi>\u0628<\/mi>\n  <mo>=<\/mo>\n  <mo stretchy=\"false\">(<\/mo>\n  <mn>9<\/mn>\n  <mo>\u060c<\/mo>\n  <mn>1<\/mn>\n  <mo>\u060c<\/mo>\n  <mn>2<\/mn>\n  <mo stretchy=\"false\">)<\/mo>\n<\/math><\/p>\n<p><code>a<\/code>  \u0648 <code>b<\/code> \u0646\u0642\u0627\u0637\u06cc \u062f\u0631 \u0641\u0636\u0627 \u0647\u0633\u062a\u0646\u062f\u060c \u0645\u062e\u062a\u0635\u0627\u062a x \u0622\u0646\u0647\u0627 \u0647\u0633\u062a\u0646\u062f <code>5<\/code> \u0648 <code>9<\/code> \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 y \u0628\u0648\u062f\u0646 \u0631\u0627 \u0645\u062e\u062a\u0635\u0627\u062a \u0645\u06cc \u06a9\u0646\u062f <code>3<\/code> \u0648 <code>1<\/code>\u060c \u0648 \u063a\u06cc\u0631\u0647 \u0631\u0648\u06cc.<\/p>\n<p>\u062f\u0631 \u06af\u0631\u0627\u0641\u06cc\u06a9 \u06a9\u0627\u0645\u067e\u06cc\u0648\u062a\u0631\u06cc\u060c \u0627\u063a\u0644\u0628\u060c <em>\u0647\u0645\u06af\u0646<\/em> \u0645\u062e\u062a\u0635\u0627\u062a \u0628\u0647 \u062c\u0627\u06cc \u0645\u062e\u062a\u0635\u0627\u062a \u062f\u06a9\u0627\u0631\u062a\u06cc \u0645\u0639\u0645\u0648\u0644\u06cc \u0642\u062f\u06cc\u0645\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0622\u0646\u0647\u0627 \u0627\u0633\u0627\u0633\u0627\u064b \u06cc\u06a9\u0633\u0627\u0646 \u0647\u0633\u062a\u0646\u062f\u060c \u0641\u0642\u0637 \u0628\u0627 \u06cc\u06a9 \u067e\u0627\u0631\u0627\u0645\u062a\u0631 \u0627\u0628\u0632\u0627\u0631 \u0627\u0636\u0627\u0641\u06cc\u060c \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u06af\u06cc \u0645\u06cc \u06af\u0648\u06cc\u06cc\u0645 \u0647\u0645\u06cc\u0634\u0647 <code>1<\/code>.<\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0627\u06af\u0631 \u0645\u062e\u062a\u0635\u0627\u062a \u0645\u0646\u0638\u0645 \u0627\u0632 <code>a<\/code> \u0647\u0633\u062a\u0646\u062f <code>(5,3,4)<\/code>\u060c \u0645\u062e\u062a\u0635\u0627\u062a \u0647\u0645\u06af\u0646 \u0645\u0631\u0628\u0648\u0637\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <code>(5,3,4,1)<\/code>.  \u062a\u0626\u0648\u0631\u06cc \u0647\u0646\u062f\u0633\u06cc \u0632\u06cc\u0627\u062f\u06cc \u067e\u0634\u062a \u0627\u06cc\u0646 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0627\u0645\u0627 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0648\u0627\u0642\u0639\u0627\u064b \u0636\u0631\u0648\u0631\u06cc \u0646\u06cc\u0633\u062a.<\/p>\n<p>\u062f\u0631 \u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u060c \u06cc\u06a9 \u0627\u0628\u0632\u0627\u0631 \u0636\u0631\u0648\u0631\u06cc \u0628\u0631\u0627\u06cc \u0646\u0645\u0627\u06cc\u0634 \u062a\u0628\u062f\u06cc\u0644\u0627\u062a \u0647\u0646\u062f\u0633\u06cc \u0647\u0633\u062a\u0646\u062f <em>\u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627<\/em>.  \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0633\u0627\u0633\u0627 \u06cc\u06a9 \u0622\u0631\u0627\u06cc\u0647 \u062f\u0648 \u0628\u0639\u062f\u06cc \u0627\u0633\u062a (\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u0627\u0646\u062f\u0627\u0632\u0647 <em>n*n<\/em>\u060c \u062f\u0627\u0634\u062a\u0646 \u062a\u0639\u062f\u0627\u062f \u0633\u0637\u0631 \u0648 \u0633\u062a\u0648\u0646 \u0628\u0631\u0627\u06cc \u0622\u0646\u0647\u0627 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0647\u0645 \u0627\u0633\u062a).<\/p>\n<p>\u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc\u060c \u0627\u063a\u0644\u0628\u060c \u0628\u0633\u06cc\u0627\u0631 \u0633\u0627\u062f\u0647 \u0647\u0633\u062a\u0646\u062f\u060c \u0645\u0627\u0646\u0646\u062f \u062c\u0645\u0639\u060c \u062a\u0641\u0631\u06cc\u0642\u060c \u0648 \u063a\u06cc\u0631\u0647. \u0627\u0645\u0627 \u0645\u0633\u0644\u0645\u0627\u064b \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0627\u06cc\u062f \u067e\u06cc\u0686\u06cc\u062f\u0647 \u062a\u0631\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0628\u0627\u0634\u062f &#8211; \u0636\u0631\u0628.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u0645\u062b\u0627\u0644 \u0647\u0627\u06cc \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0648\u0644\u06cc\u0647 \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0622<\/mi>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>6<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>9<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>&#8211;<\/mo>\n  <mtext>\u0645\u0627\u062a\u0631\u06cc\u0633 \u0646\u0645\u0648\u0646\u0647<\/mtext>\n  <mtext> <\/mtext>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>6<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>9<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>+<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>10<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>12<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>18<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>10<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>10<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>4<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>3<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>7<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>15<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>18<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>3<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>27<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>15<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>15<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>6<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>&#8211;<\/mo>\n  <mtext>\u0627\u0636\u0627\u0641\u0647 \u06a9\u0631\u062f\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633<\/mtext>\n  <mtext> <\/mtext>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>4<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>10<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>12<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>18<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>10<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>10<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>4<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>&#8211;<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>6<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>9<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>6<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>9<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>5<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>2<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>&#8211;<\/mo>\n  <mtext>\u062a\u0641\u0631\u06cc\u0642 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc<\/mtext>\n  <mtext> <\/mtext>\n  <mspace linebreak=\"newline\"><\/mspace>\n<\/math><\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646\u060c \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062a\u0645\u0627\u0645 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a \u062a\u0645\u0627\u06cc\u0644 \u062f\u0627\u0631\u0646\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u0646\u062f\u060c \u0648\u0642\u062a\u06cc \u0648\u0627\u0642\u0639\u0627\u064b \u0686\u06cc\u0632\u06cc \u0639\u0645\u0644\u06cc \u0627\u0632 \u0622\u0646 \u0628\u062e\u0648\u0627\u0647\u06cc\u062f\u060c \u0646\u0633\u0628\u062a\u0627\u064b \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0641\u0631\u0645\u0648\u0644 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p>$$<br \/>c(i,j) = \\sum_{k=1}^{n}a(i,k)*b(k,j)<br \/>$$<\/p>\n<p><code>c<\/code>  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062d\u0627\u0635\u0644\u060c <code>a<\/code> \u0648 <code>b<\/code> \u0636\u0631\u0628 \u0648 \u0636\u0631\u06cc\u0628 \u0628\u0648\u062f\u0646.<\/p>\n<p>\u062f\u0631 \u0648\u0627\u0642\u0639 \u06cc\u06a9 \u062a\u0648\u0636\u06cc\u062d \u0633\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0641\u0631\u0645\u0648\u0644 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.  \u0647\u0631 \u0639\u0646\u0635\u0631 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639 \u062d\u0627\u0635\u0644\u0636\u0631\u0628 \u062a\u0645\u0627\u0645 \u0639\u0646\u0627\u0635\u0631 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0622\u0646 \u0633\u0627\u062e\u062a <code>i<\/code>&#8211; \u0631\u062f\u06cc\u0641 \u0648 <code>j<\/code>\u0633\u062a\u0648\u0646 -\u0627\u0645.  \u0627\u06cc\u0646 \u062f\u0644\u06cc\u0644\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 <code>a(i,k)<\/code>\u060c <code>i<\/code> \u062b\u0627\u0628\u062a \u0627\u0633\u062a \u0648 <code>k<\/code> \u0628\u0631\u0627\u06cc \u062a\u06a9\u0631\u0627\u0631 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0639\u0646\u0627\u0635\u0631 \u0631\u062f\u06cc\u0641 \u0645\u0631\u0628\u0648\u0637\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0647\u0645\u06cc\u0646 \u0627\u0635\u0644 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u06a9\u0627\u0631 \u0628\u0631\u062f <code>b(k,j)<\/code>.<\/p>\n<p>\u0628\u0627 \u062f\u0627\u0646\u0633\u062a\u0646 \u0627\u06cc\u0646 \u0645\u0648\u0636\u0648\u0639\u060c \u06cc\u06a9 \u0634\u0631\u0637 \u0627\u0636\u0627\u0641\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u0631\u0622\u0648\u0631\u062f\u0647 \u0634\u0648\u062f \u062a\u0627 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645.  \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627 \u0631\u0627 \u0636\u0631\u0628 \u06a9\u0646\u06cc\u0645 <code>A<\/code> \u0648 <code>B<\/code> \u0627\u0632 \u0627\u0628\u0639\u0627\u062f <code>a*b<\/code> \u0648 <code>c*d<\/code>.  \u062a\u0639\u062f\u0627\u062f \u0639\u0646\u0627\u0635\u0631 \u062f\u0631 \u06cc\u06a9 \u0631\u062f\u06cc\u0641 \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0648\u0644 (<code>b<\/code>) \u0628\u0627\u06cc\u062f \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u0639\u0646\u0627\u0635\u0631 \u06cc\u06a9 \u0633\u062a\u0648\u0646 \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0648\u0645 \u06cc\u06a9\u0633\u0627\u0646 \u0628\u0627\u0634\u062f (<code>c<\/code>) \u062a\u0627 \u0628\u062a\u0648\u0627\u0646 \u0627\u0632 \u0641\u0631\u0645\u0648\u0644 \u0628\u0627\u0644\u0627 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/p>\n<p>\u06cc\u06a9 \u0631\u0627\u0647 \u0628\u0633\u06cc\u0627\u0631 \u062e\u0648\u0628 \u0628\u0631\u0627\u06cc \u062a\u062c\u0633\u0645 \u0627\u06cc\u0646 \u0645\u0641\u0647\u0648\u0645\u060c \u0628\u0631\u062c\u0633\u062a\u0647 \u06a9\u0631\u062f\u0646 \u0633\u0637\u0631\u0647\u0627 \u0648 \u0633\u062a\u0648\u0646\u200c\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0642\u0631\u0627\u0631 \u0627\u0633\u062a \u0627\u0632 \u0639\u0646\u0627\u0635\u0631 \u0622\u0646\u0647\u0627 \u062f\u0631 \u0636\u0631\u0628 \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0645\u0639\u06cc\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f.  \u062a\u0635\u0648\u0631 \u06a9\u0646\u06cc\u062f \u0627\u06cc\u0646 \u062f\u0648 \u0628\u0631\u062c\u0633\u062a\u0647 \u0634\u062f\u0647 \u0627\u0646\u062f <em>\u062e\u0637\u0648\u0637<\/em> \u0628\u0631 \u0631\u0648\u06cc \u06cc\u06a9\u062f\u06cc\u06af\u0631\u060c \u06af\u0648\u06cc\u06cc \u062f\u0631 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0639\u0646\u0635\u0631\u06cc \u06a9\u0647 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0631\u0647\u06af\u06cc\u0631\u06cc \u0645\u06cc \u06a9\u0646\u0646\u062f\u060c \u0645\u0648\u0642\u0639\u06cc\u062a \u0639\u0646\u0635\u0631 \u062d\u0627\u0635\u0644 \u0627\u0632 \u062c\u0645\u0639 \u0645\u062d\u0635\u0648\u0644\u0627\u062a \u0622\u0646\u0647\u0627 \u0627\u0633\u062a:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/understanding-opengl-through-python-1.png\" alt=\"\u062a\u0642\u0627\u0637\u0639 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc\" title=\"\"><\/p>\n<p>\u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0647\u0645 \u0627\u0633\u062a \u0632\u06cc\u0631\u0627 \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0639\u0628\u0627\u0631\u062a \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0647 \u0632\u0628\u0627\u0646 \u0633\u0627\u062f\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0647\u06cc\u0645: <code>A*B<\/code> (A \u0648 B \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0633\u062a\u0646\u062f)\u060c \u0645\u06cc \u06af\u0648\u06cc\u06cc\u0645:<\/p>\n<blockquote>\n<p>\u0645\u0627 A \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 B \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<\/blockquote>\n<p>\u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0627\u0633\u062a \u06a9\u0647 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0628\u0632\u0627\u0631 \u0627\u0635\u0644\u06cc \u0628\u0631\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0647\u0631 \u0634\u06cc \u062f\u0631 OpenGL \u06cc\u0627 \u0628\u0647 \u0637\u0648\u0631 \u06a9\u0644\u06cc \u0647\u0646\u062f\u0633\u0647 \u0627\u0633\u062a.<\/p>\n<p>\u0622\u062e\u0631\u06cc\u0646 \u0686\u06cc\u0632\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u062f\u0631 \u0645\u0648\u0631\u062f \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u062f\u0627\u0646\u06cc\u062f \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 a \u062f\u0627\u0631\u062f <strong>\u062e\u0646\u062b\u06cc<\/strong>.  \u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0645\u0646\u062d\u0635\u0631 \u0628\u0647 \u0641\u0631\u062f \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f (\u0645\u0627\u062a\u0631\u06cc\u0633 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f) <code>E<\/code> \u06a9\u0647 \u0648\u0642\u062a\u06cc \u0628\u0627 \u0647\u0631 \u0639\u0646\u0635\u0631 \u062f\u06cc\u06af\u0631\u06cc \u0636\u0631\u0628 \u0634\u0648\u062f <code>A<\/code> \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc \u06a9\u0646\u062f <code>A<\/code>\u0645\u0642\u062f\u0627\u0631\u060c \u06cc\u0639\u0646\u06cc:<\/p>\n<p>$$<br \/>(!\\\u0648\u062c\u0648\u062f{E}\\ \\ \\\u0628\u0631\u0627\u06cc \u0647\u0645\u0647{A})\\ E*A=A<br \/>$$<\/p>\n<blockquote>\n<p>\u0639\u0644\u0627\u0645\u062a \u062a\u0639\u062c\u0628 \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627 \u0639\u0644\u0627\u0645\u062a \u0648\u062c\u0648\u062f \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a: <strong>\u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0645\u0646\u062d\u0635\u0631 \u0628\u0647 \u0641\u0631\u062f E \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 &#8230;<\/strong><\/p>\n<\/blockquote>\n<p>\u062f\u0631 \u0635\u0648\u0631\u062a \u0636\u0631\u0628 \u0628\u0627 \u0627\u0639\u062f\u0627\u062f \u0635\u062d\u06cc\u062d \u0645\u0639\u0645\u0648\u0644\u06cc\u060c <code>E<\/code> \u0627\u0631\u0632\u0634 \u062f\u0627\u0631\u062f <code>1<\/code>.  \u062f\u0631 \u0645\u0648\u0631\u062f \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u060c E \u062f\u0627\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0632\u06cc\u0631 \u062f\u0631 \u062d\u0627\u0644\u062a \u0639\u0627\u062f\u06cc \u0627\u0633\u062a <em>\u062f\u06a9\u0627\u0631\u062a\u06cc<\/em> (E<sub>1<\/sub>) \u0648 <em>\u0645\u062e\u062a\u0635\u0627\u062a \u0647\u0645\u06af\u0646<\/em> (E<sub>2<\/sub>) \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <msub>\n    <mi>E<\/mi>\n    <mn>1<\/mn>\n  <\/msub>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <msub>\n    <mi>E<\/mi>\n    <mn>2<\/mn>\n  <\/msub>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u0647\u0631 \u062a\u0628\u062f\u06cc\u0644 \u0647\u0646\u062f\u0633\u06cc \u062f\u0627\u0631\u0627\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0628\u062f\u06cc\u0644 \u0645\u0646\u062d\u0635\u0631 \u0628\u0647 \u0641\u0631\u062f \u062e\u0648\u062f \u0627\u0633\u062a \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u0646\u0648\u0639\u06cc \u0627\u0644\u06af\u0648 \u0627\u0633\u062a \u06a9\u0647 \u0645\u0647\u0645\u062a\u0631\u06cc\u0646 \u0622\u0646\u0647\u0627 \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<ul>\n<li>\u062a\u0631\u062c\u0645\u0647<\/li>\n<li>\u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc<\/li>\n<li>\u0627\u0646\u0639\u06a9\u0627\u0633<\/li>\n<li>\u0686\u0631\u062e\u0634<\/li>\n<li>\u0634\u06cc\u06cc\u0631\u06cc\u0646\u06af<\/li>\n<\/ul>\n<h3 id=\"translation\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%b1%d8%ac%d9%85%d9%87\"><\/span>\u062a\u0631\u062c\u0645\u0647<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062a\u0631\u062c\u0645\u0647 \u0639\u0645\u0644 \u062d\u0631\u06a9\u062a \u0628\u0647 \u0645\u0639\u0646\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u06a9\u0644\u0645\u0647 \u062a\u0648\u0633\u0637 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0633\u062a.  \u062c\u0633\u0645\u06cc \u06a9\u0647 \u062a\u062d\u062a \u062a\u0623\u062b\u06cc\u0631 \u062f\u06af\u0631\u06af\u0648\u0646\u06cc \u0642\u0631\u0627\u0631 \u0645\u06cc \u06af\u06cc\u0631\u062f \u0628\u0647 \u0647\u06cc\u0686 \u0648\u062c\u0647 \u0634\u06a9\u0644 \u062e\u0648\u062f \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc \u062f\u0647\u062f \u0648 \u062c\u0647\u062a \u062e\u0648\u062f \u0631\u0627 \u0646\u06cc\u0632 \u062a\u063a\u06cc\u06cc\u0631 \u0646\u0645\u06cc \u062f\u0647\u062f &#8211; \u0641\u0642\u0637 \u062f\u0631 \u0641\u0636\u0627 \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u062f (\u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u0634\u0648\u062f. <em>\u062c\u0646\u0628\u0634<\/em> \u062f\u06af\u0631\u06af\u0648\u0646\u06cc).<\/p>\n<p>\u062a\u0631\u062c\u0645\u0647 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0641\u0631\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0632\u06cc\u0631 \u062a\u0648\u0635\u06cc\u0641 \u06a9\u0631\u062f:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u062a\u06cc<\/mi>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <msub>\n            <mi>\u062a\u06cc<\/mi>\n            <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <\/msub>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <msub>\n            <mi>\u062a\u06cc<\/mi>\n            <mi>y<\/mi>\n          <\/msub>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <msub>\n            <mi>\u062a\u06cc<\/mi>\n            <mi>z<\/mi>\n          <\/msub>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u0627\u06cc\u0646 <code>t<\/code>-s \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0645\u06cc\u0632\u0627\u0646 \u0634\u06cc\u0621 \u0627\u0633\u062a <code>x<\/code>\u060c<code>y<\/code> \u0648 <code>z<\/code> \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u06a9\u0627\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u06a9\u0631\u062f.<\/p>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u067e\u0633 \u0627\u0632 \u062a\u0628\u062f\u06cc\u0644 \u0647\u0631 \u0645\u062e\u062a\u0635\u0627\u062a\u06cc \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0631\u062c\u0645\u0647 <code>T<\/code>\u060c \u0645\u0627 \u06af\u0631\u0641\u062a\u06cc\u0645:<\/p>\n<p>$$<br \/>(x,y,z)*T=(t_x+x,t_y+y,t_z+z)<br \/>$$<\/p>\n<p>\u062a\u0631\u062c\u0645\u0647 \u0628\u0627 \u062a\u0627\u0628\u0639 OpenGL \u0632\u06cc\u0631 \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">void<\/span> <span class=\"hljs-title\">glTranslatef<\/span><span class=\"hljs-params\">(GLfloat tx, GLfloat ty, GLfloat tz)<\/span><\/span>;\n<\/code><\/pre>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u062f\u060c \u0627\u06af\u0631 \u0634\u06a9\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0631\u062c\u0645\u0647 \u0631\u0627 \u0628\u062f\u0627\u0646\u06cc\u0645\u060c \u062f\u0631\u06a9 \u062a\u0627\u0628\u0639 OpenGL \u0628\u0633\u06cc\u0627\u0631 \u0633\u0627\u062f\u0647 \u0627\u0633\u062a\u060c \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u062f\u0631 \u0645\u0648\u0631\u062f \u0647\u0645\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0647\u0627\u06cc OpenGL \u0627\u0633\u062a.<\/p>\n<blockquote>\n<p>\u0627\u0647\u0645\u06cc\u062a \u0646\u062f\u0647 <code>GLfloat<\/code>\u060c \u0627\u06cc\u0646 \u0641\u0642\u0637 \u06cc\u06a9 \u0646\u0648\u0639 \u062f\u0627\u062f\u0647 \u0647\u0648\u0634\u0645\u0646\u062f\u0627\u0646\u0647 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631 OpenGL \u0627\u0633\u062a \u0631\u0648\u06cc \u0686\u0646\u062f\u06cc\u0646 \u067e\u0644\u062a\u0641\u0631\u0645\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u062f:<\/p>\n<\/blockquote>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">typedef<\/span> <span class=\"hljs-keyword\">float<\/span> GLfloat;\n<span class=\"hljs-keyword\">typedef<\/span> <span class=\"hljs-keyword\">double<\/span> GLdouble;\n<span class=\"hljs-keyword\">typedef<\/span> someType GLsomeType;\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u06cc\u06a9 \u0627\u0642\u062f\u0627\u0645 \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a \u0632\u06cc\u0631\u0627 \u0647\u0645\u0647 \u0633\u06cc\u0633\u062a\u0645 \u0647\u0627 \u0641\u0636\u0627\u06cc \u0630\u062e\u06cc\u0631\u0647 \u0633\u0627\u0632\u06cc \u06cc\u06a9\u0633\u0627\u0646\u06cc \u0628\u0631\u0627\u06cc a \u0646\u062f\u0627\u0631\u0646\u062f <code>char<\/code>\u060c \u0645\u062b\u0644\u0627.<\/p>\n<h3 id=\"rotation\"><span class=\"ez-toc-section\" id=\"%da%86%d8%b1%d8%ae%d8%b4\"><\/span>\u0686\u0631\u062e\u0634<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0686\u0631\u062e\u0634 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0645\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647\u200c\u062a\u0631 \u0627\u0633\u062a\u060c \u0632\u06cc\u0631\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0648\u0627\u0642\u0639\u06cc\u062a \u0633\u0627\u062f\u0647 \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a \u0631\u0648\u06cc 2 \u0639\u0627\u0645\u0644:<\/p>\n<ul>\n<li><strong>\u0645\u062d\u0648\u0631:<\/strong> \u062d\u0648\u0644 \u0686\u0647 \u062e\u0637\u06cc \u062f\u0631 \u0641\u0636\u0627\u06cc \u0633\u0647 \u0628\u0639\u062f\u06cc (\u06cc\u0627 \u0646\u0642\u0637\u0647 \u0627\u06cc \u062f\u0631 \u0641\u0636\u0627\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc) \u062e\u0648\u0627\u0647\u06cc\u0645 \u0686\u0631\u062e\u06cc\u062f<\/li>\n<li><strong>\u0645\u06cc\u0632\u0627\u0646:<\/strong> \u0686\u0642\u062f\u0631 (\u0628\u0631 \u062d\u0633\u0628 \u062f\u0631\u062c\u0647 \u06cc\u0627 \u0631\u0627\u062f\u06cc\u0627\u0646) \u062f\u0631 \u062d\u0627\u0644 \u0686\u0631\u062e\u0634 \u062e\u0648\u0627\u0647\u06cc\u0645 \u0628\u0648\u062f<\/li>\n<\/ul>\n<p>\u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644\u060c \u0627\u0628\u062a\u062f\u0627 \u0628\u0627\u06cc\u062f \u0686\u0631\u062e\u0634 \u0631\u0627 \u062f\u0631 \u0641\u0636\u0627\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0631\u0627\u06cc \u0622\u0646 \u0628\u0647 \u06a9\u0645\u06cc \u0645\u062b\u0644\u062b\u0627\u062a \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u06a9 \u0645\u0631\u062c\u0639 \u0633\u0631\u06cc\u0639 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/understanding-opengl-through-python-2.png\" alt=\"\" title=\"\"><\/p>\n<blockquote>\n<p>\u0627\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0645\u062b\u0644\u062b\u0627\u062a\u06cc \u0641\u0642\u0637 \u062f\u0631 \u062f\u0627\u062e\u0644 \u0645\u062b\u0644\u062b \u0642\u0627\u0626\u0645 \u0627\u0644\u0632\u0627\u0648\u06cc\u0647 \u0642\u0627\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0647\u0633\u062a\u0646\u062f (\u06cc\u06a9\u06cc \u0627\u0632 \u0632\u0648\u0627\u06cc\u0627 \u0628\u0627\u06cc\u062f 90 \u062f\u0631\u062c\u0647 \u0628\u0627\u0634\u062f).<\/p>\n<\/blockquote>\n<p>\u0645\u0627\u062a\u0631\u06cc\u0633 \u0686\u0631\u062e\u0634 \u067e\u0627\u06cc\u0647 \u0628\u0631\u0627\u06cc \u0686\u0631\u062e\u0627\u0646\u062f\u0646 \u06cc\u06a9 \u062c\u0633\u0645 \u062f\u0631 \u0641\u0636\u0627\u06cc \u062f\u0648\u0628\u0639\u062f\u06cc \u062d\u0648\u0644 \u0631\u0623\u0633 (<code>0,0<\/code>) \u0628\u0627 \u0632\u0627\u0648\u06cc\u0647 <code>A<\/code> \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<blockquote>\n<p>\u0628\u0627\u0632 \u0647\u0645\u060c \u0633\u0637\u0631 3 \u0648 \u0633\u062a\u0648\u0646 3 \u0641\u0642\u0637 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u062a\u0628\u062f\u06cc\u0644\u200c\u0647\u0627\u06cc \u062a\u0631\u062c\u0645\u0647 \u0631\u0627 \u0631\u0648\u06cc \u0647\u0645 \u0628\u06af\u0630\u0627\u0631\u06cc\u0645 \u0631\u0648\u06cc \u0628\u0627\u0644\u0627\u062a\u0631 \u0627\u0632 \u0633\u0627\u06cc\u0631 \u062a\u0628\u062f\u06cc\u0644\u200c\u0647\u0627 (\u06a9\u0647 \u0645\u0627 \u062f\u0631 OpenGL \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645)\u060c \u0627\u06af\u0631 \u0628\u0647 \u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u062f\u0631\u06a9 \u0646\u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0686\u0631\u0627 \u0622\u0646\u0647\u0627 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0622\u0646\u062c\u0627 \u0647\u0633\u062a\u0646\u062f\u060c \u0645\u0634\u06a9\u0644\u06cc \u0646\u06cc\u0633\u062a.  \u0686\u06cc\u0632\u0647\u0627 \u0628\u0627\u06cc\u062f \u062f\u0631 \u0645\u062b\u0627\u0644 \u062a\u0628\u062f\u06cc\u0644 \u062a\u0631\u06a9\u06cc\u0628\u06cc \u0631\u0648\u0634\u0646 \u0634\u0648\u0646\u062f.<\/p>\n<\/blockquote>\n<p>\u0647\u0645\u0647 \u0627\u06cc\u0646\u0647\u0627 \u062f\u0631 \u0641\u0636\u0627\u06cc \u062f\u0648 \u0628\u0639\u062f\u06cc \u0628\u0648\u062f\u060c \u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u062d\u0631\u06a9\u062a \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u0628\u0647 \u0641\u0636\u0627\u06cc \u0633\u0647 \u0628\u0639\u062f\u06cc  \u062f\u0631 \u0641\u0636\u0627\u06cc \u0633\u0647 \u0628\u0639\u062f\u06cc \u0628\u0627\u06cc\u062f \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u062f \u06cc\u06a9 \u0634\u06cc \u0631\u0627 \u0628\u0647 \u062f\u0648\u0631 \u062e\u0648\u062f \u0628\u0686\u0631\u062e\u0627\u0646\u062f <strong>\u0647\u0631<\/strong> \u062e\u0637<\/p>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u06cc\u06a9 \u0645\u0631\u062f \u062e\u0631\u062f\u0645\u0646\u062f \u06cc\u06a9 \u0628\u0627\u0631 \u06af\u0641\u062a: &#8220;\u0633\u0627\u062f\u0647 \u0648 \u0627\u062d\u0645\u0642\u0627\u0646\u0647 \u0646\u06af\u0647 \u062f\u0627\u0631!&#8221;  \u062e\u0648\u0634\u0628\u062e\u062a\u0627\u0646\u0647\u060c \u0634\u0639\u0628\u062f\u0647 \u0628\u0627\u0632\u0627\u0646 \u0631\u06cc\u0627\u0636\u06cc \u0628\u0631\u0627\u06cc \u06cc\u06a9 \u0628\u0627\u0631 \u0622\u0646 \u0631\u0627 \u0633\u0627\u062f\u0647 \u0648 \u0627\u062d\u0645\u0642\u0627\u0646\u0647 \u0646\u06af\u0647 \u062f\u0627\u0634\u062a\u0646\u062f.<\/p>\n<p>\u0647\u0631 \u0686\u0631\u062e\u0634 \u062d\u0648\u0644 \u06cc\u06a9 \u062e\u0637 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0686\u0646\u062f \u062a\u0628\u062f\u06cc\u0644 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f:<\/p>\n<ul>\n<li>\u0686\u0631\u062e\u0634 \u062d\u0648\u0644 \u0645\u062d\u0648\u0631 x<\/li>\n<li>\u0686\u0631\u062e\u0634 \u062d\u0648\u0644 \u0645\u062d\u0648\u0631 y<\/li>\n<li>\u0686\u0631\u062e\u0634 \u062d\u0648\u0644 \u0645\u062d\u0648\u0631 z<\/li>\n<li>\u062a\u0631\u062c\u0645\u0647 \u0647\u0627\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f\u06cc (\u06a9\u0647 \u0628\u0639\u062f\u0627\u064b \u0628\u0647 \u0622\u0646\u0647\u0627 \u067e\u0631\u062f\u0627\u062e\u062a\u0647 \u062e\u0648\u0627\u0647\u062f \u0634\u062f)<\/li>\n<\/ul>\n<p>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646\u060c \u062a\u0646\u0647\u0627 \u0633\u0647 \u0686\u06cc\u0632\u06cc \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0686\u0631\u062e\u0634 \u0633\u0647 \u0628\u0639\u062f\u06cc \u0628\u0627\u06cc\u062f \u0628\u0633\u0627\u0632\u06cc\u0645\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0686\u0631\u062e\u0634 \u062d\u0648\u0644 <code>x<\/code>\u060c <code>y<\/code>\u060c \u0648 <code>z<\/code> \u0645\u062d\u0648\u0631 \u062a\u0648\u0633\u0637 \u06cc\u06a9 \u0632\u0627\u0648\u06cc\u0647 <code>A<\/code>:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <msub>\n    <mi>\u0622\u0631<\/mi>\n    <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <\/msub>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <msub>\n    <mi>\u0622\u0631<\/mi>\n    <mi>y<\/mi>\n  <\/msub>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <msub>\n    <mi>\u0622\u0631<\/mi>\n    <mi>z<\/mi>\n  <\/msub>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mi>\u0633<\/mi>\n          <mi>\u0645\u0646<\/mi>\n          <mi>n<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mi>\u062c<\/mi>\n          <mi>o<\/mi>\n          <mi>\u0633<\/mi>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u0686\u0631\u062e\u0634 \u0633\u0647 \u0628\u0639\u062f\u06cc \u0628\u0627 \u062a\u0627\u0628\u0639 OpenGL \u0632\u06cc\u0631 \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">void<\/span> <span class=\"hljs-title\">glRotatef<\/span><span class=\"hljs-params\">(GLfloat angle, GLfloat x, GLfloat y, GLfloat z)<\/span><\/span>;\n<\/code><\/pre>\n<ul>\n<li><code>angle<\/code>: \u0632\u0627\u0648\u06cc\u0647 \u0686\u0631\u062e\u0634 \u0628\u0631 \u062d\u0633\u0628 \u062f\u0631\u062c\u0647 (0-360)<\/li>\n<li><code>x,y,z<\/code>: \u0628\u0631\u062f\u0627\u0631\u06cc \u06a9\u0647 \u0686\u0631\u062e\u0634 \u062d\u0648\u0644 \u0622\u0646 \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f<\/li>\n<\/ul>\n<h3 id=\"scaling\"><span class=\"ez-toc-section\" id=\"%d9%85%d9%82%db%8c%d8%a7%d8%b3_%d8%a8%d9%86%d8%af%db%8c\"><\/span>\u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc \u0639\u0645\u0644 \u0636\u0631\u0628 \u0647\u0631 \u0628\u0639\u062f \u0634\u06cc \u0647\u062f\u0641 \u062f\u0631 a \u0627\u0633\u062a <em>\u0627\u0633\u06a9\u0627\u0644\u0631<\/em>.  \u0627\u06cc\u0646 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0627\u0634\u062f <code>&lt;1<\/code> \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0634\u06cc \u0631\u0627 \u06a9\u0648\u0686\u06a9 \u06a9\u0646\u06cc\u0645\u060c \u0648 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0627\u0634\u062f <code>&gt;1<\/code> \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0634\u06cc \u0631\u0627 \u0628\u0632\u0631\u06af \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0641\u0631\u0645 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0632\u06cc\u0631 \u062a\u0648\u0635\u06cc\u0641 \u06a9\u0631\u062f:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0627\u0633<\/mi>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <msub>\n            <mi>\u0633<\/mi>\n            <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n          <\/msub>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <msub>\n            <mi>\u0633<\/mi>\n            <mi>y<\/mi>\n          <\/msub>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <msub>\n            <mi>\u0633<\/mi>\n            <mi>z<\/mi>\n          <\/msub>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p><em>\u0633<sub>\u0627\u06cc\u06a9\u0633<\/sub><\/em>\u060c <em>\u0633<sub>y<\/sub><\/em>\u060c <em>\u0633<sub>z<\/sub><\/em>  \u0627\u0633\u06a9\u0627\u0644\u0631\u0647\u0627\u06cc\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0628\u0627 \u0639\u062f\u062f \u0636\u0631\u0628 \u0645\u06cc \u0634\u0648\u0646\u062f <code>x<\/code>\u060c <code>y<\/code>\u060c \u0648 <code>z<\/code> \u0645\u0642\u0627\u062f\u06cc\u0631 \u0634\u06cc \u0645\u0648\u0631\u062f \u0646\u0638\u0631<\/p>\n<p>\u0628\u0639\u062f \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u0647\u0631 \u0645\u062e\u062a\u0635\u0627\u062a\u06cc \u0631\u0627 \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f\u06cc\u0645 <code>S<\/code> \u0645\u0627 \u06af\u0631\u0641\u062a\u06cc\u0645:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mo stretchy=\"false\">(<\/mo>\n  <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <mo>\u060c<\/mo>\n  <mi>y<\/mi>\n  <mo>\u060c<\/mo>\n  <mi>z<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n  <mo>\u2217<\/mo>\n  <mi>\u0627\u0633<\/mi>\n  <mo>=<\/mo>\n  <mo stretchy=\"false\">(<\/mo>\n  <msub>\n    <mi>\u0633<\/mi>\n    <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <\/msub>\n  <mo>\u2217<\/mo>\n  <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <mo>\u060c<\/mo>\n  <msub>\n    <mi>\u0633<\/mi>\n    <mi>y<\/mi>\n  <\/msub>\n  <mo>\u2217<\/mo>\n  <mi>y<\/mi>\n  <mo>\u060c<\/mo>\n  <msub>\n    <mi>\u0633<\/mi>\n    <mi>z<\/mi>\n  <\/msub>\n  <mo>\u2217<\/mo>\n  <mi>z<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n<\/math><\/p>\n<p>\u0627\u06cc\u0646 \u062a\u0628\u062f\u06cc\u0644 \u0628\u0647 \u0648\u06cc\u0698\u0647 \u0647\u0646\u06af\u0627\u0645 \u0645\u0642\u06cc\u0627\u0633 \u0628\u0646\u062f\u06cc \u06cc\u06a9 \u0634\u06cc \u0628\u0631 \u0627\u0633\u0627\u0633 \u0641\u0627\u06a9\u062a\u0648\u0631 \u0645\u0641\u06cc\u062f \u0627\u0633\u062a <em>\u06a9<\/em> (\u0627\u06cc\u0646 \u0628\u062f\u0627\u0646 \u0645\u0639\u0646\u0627\u0633\u062a \u06a9\u0647 \u062c\u0633\u0645 \u062d\u0627\u0635\u0644 \u062f\u0648 \u0628\u0631\u0627\u0628\u0631 \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0633\u062a)\u060c \u0627\u06cc\u0646 \u0628\u0627 \u062a\u0646\u0638\u06cc\u0645 \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u062f <em>\u0633<sub>\u0627\u06cc\u06a9\u0633<\/sub><\/em>=<em>\u0633<sub>y<\/sub><\/em>=<em>\u0633<sub>z<\/sub><\/em>=<em>\u06a9<\/em>:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mo stretchy=\"false\">(<\/mo>\n  <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <mo>\u060c<\/mo>\n  <mi>y<\/mi>\n  <mo>\u060c<\/mo>\n  <mi>z<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n  <mo>\u2217<\/mo>\n  <mi>\u0627\u0633<\/mi>\n  <mo>=<\/mo>\n  <mo stretchy=\"false\">(<\/mo>\n  <msub>\n    <mi>\u0633<\/mi>\n    <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <\/msub>\n  <mo>\u2217<\/mo>\n  <mi>\u0627\u06cc\u06a9\u0633<\/mi>\n  <mo>\u060c<\/mo>\n  <msub>\n    <mi>\u0633<\/mi>\n    <mi>y<\/mi>\n  <\/msub>\n  <mo>\u2217<\/mo>\n  <mi>y<\/mi>\n  <mo>\u060c<\/mo>\n  <msub>\n    <mi>\u0633<\/mi>\n    <mi>z<\/mi>\n  <\/msub>\n  <mo>\u2217<\/mo>\n  <mi>z<\/mi>\n  <mo stretchy=\"false\">)<\/mo>\n<\/math><\/p>\n<p>\u06cc\u06a9 \u0645\u0648\u0631\u062f \u062e\u0627\u0635 \u0627\u0632 \u067e\u0648\u0633\u062a\u0647 \u067e\u0648\u0633\u062a\u0647 \u0634\u062f\u0646 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a <em>\u0627\u0646\u0639\u06a9\u0627\u0633<\/em>.  \u0628\u0627 \u062a\u0646\u0638\u06cc\u0645 \u06cc\u0627 \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u062f <em>\u0633<sub>\u0627\u06cc\u06a9\u0633<\/sub><\/em>\u060c <em>\u0633<sub>y<\/sub><\/em>\u060c \u06cc\u0627 <em>\u0633<sub>z<\/sub><\/em>  \u0628\u0647 <code>-1<\/code>.  \u0627\u06cc\u0646 \u0641\u0642\u0637 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0627 \u0639\u0644\u0627\u0645\u062a \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u062e\u062a\u0635\u0627\u062a \u062c\u0633\u0645 \u0631\u0627 \u0645\u0639\u06a9\u0648\u0633 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0628\u0647 \u0639\u0628\u0627\u0631\u062a \u0633\u0627\u062f\u0647 \u062a\u0631\u060c \u0645\u0627 \u0634\u06cc \u0631\u0627 \u0642\u0631\u0627\u0631 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0631\u0648\u06cc \u0637\u0631\u0641 \u062f\u06cc\u06af\u0631 <code>x<\/code>\u060c <code>y<\/code>\u060c \u06cc\u0627 <code>z<\/code> \u0645\u062d\u0648\u0631.<\/p>\n<p>\u0627\u06cc\u0646 \u062f\u06af\u0631\u06af\u0648\u0646\u06cc \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0627\u062f \u062a\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0633\u0637\u062d \u0628\u0627\u0632\u062a\u0627\u0628\u06cc \u06a9\u0627\u0631 \u06a9\u0646\u062f\u060c \u0627\u0645\u0627 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u0648\u0627\u0642\u0639\u0627\u064b \u0628\u0647 \u0622\u0646 \u0646\u06cc\u0627\u0632 \u0646\u062f\u0627\u0631\u06cc\u0645.<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">void<\/span> <span class=\"hljs-title\">glScalef<\/span><span class=\"hljs-params\">(GLfloat sx, GLfloat sy, GLfloat sz)<\/span><\/span>;\n<\/code><\/pre>\n<h2 id=\"compositetransformations\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%a8%d8%af%db%8c%d9%84_%d9%87%d8%a7%db%8c_%d9%85%d8%b1%da%a9%d8%a8\"><\/span>\u062a\u0628\u062f\u06cc\u0644 \u0647\u0627\u06cc \u0645\u0631\u06a9\u0628<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u062a\u0628\u062f\u06cc\u0644 \u0647\u0627\u06cc \u0645\u0631\u06a9\u0628\u060c \u062a\u0628\u062f\u06cc\u0644 \u0647\u0627\u06cc\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0627\u0632 \u0628\u06cc\u0634 \u0627\u0632 1 \u062a\u0628\u062f\u06cc\u0644 \u0627\u0633\u0627\u0633\u06cc \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0646\u062f (\u0630\u06a9\u0631 \u0634\u062f\u0647 \u062f\u0631 \u0628\u0627\u0644\u0627).  \u062a\u062d\u0648\u0644\u0627\u062a <code>A<\/code> \u0648 <code>B<\/code> \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0645\u0631\u0628\u0648\u0637\u0647 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u06cc \u0634\u0648\u0646\u062f <code>M_a<\/code> \u0648 <code>M_b<\/code>.<\/p>\n<p>\u0627\u06cc\u0646 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u0646\u0637\u0642\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0633\u0627\u062f\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0628\u0631\u0633\u062f\u060c \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644 \u0645\u0648\u0627\u0631\u062f\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u06af\u06cc\u062c \u06a9\u0646\u0646\u062f\u0647 \u0628\u0627\u0634\u062f.  \u0645\u062b\u0644\u0627:<\/p>\n<ul>\n<li>\u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0642\u0627\u0628\u0644 \u062a\u0639\u0648\u06cc\u0636 \u0646\u06cc\u0633\u062a:<\/li>\n<\/ul>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u0622<\/mi>\n  <mo>\u2217<\/mo>\n  <mi>\u0628<\/mi>\n  <mo>\u2260<\/mo>\n  <mi>\u0628<\/mi>\n  <mo>\u2217<\/mo>\n  <mi>\u0622<\/mi>\n  <mtext> <\/mtext>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mtext>A \u0648 B \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0633\u062a\u0646\u062f<\/mtext>\n<\/math><\/p>\n<ul>\n<li>\u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u0627\u06cc\u0646 \u062a\u0628\u062f\u06cc\u0644 \u0647\u0627 \u06cc\u06a9 \u062a\u0628\u062f\u06cc\u0644 \u0645\u0639\u06a9\u0648\u0633 \u062f\u0627\u0631\u0646\u062f.  \u062a\u0628\u062f\u06cc\u0644 \u0645\u0639\u06a9\u0648\u0633 \u062a\u0628\u062f\u06cc\u0644\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062a\u0628\u062f\u06cc\u0644 \u0627\u0635\u0644\u06cc \u0631\u0627 \u062e\u0646\u062b\u06cc \u0645\u06cc \u06a9\u0646\u062f:<\/li>\n<\/ul>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u062a\u06cc<\/mi>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u0628<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u062c<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <msup>\n    <mi>\u062a\u06cc<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mo>&#8211;<\/mo>\n      <mn>1<\/mn>\n    <\/mrow>\n  <\/msup>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0628<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u062c<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mi>E<\/mi>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mtext> <\/mtext>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mtext> <\/mtext>\n  <mspace linebreak=\"newline\"><\/mspace>\n  <mi>\u062a\u06cc<\/mi>\n  <mo>\u2217<\/mo>\n  <msup>\n    <mi>\u062a\u06cc<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mo>&#8211;<\/mo>\n      <mn>1<\/mn>\n    <\/mrow>\n  <\/msup>\n  <mo>=<\/mo>\n  <mi>E<\/mi>\n<\/math><\/p>\n<ul>\n<li>\u0648\u0642\u062a\u06cc \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06cc\u06a9 \u062a\u0628\u062f\u06cc\u0644 \u0645\u0631\u06a9\u0628 \u0631\u0627 \u0645\u0639\u06a9\u0648\u0633 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0627\u06cc\u062f \u062a\u0631\u062a\u06cc\u0628 \u0639\u0646\u0627\u0635\u0631 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f\u0647 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u06cc\u0645:<\/li>\n<\/ul>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mo stretchy=\"false\">(<\/mo>\n  <mi>\u0622<\/mi>\n  <mo>\u2217<\/mo>\n  <mi>\u0628<\/mi>\n  <mo>\u2217<\/mo>\n  <mi>\u0633\u06cc<\/mi>\n  <msup>\n    <mo stretchy=\"false\">)<\/mo>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mo>&#8211;<\/mo>\n      <mn>1<\/mn>\n    <\/mrow>\n  <\/msup>\n  <mo>=<\/mo>\n  <msup>\n    <mi>\u0633\u06cc<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mo>&#8211;<\/mo>\n      <mn>1<\/mn>\n    <\/mrow>\n  <\/msup>\n  <mo>\u2217<\/mo>\n  <msup>\n    <mi>\u0628<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mo>&#8211;<\/mo>\n      <mn>1<\/mn>\n    <\/mrow>\n  <\/msup>\n  <mo>\u2217<\/mo>\n  <msup>\n    <mi>\u0622<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mo>&#8211;<\/mo>\n      <mn>1<\/mn>\n    <\/mrow>\n  <\/msup>\n<\/math><\/p>\n<p>\u0646\u06a9\u062a\u0647 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 &#8211; \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0647\u0645 \u0627\u0633\u062a\u060c \u062f\u0631\u0633\u062a \u0645\u0627\u0646\u0646\u062f \u0635\u0639\u0648\u062f \u0628\u0647 \u0637\u0628\u0642\u0647 \u062e\u0627\u0635\u06cc \u0627\u0632 \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0645\u0627\u0646.<\/p>\n<p>\u0627\u06af\u0647 \u062a\u0648 \u0647\u0633\u062a\u06cc \u0631\u0648\u06cc \u0637\u0628\u0642\u0647 \u0627\u0648\u0644\u060c \u0648 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u0628\u0647 \u0637\u0628\u0642\u0647 \u0686\u0647\u0627\u0631\u0645 \u0628\u0631\u0633\u06cc\u062f\u060c \u0627\u0628\u062a\u062f\u0627 \u0628\u0627\u06cc\u062f \u0628\u0647 \u0637\u0628\u0642\u0647 \u0633\u0648\u0645 \u0648 \u0633\u067e\u0633 \u0628\u0647 \u0637\u0628\u0642\u0647 \u0686\u0647\u0627\u0631\u0645 \u0628\u0631\u0648\u06cc\u062f.<\/p>\n<p>\u0627\u0645\u0627 \u0627\u06af\u0631 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u0628\u0647 \u0637\u0628\u0642\u0647 \u062f\u0648\u0645 \u0628\u0631\u06af\u0631\u062f\u06cc\u062f\u060c \u0628\u0627\u06cc\u062f \u0628\u0647 \u0637\u0628\u0642\u0647 \u0633\u0648\u0645 \u0648 \u0633\u067e\u0633 \u0628\u0647 \u0637\u0628\u0642\u0647 \u062f\u0648\u0645 (\u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 \u062a\u0648\u067e\u0648\u0644\u0648\u0698\u06cc\u06a9 \u0645\u0639\u06a9\u0648\u0633) \u0628\u0631\u0648\u06cc\u062f.<\/p>\n<h2 id=\"transformationsthatinvolveareferralpoint\"><span class=\"ez-toc-section\" id=\"%d8%af%da%af%d8%b1%da%af%d9%88%d9%86%db%8c_%d9%87%d8%a7%db%8c%db%8c_%da%a9%d9%87_%d8%b4%d8%a7%d9%85%d9%84_%db%8c%da%a9_%d9%86%d9%82%d8%b7%d9%87_%d8%a7%d8%b1%d8%ac%d8%a7%d8%b9_%d9%87%d8%b3%d8%aa%d9%86%d8%af\"><\/span>\u062f\u06af\u0631\u06af\u0648\u0646\u06cc \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0634\u0627\u0645\u0644 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0627\u0631\u062c\u0627\u0639 \u0647\u0633\u062a\u0646\u062f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0642\u0628\u0644\u0627 \u0630\u06a9\u0631 \u0634\u062f\u060c \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u06cc\u06a9 \u062a\u0628\u062f\u06cc\u0644 \u0628\u0627\u06cc\u062f \u0646\u0633\u0628\u062a \u0628\u0647 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u062e\u0627\u0635 \u062f\u0631 \u0641\u0636\u0627 \u0627\u0646\u062c\u0627\u0645 \u0634\u0648\u062f\u060c \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644 \u0686\u0631\u062e\u0634 \u062d\u0648\u0644 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0627\u0631\u062c\u0627\u0639 <code>A=(a,b,c)<\/code> \u062f\u0631 \u0641\u0636\u0627\u06cc \u0633\u0647 \u0628\u0639\u062f\u06cc\u060c \u0646\u0647 \u0645\u0628\u062f\u0627 <code>O=(0,0,0)<\/code>\u060c \u0628\u0627\u06cc\u062f \u0622\u0646 \u0646\u0642\u0637\u0647 \u0627\u0631\u062c\u0627\u0639 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u06cc\u0645 <code>A<\/code> \u0628\u0647 <code>O<\/code> \u0628\u0627 \u062a\u0631\u062c\u0645\u0647 \u0647\u0645\u0647 \u0686\u06cc\u0632 \u062a\u0648\u0633\u0637 <code>T(-a,-b,-c)<\/code>.<\/p>\n<p>\u0633\u067e\u0633 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0647\u0631 \u062a\u063a\u06cc\u06cc\u0631\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645\u060c \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u0648 \u0648\u0642\u062a\u06cc \u06a9\u0627\u0631\u0645\u0627\u0646 \u062a\u0645\u0627\u0645 \u0634\u062f\u060c \u0647\u0645\u0647 \u0686\u06cc\u0632 \u0631\u0627 \u062f\u0648\u0628\u0627\u0631\u0647 \u062a\u0631\u062c\u0645\u0647 \u06a9\u0646\u06cc\u0645 <code>T(a,b,c)<\/code>\u060c \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0645\u0646\u0634\u0627\u0621 \u0627\u0635\u0644\u06cc <code>O<\/code> \u062f\u0648\u0628\u0627\u0631\u0647 \u0645\u062e\u062a\u0635\u0627\u062a \u0631\u0627 \u062f\u0627\u0631\u062f <code>(0,0,0)<\/code>.<\/p>\n<p>\u0634\u06a9\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0627\u06cc\u0646 \u0645\u062b\u0627\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\">\n  <mi>\u062a\u06cc<\/mi>\n  <mo>\u2217<\/mo>\n  <mi>\u0645<\/mi>\n  <mo>\u2217<\/mo>\n  <msup>\n    <mi>\u062a\u06cc<\/mi>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mo>&#8211;<\/mo>\n      <mn>1<\/mn>\n    <\/mrow>\n  <\/msup>\n  <mo>=<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u0628<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mo>&#8211;<\/mo>\n          <mi>\u062c<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n  <mo>\u2217<\/mo>\n  <mi>\u0645<\/mi>\n  <mo>\u2217<\/mo>\n  <mrow>\n    <mo>(<\/mo>\n    <mtable rowspacing=\"4pt\" columnspacing=\"1em\">\n      <mtr>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u0622<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u0628<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n        <mtd>\n          <mi>\u062c<\/mi>\n        <\/mtd>\n      <\/mtr>\n      <mtr>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>0<\/mn>\n        <\/mtd>\n        <mtd>\n          <mn>1<\/mn>\n        <\/mtd>\n      <\/mtr>\n    <\/mtable>\n    <mo>)<\/mo>\n  <\/mrow>\n<\/math><\/p>\n<p>\u062c\u0627\u06cc\u06cc \u06a9\u0647 <code>M<\/code> \u062a\u062d\u0648\u0644\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u0631\u0648\u06cc \u06cc\u06a9 \u0634\u06cc<\/p>\n<p>\u0646\u06a9\u062a\u0647 \u0627\u0635\u0644\u06cc \u06cc\u0627\u062f\u06af\u06cc\u0631\u06cc \u0627\u06cc\u0646 \u0639\u0645\u0644\u06cc\u0627\u062a \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u0637\u0648\u0631 \u06a9\u0627\u0645\u0644 \u062f\u0631\u06a9 \u06a9\u0646\u06cc\u062f \u06a9\u0647 OpenGL \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n<h2 id=\"modelingdemonstration\"><span class=\"ez-toc-section\" id=\"%d9%86%d9%85%d8%a7%db%8c%d8%b4_%d9%85%d8%af%d9%84%db%8c%d9%86%da%af\"><\/span>\u0646\u0645\u0627\u06cc\u0634 \u0645\u062f\u0644\u06cc\u0646\u06af<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u0627 \u0648\u062c\u0648\u062f \u0647\u0645\u0647 \u0627\u06cc\u0646 \u0645\u0648\u0627\u0631\u062f\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u0628\u0647 \u06cc\u06a9 \u0646\u0645\u0627\u06cc\u0634 \u0645\u062f\u0644 \u0633\u0627\u0632\u06cc \u0633\u0627\u062f\u0647 \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0647\u0631 \u06a9\u0627\u0631\u06cc \u0628\u0627 OpenGL \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u0627\u06cc\u062a\u0648\u0646\u060c \u0627\u0632 \u062f\u0648 \u0645\u0627\u0698\u0648\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 &#8211; PyGame \u0648 PyOpenGL:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-meta\">$<\/span><span class=\"bash\"> python3 -m pip install -U pygame --user<\/span>\n<span class=\"hljs-meta\">$<\/span><span class=\"bash\"> python3 -m pip install PyOpenGL PyOpenGL_accelerate<\/span>\n<\/code><\/pre>\n<p>\u0632\u06cc\u0631\u0627 \u062e\u0627\u0644\u06cc \u06a9\u0631\u062f\u0646 3 \u06a9\u062a\u0627\u0628 \u062a\u0626\u0648\u0631\u06cc \u06af\u0631\u0627\u0641\u06cc\u06a9 \u0627\u0636\u0627\u0641\u06cc \u0627\u0633\u062a \u0631\u0648\u06cc \u062e\u0648\u062f\u062a\u0627\u0646\u060c \u0645\u0627 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 PyGame \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u0627\u06cc\u0646 \u0627\u0633\u0627\u0633\u0627 \u0641\u0642\u0637 \u06a9\u0648\u062a\u0627\u0647 \u062e\u0648\u0627\u0647\u062f \u0634\u062f process \u0627\u0632 \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647 \u067e\u0631\u0648\u0698\u0647 \u06af\u0631\u0641\u062a\u0647 \u062a\u0627 \u0645\u062f\u0644 \u0633\u0627\u0632\u06cc \u0648 \u0645\u062a\u062d\u0631\u06a9 \u0633\u0627\u0632\u06cc \u0648\u0627\u0642\u0639\u06cc.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0634\u0631\u0648\u0639\u060c \u0645\u0627 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645 import \u0647\u0645\u0647 \u0686\u06cc\u0632 \u0644\u0627\u0632\u0645 \u0627\u0632 OpenGL \u0648 PyGame:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> pygame <span class=\"hljs-keyword\">as<\/span> pg\n<span class=\"hljs-keyword\">from<\/span> pygame.<span class=\"hljs-built_in\">locals<\/span> <span class=\"hljs-keyword\">import<\/span> *\n\n<span class=\"hljs-keyword\">from<\/span> OpenGL.GL <span class=\"hljs-keyword\">import<\/span> *\n<span class=\"hljs-keyword\">from<\/span> OpenGL.GLU <span class=\"hljs-keyword\">import<\/span> *\n<\/code><\/pre>\n<p>\u062f\u0631 \u0645\u062b\u0627\u0644 \u0632\u06cc\u0631 \u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u062f\u0644 \u0633\u0627\u0632\u06cc \u0627\u0634\u06cc\u0627\u0621 \u063a\u06cc\u0631 \u0645\u062a\u0639\u0627\u0631\u0641\u060c \u062a\u0646\u0647\u0627 \u0686\u06cc\u0632\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u062f\u0627\u0646\u06cc\u0645 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0634\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0642\u0637\u0639\u0627\u062a \u06a9\u0648\u0686\u06a9\u062a\u0631 \u0648 \u0633\u0627\u062f\u0647 \u062a\u0631 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0627 \u0647\u0646\u0648\u0632 \u0646\u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0686\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u0646\u062f\u060c \u0645\u0646 \u0628\u0631\u062e\u06cc \u0627\u0632 \u062a\u0639\u0627\u0631\u06cc\u0641 \u0633\u0637\u062d \u0633\u0637\u062d \u0631\u0627 \u062f\u0631 \u062e\u0648\u062f \u06a9\u062f \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u0645\u060c \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u062f \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 OpenGL \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.  \u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0628\u0639\u062f\u06cc\u060c \u0647\u0645\u0647 \u0627\u06cc\u0646\u0647\u0627 \u0628\u0647 \u062a\u0641\u0635\u06cc\u0644 \u067e\u0648\u0634\u0634 \u062f\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u062f \u0634\u062f &#8211; \u0627\u06cc\u0646 \u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 \u0627\u06cc\u062f\u0647 \u0627\u0648\u0644\u06cc\u0647 \u0627\u0632 \u0631\u0648\u0634 \u06a9\u0627\u0631 \u0628\u0627 OpenGL \u0628\u0647 \u0634\u0645\u0627 \u0627\u0631\u0627\u0626\u0647 \u062f\u0647\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">draw_gun<\/span>():<\/span>\n    \n    \n    \n    ambient_coeffsGray = (<span class=\"hljs-number\">0.3<\/span>, <span class=\"hljs-number\">0.3<\/span>, <span class=\"hljs-number\">0.3<\/span>, <span class=\"hljs-number\">1<\/span>)\n    diffuse_coeffsGray = (<span class=\"hljs-number\">0.5<\/span>, <span class=\"hljs-number\">0.5<\/span>, <span class=\"hljs-number\">0.5<\/span>, <span class=\"hljs-number\">1<\/span>)\n    specular_coeffsGray = (<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>)\n    glMaterialfv(GL_FRONT, GL_AMBIENT, ambient_coeffsGray)\n    glMaterialfv(GL_FRONT, GL_DIFFUSE, diffuse_coeffsGray)\n    glMaterialfv(GL_FRONT, GL_SPECULAR, specular_coeffsGray)\n    glMateriali(GL_FRONT, GL_SHININESS, <span class=\"hljs-number\">1<\/span>)\n\n    \n    \n    \n    \n    \n    \n    \n    glPushMatrix()\n\n    glPushMatrix()\n    glTranslatef(<span class=\"hljs-number\">3.1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1.75<\/span>)\n    glRotatef(<span class=\"hljs-number\">90<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>)\n    glScalef(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">5<\/span>)\n    glScalef(<span class=\"hljs-number\">0.2<\/span>, <span class=\"hljs-number\">0.2<\/span>, <span class=\"hljs-number\">0.2<\/span>)\n    glutSolidTorus(<span class=\"hljs-number\">0.2<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">10<\/span>)\n    glPopMatrix()\n\n    glPushMatrix()\n    glTranslatef(<span class=\"hljs-number\">2.5<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1.75<\/span>)\n    glScalef(<span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">1<\/span>)\n    glutSolidCube(<span class=\"hljs-number\">1<\/span>)\n    glPopMatrix()\n\n    glPushMatrix()\n    glTranslatef(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>)\n    glRotatef(<span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>)\n    glScalef(<span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">1<\/span>)\n    glutSolidCube(<span class=\"hljs-number\">1<\/span>)\n\n    glPopMatrix()\n\n    glPushMatrix()\n    glTranslatef(<span class=\"hljs-number\">0.8<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0.8<\/span>)\n    glRotatef(<span class=\"hljs-number\">90<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0<\/span>)\n    glScalef(<span class=\"hljs-number\">0.5<\/span>, <span class=\"hljs-number\">0.5<\/span>, <span class=\"hljs-number\">0.5<\/span>)\n    glutSolidTorus(<span class=\"hljs-number\">0.2<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">10<\/span>, <span class=\"hljs-number\">10<\/span>)\n    glPopMatrix()\n\n    glPushMatrix()\n    glTranslatef(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1.5<\/span>)\n    glRotatef(<span class=\"hljs-number\">90<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>)\n    glScalef(<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">4<\/span>)\n    glutSolidCube(<span class=\"hljs-number\">1<\/span>)\n    glPopMatrix()\n\n    glPushMatrix()\n    glRotatef(<span class=\"hljs-number\">8<\/span>, <span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">0<\/span>)\n    glScalef(<span class=\"hljs-number\">1.1<\/span>, <span class=\"hljs-number\">0.8<\/span>, <span class=\"hljs-number\">3<\/span>)\n    glutSolidCube(<span class=\"hljs-number\">1<\/span>)\n    glPopMatrix()\n\n    glPopMatrix()\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">main<\/span>():<\/span>\n    \n    pg.init()\n    \n    glutInit(sys.argv)\n    \n    display = (<span class=\"hljs-number\">800<\/span>,<span class=\"hljs-number\">600<\/span>)\n    pg.display.set_mode(display, DOUBLEBUF|OPENGL)\n    glClearColor(<span class=\"hljs-number\">0.1<\/span>,<span class=\"hljs-number\">0.1<\/span>,<span class=\"hljs-number\">0.1<\/span>,<span class=\"hljs-number\">0.3<\/span>)\n    gluPerspective(<span class=\"hljs-number\">45<\/span>, (display(<span class=\"hljs-number\">0<\/span>)\/display(<span class=\"hljs-number\">1<\/span>)), <span class=\"hljs-number\">0.1<\/span>, <span class=\"hljs-number\">50.0<\/span>)\n    gluLookAt(<span class=\"hljs-number\">5<\/span>,<span class=\"hljs-number\">5<\/span>,<span class=\"hljs-number\">3<\/span>,<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">0<\/span>,<span class=\"hljs-number\">1<\/span>)\n\n    glTranslatef(<span class=\"hljs-number\">0.0<\/span>,<span class=\"hljs-number\">0.0<\/span>, -<span class=\"hljs-number\">5<\/span>)\n    <span class=\"hljs-keyword\">while<\/span> <span class=\"hljs-literal\">True<\/span>:\n        \n        <span class=\"hljs-keyword\">for<\/span> event <span class=\"hljs-keyword\">in<\/span> pg.event.get():\n            <span class=\"hljs-keyword\">if<\/span> event.<span class=\"hljs-built_in\">type<\/span> == pg.QUIT:\n                pg.quit()\n                quit()\n\n        \n        glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)\n        \n        draw_gun()\n        \n        \n        pg.display.flip()\n        pg.time.wait(<span class=\"hljs-number\">10<\/span>)\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u062f\u0633\u062a\u0647 \u0627\u0632 \u06a9\u062f\u0647\u0627 \u0628\u0647 \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/understanding-opengl-through-python-3.png\" alt=\"\u0634\u06cc \u0631\u0633\u0645 \u0634\u062f\u0647\" title=\"\"><\/p>\n<h2 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>OpenGL \u0628\u0633\u06cc\u0627\u0631 \u0642\u062f\u06cc\u0645\u06cc \u0627\u0633\u062a \u0648 \u0622\u0645\u0648\u0632\u0634 \u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0622\u0646\u0644\u0627\u06cc\u0646 \u067e\u06cc\u062f\u0627 \u0646\u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f \u0631\u0648\u06cc \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0622\u0646 \u0628\u0647 \u062f\u0631\u0633\u062a\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f \u0648 \u0622\u0646 \u0631\u0627 \u062f\u0631\u06a9 \u06a9\u0631\u062f \u0632\u06cc\u0631\u0627 \u062a\u0645\u0627\u0645 \u0633\u06af \u0647\u0627\u06cc \u0628\u0631\u062a\u0631 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 \u062f\u0631 \u0641\u0646 \u0622\u0648\u0631\u06cc \u0647\u0627\u06cc \u062c\u062f\u06cc\u062f \u062a\u0627 \u0632\u0627\u0646\u0648 \u0639\u0645\u06cc\u0642 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0635\u062d\u06cc\u062d \u0627\u0632 OpenGL\u060c \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062f\u0631\u06a9 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0627\u0648\u0644\u06cc\u0647 \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u0647\u0627 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u062a\u0648\u0627\u0628\u0639 OpenGL \u0627\u0633\u062a.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0639\u0645\u0644\u06cc\u0627\u062a \u0627\u0635\u0644\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 (\u062a\u0631\u062c\u0645\u0647\u060c \u0686\u0631\u062e\u0634\u060c \u0648 \u0645\u0642\u06cc\u0627\u0633\u200c\u0628\u0646\u062f\u06cc) \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u062a\u0628\u062f\u06cc\u0644\u200c\u0647\u0627 \u0648 \u062a\u0628\u062f\u06cc\u0644\u200c\u0647\u0627\u06cc \u062a\u0631\u06a9\u06cc\u0628\u06cc \u06a9\u0647 \u0634\u0627\u0645\u0644 \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0627\u0631\u062c\u0627\u0639 \u0647\u0633\u062a\u0646\u062f \u0631\u0627 \u067e\u0648\u0634\u0634 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc\u0645.<\/p>\n<p>\u062f\u0631 \u0645\u0642\u0627\u0644\u0647 \u0628\u0639\u062f\u06cc\u060c \u0645\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.pygame.org\">PyGame<\/a> \u0648 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"http:\/\/pyopengl.sourceforge.net\/\">PyOpenGL<\/a> \u0628\u0631\u0627\u06cc \u0645\u0642\u062f\u0627\u0631\u062f\u0647\u06cc \u0627\u0648\u0644\u06cc\u0647 \u06cc\u06a9 \u067e\u0631\u0648\u0698\u0647\u060c \u062a\u0631\u0633\u06cc\u0645 \u0627\u0634\u06cc\u0627\u060c \u0645\u062a\u062d\u0631\u06a9 \u0633\u0627\u0632\u06cc \u0622\u0646\u0647\u0627 \u0648 \u063a\u06cc\u0631\u0647!<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-19 18:12:05<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;16007&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u062f\u0631\u06a9 OpenGL \u0627\u0632 \u0637\u0631\u06cc\u0642 \u067e\u0627\u06cc\u062a\u0648\u0646&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} ({count} \u0631\u0627\u06cc)&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 10<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u067e\u06cc\u0631\u0648 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u0648\u0633\u0637 \u0645\u062d\u0645\u062f \u062c\u0646\u06cc\u062f \u062e\u0627\u0644\u062f\u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u067e\u0627\u06cc\u0647 OpenGL \u0645\u0641\u0627\u0647\u06cc\u0645 \u0648 \u062a\u0646\u0638\u06cc\u0645\u0627\u062a \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u060c \u0627\u06a9\u0646\u0648\u0646 \u0645\u0627 \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u0686\u06af\u0648\u0646\u06af\u06cc \u0633\u0627\u062e\u062a \u0628\u06cc\u0634\u062a\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u0628\u0648\u062f \u0645\u062c\u062a\u0645\u0639 \u0627\u0634\u06cc\u0627\u0621 \u0648 \u0686\u06af\u0648\u0646\u06af\u06cc \u062c\u0627\u0646 \u062f\u0627\u062f\u0646 \u0622\u0646\u0647\u0627 \u0631\u0627 OpenGL \u0628\u0633\u06cc\u0627\u0631 \u0642\u062f\u06cc\u0645\u06cc \u0627\u0633\u062a \u0648 \u0622\u0645\u0648\u0632\u0634 \u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0622\u0646\u0644\u0627\u06cc\u0646 \u067e\u06cc\u062f\u0627 \u0646\u062e\u0648\u0627\u0647\u06cc\u062f \u06a9\u0631\u062f \u0631\u0648\u06cc \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":16008,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-16007","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-programming"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/16007","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=16007"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/16007\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/16008"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=16007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=16007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=16007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}