{"id":19775,"date":"2018-04-06T21:26:38","date_gmt":"2018-04-07T02:26:38","guid":{"rendered":"http:\/\/blog.kenperlin.com\/?p=19775"},"modified":"2018-04-06T21:26:38","modified_gmt":"2018-04-07T02:26:38","slug":"math-with-my-brother-part-3","status":"publish","type":"post","link":"http:\/\/blog.kenperlin.com\/?p=19775","title":{"rendered":"Math with my brother, part 3"},"content":{"rendered":"<p>In the world of computer graphics, it gets more and more difficult to place the vertices of a simplex as the number of dimensions increases.  In one dimension, it&#8217;s easy.  You can just draw a line from x = -1 to x = +1.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2018\/04\/simplex1.png\"><\/center><\/p>\n<p>For two dimensions it&#8217;s a little more difficult, but still pretty easy.  To create a regular triangle you go around a circle, marking off a vertex every third of the way around.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2018\/04\/simplex2.png\"><\/center><\/p>\n<p>Starting with three dimensions it starts to get harder. To create a regular tetrahedron you need to resort to some fancy tricks. One trick is to first make a cube, and then use only half of its vertices. The edges of the tetrahedron are just diagonals of the cube&#8217;s faces.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2018\/04\/simplex31.png\" alt=\"simplex3\"><\/center><\/p>\n<p>But once you get to four dimensions, those tricks don&#8217;t really work anymore. Which is very discouraging if you like doing things with simplex shapes.<\/p>\n<p>But then my brother told me how they make simplex shapes in his field, and it is completely awesome. More tomorrow.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the world of computer graphics, it gets more and more difficult to place the vertices of a simplex as the number of dimensions increases. In one dimension, it&#8217;s easy. You can just draw a line from x = -1 to x = +1. For two dimensions it&#8217;s a little more difficult, but still pretty &hellip; <a href=\"http:\/\/blog.kenperlin.com\/?p=19775\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Math with my brother, part 3&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/19775"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=19775"}],"version-history":[{"count":3,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/19775\/revisions"}],"predecessor-version":[{"id":19782,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/19775\/revisions\/19782"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=19775"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=19775"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=19775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}