{"id":2045,"date":"2008-02-04T20:24:36","date_gmt":"2008-02-05T04:24:36","guid":{"rendered":"http:\/\/www.ogre.nu\/wp\/?p=2045"},"modified":"2008-02-04T20:25:34","modified_gmt":"2008-02-05T04:25:34","slug":"negative-curves","status":"publish","type":"post","link":"https:\/\/bendwavy.org\/wp\/?p=2045","title":{"rendered":"negative curves"},"content":{"rendered":"<p>For years I&#8217;ve wished to learn enough hyperbolic geometry to write a simple ray-tracer.  Recently a post on <i>comp.graphics.algorithms<\/i> advised me to look up <i>Euclidean and Non-Euclidean Geometry<\/i> by Patrick J. Ryan; I was pleased to find that its subtitle is <i>An Analytic Approach<\/i>.  Indeed it gives most of what I was looking for; though it relies so much on cross products that extending from two dimensions to three may be difficult.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For years I&#8217;ve wished to learn enough hyperbolic geometry to write a simple ray-tracer. Recently a post on comp.graphics.algorithms advised me to look up Euclidean and Non-Euclidean Geometry by Patrick J. Ryan; I was pleased to find that its subtitle &hellip; <a href=\"https:\/\/bendwavy.org\/wp\/?p=2045\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-2045","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/2045","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2045"}],"version-history":[{"count":0,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=\/wp\/v2\/posts\/2045\/revisions"}],"wp:attachment":[{"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2045"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2045"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bendwavy.org\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}