{"id":561,"date":"2017-02-13T10:52:34","date_gmt":"2017-02-13T02:52:34","guid":{"rendered":"http:\/\/www.cgdev.net\/blog\/?p=561"},"modified":"2017-02-14T11:13:30","modified_gmt":"2017-02-14T03:13:30","slug":"line-plane-intersection","status":"publish","type":"post","link":"https:\/\/www.cgdev.net\/blog\/561.html","title":{"rendered":"Line\u2013plane intersection"},"content":{"rendered":"<p>Suppose we have a Line:<\/p>\n<pre>P = P1 + tL<\/pre>\n<p>and a plane:<\/p>\n<pre>N \u2022 (P - P2) = 0<\/pre>\n<p>We can substitute P into the plane equation:<\/p>\n<pre>N \u2022 (P1 + tL - P2) = 0<\/pre>\n<p>Solve for t:<\/p>\n<pre>t = (N \u2022 (P2 - P1)) \/ (N \u2022 L)<\/pre>\n<p>The point of intersection is:<\/p>\n<pre>P = P1 + ((N \u2022 (P2 - P1)) \/ (N \u2022 L)) L<\/pre>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Suppose we have a Line: P = P1 + tL and a plane: N \u2022 (P &#8211; P2) = 0 We can substitute P into the plane equation: N \u2022 (P1 + tL &#8211; P2) = 0 Solve for t: t = (N \u2022 (P2 &#8211; P1)) \/ (N \u2022 L) The point of intersection [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-561","post","type-post","status-publish","format-standard","hentry","category-graphics"],"_links":{"self":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts\/561","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/comments?post=561"}],"version-history":[{"count":0,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts\/561\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/media?parent=561"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/categories?post=561"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/tags?post=561"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}