{"id":2573,"date":"2016-09-13T07:15:55","date_gmt":"2016-09-13T07:15:55","guid":{"rendered":"http:\/\/www.raymaps.com\/?p=2573"},"modified":"2016-09-14T04:26:33","modified_gmt":"2016-09-14T04:26:33","slug":"how-to-find-point-of-intersection-of-two-lines","status":"publish","type":"post","link":"https:\/\/www.raymaps.com\/index.php\/how-to-find-point-of-intersection-of-two-lines\/","title":{"rendered":"How to Find Point of Intersection of Two Lines"},"content":{"rendered":"

Finding the point of intersection of two lines has many important application such as in Ray-Tracing Simulation. \u00a0Two lines always intersect at some point unless they are absolutely parallel, like the rails of a railway track. We start with writing the equations of the two lines in slope-intercept form.<\/p>\n

y1=b1+m1*x1<\/p>\n

y2=b2+m2*x2<\/p>\n

\"straight-lines\"<\/a><\/p>\n

Here m1 and m2 are the slopes of the two lines and b1 and b2 are their y-intercepts. At the point of intesection y1=y2, so we have.<\/p>\n

b1+m1*x1=b2+m2*x2<\/p>\n

But at \u00a0the point of intersection x1=x2 as well, so replacing x1 and x2 with x we have.<\/p>\n

b1+m1*x=b2+m2*x<\/p>\n

or<\/p>\n

b1-b2=-x*(m1-m2)<\/p>\n

or<\/p>\n

x=-(b1-b2)\/(m1-m2)<\/p>\n

Once the x-component of the point of intersection is found we can easily find the y-component by substituting x in any of the two line equations above.<\/p>\n

y=b1+m1*x<\/p>\n

In future posts we would like to discuss the cases of intersection of two surfaces and the intersection of two volumes.<\/p>\n","protected":false},"excerpt":{"rendered":"

Finding the point of intersection of two lines has many important application such as in Ray-Tracing Simulation. \u00a0Two lines always intersect at some point unless they are absolutely parallel, like the rails of a railway track. We start with writing the equations of the two lines in slope-intercept form. y1=b1+m1*x1 y2=b2+m2*x2 Here m1 and m2 are the slopes of the two lines and b1 and b2 are their y-intercepts. At the point of intesection y1=y2, so we have. b1+m1*x1=b2+m2*x2 But at \u00a0the point of intersection x1=x2 as well, so replacing x1 and x2 with x we have. b1+m1*x=b2+m2*x or b1-b2=-x*(m1-m2) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[81],"tags":[123,122,97],"class_list":["post-2573","post","type-post","status-publish","format-standard","hentry","category-fundamentals","tag-electromagnetic","tag-poi","tag-ray-tracing"],"_links":{"self":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/2573","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/comments?post=2573"}],"version-history":[{"count":8,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/2573\/revisions"}],"predecessor-version":[{"id":2582,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/posts\/2573\/revisions\/2582"}],"wp:attachment":[{"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/media?parent=2573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/categories?post=2573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.raymaps.com\/index.php\/wp-json\/wp\/v2\/tags?post=2573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}