{"id":1758,"date":"2016-02-01T23:36:04","date_gmt":"2016-02-02T05:36:04","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=1758"},"modified":"2016-02-01T23:36:04","modified_gmt":"2016-02-02T05:36:04","slug":"look-around-you-spherical-videos-and-moebius-transformations","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/02\/01\/look-around-you-spherical-videos-and-moebius-transformations\/","title":{"rendered":"Look Around You: Spherical Videos and M\u00f6bius Transformations"},"content":{"rendered":"<div id=\"attachment_1764\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/twitter.com\/henryseg\/status\/689238958249644032\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1764\" class=\"size-full wp-image-1764\" src=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/02\/spherical-video.png?resize=600%2C300\" alt=\"A spherical photo, cut and pasted onto your rectangular screen. Image: Henry Segerman.\" width=\"600\" height=\"300\" srcset=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/02\/spherical-video.png?w=600&amp;ssl=1 600w, https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/02\/spherical-video.png?resize=300%2C150&amp;ssl=1 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><p id=\"caption-attachment-1764\" class=\"wp-caption-text\">A spherical photo hit with the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Exponential_function#Complex_plane\">complex exponential function<\/a>. Image: Henry Segerman.<\/p><\/div>\n<p>I\u2019ve lost count of the number of times I\u2019ve watched the short video \u201c<a href=\"http:\/\/www.ima.umn.edu\/~arnold\/moebius\/\"><span class=\"s2\">M\u00f6bius transformations revealed<\/span><\/a>\u201d by Douglas Arnold and Jonathan Rogness.<br \/>\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/0z1fIsUNhO4?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span><br \/>\nIt is a beautiful tribute to <a href=\"http:\/\/jeremykun.com\/2011\/07\/23\/mobius-transformations\/\"><span class=\"s2\">beautiful functions<\/span><\/a>. As a complex analysis and hyperbolic geometry fangirl, I am contractually required to get a little misty-eyed when I think about M\u00f6bius transformations.<\/p>\n<p>I thought &#8220;M\u00f6bius transformations revealed&#8221; was the pinnacle of M\u00f6bius transformation-related video until\u00a0<a href=\"http:\/\/www.segerman.org\/\">Henry Segerman<\/a>\u00a0posted this one last month.<\/p>\n<p><span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/oVwmF_vrZh0?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span><br \/>\n(It took me a while\u00a0to realize that if you&#8217;re on a computer and your browser supports it, you can push the arrows in the compass at the top left of the frame to look around the sphere. For phones it&#8217;s a little different. My iPhone shows the full frame, but I think on Android devices, you can see different parts of the video by moving your phone around. Your mileage may vary.)<\/p>\n<p>M\u00f6bius transformations turn out to be the answer to some tricky problems that come up in spherical video, namely, how to zoom or rotate the way you would with rectangular videos. Like Frank Farris&#8217;\u00a0book <em><a href=\"http:\/\/blogs.scientificamerican.com\/roots-of-unity\/creating-symmetry-frank-farris\/\">Creating Symmetry<\/a>, <\/em>the mathematics inspires\u00a0the creation of beautiful and interesting images. Segerman wrote a guest post about using <a href=\"http:\/\/elevr.com\/spherical-video-editing-effects-with-mobius-transformations\/\"><span class=\"s2\">M\u00f6bius transformations in spherical video editing<\/span><\/a> on the <a href=\"http:\/\/elevr.com\/\"><span class=\"s2\">eleVR<\/span><\/a> <a href=\"http:\/\/elevr.com\/blog\/\"><span class=\"s2\">blog<\/span><\/a>. EleVR is the virtual reality research group\u00a0of Emily Eifler, Vi Hart, <a href=\"http:\/\/blogs.ams.org\/blogonmathblogs\/2014\/06\/11\/fibonacci-lemonade-andrea-hawksley\/\">Andrea Hawksley<\/a>, and Elijah Butterfield, the team\u00a0behind <a href=\"http:\/\/elevr.com\/hypernom\/\"><span class=\"s2\">Hypernom<\/span><\/a>, <a href=\"http:\/\/aperiodical.com\/2015\/07\/hypernom\/\">a game where you try to eat the cells of four-dimensional Platonic solids<\/a>\u00a0and\u00a0other VR endeavors. Their blog documents the fascinating challenges, both mathematical and logistical, of creating and interacting with spherical videos. I love the <a href=\"http:\/\/elevr.com\/sphere-a-day\/\"><span class=\"s2\">Sphere-a-day<\/span><\/a> post in which Eifler talks about how different spherical videos feel to her\u00a0as a creator:<\/p>\n<blockquote><p>Many of the daily spherical videos so far feel more like \u2018Come hang out with me while I do this thing I would be doing anyway,\u2019 the largest number falling into the \u2018I am making art and the camera is running\u2019 category which reveals a lot about how I spend my life, something I never let happen when I was making flat video. In flat video I kept video Emily and RL Emily very separate, but not so in spherical.<span class=\"Apple-converted-space\">\u00a0 <\/span>Its feels like documentation without translation into textual or verbal language and the non-framed non-presentational all seeing eye of the camera makes me feel more relaxed, more open, and frankly just more adventurous and laissez faire about what I can shoot with it. Nothing gets cropped out, nothing gets left behind.<\/p><\/blockquote>\n<p>Spherical videos already offer viewers the opportunity to interact with videos in new ways, but using M\u00f6bius transformations on them gives creators new ways\u00a0to tell stories. With the help of the eleVR-ers, Segerman illustrates this beautifully in a\u00a0spherical <a href=\"https:\/\/en.wikipedia.org\/wiki\/Droste_effect\">Droste<\/a> video where you feel like you&#8217;re taking an endless scroll through a time loop.<\/p>\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/qvh-EAipIUk?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<p>To watch more spherical videos, check out Eifler\u2019s YouTube channel\u00a0<a href=\"https:\/\/www.youtube.com\/user\/BlinkPopShift\/featured\"><span class=\"s2\">BlinkPopShift<\/span><\/a>, <a href=\"https:\/\/www.youtube.com\/user\/henryseg\/featured\">Segerman&#8217;s channel<\/a>, and the <a href=\"https:\/\/www.youtube.com\/channel\/UCGSW-G716AyjUlNJCNl-mAg\/featured\"><span class=\"s2\">eleVR<\/span><\/a> channel.<\/p>\n<div id=\"attachment_1765\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/twitter.com\/henryseg\/status\/694374720116895744\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1765\" class=\"size-full wp-image-1765\" src=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/02\/CaLqIJ0UsAAPiMm.jpg?resize=600%2C300\" alt=\"A spherical picture hit with a Schottky function. Image: Henry Segerman.\" width=\"600\" height=\"300\" srcset=\"https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/02\/CaLqIJ0UsAAPiMm.jpg?w=600&amp;ssl=1 600w, https:\/\/i0.wp.com\/blogs.ams.org\/blogonmathblogs\/files\/2016\/02\/CaLqIJ0UsAAPiMm.jpg?resize=300%2C150&amp;ssl=1 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/a><p id=\"caption-attachment-1765\" class=\"wp-caption-text\">A spherical picture hit with a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Schottky_group\">Schottky group<\/a>. Image: Henry Segerman.<\/p><\/div>\n<p>Spherical video is still young, and people are still discovering <a href=\"https:\/\/twitter.com\/henryseg\/status\/694374720116895744\">new ways to make art with it<\/a>. I can&#8217;t wait to see what\u00a0comes next. Now get out of here <a href=\"https:\/\/youtu.be\/wjeeMlHsYjE\">and<\/a> <a href=\"https:\/\/www.youtube.com\/watch?v=Jcq72JPD8Kg\">go<\/a> <a href=\"https:\/\/www.youtube.com\/watch?v=WCjHtFa30GM\">watch<\/a> <a href=\"https:\/\/www.youtube.com\/watch?v=KP6g33aIP4w\">something<\/a>!<\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>","protected":false},"excerpt":{"rendered":"<p>I\u2019ve lost count of the number of times I\u2019ve watched the short video \u201cM\u00f6bius transformations revealed\u201d by Douglas Arnold and Jonathan Rogness. It is a beautiful tribute to beautiful functions. As a complex analysis and hyperbolic geometry fangirl, I am &hellip; <a href=\"https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/02\/01\/look-around-you-spherical-videos-and-moebius-transformations\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" data-url=https:\/\/blogs.ams.org\/blogonmathblogs\/2016\/02\/01\/look-around-you-spherical-videos-and-moebius-transformations\/><\/div>\n","protected":false},"author":61,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[372,4],"tags":[453,522,520,521,142,523,518,193,519],"class_list":["post-1758","post","type-post","status-publish","format-standard","hentry","category-math-communication","category-mathematics-and-the-arts","tag-andrea-hawksley","tag-droste-effect","tag-elevr","tag-emily-eifler","tag-henry-segerman","tag-moebius-transformations","tag-spherical-video","tag-vi-hart","tag-virtual-reality"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3tW3N-sm","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/1758","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/users\/61"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/comments?post=1758"}],"version-history":[{"count":6,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/1758\/revisions"}],"predecessor-version":[{"id":1766,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/posts\/1758\/revisions\/1766"}],"wp:attachment":[{"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/media?parent=1758"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/categories?post=1758"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ams.org\/blogonmathblogs\/wp-json\/wp\/v2\/tags?post=1758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}