{"id":945,"date":"2007-01-18T16:27:40","date_gmt":"2007-01-18T21:27:40","guid":{"rendered":"http:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/18\/945\/"},"modified":"2008-04-19T18:18:10","modified_gmt":"2008-04-19T22:18:10","slug":"polar-coordinates-of-austin-texas","status":"publish","type":"post","link":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/18\/945\/","title":{"rendered":"Polar Coordinates of Austin, Texas [square]"},"content":{"rendered":"<div align=\"center\">\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar8.jpg\"\/><br \/>\n<i>8 tiled map<\/i>\n<\/div>\n<p>I recently read through the work of <a href=\"http:\/\/digitalurban.blogspot.com\/\" >Dr. Andrew Hudson-Smith<\/a> (located at the <a href=\"http:\/\/www.casa.ucl.ac.uk\">Center for Advanced Spatial Analysis<\/a> in London).  I was intrigued by his use of Polar Coordinates to create <a href=\"http:\/\/digitalurban.blogspot.com\/search\/label\/Panoramas%2090-100\">panoramas<\/a> and <a href=\"http:\/\/www.photojojo.com\/content\/tutorials\/create-your-own-panorama-planets\/\">synthetic planets<\/a>.  I had been shown how to make the panoramas before, but I hadn&#8217;t actually figured out how I could incorporate my current work with this design technique.  After some experimenting I figured out some interesting new methods to display tessellated aerial photography using the Polar Coordinates filter.  The results are quite amazing and show definite promise for further research&#8230;<\/p>\n<p><ul><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/02\/14\/963\/\">A periodic shift in Polar Roses for Valentines Day<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/23\/951\/\">Polar Coordinates of the Delmar Loop in University City, Missouri [icositetragon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/22\/949\/\">Polar Coordinates of Harvard University [dodecagon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/21\/948\/\">Polar Coordinates of the George Washington University [octagon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/20\/947\/\">Polar Coordinates of the Super Dome in New Orleans, Louisiana [hexagon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/19\/946\/\">Polar Coordinates of Charleston, West Virginia [diamond]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/18\/945\/\">Polar Coordinates of Austin, Texas [square]<\/a><\/li><\/ul><\/p>\n<p>For this experiment I used the &#8220;zoom&#8221; of <a href=\"http:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/14\/944\/\">Austin Quilt #2<\/a> (a <a href=\"http:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/category\/renderings\/quilt\/square\/\">square<\/a> quilt projection) as my test tessellation to begin working with.  I could have used any zoom from any previously made map, but since it was snowing in Austin yesterday, I thought it would be ironic to use the <i>Polar<\/i> Coordinates filter.<\/p>\n<p>The process to create the panorama planets is relatively <a href=\"http:\/\/www.photojojo.com\/content\/tutorials\/create-your-own-panorama-planets\/\">simple<\/a>:<br \/>\n&#8211; Stitch together series of photographs<br \/>\n&#8211; Reduce the panorama (by default a rectangle) to a square<br \/>\n&#8211; Apply Polar Coordinates filter in Photoshop<\/p>\n<p>What makes my experiments unique is that instead of stitching together a photograph, I am  I am stitching together perfectly symmetrical square tiles (composed of tessellated aerial photography) to create a rectangle.  Moreover, I am maintaining perfect ratios throughout: 1:1, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, and 8:1.  For example, the source tile is 800&#215;800 and for each polar coordinate created (below) I merely added one more tile to rectangle ([1600, 2400, 3200, 4000, 4800, 5600, 6400]x800).<\/p>\n<p>For each ratio there are three images shown below:<br \/>\n&#8211; Rectangle with number of tiles<br \/>\n&#8211; Conversion of the Rectangle to Square<br \/>\n&#8211; Application of Polar Coordinates filter<\/p>\n<p>Note: The first image of each ratio below appears to reduce in size after each tile has been been added.  In order to maintain a constant width on my website, I&#8217;ve chosen to reduce each rectangle to 800 pixels in width (otherwise this entry would be 6400 pixels wide right now!).  When originally manipulating the rectangles they were not reduced in size. Essentially, it was done to show the scale of the panorama at a fixed width of 800 pixels.<\/p>\n<p><font size=\"5\">1 : 1<\/font><\/p>\n<div align=\"center\">\n:Original:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/austinquilt2-zoom.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar.jpg\"\/>\n<\/div>\n<p><font size=\"5\">2 : 1<\/font><\/p>\n<div align=\"center\">\n:Rectangle 2 Tiles Wide (reduced from: 1600&#215;800):<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_rectangle2.jpg\"\/><\/p>\n<p>:Rectangle reduced to a Square:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_square2.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar2.jpg\"\/>\n<\/div>\n<p><font size=\"5\">3 : 1<\/font><\/p>\n<div align=\"center\">\n:Rectangle 3 Tiles Wide (reduced from:2400&#215;800):<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_rectangle3.jpg\"\/><\/p>\n<p>:Rectangle reduced to a Square:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_square3.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar3.jpg\"\/>\n<\/div>\n<p><font size=\"5\">4 : 1<\/font><\/p>\n<div align=\"center\">\n:Rectangle 4 Tiles Wide (reduced from: 3200&#215;800):<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_rectangle4.jpg\"\/><\/p>\n<p>:Rectangle reduced to a Square:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_square4.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar4.jpg\"\/>\n<\/div>\n<p><font size=\"5\">5 : 1<\/font><\/p>\n<div align=\"center\">\n:Rectangle 5 Tiles Wide (reduced from: 4000&#215;800):<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_rectangle5.jpg\"\/><\/p>\n<p>:Rectangle reduced to a Square:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_square5.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar5.jpg\"\/>\n<\/div>\n<p><font size=\"5\">6 : 1<\/font><\/p>\n<div align=\"center\">\n:Rectangle 6 Tiles Wide (reduced from: 4800&#215;800):<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_rectangle6.jpg\"\/><\/p>\n<p>:Rectangle reduced to a Square:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_square6.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar6.jpg\"\/>\n<\/div>\n<p><font size=\"5\">7 : 1<\/font><\/p>\n<div align=\"center\">\n:Rectangle 7 Tiles Wide (reduced from: 5600&#215;800):<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_rectangle7.jpg\"\/><\/p>\n<p>:Rectangle reduced to a Square:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_square7.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar7.jpg\"\/>\n<\/div>\n<p><font size=\"5\">8 : 1<\/font><\/p>\n<div align=\"center\">\n:Rectangle 8 Tiles Wide (reduced from: 6400&#215;800):<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_rectangle8.jpg\"\/><\/p>\n<p>:Rectangle reduced to a Square:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_square8.jpg\"\/><\/p>\n<p>:Converts To:<br \/>\n<img decoding=\"async\" src=\"http:\/\/nikolasschiller.com\/posters\/polar\/austin_polar8.jpg\"\/>\n<\/div>\n<p>I am excited about what directions this technique might take my cartographic activities :)  My next experiment will be to see how the application of the Polar Coordinates filter will effect each geometry of the quilt projection.  This experiment was conducted using the <a href=\"http:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/category\/renderings\/quilt\/square\/\">square<\/a> quilt projection, up next with be the <a href=\"http:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/category\/renderings\/quilt\/diamond\/\">diamond<\/a>.  The results should be interesting.<\/p>\n<p>Related:<br \/>\n<ul><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/02\/14\/963\/\">A periodic shift in Polar Roses for Valentines Day<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/23\/951\/\">Polar Coordinates of the Delmar Loop in University City, Missouri [icositetragon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/22\/949\/\">Polar Coordinates of Harvard University [dodecagon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/21\/948\/\">Polar Coordinates of the George Washington University [octagon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/20\/947\/\">Polar Coordinates of the Super Dome in New Orleans, Louisiana [hexagon]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/19\/946\/\">Polar Coordinates of Charleston, West Virginia [diamond]<\/a><\/li><li><a href=\"https:\/\/www.nikolasschiller.com\/blog\/index.php\/archives\/2007\/01\/18\/945\/\">Polar Coordinates of Austin, Texas [square]<\/a><\/li><\/ul><\/p>\n","protected":false},"excerpt":{"rendered":"<p>8 tiled map I recently read through the work of Dr. Andrew Hudson-Smith (located at the Center for Advanced Spatial Analysis in London). I was intrigued by his use of Polar Coordinates to create panoramas and synthetic planets. I had been shown how to make the panoramas before, but I hadn&#8217;t actually figured out how [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[248,16,1,249,7,4,231,74],"tags":[],"class_list":["post-945","post","type-post","status-publish","format-standard","hentry","category-austin","category-design","category-general","category-polar-coordinates","category-quilt","category-renderings","category-square","category-texas"],"aioseo_notices":[],"views":472,"_links":{"self":[{"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/posts\/945","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/comments?post=945"}],"version-history":[{"count":0,"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/posts\/945\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/media?parent=945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/categories?post=945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.nikolasschiller.com\/blog\/index.php\/wp-json\/wp\/v2\/tags?post=945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}