{"id":28,"date":"2009-12-19T23:54:46","date_gmt":"2009-12-19T22:54:46","guid":{"rendered":"http:\/\/www.clodo.it\/blog\/?p=28"},"modified":"2024-04-09T16:02:11","modified_gmt":"2024-04-09T15:02:11","slug":"sphere-spirals-1958-mc-escher","status":"publish","type":"post","link":"https:\/\/www.clodo.it\/blog\/sphere-spirals-1958-mc-escher\/","title":{"rendered":"Povray Render &#8211; Sphere spirals, 1958, MC Escher"},"content":{"rendered":"<p class=\"bbc_center\"><img decoding=\"async\" class=\"bbc_img\" src=\"https:\/\/www.clodo.it\/host\/images\/888f931352de50468def1d25cc9bfcbca84e74c7.png\" alt=\"Immagine inviata\" \/><\/p>\n<p><a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clodo.it\/host\/index.php?id=eef180ea19e06277365f6e2150be5ce6449cbfdc.jpg\" rel=\"nofollow external\"><img decoding=\"async\" class=\"bbc_img\" src=\"https:\/\/www.clodo.it\/host\/thumbs\/eef180ea19e06277365f6e2150be5ce6449cbfdc.jpg\" alt=\"Immagine inviata\" \/><\/a> <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clodo.it\/host\/index.php?id=a7e3604c703a7962d3871235598817e83d6a7ac5.jpg\" rel=\"nofollow external\"><img decoding=\"async\" class=\"bbc_img\" src=\"https:\/\/www.clodo.it\/host\/thumbs\/a7e3604c703a7962d3871235598817e83d6a7ac5.jpg\" alt=\"Immagine inviata\" \/><\/a> <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clodo.it\/host\/index.php?id=2708ebba24810cdd3933b790a44be378f6aeaf45.jpg\" rel=\"nofollow external\"><img decoding=\"async\" class=\"bbc_img\" src=\"https:\/\/www.clodo.it\/host\/thumbs\/2708ebba24810cdd3933b790a44be378f6aeaf45.jpg\" alt=\"Immagine inviata\" \/><\/a> <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clodo.it\/host\/index.php?id=2b5131cdae858ec0a6ddf390a4f15bf79b9a363d.jpg\" rel=\"nofollow external\"><img decoding=\"async\" class=\"bbc_img\" src=\"https:\/\/www.clodo.it\/host\/thumbs\/2b5131cdae858ec0a6ddf390a4f15bf79b9a363d.jpg\" alt=\"Immagine inviata\" \/><\/a> <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clodo.it\/host\/index.php?id=b49db2aceee0416d4fb3c78d01f0759679ff58b8.jpg\" rel=\"nofollow external\"><img decoding=\"async\" class=\"bbc_img\" src=\"https:\/\/www.clodo.it\/host\/thumbs\/b49db2aceee0416d4fb3c78d01f0759679ff58b8.jpg\" alt=\"Immagine inviata\" \/>\u00a0<\/a><\/p>\n<p><video controls=\"controls\" width=\"640\" height=\"150\"><source src=\"https:\/\/www.clodo.it\/files\/Clodo\/projects\/escher_sphere_spirals\/escher_sphere_spirals.mp4\" type=\"video\/mp4\" \/>Your browser does not support HTML5 video.<\/video><\/p>\n<p><a href=\"https:\/\/www.clodo.it\/files\/Clodo\/projects\/escher_sphere_spirals\/escher_sphere_spirals.mp4\">Download MP4<\/a><\/p>\n<p>Rendering di una <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/it.wikipedia.org\/wiki\/Isosuperficie\" rel=\"nofollow external\">isosuperficie<\/a> ispirata da un&#8217;opera di <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.flickr.com\/photos\/transphormetic\/279762196\/\" rel=\"nofollow external\">Escher, Sphere Spirals.<\/a><br \/>\nFormule per Povray da <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/hof.povray.org\/Riemann_Sphere-Isosurface.html\" rel=\"nofollow external\">&#8220;Almost Sphere Spirals&#8221;<\/a> by <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/home.online.no\/%7Et-o-k\/index.html\" rel=\"nofollow external\">Tor Olav Kristensen<\/a> (2002)<\/p>\n<p class=\"citation\">&#8216;Tor Olav Kristensen&#8217; said<\/p>\n<blockquote class=\"ipsBlockquote built\" data-author=\"'Tor Olav Kristensen'\"><p>An isosurface shape inspired by M.C. Escher&#8217;s &#8220;Sphere Spirals&#8221; (&#8220;Bolspiralen&#8221;) woodcut print from 1958. The edges of the four spiraling bands on the sphere can be formed by an inverse stereographic projection of eight infinite logarithmic spirals in a complex plane tangent to a Riemann Sphere onto it&#8217;s surface. I found some useful information about this shape <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clowder.net\/hop\/Riemann\/Riemann.html\" rel=\"nofollow external\">here<\/a>.<\/p><\/blockquote>\n<p>Shot 1: Twisting rate a 1.5, 4 bande. 1920 x 1080. Rendering: 2 ore circa.<br \/>\nShot 2: Twisting rate a 0.1, 1 banda. 1920 x 1080. Rendering: 20 ore circa.<br \/>\nShot 3: Twisting rate a 0.5, 4 bande. 1920 x 1080. Rendering: 8 ore circa.<br \/>\nShot 4: Twisting rate a 1.9, 12 bande. 1920 x 1080. Rendering: 1 ora circa.<br \/>\nShot 5: Twisting rate a 1.0, 4 bande, fog. 1920 x 1080. Rendering: 8 ore circa.<br \/>\nAnimazione: Twisting rate variabile da 1 a 3, 4 bande. 640 x 360, 30 fps, 600 fotogrammi (20 sec). Rendering: 2-3 settimane su 3 macchine circa, tempo variabile da 3 ore a mezz&#8217;ora per ogni fotogramma.<\/p>\n<p>Tutti con antialiasing di default, senza radiosit\u00e0.<br \/>\nIn dettaglio, i riflessi non incidono particolarmente nei tempi di rendering. E&#8217; l&#8217;isosuperficie che &#8220;ammazza&#8221;, in particolare con bassi valori di twisting rate.<\/p>\n<p>Sorgenti (<a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.povray.org\/\" rel=\"nofollow external\">PovRay<\/a> 3.6 richiesto, 3.7 consigliato): <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clodo.it\/files\/Clodo\/projects\/escher_sphere_spirals\/escher_sphere_spirals.ini\" rel=\"nofollow external\">ini<\/a>, <a class=\"bbc_url\" title=\"link esterno\" href=\"https:\/\/www.clodo.it\/files\/Clodo\/projects\/escher_sphere_spirals\/escher_sphere_spirals.pov\" rel=\"nofollow external\">pov<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0 Your browser does not support HTML5 video. Download MP4 Rendering di una isosuperficie ispirata da un&#8217;opera di Escher, Sphere Spirals. Formule per Povray da &#8220;Almost Sphere Spirals&#8221; by Tor Olav Kristensen (2002) &#8216;Tor Olav Kristensen&#8217; said An isosurface shape inspired by M.C. Escher&#8217;s &#8220;Sphere Spirals&#8221; (&#8220;Bolspiralen&#8221;) woodcut print from 1958. The edges of the &hellip; <a href=\"https:\/\/www.clodo.it\/blog\/sphere-spirals-1958-mc-escher\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Povray Render &#8211; Sphere spirals, 1958, MC Escher<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":499,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10,3],"tags":[18,17],"uagb_featured_image_src":{"full":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere.jpg",1328,749,false],"thumbnail":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere-150x150.jpg",150,150,true],"medium":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere-300x169.jpg",300,169,true],"medium_large":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere-768x433.jpg",660,372,true],"large":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere-1024x578.jpg",660,373,true],"1536x1536":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere.jpg",1328,749,false],"2048x2048":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere.jpg",1328,749,false],"post-thumbnail":["https:\/\/www.clodo.it\/blog\/wp-content\/uploads\/2009\/12\/feature-povray_isosphere-825x510.jpg",825,510,true]},"uagb_author_info":{"display_name":"Clodo","author_link":"https:\/\/www.clodo.it\/blog\/author\/clodo\/"},"uagb_comment_info":1,"uagb_excerpt":"\u00a0 Your browser does not support HTML5 video. Download MP4 Rendering di una isosuperficie ispirata da un&#8217;opera di Escher, Sphere Spirals. Formule per Povray da &#8220;Almost Sphere Spirals&#8221; by Tor Olav Kristensen (2002) &#8216;Tor Olav Kristensen&#8217; said An isosurface shape inspired by M.C. Escher&#8217;s &#8220;Sphere Spirals&#8221; (&#8220;Bolspiralen&#8221;) woodcut print from 1958. The edges of the&hellip;","_links":{"self":[{"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/posts\/28"}],"collection":[{"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/comments?post=28"}],"version-history":[{"count":6,"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/posts\/28\/revisions"}],"predecessor-version":[{"id":526,"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/posts\/28\/revisions\/526"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/media\/499"}],"wp:attachment":[{"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/media?parent=28"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/categories?post=28"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.clodo.it\/blog\/wp-json\/wp\/v2\/tags?post=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}