{"id":2331,"date":"2014-01-30T16:38:27","date_gmt":"2014-01-30T16:38:27","guid":{"rendered":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/?post_type=portfolio&#038;p=2331"},"modified":"2020-08-20T10:39:49","modified_gmt":"2020-08-20T08:39:49","slug":"fluid_control_msc_thesis","status":"publish","type":"portfolio","link":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/gfx\/fluid_control_msc_thesis\/","title":{"rendered":"Real time fluid simulation and control using the Navier-Stokes equations MSc thesis (2012)"},"content":{"rendered":"<div  class='avia-slideshow av-10b3azv-490efbcdd5b3ee525b8af20f314508b5 avia-slideshow-entry_with_sidebar av_slideshow avia-slide-slider  avia-builder-el-0  el_before_av_hr  avia-builder-el-first  av-slideshow-ui av-control-default av-slideshow-autoplay av-loop-endless av-loop-manual-endless av-default-height-applied avia-slideshow-1' data-slideshow-options=\"{&quot;animation&quot;:&quot;slide&quot;,&quot;autoplay&quot;:true,&quot;loop_autoplay&quot;:&quot;endless&quot;,&quot;interval&quot;:5,&quot;loop_manual&quot;:&quot;manual-endless&quot;,&quot;autoplay_stopper&quot;:false,&quot;noNavigation&quot;:false,&quot;bg_slider&quot;:false,&quot;keep_padding&quot;:false,&quot;hoverpause&quot;:false,&quot;show_slide_delay&quot;:0}\"  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><ul class='avia-slideshow-inner ' style='padding-bottom: 38.028169014085%;'><li  class='avia-slideshow-slide av-10b3azv-490efbcdd5b3ee525b8af20f314508b5__0  slide-1 slide-odd'><div data-rel='slideshow-1' class='avia-slide-wrap '   ><img decoding=\"async\" fetchpriority=\"high\" class=\"wp-image-2319 avia-img-lazy-loading-not-2319\"  src=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/gpu_fluid_big-710x270.png\" width=\"710\" height=\"270\" title='gpu_fluid_big' alt='Fluid Control'  itemprop=\"thumbnailUrl\"   \/><\/div><\/li><li  class='avia-slideshow-slide av-10b3azv-490efbcdd5b3ee525b8af20f314508b5__1  slide-2 slide-even'><div data-rel='slideshow-1' class='avia-slide-wrap '   ><img decoding=\"async\" fetchpriority=\"high\" class=\"wp-image-2370 avia-img-lazy-loading-not-2370\"  src=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/fluid-eg-710x270.png\" width=\"710\" height=\"270\" title='fluid-eg' alt=''  itemprop=\"thumbnailUrl\"   \/><\/div><\/li><\/ul><div class='avia-slideshow-arrows avia-slideshow-controls' ><a href='#prev' class='prev-slide  avia-svg-icon avia-font-svg_entypo-fontello' data-av_svg_icon='left-open-big' data-av_iconset='svg_entypo-fontello' tabindex='-1' title=\"Previous\"><svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15\" height=\"32\" viewBox=\"0 0 15 32\" preserveAspectRatio=\"xMidYMid meet\" aria-labelledby='av-svg-title-1' aria-describedby='av-svg-desc-1' 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0l12.544 12.608q0.768 0.832 0 1.6l-12.544 12.608q-0.704 0.832-1.536 0-0.832-0.704 0-1.536z\"><\/path>\n<\/svg><span class='avia_hidden_link_text'>Next<\/span><\/a><\/div><div class='avia-slideshow-dots avia-slideshow-controls'><a href='#1' class='goto-slide active' >1<\/a><a href='#2' class='goto-slide ' >2<\/a><\/div><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-u5ceqj-41b166a49585070d335a32baa926acd1\">\n#top .hr.hr-invisible.av-u5ceqj-41b166a49585070d335a32baa926acd1{\nheight:25px;\n}\n<\/style>\n<div  class='hr av-u5ceqj-41b166a49585070d335a32baa926acd1 hr-invisible  avia-builder-el-1  el_after_av_slideshow  el_before_av_one_full '><span class='hr-inner '><span class=\"hr-inner-style\"><\/span><\/span><\/div>\n<div  class='flex_column av-svetez-734b128cf4112c1aac1e71716b56cbb6 av_one_full  avia-builder-el-2  el_after_av_hr  el_before_av_hr  first flex_column_div  '     ><p>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-2ow4sb-a09dda27ad6af03c0fc87db9db364014\">\n#top .av-special-heading.av-2ow4sb-a09dda27ad6af03c0fc87db9db364014{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-2ow4sb-a09dda27ad6af03c0fc87db9db364014 .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-2ow4sb-a09dda27ad6af03c0fc87db9db364014 .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-2ow4sb-a09dda27ad6af03c0fc87db9db364014 av-special-heading-h3 meta-heading  avia-builder-el-3  el_before_av_textblock  avia-builder-el-first '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Abstract<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-pi8gnv-0153cad67b205bec1969f1ca866ed68d '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p style=\"text-align: justify;\"><span class='av_dropcap2 av-av_dropcap2-21c86f7a1fbddaa06b9d9923710e6bba'>W<\/span>hen observing natural phenomena in our everyday life involving\u00a0complex fluid flows, one may feel that it ought to be immensely difficult\u00a0to understand the underlying laws of fluid motion. More than a hundred\u00a0years ago, Claude-Louis Navier and Sir George Stokes came up with\u00a0a short universal formula that describes the motion of incompressible\u00a0fluids. This made us realize that these underlying rules are surprisingly\u00a0simple: even the most difficult looking flows can be understood by the\u00a0evaluation of only three terms. Implementing a fluid simulation program\u00a0on computer hardware based on this equation is not a trivial problem,\u00a0however, it is quite rewarding: these simulation programs serve a vast array\u00a0of applications in physics- and engineering-related problems. In this thesis,\u00a0based on previous research work, we show a highly parallel framework that is\u00a0capable of giving an effective numerical solution of the Navier-Stokes equations.\u00a0Here we also address the fluid control problem, where, alongside simulating\u00a0the motion of fluids, an arbitrary density distribution (a shape of\u00a0any kind) is given, and forces are exerted on the system with the intention\u00a0that the fluid would sooner or later take this form. Prior research work\u00a0had shown that the problem is of enormous difficulty due to multiple\u00a0reasons: first, every region is tightly bound to its neighborhood, therefore\u00a0a force that acts upon a point in space will also have effect on nearby\u00a0regions, therefore making the controlling process unpredictable. Second, it\u00a0also a desirable, but ambivalent requirement that the controlling external\u00a0force field should make the fluid flow realistic, even though it is highly\u00a0improbable that a given volume of water would suddenly flow exactly into\u00a0a shape of a human face or a skyscraper. Utilizing highly sophisticated\u00a0mathematical methods from different fields such as optimization and\u00a0control theory, current state of the art methods are able to give visually\u00a0pleasing results at the cost of 5 to 7 minutes of computation time per frame,\u00a0effectively taking more than two hours of time for every second of video footage.\u00a0In this thesis work, we present a novel solution for the fluid control\u00a0problem, making it possible to solve it in real time, even on home computers with limited processing power.<\/p>\n<\/div><\/section><\/p><\/div>\n<div  class='hr av-omopbf-837cf2fe353f6030bc22ff4dfb8d56c2 hr-default  avia-builder-el-5  el_after_av_one_full  el_before_av_one_full '><span class='hr-inner '><span class=\"hr-inner-style\"><\/span><\/span><\/div>\n<div  class='flex_column av-81twb-48a0d7048f32f83f6d8634928f04bdf5 av_one_full  avia-builder-el-6  el_after_av_hr  el_before_av_one_third  first flex_column_div  '     ><style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-kxf19n-1b56a79657903a1cad1026dc1b2abbcb\">\n#top .av-special-heading.av-kxf19n-1b56a79657903a1cad1026dc1b2abbcb{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-kxf19n-1b56a79657903a1cad1026dc1b2abbcb .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-kxf19n-1b56a79657903a1cad1026dc1b2abbcb .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-kxf19n-1b56a79657903a1cad1026dc1b2abbcb av-special-heading-h3 meta-heading  avia-builder-el-7  avia-builder-el-no-sibling '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Resources<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><\/div>\n<div  class='flex_column av-ioaq3f-133134720044fff43bd10e39e9b3ada1 av_one_third  avia-builder-el-8  el_after_av_one_full  el_before_av_one_third  first flex_column_div  column-top-margin'     ><p>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-6hw0b-2ec44377a7e087b92c515e6169dab538\">\n.avia-image-container.av-6hw0b-2ec44377a7e087b92c515e6169dab538 img.avia_image{\nbox-shadow:none;\n}\n.avia-image-container.av-6hw0b-2ec44377a7e087b92c515e6169dab538 .av-image-caption-overlay-center{\ncolor:#ffffff;\n}\n<\/style>\n<div  class='avia-image-container av-6hw0b-2ec44377a7e087b92c515e6169dab538 av-styling- av-img-linked avia_animated_image av-animated-when-visible-95 left-to-right avia-align-center  avia-builder-el-9  el_before_av_textblock  avia-builder-el-first '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><a href=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/zsolnai_msc_thesis.pdf\" class='avia_image '  target=\"_blank\"  rel=\"noopener noreferrer\" aria-label='zsolnai_msc_thesis'><img decoding=\"async\" width=\"212\" height=\"300\" fetchpriority=\"high\" class='wp-image-2602 avia-img-lazy-loading-not-2602 avia_image ' src=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/zsolnai_msc_thesis-212x300.png\" alt='' title='zsolnai_msc_thesis'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/zsolnai_msc_thesis-212x300.png 212w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/zsolnai_msc_thesis-499x705.png 499w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/zsolnai_msc_thesis-450x635.png 450w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/01\/zsolnai_msc_thesis.png 568w\" sizes=\"(max-width: 212px) 100vw, 212px\" \/><\/a><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-g39yjf-7481107d0291383c5ec489324063fde7 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p style=\"text-align: center;\"><strong>Thesis<\/strong><\/p>\n<\/div><\/section><\/p><\/div>\n\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-e1ha3v-e4e3f597f7a4fc64a75683372359b51e\">\n.flex_column.av-e1ha3v-e4e3f597f7a4fc64a75683372359b51e{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-e1ha3v-e4e3f597f7a4fc64a75683372359b51e av_one_third  avia-builder-el-11  el_after_av_one_third  el_before_av_one_third  flex_column_div av-zero-column-padding  column-top-margin'     ><p>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-178z6j-4ba6ab7949514f2c8855f071f2c633d3\">\n.avia-image-container.av-178z6j-4ba6ab7949514f2c8855f071f2c633d3 img.avia_image{\nbox-shadow:none;\n}\n.avia-image-container.av-178z6j-4ba6ab7949514f2c8855f071f2c633d3 .av-image-caption-overlay-center{\ncolor:#ffffff;\n}\n<\/style>\n<div  class='avia-image-container av-178z6j-4ba6ab7949514f2c8855f071f2c633d3 av-styling- av-img-linked avia_animated_image av-animated-when-visible-95 left-to-right avia-align-center  avia-builder-el-12  el_before_av_textblock  avia-builder-el-first '   itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\" ><div class=\"avia-image-container-inner\"><div class=\"avia-image-overlay-wrap\"><a href=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/07\/fluid_gpl.zip\" class='avia_image '  target=\"_blank\"  rel=\"noopener noreferrer\" aria-label='code-icon'><img decoding=\"async\" width=\"300\" height=\"279\" fetchpriority=\"high\" class='wp-image-2653 avia-img-lazy-loading-not-2653 avia_image ' src=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/code-icon-300x279.png\" alt='' title='code-icon'   itemprop=\"thumbnailUrl\" srcset=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/code-icon-300x279.png 300w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/code-icon-705x656.png 705w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/code-icon-450x419.png 450w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/code-icon.png 714w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-agmfnf-724b1726cd8a4a6a706220e57ad63104 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p style=\"text-align: center;\"><b>Code (Standalone)<br \/>\n<\/b><\/p>\n<\/div><\/section><\/p><\/div>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-e1ha3v-e4e3f597f7a4fc64a75683372359b51e\">\n.flex_column.av-e1ha3v-e4e3f597f7a4fc64a75683372359b51e{\nborder-radius:0px 0px 0px 0px;\npadding:0px 0px 0px 0px;\n}\n<\/style>\n<div  class='flex_column av-e1ha3v-e4e3f597f7a4fc64a75683372359b51e av_one_third  avia-builder-el-14  el_after_av_one_third  el_before_av_video  flex_column_div av-zero-column-padding  column-top-margin'     ><p>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-178z6j-99ef4485cb0c1d0d9e1e0a743709d76f\">\n.avia-image-container.av-178z6j-99ef4485cb0c1d0d9e1e0a743709d76f img.avia_image{\nbox-shadow:none;\n}\n.avia-image-container.av-178z6j-99ef4485cb0c1d0d9e1e0a743709d76f .av-image-caption-overlay-center{\ncolor:#ffffff;\n}\n<\/style>\n<div  class='avia-image-container av-178z6j-99ef4485cb0c1d0d9e1e0a743709d76f av-styling- av-img-linked avia_animated_image av-animated-when-visible-95 left-to-right avia-align-center  avia-builder-el-15  el_before_av_textblock  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450w, https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp\/wp-content\/uploads\/2014\/02\/code-icon.png 714w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-agmfnf-724b1726cd8a4a6a706220e57ad63104 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p style=\"text-align: center;\"><b>Blender version (redirect)<br \/>\n<\/b><\/p>\n<\/div><\/section><\/p><\/div><div  class='avia-video av-9wcesb-e2efb538aec2d3849b0b02822d73222a avia-video-16-9 av-no-preview-image avia-video-load-always av-lazyload-immediate av-lazyload-video-embed'  itemprop=\"video\" itemtype=\"https:\/\/schema.org\/VideoObject\"  data-original_url='https:\/\/www.youtube.com\/watch?v=xjiFVSSMkfI'><script type='text\/html' class='av-video-tmpl'><div class='avia-iframe-wrap'><iframe loading=\"lazy\" title=\"Control of Newtonian fluids with minimum force impact using the Navier Stokes equations\" width=\"1500\" height=\"844\" src=\"https:\/\/www.youtube.com\/embed\/xjiFVSSMkfI?feature=oembed&autoplay=0&loop=0&controls=1&mute=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/script><div class='av-click-to-play-overlay'><div class=\"avia_playpause_icon\"><\/div><\/div><\/div><\/p>\n<div  class='avia-video av-86dm57-776c82262c0752d1882a513bb1e59154 avia-video-16-9 av-no-preview-image avia-video-load-always av-lazyload-immediate av-lazyload-video-embed'  itemprop=\"video\" itemtype=\"https:\/\/schema.org\/VideoObject\"  data-original_url='https:\/\/www.youtube.com\/watch?v=7SFw6sdyzcQ'><script type='text\/html' class='av-video-tmpl'><div class='avia-iframe-wrap'><iframe loading=\"lazy\" title=\"Real-time Control and Stopping of Fluids by K\u00e1roly Zsolnai and L\u00e1szl\u00f3 Szirmay-Kalos\" width=\"1500\" height=\"844\" src=\"https:\/\/www.youtube.com\/embed\/7SFw6sdyzcQ?feature=oembed&autoplay=0&loop=0&controls=1&mute=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/script><div class='av-click-to-play-overlay'><div class=\"avia_playpause_icon\"><\/div><\/div><\/div>\n<div  class='avia-video av-86dm57-b2316585b89c4fbd4ba6d5402d8219b0 avia-video-16-9 av-no-preview-image avia-video-load-always av-lazyload-immediate av-lazyload-video-embed'  itemprop=\"video\" itemtype=\"https:\/\/schema.org\/VideoObject\"  data-original_url='https:\/\/www.youtube.com\/watch?v=lxNEWuO6xQk'><script type='text\/html' class='av-video-tmpl'><div class='avia-iframe-wrap'><iframe loading=\"lazy\" title=\"Controllable Fluid and Smoke Simulations | Two Minute Papers #145\" width=\"1500\" height=\"844\" src=\"https:\/\/www.youtube.com\/embed\/lxNEWuO6xQk?feature=oembed&autoplay=0&loop=0&controls=1&mute=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div><\/script><div class='av-click-to-play-overlay'><div class=\"avia_playpause_icon\"><\/div><\/div><\/div>\n<div  class='flex_column av-59a6fv-d5568bfca18d390e974aa8eb8b8c5098 av_one_full  avia-builder-el-20  el_after_av_video  avia-builder-el-last  first flex_column_div  '     ><p>\n<style type=\"text\/css\" data-created_by=\"avia_inline_auto\" id=\"style-css-av-h4wl7-bb33378aa7ef42fbe0938b588aa8ef1a\">\n#top .av-special-heading.av-h4wl7-bb33378aa7ef42fbe0938b588aa8ef1a{\npadding-bottom:10px;\n}\nbody .av-special-heading.av-h4wl7-bb33378aa7ef42fbe0938b588aa8ef1a .av-special-heading-tag .heading-char{\nfont-size:25px;\n}\n.av-special-heading.av-h4wl7-bb33378aa7ef42fbe0938b588aa8ef1a .av-subheading{\nfont-size:15px;\n}\n<\/style>\n<div  class='av-special-heading av-h4wl7-bb33378aa7ef42fbe0938b588aa8ef1a av-special-heading-h3 meta-heading  avia-builder-el-21  el_before_av_textblock  avia-builder-el-first '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >BibTeX<\/h3><div class=\"special-heading-border\"><div class=\"special-heading-inner-border\"><\/div><\/div><\/div><br \/>\n<section  class='av_textblock_section av-2t30vv-368ac109d7048df467693fb005610a98 '   itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/CreativeWork\" ><div class='avia_textblock'  itemprop=\"text\" ><p>Please <a href=\"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/gfx\/real_time_fluid_control_eg\/\"><strong>click here<\/strong><\/a> to obtain the citable version of this paper.<\/p>\n<\/div><\/section><\/p><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":2319,"template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"tags":[],"portfolio_category":[],"portfolio_tag":[],"portfolio_entries":[],"class_list":["post-2331","portfolio","type-portfolio","status-publish","has-post-thumbnail","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/portfolio\/2331","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/portfolio"}],"about":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/types\/portfolio"}],"author":[{"embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":25,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/portfolio\/2331\/revisions"}],"predecessor-version":[{"id":5011,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/portfolio\/2331\/revisions\/5011"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/media\/2319"}],"wp:attachment":[{"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/media?parent=2331"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/tags?post=2331"},{"taxonomy":"portfolio_category","embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/portfolio_category?post=2331"},{"taxonomy":"portfolio_tag","embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/portfolio_tag?post=2331"},{"taxonomy":"portfolio_entries","embeddable":true,"href":"https:\/\/users.cg.tuwien.ac.at\/zsolnai\/wp-json\/wp\/v2\/portfolio_entries?post=2331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}