{"version":"1.0","provider_name":"Microsoft Research","provider_url":"https:\/\/www.microsoft.com\/en-us\/research","author_name":"Yang Liu","author_url":"https:\/\/www.microsoft.com\/en-us\/research\/people\/yangliu\/","title":"On Centroidal Voronoi Tessellation\"\u201dEnergy Smoothness and Fast Computation - Microsoft Research","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"fhiZtap2TE\"><a href=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/centroidal-voronoi-tessellation-energy-smoothness-fast-computation\/\">On Centroidal Voronoi Tessellation&#8221;\u201dEnergy Smoothness and Fast Computation<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/centroidal-voronoi-tessellation-energy-smoothness-fast-computation\/embed\/#?secret=fhiZtap2TE\" width=\"600\" height=\"338\" title=\"&#8220;On Centroidal Voronoi Tessellation&#8221;\u201dEnergy Smoothness and Fast Computation&#8221; &#8212; Microsoft Research\" data-secret=\"fhiZtap2TE\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/* ]]> *\/\n<\/script>\n","description":"Centroidal Voronoi tessellation (CVT) is a particular type of Voronoi tessellation that has many applications in computational sciences and engineering, including computer graphics. The prevailing method for computing CVT is Lloyd\u2019s method, which has linear convergence and is inefficient in practice. We develop new efficient methods for CVT computation and demonstrate the fast convergence of [&hellip;]"}