<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
  <head>
    <meta http-equiv="Content-Type" content="application/xhtml+xml; charset=utf-8"/>
    <title>Project-Team:ALICE</title>
    <link rel="stylesheet" href="../static/css/raweb.css" type="text/css"/>
    <meta name="description" content="New Results - Hex-dominant meshing: Mind the gap!"/>
    <meta name="dc.title" content="New Results - Hex-dominant meshing: Mind the gap!"/>
    <meta name="dc.creator" content="Nicolas Ray"/>
    <meta name="dc.creator" content="Dmitry Sokolov"/>
    <meta name="dc.creator" content="Maxence Reberol"/>
    <meta name="dc.creator" content="Franck Ledoux"/>
    <meta name="dc.creator" content="Bruno Lévy"/>
    <meta name="dc.subject" content=""/>
    <meta name="dc.publisher" content="INRIA"/>
    <meta name="dc.date" content="(SCHEME=ISO8601) 2018-01"/>
    <meta name="dc.type" content="Report"/>
    <meta name="dc.language" content="(SCHEME=ISO639-1) en"/>
    <meta name="projet" content="ALICE"/>
    <script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-MML-AM_CHTML">
      <!--MathJax-->
    </script>
  </head>
  <body>
    <div class="tdmdiv">
      <div class="logo">
        <a href="http://www.inria.fr">
          <img style="align:bottom; border:none" src="../static/img/icons/logo_INRIA-coul.jpg" alt="Inria"/>
        </a>
      </div>
      <div class="TdmEntry">
        <div class="tdmentete">
          <a href="uid0.html">Project-Team Alice</a>
        </div>
        <span>
          <a href="uid1.html">Team, Visitors, External Collaborators</a>
        </span>
      </div>
      <div class="TdmEntry">
        <a href="./uid3.html">Overall Objectives</a>
      </div>
      <div class="TdmEntry">Research Program<ul><li><a href="uid5.html&#10;&#9;&#9;  ">Introduction</a></li><li><a href="uid8.html&#10;&#9;&#9;  ">Geometry Processing for Engineering</a></li><li><a href="uid9.html&#10;&#9;&#9;  ">Computer Graphics</a></li></ul></div>
      <div class="TdmEntry">Application Domains<ul><li><a href="uid11.html&#10;&#9;&#9;  ">Geometric Tools for Simulating Physics with a Computer</a></li><li><a href="uid12.html&#10;&#9;&#9;  ">Fabrication</a></li></ul></div>
      <div class="TdmEntry">
        <a href="./uid14.html">Highlights of the Year</a>
      </div>
      <div class="TdmEntry">New Software and Platforms<ul><li><a href="uid17.html&#10;&#9;&#9;  ">Graphite</a></li><li><a href="uid21.html&#10;&#9;&#9;  ">GEOGRAM</a></li><li><a href="uid25.html&#10;&#9;&#9;  ">OpenNL</a></li><li><a href="uid29.html&#10;&#9;&#9;  ">IceSL</a></li><li><a href="uid33.html&#10;&#9;&#9;  ">LibSL</a></li><li><a href="uid36.html&#10;&#9;&#9;  ">3DPrintScaffoldings</a></li><li><a href="uid41.html&#10;&#9;&#9;  ">VORPALINE</a></li></ul></div>
      <div class="TdmEntry">New Results<ul><li class="tdmActPage"><a href="uid46.html&#10;&#9;&#9;  ">Hex-dominant meshing: Mind the gap!</a></li><li><a href="uid48.html&#10;&#9;&#9;  ">Meshless Voronoi on the GPU</a></li><li><a href="uid50.html&#10;&#9;&#9;  ">Computational Optimal Transport</a></li></ul></div>
      <div class="TdmEntry">Partnerships and Cooperations<ul><li><a href="uid52.html&#10;&#9;&#9;  ">National Initiatives</a></li><li><a href="uid56.html&#10;&#9;&#9;  ">International Research Visitors</a></li></ul></div>
      <div class="TdmEntry">Dissemination<ul><li><a href="uid61.html&#10;&#9;&#9;  ">Promoting Scientific Activities</a></li><li><a href="uid76.html&#10;&#9;&#9;  ">Teaching - Supervision - Juries</a></li></ul></div>
      <div class="TdmEntry">
        <div>Bibliography</div>
      </div>
      <div class="TdmEntry">
        <ul>
          <li>
            <a id="tdmbibentmajor" href="bibliography.html">Major publications</a>
          </li>
          <li>
            <a id="tdmbibentyear" href="bibliography.html#year">Publications of the year</a>
          </li>
          <li>
            <a id="tdmbibentfoot" href="bibliography.html#References">References in notes</a>
          </li>
        </ul>
      </div>
    </div>
    <div id="main">
      <div class="mainentete">
        <div id="head_agauche">
          <small><a href="http://www.inria.fr">
	    
	    Inria
	  </a> | <a href="../index.html">
	    
	    Raweb 
	    2018</a> | <a href="http://www.inria.fr/en/teams/alice">Presentation of the Project-Team ALICE</a> | <a href="http://alice.loria.fr">ALICE Web Site
	  </a></small>
        </div>
        <div id="head_adroite">
          <table class="qrcode">
            <tr>
              <td>
                <a href="alice.xml">
                  <img style="align:bottom; border:none" alt="XML" src="../static/img/icons/xml_motif.png"/>
                </a>
              </td>
              <td>
                <a href="alice.pdf">
                  <img style="align:bottom; border:none" alt="PDF" src="IMG/qrcode-alice-pdf.png"/>
                </a>
              </td>
              <td>
                <a href="../alice/alice.epub">
                  <img style="align:bottom; border:none" alt="e-pub" src="IMG/qrcode-alice-epub.png"/>
                </a>
              </td>
            </tr>
            <tr>
              <td/>
              <td>PDF
</td>
              <td>e-Pub
</td>
            </tr>
          </table>
        </div>
      </div>
      <!--FIN du corps du module-->
      <br/>
      <div class="bottomNavigation">
        <div class="tail_aucentre">
          <a href="./uid41.html" accesskey="P"><img style="align:bottom; border:none" alt="previous" src="../static/img/icons/previous_motif.jpg"/> Previous | </a>
          <a href="./uid0.html" accesskey="U"><img style="align:bottom; border:none" alt="up" src="../static/img/icons/up_motif.jpg"/>  Home</a>
          <a href="./uid48.html" accesskey="N"> | Next <img style="align:bottom; border:none" alt="next" src="../static/img/icons/next_motif.jpg"/></a>
        </div>
        <br/>
      </div>
      <div id="textepage">
        <!--DEBUT2 du corps du module-->
        <h2>Section: 
      New Results</h2>
        <h3 class="titre3">Hex-dominant meshing: Mind the gap!</h3>
        <p class="participants"><span class="part">Participants</span> :
	Nicolas Ray, Dmitry Sokolov, Maxence Reberol, Franck Ledoux, Bruno Lévy.</p>
        <p>We proposed a robust pipeline that can generate hex-dominant meshes from any global parameterization of a tetrahedral mesh (Figure <a title="Hex-dominant meshing: Mind the gap!" href="./uid46.html#uid47">1</a>). We focus on robustness in order to be able to benchmark different parameterizations on a large database. Our main contribution is a new method that integrates the hexahedra (extracted from the parameterization) into the original object. The main difficulty is to produce the boundary of the result, composed of both faces of hexahedra and tetrahedra. Obviously, this surface must be a good approximation of the original object but, more importantly, it must be possible to remesh the volume bounded by this surface minus the extracted hexahedra (called void). We enforce these properties by carefully tracking and eliminating all possibilities of failure at each step of our pipeline.</p>
        <p>We tested our method on a large collection of objects (200+) with different settings. In most cases, we obtained results of very good quality as compared to the state-of-the-art solutions.</p>
        <div align="center" style="margin-top:10px">
          <a name="uid47">
            <!--...-->
          </a>
          <table title="" class="objectContainer">
            <caption align="bottom"><strong>Figure
	1. </strong>Our hexahedral-dominant meshing procedure: Start from an input tetrahedral mesh. Compute a global parameterization
<b>(a)</b>. Extract hexahedra by contouring the isovalues of the parameterization. Isolate the boundary of the void (in red), i.e., the volume with a
degenerate / singular parameterization <b>(b)</b> (also called “gap” or “cavity”), shown in red. Remesh the void and stitch it into the hexahedral
mesh <b>(c)</b>.</caption>
            <tr align="center">
              <td>
                <table>
                  <tr>
                    <td style="height:3px;" align="center">
                      <img style="width:170.7974pt" alt="IMG/teasercrop.jpg" src="IMG/teasercrop.jpg"/>
                    </td>
                    <td style="height:3px;" align="center">
                      <img style="width:128.1013pt" alt="IMG/r2_block.jpg" src="IMG/r2_block.jpg"/>
                    </td>
                  </tr>
                </table>
              </td>
            </tr>
          </table>
        </div>
      </div>
      <!--FIN du corps du module-->
      <br/>
      <div class="bottomNavigation">
        <div class="tail_aucentre">
          <a href="./uid41.html" accesskey="P"><img style="align:bottom; border:none" alt="previous" src="../static/img/icons/previous_motif.jpg"/> Previous | </a>
          <a href="./uid0.html" accesskey="U"><img style="align:bottom; border:none" alt="up" src="../static/img/icons/up_motif.jpg"/>  Home</a>
          <a href="./uid48.html" accesskey="N"> | Next <img style="align:bottom; border:none" alt="next" src="../static/img/icons/next_motif.jpg"/></a>
        </div>
        <br/>
      </div>
    </div>
  </body>
</html>
