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<!DOCTYPE html>
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<h1 class="page-title">Class: DEC</h1>
<section>
<header>
<h2>
<span class="ancestors"><a href="module-Core.html">Core</a>.</span>
DEC
</h2>
<div class="class-description"><p>This class contains methods to build common <a href="https://cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf">discrete exterior calculus</a> operators.</p></div>
</header>
<article>
<div class="container-overview">
<hr>
<dt>
<h4 class="name" id="DEC"><span class="type-signature"></span>new DEC()</h4>
</dt>
<dd>
<dl class="details">
</dl>
</dd>
</div>
<h3 class="subsection-title">Methods</h3>
<dl>
<hr>
<dt>
<h4 class="name" id=".buildHodgeStar0Form"><span class="type-signature"><static> </span>buildHodgeStar0Form(geometry, vertexIndex)</h4>
</dt>
<dd>
<div class="description">
<p>Builds a sparse diagonal matrix encoding the Hodge operator on 0-forms.<br>
By convention, the area of a vertex is 1.</p>
</div>
<h5>Parameters:</h5>
<table class="params table table-striped">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>geometry</code></td>
<td class="type">
<span class="param-type"><a href="module-Core.Geometry.html">module:Core.Geometry</a></span>
</td>
<td class="description last"><p>The geometry of a mesh.</p></td>
</tr>
<tr>
<td class="name"><code>vertexIndex</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last"><p>A dictionary mapping each vertex of a mesh to a unique index.</p></td>
</tr>
</tbody>
</table>
<dl class="details">
</dl>
<h5>Returns:</h5>
<dl>
<dt>
Type
</dt>
<dd>
<span class="param-type"><a href="module-LinearAlgebra.SparseMatrix.html">module:LinearAlgebra.SparseMatrix</a></span>
</dd>
</dl>
</dd>
<hr>
<dt>
<h4 class="name" id=".buildHodgeStar1Form"><span class="type-signature"><static> </span>buildHodgeStar1Form(geometry, edgeIndex)</h4>
</dt>
<dd>
<div class="description">
<p>Builds a sparse diagonal matrix encoding the Hodge operator on 1-forms.</p>
</div>
<h5>Parameters:</h5>
<table class="params table table-striped">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>geometry</code></td>
<td class="type">
<span class="param-type"><a href="module-Core.Geometry.html">module:Core.Geometry</a></span>
</td>
<td class="description last"><p>The geometry of a mesh.</p></td>
</tr>
<tr>
<td class="name"><code>edgeIndex</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last"><p>A dictionary mapping each edge of a mesh to a unique index.</p></td>
</tr>
</tbody>
</table>
<dl class="details">
</dl>
<h5>Returns:</h5>
<dl>
<dt>
Type
</dt>
<dd>
<span class="param-type"><a href="module-LinearAlgebra.SparseMatrix.html">module:LinearAlgebra.SparseMatrix</a></span>
</dd>
</dl>
</dd>
<hr>
<dt>
<h4 class="name" id=".buildHodgeStar2Form"><span class="type-signature"><static> </span>buildHodgeStar2Form(geometry, faceIndex)</h4>
</dt>
<dd>
<div class="description">
<p>Builds a sparse diagonal matrix encoding the Hodge operator on 2-forms.<br>
By convention, the area of a vertex is 1.</p>
</div>
<h5>Parameters:</h5>
<table class="params table table-striped">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>geometry</code></td>
<td class="type">
<span class="param-type"><a href="module-Core.Geometry.html">module:Core.Geometry</a></span>
</td>
<td class="description last"><p>The geometry of a mesh.</p></td>
</tr>
<tr>
<td class="name"><code>faceIndex</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last"><p>A dictionary mapping each face of a mesh to a unique index.</p></td>
</tr>
</tbody>
</table>
<dl class="details">
</dl>
<h5>Returns:</h5>
<dl>
<dt>
Type
</dt>
<dd>
<span class="param-type"><a href="module-LinearAlgebra.SparseMatrix.html">module:LinearAlgebra.SparseMatrix</a></span>
</dd>
</dl>
</dd>
<hr>
<dt>
<h4 class="name" id=".buildExteriorDerivative0Form"><span class="type-signature"><static> </span>buildExteriorDerivative0Form(geometry, edgeIndex, vertexIndex)</h4>
</dt>
<dd>
<div class="description">
<p>Builds a sparse matrix encoding the exterior derivative on 0-forms.</p>
</div>
<h5>Parameters:</h5>
<table class="params table table-striped">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>geometry</code></td>
<td class="type">
<span class="param-type"><a href="module-Core.Geometry.html">module:Core.Geometry</a></span>
</td>
<td class="description last"><p>The geometry of a mesh.</p></td>
</tr>
<tr>
<td class="name"><code>edgeIndex</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last"><p>A dictionary mapping each edge of a mesh to a unique index.</p></td>
</tr>
<tr>
<td class="name"><code>vertexIndex</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last"><p>A dictionary mapping each vertex of a mesh to a unique index.</p></td>
</tr>
</tbody>
</table>
<dl class="details">
</dl>
<h5>Returns:</h5>
<dl>
<dt>
Type
</dt>
<dd>
<span class="param-type"><a href="module-LinearAlgebra.SparseMatrix.html">module:LinearAlgebra.SparseMatrix</a></span>
</dd>
</dl>
</dd>
<hr>
<dt>
<h4 class="name" id=".buildExteriorDerivative1Form"><span class="type-signature"><static> </span>buildExteriorDerivative1Form(geometry, faceIndex, edgeIndex)</h4>
</dt>
<dd>
<div class="description">
<p>Builds a sparse matrix encoding the exterior derivative on 1-forms.</p>
</div>
<h5>Parameters:</h5>
<table class="params table table-striped">
<thead>
<tr>
<th>Name</th>
<th>Type</th>
<th class="last">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="name"><code>geometry</code></td>
<td class="type">
<span class="param-type"><a href="module-Core.Geometry.html">module:Core.Geometry</a></span>
</td>
<td class="description last"><p>The geometry of a mesh.</p></td>
</tr>
<tr>
<td class="name"><code>faceIndex</code></td>
<td class="type">
<span class="param-type">Object</span>
</td>
<td class="description last"><p>A dictionary mapping each face of a mesh to a unique index.</p></td>
</tr>
<tr>