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	<h1 class="page-title">Class: Geometry</h1>
<section>

<header>
    
        <h2>
            <span class="ancestors"><a href="module-Core.html">Core</a>.</span>
        
        Geometry
        </h2>
        
    
</header>


<article>
    <div class="container-overview">
    
        
<hr>
<dt>
    <h4 class="name" id="Geometry"><span class="type-signature"></span>new Geometry(mesh, positions, normalizePositions)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>This class represents the geometry of a <a href="module-Core.Mesh.html">Mesh</a>. This includes information such<br>
as the position of vertices as well as methods to compute edge lengths, corner<br>
angles, face area, normals, discrete curvatures etc.</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>mesh</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Mesh.html">module:Core.Mesh</a></span>


            </td>

            
            <td class="description last"><p>The mesh this class describes the geometry of.</p></td>
        </tr>

    
        <tr>
            
                <td class="name"><code>positions</code></td>
            

            <td class="type">
            
                
<span class="param-type">Array.&lt;<a href="module-LinearAlgebra.Vector.html">module:LinearAlgebra.Vector</a>></span>


            </td>

            
            <td class="description last"><p>An array containing the position of each vertex in a mesh.</p></td>
        </tr>

    
        <tr>
            
                <td class="name"><code>normalizePositions</code></td>
            

            <td class="type">
            
                
<span class="param-type">boolean</span>


            </td>

            
            <td class="description last"><p>flag to indicate whether positions should be normalized. Default value is true.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

    <h5 class="subsection-title">Properties:</h5>

    <dl>

<table class="props table table-striped">
    <thead>
    <tr>
        
        <th>Name</th>
        

        <th>Type</th>

        
        <th class="last">Description</th>
    </tr>
    </thead>

    <tbody>
    

        <tr>
            
                <td class="name"><code>mesh</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Mesh.html">module:Core.Mesh</a></span>


            </td>

            
            <td class="description last"><p>The mesh this class describes the geometry of.</p></td>
        </tr>

    
        <tr>
            
                <td class="name"><code>positions</code></td>
            

            <td class="type">
            
                
<span class="param-type">Object</span>


            </td>

            
            <td class="description last"><p>A dictionary mapping each vertex to a normalized position.</p></td>
        </tr>

    
    </tbody>
</table>
</dl>

    
</dl>


</dd>

    
    </div>

    
        <h3 class="subsection-title">Methods</h3>

        <dl>
            
<hr>
<dt>
    <h4 class="name" id="vector"><span class="type-signature"></span>vector(h)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the vector along a halfedge.</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>h</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Halfedge.html">module:Core.Halfedge</a></span>


            </td>

            
            <td class="description last"><p>The halfedge along which the vector needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="length"><span class="type-signature"></span>length(e)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the length of an edge.</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>e</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Edge.html">module:Core.Edge</a></span>


            </td>

            
            <td class="description last"><p>The edge whose length needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="midpoint"><span class="type-signature"></span>midpoint(e)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the midpoint of an edge.</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>e</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Edge.html">module:Core.Edge</a></span>


            </td>

            
            <td class="description last"><p>The edge whose midpoint needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="meanEdgeLength"><span class="type-signature"></span>meanEdgeLength()</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the mean edge length of all the edges in a mesh.</p>
    </div>
    

<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="area"><span class="type-signature"></span>area(f)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the area of a face.</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>f</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Face.html">module:Core.Face</a></span>


            </td>

            
            <td class="description last"><p>The face whose area needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="totalArea"><span class="type-signature"></span>totalArea()</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the total surface area of a mesh.</p>
    </div>
    

<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="faceNormal"><span class="type-signature"></span>faceNormal(f)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the normal of a face.</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>f</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Face.html">module:Core.Face</a></span>


            </td>

            
            <td class="description last"><p>The face whose normal needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="centroid"><span class="type-signature"></span>centroid(f)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the centroid of a face.</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>f</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Face.html">module:Core.Face</a></span>


            </td>

            
            <td class="description last"><p>The face whose centroid needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="circumcenter"><span class="type-signature"></span>circumcenter(f)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the circumcenter of a face.</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>f</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Face.html">module:Core.Face</a></span>


            </td>

            
            <td class="description last"><p>The face whose circumcenter needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="orthonormalBases"><span class="type-signature"></span>orthonormalBases(f)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes an orthonormal bases for a face.</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>f</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Face.html">module:Core.Face</a></span>


            </td>

            
            <td class="description last"><p>The face on which the orthonormal bases needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<div class="param-desc">
    <p>An array containing two orthonormal vectors tangent to the face.</p>
</div>


<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">Array.&lt;<a href="module-LinearAlgebra.Vector.html">module:LinearAlgebra.Vector</a>></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="angle"><span class="type-signature"></span>angle(c)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the angle (in radians) at a corner.</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>c</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Corner.html">module:Core.Corner</a></span>


            </td>

            
            <td class="description last"><p>The corner at which the angle needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<div class="param-desc">
    <p>The angle clamped between 0 and π.</p>
</div>


<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="cotan"><span class="type-signature"></span>cotan(h)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the cotangent of the angle opposite to a halfedge.</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>h</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Halfedge.html">module:Core.Halfedge</a></span>


            </td>

            
            <td class="description last"><p>The halfedge opposite to the angle whose cotangent needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="dihedralAngle"><span class="type-signature"></span>dihedralAngle(h)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the signed angle (in radians) between two adjacent faces.</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>h</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Halfedge.html">module:Core.Halfedge</a></span>


            </td>

            
            <td class="description last"><p>The halfedge (shared by the two adjacent faces) on which<br>
the dihedral angle is computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<div class="param-desc">
    <p>The dihedral angle.</p>
</div>


<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="barycentricDualArea"><span class="type-signature"></span>barycentricDualArea(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the barycentric dual area of a vertex.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex whose barycentric dual area needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="circumcentricDualArea"><span class="type-signature"></span>circumcentricDualArea(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the circumcentric dual area of a vertex.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex whose circumcentric dual area needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

	<dt class="tag-see method-doc-label method-doc-details-label">See:</dt>
	<dd class="tag-see">
		<ul>
			<li><a href="http://cs.cmu.edu/~kmcrane/Projects/Other/TriangleAreasCheatSheet.pdf">http://cs.cmu.edu/~kmcrane/Projects/Other/TriangleAreasCheatSheet.pdf</a></li>
			</ul>
	</dd>
	

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="vertexNormalEquallyWeighted"><span class="type-signature"></span>vertexNormalEquallyWeighted(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the normal at a vertex using the &quot;equally weighted&quot; method.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex on which the normal needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="vertexNormalAreaWeighted"><span class="type-signature"></span>vertexNormalAreaWeighted(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the normal at a vertex using the &quot;face area weights&quot; method.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex on which the normal needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="vertexNormalAngleWeighted"><span class="type-signature"></span>vertexNormalAngleWeighted(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the normal at a vertex using the &quot;tip angle weights&quot; method.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex on which the normal needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="vertexNormalGaussCurvature"><span class="type-signature"></span>vertexNormalGaussCurvature(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the normal at a vertex using the &quot;gauss curvature&quot; method.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex on which the normal needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="vertexNormalMeanCurvature"><span class="type-signature"></span>vertexNormalMeanCurvature(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the normal at a vertex using the &quot;mean curvature&quot; method (same as the &quot;area gradient&quot; method).</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex on which the normal needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="vertexNormalSphereInscribed"><span class="type-signature"></span>vertexNormalSphereInscribed(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the normal at a vertex using the &quot;inscribed sphere&quot; method.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex on which the normal needs to be computed.</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.Vector.html">module:LinearAlgebra.Vector</a></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="angleDefect"><span class="type-signature"></span>angleDefect(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the angle defect at a vertex (= 2π minus the sum of incident angles<br>
at an interior vertex or π minus the sum of incident angles at a boundary vertex).</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex whose angle defect needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="scalarGaussCurvature"><span class="type-signature"></span>scalarGaussCurvature(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the (integrated) scalar gauss curvature at a vertex.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex whose gauss curvature needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="scalarMeanCurvature"><span class="type-signature"></span>scalarMeanCurvature(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the (integrated) scalar mean curvature at a vertex.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex whose mean curvature needs to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="totalAngleDefect"><span class="type-signature"></span>totalAngleDefect()</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the total angle defect (= 2π times the euler characteristic of the mesh).</p>
    </div>
    

<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">number</span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="principalCurvatures"><span class="type-signature"></span>principalCurvatures(v)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Computes the (pointwise) minimum and maximum principal curvature values at a vertex.</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>v</code></td>
            

            <td class="type">
            
                
<span class="param-type"><a href="module-Core.Vertex.html">module:Core.Vertex</a></span>


            </td>

            
            <td class="description last"><p>The vertex on which the principal curvatures need to be computed.</p></td>
        </tr>

    
    </tbody>
</table>

    
<dl class="details">
    

</dl>


    <h5>Returns:</h5>
    
            
<div class="param-desc">
    <p>An array containing the minimum and maximum principal curvature values at a vertex.</p>
</div>


<dl>
    <dt>
        Type
    </dt>
    <dd>
        
<span class="param-type">Array.&lt;number></span>


    </dd>
</dl>


</dd>

        
<hr>
<dt>
    <h4 class="name" id="laplaceMatrix"><span class="type-signature"></span>laplaceMatrix(vertexIndex)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Builds a sparse laplace matrix. The laplace operator is negative semidefinite;<br>
instead we build a positive definite matrix by multiplying the entries of the<br>
laplace matrix by -1 and shifting the diagonal elements by a small constant (e.g. 1e-8).</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>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="massMatrix"><span class="type-signature"></span>massMatrix(vertexIndex)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Builds a sparse diagonal mass matrix containing the barycentric dual area of each vertex<br>
of a mesh.</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>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="complexLaplaceMatrix"><span class="type-signature"></span>complexLaplaceMatrix(vertexIndex)</h4>
    
    
</dt>
<dd>

    
    <div class="description">
        <p>Builds a sparse complex laplace matrix. The laplace operator is negative semidefinite;<br>
instead we build a positive definite matrix by multiplying the entries of the<br>
laplace matrix by -1 and shifting the diagonal elements by a small constant (e.g. 1e-8).</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>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.ComplexSparseMatrix.html">module:LinearAlgebra.ComplexSparseMatrix</a></span>


    </dd>
</dl>


</dd>

        </dl>
    

</article>

</section>


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