/*!

\page cutting_quadrangles_page Cutting quadrangles

\n This operation allows cutting one or several quadrangle elements
into two or four triangles.

<em>To cut quadrangles:</em>
<ol>
<li>Display a mesh, a 2D sub-mesh or a group of faces in the 3D viewer.</li>
<li>In the \b Modification menu select the <b>Cutting of quadrangles</b> item or
click <em>"Cutting of quadrangles"</em> button in the toolbar.

\image html image82.png
<center><em>"Cutting of quadrangles" button</em></center>

The following dialog box will appear:

\image html a-cuttingofquadrangles.png

<ul>
<li>The main list contains the list of quadrangles selected for cutting. You can
  click on an quadrangle in the 3D viewer and it will be highlighted (lock Shift
  keyboard button to select several quadrangles). Click \b Add button and the ID of
  this quadrangle will be added to the list. To remove a selected element or elements
  from the list click \b Remove button. <b>Sort list</b> button allows to sort the
  list of IDs. \b Filter button allows to apply a definite filter to the selection of
  quadrangles.</li> 
<li><b>Apply to all</b> check box allows to cut all quadrangles of the selected mesh,
  sub-mesh or group.</li> 
<li>\b Preview provides a preview of cutting in the viewer. It is disabled for <b>Cut
    into 4 triangles</b> as this cutting way implies no ambiguity.</li>
</ul>

<ul>
<li>\b Criterion defines a cutting way.
<ul>
<li><b>Cut into 4 triangles</b> selects cutting the quadrangle into four triangles by
  inserting a new node at the center of quadrangle. The other options selects cutting
  the quadrangle into two triangles by connecting nodes of either of the two diagonals.
<li><b>Use diagonal 1-3</b> and <b>Use diagonal 2-4</b> allows to specify the
  opposite corners which will be connected to form two new triangles.</li>
<li><b>Use numeric functor</b> allows to choose a quality metric which will be
  optimized when choosing a diagonal for cutting a quadrangle. 
  <ul>
    <li><b>Minimum diagonal</b> cuts by the shortest diagonal.</li>
    <li><b>Aspect Ratio</b> cuts by the diagonal splitting the quadrangle into
      triangles with \ref aspect_ratio_page "Aspect Ratio" closer to 1.</li>
    <li><b>Minimum Angle</b> cuts by the diagonal splitting the quadrangle into
      triangles with \ref minimum_angle_page "Minimum Angle" closer to 60
      degrees.</li> 
    <li><b>Skew</b> cuts by the diagonal splitting the quadrangle into triangles
      with \ref skew_page "Skew" closer to 0.0 degrees.</li>
  </ul>
</li>
</ul>
</li>
<li><b>Select from</b> allows to choose a sub-mesh or an existing group whose
  quadrangle elements will be automatically added to the main list.</li>
</ul>

</li>
<li>Click the \b Apply or <b>Apply and Close</b> button to confirm the operation.</li>
</ol>

\image html image52.jpg "The chosen quadrangular element"

\image html image51.jpg "Two resulting triangular elements"

<br><b>See Also</b> a sample TUI Script of a 
\ref tui_cutting_quadrangles "Cutting Quadrangles" operation.  

*/