/*!

\page extrusion_page Extrusion

\n Extrusion is used to build mesh elements of plus one
dimension than the input ones. Boundary elements around generated
mesh of plus one dimension are additionally created. All created
elements can be automatically grouped. Extrusion can be used to create
a \ref extrusion_struct "structured mesh from scratch".

\image html extrusion_box.png "If you extrude several quadrangles, you get exactly the same mesh as if you meshed a geometrical box (except for that the initial quadrangles can be incorrectly oriented): quadrangles and segments are created on the boundary of the generated mesh"

<p>Any node, segment or 2D element can be extruded. Each type of
elements is extruded into a corresponding type of result elements:
<table>
<tr><td><b>Extruded element</b></td><td><b> Result element </b></td></tr>
<tr><td>Node              </td><td> Segment </td></tr>
<tr><td>Segment           </td><td> Quadrilateral </td></tr>
<tr><td>Triangle          </td><td> Pentahedron </td></tr>
<tr><td>Quadrilateral     </td><td> Hexahedron </td></tr>
<tr><td>Polygon           </td><td> Polyhedron </td></tr>
<tr><td>Hexagonal polygon </td><td> Hexagonal prism </td></tr>
</table>

<em>To use extrusion:</em>
<ol>
<li>From the \b Modification menu choose the \b Extrusion item or click
<em>"Extrusion"</em> button in the toolbar. 

<center>
\image html image91.png
<em>"Extrusion" button</em>
</center>

The following dialog will appear:

\image html extrusionalongaline1.png

</li>

<li>In this dialog:
<ul>
  <li>Specify \b Nodes, \b Edges and \b Faces, which will be extruded, by one
    of following means:
    <ul>
      <li><b>Select the whole mesh, sub-mesh or group</b> activating the
        corresponding check-box.</li>
      <li>Choose mesh elements with the mouse in the 3D Viewer. It is
        possible to select a whole area with a mouse frame.</li> 
      <li>Input the element IDs directly in <b>Node IDs</b>, <b>Edge
        IDs</b> and <b>Face IDs</b> fields. The selected elements will
        be highlighted in the viewer, if the mesh is shown there.</li> 
      <li>Apply Filters. <b>Set filter</b> button allows to apply a
        filter to the selection of elements. See more about filters in
        the \ref filtering_elements "Selection filters" page.</li> 
    </ul>
  </li>
  <li>If the <b>Extrusion to Distance</b> radio button is selected
    - specify the translation vector by which the elements will be extruded.
  </li>
  <p><br></p>

\image html extrusionalongaline2.png  

 <li>If the <b>Extrusion Along Vector</b> radio button is selected
    <ul>
      <li>specify the coordinates of the \b Vector along which the elements
        will be extruded, either directly or by selecting the mesh face (the
        normal to the face will define the vector),</li>
      <li>specify the \b Distance of extrusion along the vector (it can
        be negative).</li>
    </ul>
  </li>
  <p><br></p>

\image html extrusionalongaline3.png  
  
  <li>If the <b>Extrusion By Normal</b> radio button is selected,
    every node of the selected faces is extruded along the \a average
    of the \a normal vectors to the faces sharing the node. (Nodes and
    edges cannot be extruded in this mode.)
    <ul>
      <li>Specify the \b Distance of extrusion (it can be negative),</li>
      <li>Use <b>Along average normal</b> check-box to specify along
        which vector the distance is measured.
        <ul>
          <li>If it is \a activated the distance is measured along the
            average normal mentioned above. </li>
          <li>If it is \a deactivated every node is extruded along the
            average normal till its intersection with a virtual plane obtained
            by translation of the face sharing the node along its own normal
            by the \b Distance.</li>
        </ul>
        The picture below shows a cross-section of a 2D mesh extruded
        with <b>Along average normal</b> activated (to the left) and
        deactivated (to the right). 

        \image html extrusionbynormal_alongavgnorm.png "'Along average normal' activated (to the left) and deactivated (to the right)"
        <p></li>

      <li><b>Use only input elements</b> check-box specifies what
        elements will be used to compute the average normal.<ul>
          <li> If it is \a activated only selected faces, among faces
            sharing the node, are used to compute the average normal at
            the node. </li>
          <li>Else all faces sharing the node are used.</li></ul>

        The picture below shows a cross-section of a 2D mesh the upper
        plane of which is extruded with <b>Use only input elements</b>
        activated (to the left) and deactivated (to the right). 

        \image html extrusionbynormal_useonly.png "'Use only input elements' activated (to the left) and deactivated (to the right)"
        <p></li>
  </li>
  </ul>

  <li>Specify the <b>Number of steps</b>.</li>
  <li>If you activate <b>Generate Groups</b> check-box, the <em>result elements</em>
    created from <em>selected elements</em> contained in groups will be
    included into new groups named by pattern "<old group
    name>_extruded" and "<old group name>_top". For example if a
    selected quadrangle is included in \a g_Faces group (see figures
    below) then result hexahedra will be included in \a
    g_Faces_extruded group and a quadrangle created at the "top" of
    extruded mesh will be included in \a g_Faces_top group. <br> 
\image html extrusion_groups.png
\image html extrusion_groups_res.png
    <p> This check-box is active only if there are some groups in the mesh.
  </li>
</ul>

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

\anchor extrusion_struct
<h2>Example: creation of a structured mesh from scratch</h2>

\image html image75.jpg "A node is extruded into a line of segments"
<br>
\image html image76.jpg "The line of segments is extruded into a quadrangle mesh"
<br>
\image html image77.jpg "The quadrangle mesh is revolved into a hexahedral mesh"


<br><b>See Also</b> a sample TUI Script of an 
\ref tui_extrusion "Extrusion" operation. 

*/