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/*!
\page extrusion_page Extrusion
\n Extrusion is used to build mesh elements of plus one
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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".
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\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"
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<p>Any node, segment or 2D element can be extruded. Each type of
elements is extruded into a corresponding type of result elements:
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<table>
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<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>
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<tr><td>Hexagonal polygon </td><td> Hexagonal prism </td></tr>
</table>
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When 2D elements are extruded, in addition to 3D elements segments are
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created on the ribs of the resulting 3D mesh. Free edges of input 2D elements
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generate logically horizontal rib segments. Logically vertical rib
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segments are generated from the nodes belonging to a sole input 2D element
(the figure below illustrates this rule).
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\image html extru_rib_segs.png "Two triangles extruded: no vertical rib segments generated from nodes #2 and #3 as they are shared by both triangles"
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<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.
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<center>
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\image html image91.png
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<em>"Extrusion" button</em>
</center>
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The following dialog will appear:
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\image html extrusionalongaline1.png
</li>
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<li>In this dialog:
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<ul>
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<li>Use \a Selection button to specify what you are going to
select at a given moment, \b Nodes, \b Edges or \b Faces.
\image html image120.png
<center><em>"Selection" button</em></center>
</li>
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<li>Specify \b Nodes, \b Edges and \b Faces, which will be extruded, by one
of following means:
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<ul>
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<li><b>Select the whole mesh, sub-mesh or group</b> activating the
corresponding check-box.</li>
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<li>Choose mesh elements with the mouse in the 3D Viewer. It is
possible to select a whole area with a mouse frame.</li>
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<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>
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<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>
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<li>If the <b>Extrusion to Distance</b> radio button is selected
- specify the translation vector by which the elements will be extruded.
</li>
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<p><br></p>
\image html extrusionalongaline2.png
<li>If the <b>Extrusion Along Vector</b> radio button is selected
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<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>
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<p><br></p>
\image html extrusionalongaline3.png
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<li>If the <b>Extrusion By Normal</b> radio button is selected,
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every node of the selected faces is extruded along the \a average
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of the \a normal vectors to the faces sharing the node. (Nodes and
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edges cannot be extruded in this mode.)
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<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
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which vector the distance is measured.
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<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
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average normal till its intersection with a virtual plane obtained
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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>
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<li><b>Use only input elements</b> check-box specifies what
elements will be used to compute the average normal.<ul>
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<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>
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</ul>
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<li>Specify the <b>Number of steps</b>.</li>
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<li>If you activate <b>Generate Groups</b> check-box, the <em>result elements</em>
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created from <em>selected elements</em> contained in groups will be
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included into new groups named by pattern "<old group
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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>
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</ul>
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<li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.</li>
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</ol>
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<p>
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\anchor extrusion_struct
<h2>Example: creation of a structured mesh from scratch</h2>
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\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"
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<br><b>See Also</b> a sample TUI Script of an
\ref tui_extrusion "Extrusion" operation.
*/