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\page extrusion_along_path_page Extrusion along a path

\n In principle, <b>Extrusion along a path</b> works in the same way
as \b Extrusion, the main difference is that we define not a vector,
but a path of extrusion which must be a 1D mesh or 1D sub-mesh. To
get an idea of how this algorithm works, examine several examples,
starting from the most simple case of extrusion along a straight edge.
In following examples the meshes will be extruded along different
paths and with different parameters.
This sample 2D mesh has two quadrangle faces and seven edges. Look
at the picture, where white digits are the node numbers and green
are the element numbers:

\image html mesh_for_extr_along_path.png

<br><center><h2>Extrusion along a straight edge</h2>(not using base point
or angles)</center>

\image html straight_before.png
<center>The image shows a 1D path mesh, built on a linear edge, and the initial 2D mesh.</center>

\image html straight_after.png
<center> The image shows the result of extrusion of two edges
(#1 and #2) of the initial mesh along the path. \n Node #1 of path mesh
has been selected as Start node.</center>

<br><center><h2>Extrusion along a curvilinear edge</h2>(with and
without angles)</center>

\image html curvi_simple_before.png
<center>The image shows a 1D path mesh, built on curvilinear edge, and
the initial  2D mesh.</center>

\image html curvi_simple_after.png
<center>The central image shows the result of extrusion of one edge
(#2) of the initial mesh along the path. \n Node #1 of path mesh has
been selected as <b>Start node</b>.</center>

\image html curvi_angles_after.png
<center>The same, but using angles {45, 45, 45, 0, -45, -45, -45}</center>

<br><center><h2>Extrusion of 2d face along a mesh builds on wire</h2></center>

In this example the path mesh has been built on a wire contains 3
edges. Node #1 is used as start node. Linear angle variation by 180
degree is applied.

\image html extr_along_wire_before.png

\image html extr_along_wire_after.png

<br><center><h2>Extrusion of 2d elements along a closed path</h2></center>

\image html circle_simple_before.png
<center>The image shows a path mesh built on a closed edge
(circle).</center>

\image html circle_simple_after.png
<center>The central image shows the result of extrusion of both faces
of the initial mesh. \n Note, that no sewing has been done, so, there are
six coincident nodes and two coincident faces in the resulting
mesh.</center>

\image html circle_angles_after.png
<center>The same, but using angles {45, -45, 45, -45, 45, -45, 45,
-45}</center>

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

\image html image101.png
<center><em>"Extrusion along a path" button</em></center>

The following dialog common for line and planar elements will appear:

\image html extrusion1.png
</li>

<li>In this dialog:
<ul>
<li>select the type of elements which will be extruded (1D or 2D),</li>
<li>specify the <b>IDs of the elements</b> which will be extruded

<ul>
<li><b>Select the whole mesh, submesh or group</b> activating this
checkbox; or</li>
<li>choose mesh elements with the mouse in the 3D Viewer. It is
possible to select a whole area with a mouse frame; or</li> 
<li>input the element IDs directly in <b>ID Elements</b> field. The selected elements will be highlighted in the
viewer; or</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 selection_filter_library_page "Selection filter library" page.</li>
</ul>

</li>
<li>define the Path along which the elements will be extruded,
\n Path definition consists of several elements:
<ul>
<li><b>Mesh or submesh</b> - 1D mesh or 1D sub-mesh, along which proceeds the extrusion</li>
<li><b>Start node</b> - the start node. It is used to define the direction of extrusion </li>
</ul>
</li>
<li>activate  <b>Generate Groups</b> checkbox if it is necessary to  copy the groups of
elements of the source mesh to the newly created one. </li>
</ul>
</li>

<li>There are two optional parameters, which can be very useful:
<ul>
<li>If the path of extrusion is curvilinear, at each iteration the
extruded shape is rotated to keep its initial angularity to the
curve. By default, the <b>Base Point</b> around which the shape is rotated is
the mass center of the shape, however, you can specify any point as
the <b>Base Point</b> and the shape will be rotated with respect to this
point.
</li>
<li>The shape can also be rotated around the path to get the resulting
mesh in a helical fashion. You can set the values of angles at the
right, add them to the list of angles at the left by pressing the <em>"Add"</em>
button and remove them from the list by pressing the <em>"Remove"</em> button. 

\image html add.png
<center><em>"Add" button</em></center>

\image html remove.png
<center><em>"Remove" button</em></center>

<b>Linear variation of the angles</b> option allows defining the angle of gradual rotation for the whole path. 
At each step the shape will be rotated by angle/nb. of steps. 

</li>
</ul>
</li>


<li>Click \b Apply or <b> Apply and Close</b>  button to confirm the operation.
Mesh edges will be extruded into
faces, faces into volumes. The external surface of the resulting 3d
mesh (if faces have been extruded) is covered with faces, and corners
with edges. If the path is closed, the resulting mesh can contain
duplicated nodes and faces, because no sewing is done.
</li>
</ol>

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

*/