/*! \page extrusion_along_path_page Extrusion along a path \n In principle, Extrusion along a path 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 the examples the sample mesh will be extruded along different paths and with different parameters. This 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

Extrusion along a straight edge

(not using base point or angles) \image html straight_before.png The image shows a 1D path mesh, built on a linear edge, and the initial 2D mesh. \image html straight_after.png 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.

Extrusion along a curvilinear edge

(with and without angles) \image html curvi_simple_before.png The image shows a 1D path mesh, built on curvilinear edge, and the initial 2D mesh. \image html curvi_simple_after.png 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 Start node. \image html curvi_angles_after.png The same, but using angles {45, 45, 45, 0, -45, -45, -45}

Extrusion of a 2D face along a mesh built on a wire

In this example the path mesh has been built on a wire containing 3 edges. Node 1 is a start node. Linear angle variation by 180 degrees has also been applied. \image html extr_along_wire_before.png Meshed wire \image html extr_along_wire_after.png The resulting extrusion

Extrusion of 2d elements along a closed path

\image html circle_simple_before.png The image shows a path mesh built on a closed edge (circle). \image html circle_simple_after.png 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. \image html circle_angles_after.png The same, but using angles {45, -45, 45, -45, 45, -45, 45, -45}
To use Extrusion along a path:

From the \b Modification menu choose the Extrusion along a path item or click "Extrusion along a path" button in the toolbar. \image html image101.png "Extrusion along a path" button The following dialog common for line and planar elements will appear: \image html extrusion_along_path_dlg.png
In this dialog:
- select the type of elements which will be extruded (1D or 2D),
- specify the IDs of the elements which will be extruded
  - Select the whole mesh, submesh or group activating this checkbox; or
  - choose mesh elements with the mouse in the 3D Viewer. It is possible to select a whole area with a mouse frame; or
  - input the element IDs directly in ID Elements field. The selected elements will be highlighted in the viewer; or
  - apply Filters. Set filter 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.
- define the \b Path along which the elements will be extruded.
  Path definition consists of several elements:
  - Mesh or submesh - 1D mesh or sub-mesh, along which proceeds the extrusion
  - Start node - the start node. It is used to define the direction of extrusion
- activate Generate Groups checkbox if it is necessary to copy the groups of elements of the source mesh to the newly created one.
There are two optional parameters, which can be very useful:
- If the path of extrusion is curvilinear, at each iteration the extruded elements are rotated to keep its initial angularity to the curve. By default, the Base Point around which the elements are rotated is the mass center of the elements, however, you can specify any point as the Base Point and the elements will be rotated with respect to this point.
  Note that it is the Base Point whos track exactly equals to the path, and all the elements being extruded just keep their relative position around the Base Point at each iteration.
- The elements 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 "Add" button and remove them from the list by pressing the "Remove" button. \image html add.png "Add" button \image html remove.png "Remove" button Linear variation of the angles option allows defining the angle of gradual rotation for the whole path. At each step the elements will be rotated by angle / nb. of steps.
Click \b Apply or Apply and Close 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.

See Also a sample TUI Script of an \ref tui_extrusion_along_path "Extrusion along a Path" operation. */