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\page extrusion_along_path_page Extrusion along a path
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\n In principle, <b>Extrusion along a path</b> works in the same way
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as \b Extrusion, the main difference is that we define not a vector,
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but a path of extrusion which must be a 1D mesh or 1D sub-mesh. To
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get an idea of how this algorithm works, examine several examples,
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starting from the most simple case of extrusion along a straight edge.
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In following examples the meshes will be extruded along different
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paths and with different parameters.
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This sample 2D mesh has two quadrangle faces and seven edges. Look
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at the picture, where white digits are the node numbers and green
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are the element numbers:
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\image html mesh_for_extr_along_path.png
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<br><center><h2>Extrusion along a straight edge</h2>(not using base point
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or angles)</center>
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\image html straight_before.png
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<center>The image shows a 1D path mesh, built on a linear edge, and the initial 2D mesh.</center>
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\image html straight_after.png
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<center> The image shows the result of extrusion of two edges
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(#1 and #2) of the initial mesh along the path. \n Node #1 of path mesh
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has been selected as Start node.</center>
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<br><center><h2>Extrusion along a curvilinear edge</h2>(with and
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without angles)</center>
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\image html curvi_simple_before.png
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<center>The image shows a 1D path mesh, built on curvilinear edge, and
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the initial 2D mesh.</center>
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\image html curvi_simple_after.png
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<center>The central image shows the result of extrusion of one edge
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(#2) of the initial mesh along the path. \n Node #1 of path mesh has
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been selected as <b>Start node</b>.</center>
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\image html curvi_angles_after.png
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<center>The same, but using angles {45, 45, 45, 0, -45, -45, -45}</center>
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<br><center><h2>Extrusion of 2d face along a mesh builds on wire</h2></center>
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In this example the path mesh has been built on a wire contains 3
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edges. Node #1 is used as start node. Linear angle variation by 180
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degree is applied.
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\image html extr_along_wire_before.png
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\image html extr_along_wire_after.png
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<br><center><h2>Extrusion of 2d elements along a closed path</h2></center>
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\image html circle_simple_before.png
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<center>The image shows a path mesh built on a closed edge
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(circle).</center>
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\image html circle_simple_after.png
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<center>The central image shows the result of extrusion of both faces
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of the initial mesh. \n Note, that no sewing has been done, so, there are
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six coincident nodes and two coincident faces in the resulting
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mesh.</center>
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\image html circle_angles_after.png
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<center>The same, but using angles {45, -45, 45, -45, 45, -45, 45,
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-45}</center>
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<br><em>To use Extrusion along a path:</em>
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<ol>
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<li>From the \b Modification menu choose the <b>Extrusion along a
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path</b> item or click <em>"Extrusion along a path"</em> button in the toolbar.
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\image html image101.png
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<center><em>"Extrusion along a path" button</em></center>
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The following dialog common for line and planar elements will appear:
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\image html extrusion1.png
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</li>
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<li>In this dialog:
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<ul>
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<li>select the type of elements which will be extruded (1D or 2D),</li>
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<li>specify the <b>IDs of the elements</b> which will be extruded
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<ul>
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<li><b>Select the whole mesh, submesh or group</b> activating this
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checkbox; or</li>
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<li>choose mesh elements with the mouse in the 3D Viewer. It is
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possible to select a whole area with a mouse frame; or</li>
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<li>input the element IDs directly in <b>ID Elements</b> field. The selected elements will be highlighted in the
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viewer; or</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
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about filters in the \ref selection_filter_library_page "Selection filter library" page.</li>
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</ul>
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</li>
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<li>define the Path along which the elements will be extruded,
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\n Path definition consists of several elements:
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<ul>
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<li><b>Mesh or submesh</b> - 1D mesh or 1D sub-mesh, along which proceeds the extrusion</li>
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<li><b>Start node</b> - the start node. It is used to define the direction of extrusion </li>
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</ul>
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</li>
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<li>activate <b>Generate Groups</b> checkbox if it is necessary to copy the groups of
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elements of the source mesh to the newly created one. </li>
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</ul>
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</li>
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<li>There are two optional parameters, which can be very useful:
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<ul>
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<li>If the path of extrusion is curvilinear, at each iteration the
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extruded shape is rotated to keep its initial angularity to the
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curve. By default, the <b>Base Point</b> around which the shape is rotated is
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the mass center of the shape, however, you can specify any point as
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the <b>Base Point</b> and the shape will be rotated with respect to this
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point.
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</li>
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<li>The shape can also be rotated around the path to get the resulting
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mesh in a helical fashion. You can set the values of angles at the
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right, add them to the list of angles at the left by pressing the <em>"Add"</em>
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button and remove them from the list by pressing the <em>"Remove"</em> button.
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\image html add.png
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<center><em>"Add" button</em></center>
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\image html remove.png
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<center><em>"Remove" button</em></center>
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<b>Linear variation of the angles</b> option allows defining the angle of gradual rotation for the whole path.
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At each step the shape will be rotated by angle/nb. of steps.
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</li>
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</ul>
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</li>
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<li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.
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Mesh edges will be extruded into
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faces, faces into volumes. The external surface of the resulting 3d
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mesh (if faces have been extruded) is covered with faces, and corners
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with edges. If the path is closed, the resulting mesh can contain
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duplicated nodes and faces, because no sewing is done.
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</li>
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</ol>
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<br><b>See Also</b> a sample TUI Script of an
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\ref tui_extrusion_along_path "Extrusion along a Path" operation.
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*/
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