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-<h1>Extrusion along a path</h1>
+<h1><img src="image101.gif" width="27px" height="24px" border="0" class="img_whs1">Extrusion along a path</h1>
-<p>In principle, Extrusion along a path works in the same way as Extrusion,
+<p>In principle, <span style="font-weight: bold;"><B>Extrusion along a path</B></span>
+ works in the same way as <span style="font-weight: bold;"><B>Extrusion</B></span>,
the main difference is that we define not a vector, but a path of extrusion
- which must be a meshed edge or wire. To get an idea of how this algorithm
- works, let's see the left image, where we have a 1D circle edge and a
- 2D hexagon to be extruded along this path (in the picture they are angular
- because we show the wireframe of the mesh). And now let's see the right
- image, showing the result of the operation. </p>
+ which must be a meshed edge. 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 all examples the same mesh 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:</p>
+
+<p><span style="margin-left: 40px;"><img src="pics/mesh_for_extr_along_path.png" x-maintain-ratio="TRUE" width="387px" height="334px" border="0" class="img_whs2"> .</span></p>
<p> </p>
-<table x-use-null-cells cellspacing="0" width="100%" class="whs1">
-<col class="whs2">
-<col class="whs2">
+<ul type="disc" class="whs3">
+
+ <li class=kadov-p><p><span style="font-weight: bold;"><B>Extrusion along
+ a straight edge</B></span> (not using base point or angles)</p></li>
+</ul>
+
+<table x-use-null-cells cellspacing="0" width="100%" class="whs4">
+<col class="whs5">
+<col class="whs5">
-<tr valign="top" class="whs3">
-<td width="50%" class="whs4">
-<p><img src="image102.gif" width="335px" height="323px" border="0" class="img_whs5"></td>
-<td width="50%" class="whs6">
-<p><img src="image104.gif" width="350px" height="323px" border="0" class="img_whs7"></td></tr>
+<tr valign="top" class="whs6">
+<td width="50%" class="whs7">
+<p class="whs8"><img src="pics/straight_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
+<td width="50%" class="whs10">
+<p class="whs11"><img src="pics/straight_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
</table>
-<p> </p>
+<p class="whs12"> </p>
+
+<p class="whs12">The left image shows a 1D path mesh, built
+ on a linear edge, and the initial 2D mesh. The right image shows the result
+ of extrusion of two edges (#1 and #2) of the initial mesh along the path.
+ Node #1 of path mesh has been selected as <span style="font-weight: bold;"><B>Start
+ node</B></span>.</p>
+
+<p class="whs12"> </p>
+
+<ul type="disc" class="whs3">
+
+ <li class=kadov-p><p><span style="font-weight: bold;"><B>Extrusion along
+ a curvilinear edge</B></span> (with and without angles)</p></li>
+</ul>
+
+<table x-use-null-cells cellspacing="0" width="100%" class="whs4">
+<col class="whs13">
+<col class="whs13">
+<col class="whs13">
+
+<tr valign="top" class="whs6">
+<td width="33.333%" class="whs14">
+<p><img src="pics/curvi_simple_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
+<td width="33.333%" class="whs15">
+<p><img src="pics/curvi_simple_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
+<td width="33.333%" class="whs16">
+<p><img src="pics/curvi_angles_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
+
+<tr valign="top" class="whs6">
+<td width="33.333%" class="whs17">
+<p>The left image shows a 1D path mesh, built on curvilinear edge, and
+ the initial 2D
+ mesh.</td>
+<td width="33.333%" class="whs18">
+<p>The central image shows the result of extrusion of one edge (#2) of
+ the initial mesh along the path. Node
+ #1 of path mesh has been selected as <span style="font-weight: bold;"><B>Start
+ node</B></span>.</td>
+<td width="33.333%" class="whs19">
+<p>The same, but using angles {45, 45, 45, 0, -45, -45, -45}</td></tr>
+</table>
+
+<p class="whs11"> </p>
+
+<ul type="disc" class="whs3">
+
+ <li class=kadov-p><p class="whs11"><span style="font-weight: bold;"><B>Extrusion
+ along a sub-mesh.</B></span></p></li>
+</ul>
+
+<table x-use-null-cells cellspacing="0" width="100%" class="whs4">
+<col class="whs5">
+<col class="whs5">
+
+<tr valign="top" class="whs6">
+<td width="50%" class="whs7">
+<p><img src="pics/edge_wire_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
+<td width="50%" class="whs10">
+<p><img src="pics/edge_wire_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
+</table>
-<p> </p>
+<p class="whs12"> </p>
+
+<p class="whs12">In this example the path mesh has been built
+ on a wire (polyline with six edges). The first edge of the wire was used
+ as <span style="font-weight: bold;"><B>Shape (edge)</B></span>, node #1 as <span
+ style="font-weight: bold;"><B>Start node</B></span>. The angles have been defined
+ as {10, 10, 10}. The middle edge (#4) of the initial mesh has been extruded.</p>
+
+<p class="whs12"> </p>
+
+<ul type="disc" class="whs3">
+
+ <li class=kadov-p><p class="whs20">Extrusion
+ of 2d elements along a sub-mesh.</p></li>
+</ul>
+
+<table x-use-null-cells cellspacing="0" width="100%" class="whs4">
+<col class="whs5">
+<col class="whs5">
+
+<tr valign="top" class="whs6">
+<td width="50%" class="whs7">
+<p><img src="pics/edge_wire_3d_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
+<td width="50%" class="whs10">
+<p><img src="pics/edge_wire_3d_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
+</table>
+
+<p class="whs12"> </p>
+
+<p class="whs12">This extrusion bases on the same path mesh
+ as in the previous example but the third edge of the wire was set as <span
+ style="font-weight: bold;"><B>Shape (edge)</B></span> and node #4 as <span style="font-weight: bold;"><B>Start
+ node</B></span>. Please note, that the extrusion has been done in direction
+ from node #4 to node #3, i.e. against the wire direction. In this example
+ both faces of the initial mesh have been extruded.</p>
+
+<p class="whs12"> </p>
+
+<ul type="disc" class="whs3">
+
+ <li class=kadov-p><p class="whs21">Extrusion of 2d elements
+ along a closed path.</p></li>
+</ul>
+
+<table x-use-null-cells cellspacing="0" width="100%" class="whs4">
+<col class="whs13">
+<col class="whs13">
+<col class="whs13">
+
+<tr valign="top" class="whs6">
+<td width="33.333%" class="whs14">
+<p><img src="pics/circle_simple_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
+<td width="33.333%" class="whs15">
+<p><img src="pics/circle_simple_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
+<td width="33.333%" class="whs16">
+<p><img src="pics/circle_angles_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
+
+<tr valign="top" class="whs6">
+<td width="33.333%" class="whs17">
+<p>The left image shows a path mesh built on a closed edge (circle).</td>
+<td width="33.333%" class="whs18">
+<p>The central image shows the result of extrusion of both faces of the
+ initial mesh. Note, that no sewing has been done, so, there are six coincident
+ nodes and two coincident faces in the resulting mesh.</td>
+<td width="33.333%" class="whs19">
+<p>The same, but using angles {45, -45, 45, -45, 45, -45, 45, -45}</td></tr>
+</table>
+
+<p class="whs12"> </p>
<p> </p>
<p class=TODO>To use Extrusion along a path:</p>
-<p class="whs8">1. From the <span style="font-weight: bold;"><B>Modification
+<p class="whs12">1. From the <span style="font-weight: bold;"><B>Modification
</B></span>menu choose the <span style="font-weight: bold;"><B>Extrusion along
- a path </B></span>item or click <img src="image101.gif" width="27px" height="24px" border="0" class="img_whs9"> button in the toolbar. The
+ a path </B></span>item or click <img src="image101.gif" width="27px" height="24px" border="0" class="img_whs1"> button in the toolbar. The
following dialog box will appear:</p>
-<p class="whs8"> </p>
+<p class="whs12"> </p>
<p class=TODO
- style="margin-left: 80px;"><img src="pics/a-extusionalongapath2.png" x-maintain-ratio="TRUE" width="434px" height="541px" border="0" class="img_whs10"></p>
+ style="margin-left: 80px;"><img src="pics/extrusion1.png" x-maintain-ratio="TRUE" width="441px" height="541px" border="0" class="img_whs22"></p>
-<p class="whs8"> </p>
+<p class="whs12"> </p>
-<p class="whs8">2. In the dialog box you should </p>
+<p class="whs12">2. In the dialog box you should </p>
-<ul type="disc" class="whs11">
+<ul type="disc" class="whs3">
- <li class=kadov-p><p class="whs12">select the type of
+ <li class=kadov-p><p class="whs23">select the type of
elements which will be extruded (1D or 2D),</p></li>
- <li class=kadov-p><p class="whs12">specify the IDs of
- the elements which will be extruded by selecting them in the 3D viewer
- or <span style="font-weight: bold;"><B>Select the whole mesh, submesh or
- grou</B></span>p,</p></li>
+ <li class=kadov-p><p class="whs23">specify the <span style="font-weight: bold;"><B>IDs
+ of the elements</B></span> which will be extruded by selecting them in the
+ 3D viewer or <span style="font-weight: bold;"><B>Select the whole mesh, submesh
+ or group</B></span>,</p></li>
+
+ <li class=kadov-p><p class="whs23">define the <span style="font-weight: bold;"><B>Path</B></span>
+ along which the elements will be extruded, </p></li>
+</ul>
+
+<p class="whs24">Path definition consists of several elements
+ </p>
+
+<ul type="disc" class="whs3">
+
+ <li class=kadov-p><p class="whs25">Mesh
+ - <span style="font-weight: normal;">containing a 1D sub-mesh on the edge,
+ along which proceeds the extrusion.</span></p></li>
+
+ <li class=kadov-p><p class="whs25">Shape
+ (edge) - <span style="font-weight: normal;">as the mesh can be complex,
+ the edge is used to define the sub-mesh for the path.</span></p></li>
- <li class=kadov-p><p class="whs12">specify the path along
- which the elements will be extruded, for this you should specify the <span
- style="font-weight: bold;"><B>Mesh</B></span>, the <span style="font-weight: bold;"><B>Shape</B></span>,
- and the <span style="font-weight: bold;"><B>Start point</B></span> for the extrusion.
- </p></li>
+ <li class=kadov-p><p class="whs25">Start
+ node - <span style="font-weight: normal;"> the
+ first or the last node on the edge. It is used to define the direction
+ of extrusion.</span></p></li>
</ul>
-<p class="whs8"> </p>
+<p class="whs12"> </p>
-<p class="whs8">3. There are two optional parameters, which
+<p class="whs12">3. There are two optional parameters, which
can be very useful.</p>
-<ul type="disc" class="whs11">
+<ul type="disc" class="whs3">
- <li class=kadov-p><p class="whs12">If the path of extrusion
+ <li class=kadov-p><p class="whs23">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 <span style="font-weight: bold;"><B>Base
- point</B></span> around which the shape is rotated is the mass center of the
+ Point</B></span> around which the shape is rotated is the mass center of the
shape, however, you can specify any point as the <span style="font-weight: bold;"><B>Base
Point</B></span> and the shape will be rotated with respect to this point.</p></li>
- <li class=kadov-p><p class="whs12">The shape can also
+ <li class=kadov-p><p class="whs23">The shape can also
be rotated around the path to get the resulting mesh in a helical fashion.
- At the picture above we see both "oblique-angled" and "right-angled"
- mesh elements because <span style="font-weight: bold;"><B>Rotation Angles</B></span>
- have not been set for all iterations. You set the values of the angles
- at the right and add them to the list of angles at the left by pressing
- the <img src="image105.gif" width="26px" height="25px" border="0" class="img_whs13"> button and remove the values from the list by pressing
- the <img src="image106.gif" width="29px" height="28px" border="0" class="img_whs14"> button. </p></li>
+ You can set the values of angles at the right, add them to the list of
+ angles at the left by pressing the <img src="image105.gif" width="26px" height="25px" border="0" class="img_whs26"> button and remove them
+ from the list by pressing the <img src="image106.gif" width="29px" height="28px" border="0" class="img_whs27"> button. </p></li>
</ul>
-<p class="whs8">4. Click the <span style="font-weight: bold;"><B>Apply
- </B></span>or <span style="font-weight: bold;"><B>OK </B></span>button.</p>
+<p class="whs12">4. Click the <span style="font-weight: bold;"><B>Apply
+ </B></span>or <span style="font-weight: bold;"><B>OK </B></span>button. 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.</p>
-<p class="whs8"> </p>
+<p class="whs12"> </p>
<p> <span style="font-weight: bold;"><B>See
Also</B></span> a sample TUI Script of an <a href="modifying_meshes.htm#bookmark10">Extrusion
