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117 <h1><img src="image101.gif" width="27px" height="24px" border="0" class="img_whs1">Extrusion along a path</h1>
119 <p>In principle, <span style="font-weight: bold;"><B>Extrusion along a path</B></span>
120 works in the same way as <span style="font-weight: bold;"><B>Extrusion</B></span>,
121 the main difference is that we define not a vector, but a path of extrusion
122 which must be a meshed edge. To get an idea of how this algorithm works,
123 examine several examples, starting from the most simple case of extrusion
124 along a straight edge. In all examples the same mesh will be extruded
125 along different paths and with different parameters. This sample 2D mesh
126 has two quadrangle faces and seven edges. Look at the picture, where white
127 digits are the node numbers and green are the element numbers:</p>
129 <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>
133 <ul type="disc" class="whs3">
135 <li class=kadov-p><p><span style="font-weight: bold;"><B>Extrusion along
136 a straight edge</B></span> (not using base point or angles)</p></li>
139 <table x-use-null-cells cellspacing="0" width="100%" class="whs4">
143 <tr valign="top" class="whs6">
144 <td width="50%" class="whs7">
145 <p class="whs8"><img src="pics/straight_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
146 <td width="50%" class="whs10">
147 <p class="whs11"><img src="pics/straight_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
150 <p class="whs12"> </p>
152 <p class="whs12">The left image shows a 1D path mesh, built
153 on a linear edge, and the initial 2D mesh. The right image shows the result
154 of extrusion of two edges (#1 and #2) of the initial mesh along the path.
155 Node #1 of path mesh has been selected as <span style="font-weight: bold;"><B>Start
158 <p class="whs12"> </p>
160 <ul type="disc" class="whs3">
162 <li class=kadov-p><p><span style="font-weight: bold;"><B>Extrusion along
163 a curvilinear edge</B></span> (with and without angles)</p></li>
166 <table x-use-null-cells cellspacing="0" width="100%" class="whs4">
171 <tr valign="top" class="whs6">
172 <td width="33.333%" class="whs14">
173 <p><img src="pics/curvi_simple_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
174 <td width="33.333%" class="whs15">
175 <p><img src="pics/curvi_simple_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
176 <td width="33.333%" class="whs16">
177 <p><img src="pics/curvi_angles_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
179 <tr valign="top" class="whs6">
180 <td width="33.333%" class="whs17">
181 <p>The left image shows a 1D path mesh, built on curvilinear edge, and
184 <td width="33.333%" class="whs18">
185 <p>The central image shows the result of extrusion of one edge (#2) of
186 the initial mesh along the path. Node
187 #1 of path mesh has been selected as <span style="font-weight: bold;"><B>Start
188 node</B></span>.</td>
189 <td width="33.333%" class="whs19">
190 <p>The same, but using angles {45, 45, 45, 0, -45, -45, -45}</td></tr>
193 <p class="whs11"> </p>
195 <ul type="disc" class="whs3">
197 <li class=kadov-p><p class="whs11"><span style="font-weight: bold;"><B>Extrusion
198 along a sub-mesh.</B></span></p></li>
201 <table x-use-null-cells cellspacing="0" width="100%" class="whs4">
205 <tr valign="top" class="whs6">
206 <td width="50%" class="whs7">
207 <p><img src="pics/edge_wire_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
208 <td width="50%" class="whs10">
209 <p><img src="pics/edge_wire_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
212 <p class="whs12"> </p>
214 <p class="whs12">In this example the path mesh has been built
215 on a wire (polyline with six edges). The first edge of the wire was used
216 as <span style="font-weight: bold;"><B>Shape (edge)</B></span>, node #1 as <span
217 style="font-weight: bold;"><B>Start node</B></span>. The angles have been defined
218 as {10, 10, 10}. The middle edge (#4) of the initial mesh has been extruded.</p>
220 <p class="whs12"> </p>
222 <ul type="disc" class="whs3">
224 <li class=kadov-p><p class="whs20">Extrusion
225 of 2d elements along a sub-mesh.</p></li>
228 <table x-use-null-cells cellspacing="0" width="100%" class="whs4">
232 <tr valign="top" class="whs6">
233 <td width="50%" class="whs7">
234 <p><img src="pics/edge_wire_3d_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
235 <td width="50%" class="whs10">
236 <p><img src="pics/edge_wire_3d_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
239 <p class="whs12"> </p>
241 <p class="whs12">This extrusion bases on the same path mesh
242 as in the previous example but the third edge of the wire was set as <span
243 style="font-weight: bold;"><B>Shape (edge)</B></span> and node #4 as <span style="font-weight: bold;"><B>Start
244 node</B></span>. Please note, that the extrusion has been done in direction
245 from node #4 to node #3, i.e. against the wire direction. In this example
246 both faces of the initial mesh have been extruded.</p>
248 <p class="whs12"> </p>
250 <ul type="disc" class="whs3">
252 <li class=kadov-p><p class="whs21">Extrusion of 2d elements
253 along a closed path.</p></li>
256 <table x-use-null-cells cellspacing="0" width="100%" class="whs4">
261 <tr valign="top" class="whs6">
262 <td width="33.333%" class="whs14">
263 <p><img src="pics/circle_simple_before.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
264 <td width="33.333%" class="whs15">
265 <p><img src="pics/circle_simple_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td>
266 <td width="33.333%" class="whs16">
267 <p><img src="pics/circle_angles_after.png" x-maintain-ratio="TRUE" width="389px" height="334px" border="0" class="img_whs9"></td></tr>
269 <tr valign="top" class="whs6">
270 <td width="33.333%" class="whs17">
271 <p>The left image shows a path mesh built on a closed edge (circle).</td>
272 <td width="33.333%" class="whs18">
273 <p>The central image shows the result of extrusion of both faces of the
274 initial mesh. Note, that no sewing has been done, so, there are six coincident
275 nodes and two coincident faces in the resulting mesh.</td>
276 <td width="33.333%" class="whs19">
277 <p>The same, but using angles {45, -45, 45, -45, 45, -45, 45, -45}</td></tr>
280 <p class="whs12"> </p>
284 <p class=TODO>To use Extrusion along a path:</p>
286 <p class="whs12">1. From the <span style="font-weight: bold;"><B>Modification
287 </B></span>menu choose the <span style="font-weight: bold;"><B>Extrusion along
288 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
289 following dialog box will appear:</p>
291 <p class="whs12"> </p>
294 style="margin-left: 80px;"><img src="pics/extrusion1.png" x-maintain-ratio="TRUE" width="441px" height="541px" border="0" class="img_whs22"></p>
296 <p class="whs12"> </p>
298 <p class="whs12">2. In the dialog box you should </p>
300 <ul type="disc" class="whs3">
302 <li class=kadov-p><p class="whs23">select the type of
303 elements which will be extruded (1D or 2D),</p></li>
305 <li class=kadov-p><p class="whs23">specify the <span style="font-weight: bold;"><B>IDs
306 of the elements</B></span> which will be extruded by selecting them in the
307 3D viewer or <span style="font-weight: bold;"><B>Select the whole mesh, submesh
308 or group</B></span>,</p></li>
310 <li class=kadov-p><p class="whs23">define the <span style="font-weight: bold;"><B>Path</B></span>
311 along which the elements will be extruded, </p></li>
314 <p class="whs24">Path definition consists of several elements
317 <ul type="disc" class="whs3">
319 <li class=kadov-p><p class="whs25">Mesh
320 - <span style="font-weight: normal;">containing a 1D sub-mesh on the edge,
321 along which proceeds the extrusion.</span></p></li>
323 <li class=kadov-p><p class="whs25">Shape
324 (edge) - <span style="font-weight: normal;">as the mesh can be complex,
325 the edge is used to define the sub-mesh for the path.</span></p></li>
327 <li class=kadov-p><p class="whs25">Start
328 node - <span style="font-weight: normal;"> the
329 first or the last node on the edge. It is used to define the direction
330 of extrusion.</span></p></li>
333 <p class="whs12"> </p>
335 <p class="whs12">3. There are two optional parameters, which
336 can be very useful.</p>
338 <ul type="disc" class="whs3">
340 <li class=kadov-p><p class="whs23">If the path of extrusion
341 is curvilinear, at each iteration the extruded shape is rotated to keep
342 its initial angularity to the curve. By default, the <span style="font-weight: bold;"><B>Base
343 Point</B></span> around which the shape is rotated is the mass center of the
344 shape, however, you can specify any point as the <span style="font-weight: bold;"><B>Base
345 Point</B></span> and the shape will be rotated with respect to this point.</p></li>
347 <li class=kadov-p><p class="whs23">The shape can also
348 be rotated around the path to get the resulting mesh in a helical fashion.
349 You can set the values of angles at the right, add them to the list of
350 angles at the left by pressing the <img src="image105.gif" width="26px" height="25px" border="0" class="img_whs26"> button and remove them
351 from the list by pressing the <img src="image106.gif" width="29px" height="28px" border="0" class="img_whs27"> button. </p></li>
354 <p class="whs12">4. Click the <span style="font-weight: bold;"><B>Apply
355 </B></span>or <span style="font-weight: bold;"><B>OK </B></span>button. Mesh edges
356 will be extruded into faces, faces into volumes. The external surface
357 of the resulting 3d mesh (if faces have been extruded) is covered with
358 faces, and corners with edges. If the path is closed, the resulting mesh
359 can contain duplicated nodes and faces, because no sewing is done.</p>
361 <p class="whs12"> </p>
363 <p> <span style="font-weight: bold;"><B>See
364 Also</B></span> a sample TUI Script of an <a href="modifying_meshes.htm#bookmark10">Extrusion
365 along a Path</a> operation. </p>
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