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-</script>\r
-<h1>Pattern mapping</h1>\r
-\r
-<h3>About patterns</h3>\r
-\r
-<p><img src="i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> The pattern describes a mesh to generate: positions of \r
- nodes within a geometrical domain and nodal connectivity of elements. \r
- As well, a pattern specifies the so-called key-points, i.e. nodes that \r
- will be located at geometrical vertices. Pattern description is stored \r
- in <pattern_name>.smp file.</p>\r
-\r
-<p> </p>\r
-\r
-<p>The smp file contains 4 sections:</p>\r
-\r
-<p> </p>\r
-\r
-<p class="whs2">1. The first line holds the number of nodes \r
- (N).</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">2. The next N lines describe nodes coordinates. \r
- Each line holds 2 coordinates of a node.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">3. A key-points line: indices of nodes to \r
- be mapped on geometrical vertices. An index n refers to a node described \r
- on an n-th line of section 2. The first node index is zero.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">4. The rest lines describe nodal connectivity \r
- of elements, one line for an element. A line holds indices of nodes forming \r
- an element. An index n refers to a node described on an n-th line of the \r
- section 2. The first node index is zero. There must be 3 or 4 indices \r
- on a line: only 2d elements are allowed.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p>The 2D pattern must contain at least one element and at least one key-point. \r
- All key-points must lay on boundaries.</p>\r
-\r
-<p> </p>\r
-\r
-<p>An example of a simple smp file and a preview of a pattern described \r
- in this file:</p>\r
-\r
-<p> </p>\r
-\r
-<p><img src="image94.gif" width="626px" height="471px" border="0" class="img_whs3"></p>\r
-\r
-<p> </p>\r
-\r
-<p> </p>\r
-\r
-<h3>Application of pattern mapping</h3>\r
-\r
-<p class=TODO>To apply pattern mapping to a geometrical object:</p>\r
-\r
-<p class=TODO> </p>\r
-\r
-<p class="whs2">1. From the <span style="font-weight: bold;"><B>Modification \r
- </B></span>menu choose the <span style="font-weight: bold;"><B>Pattern Mapping \r
- </B></span>item or click <img src="image98.gif" width="22px" height="28px" border="0" class="img_whs4"> button in the toolbar. The following \r
- dialog box shall appear:</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<table x-use-null-cells cellspacing="0" width="64.066%" class="whs5">\r
-<col class="whs6">\r
-<col class="whs7">\r
-\r
-<tr valign="top" class="whs8">\r
-<td width="56.089%" class="whs9">\r
-<p class="whs10"><img src="pics/patternmapping1.png" x-maintain-ratio="TRUE" width="306px" height="632px" border="0" class="img_whs11"></td>\r
-<td width="43.911%" class="whs12">\r
-<p><img src="pics/patternmapping2.png" x-maintain-ratio="TRUE" width="306px" height="670px" border="0" class="img_whs13"></td></tr>\r
-</table>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p>To apply a pattern to a geometrical object, you should specify:</p>\r
-\r
-<p class="whs2">- a face having the number of vertices equal \r
- to the number of key-points in the pattern; the number of key-points on \r
- internal boundaries of a pattern must also be equal to the number of vertices \r
- on internal boundaries of a face;</p>\r
-\r
-<p class="whs2">- a vertex to which the first key-point should \r
- be mapped,</p>\r
-\r
-<p class="whs2">- reverse or not the order of key-points. \r
- (The order of vertices of a face is counterclockwise looking from outside).</p>\r
-\r
-<p> </p>\r
-\r
-<p>Then you either load a .smp pattern file previously created manually \r
- by clicking on the <img src="image108.gif" width="34px" height="34px" border="0" class="img_whs14"> button, or click on the <span style="font-weight: bold;"><B>New</B></span> \r
- button for automatic generation.</p>\r
-\r
-<p>For an automatic generation you just specify a geometrical face having \r
- a mesh built on it. Mesh nodes lying on face vertices become key-points. \r
- Additionally, you may choose the way of getting nodes coordinates by <span \r
- style="font-weight: bold;"><B>projecting nodes on the face</B></span> instead \r
- of using "positions on face" generated by mesher (if there is \r
- any). Faces having a seam edge can\92t be used for automatic pattern creation.</p>\r
-\r
-<p> </p>\r
-\r
-<p>When creating a pattern from an existing mesh, there are two possible \r
- cases:</p>\r
-\r
-<p> </p>\r
-\r
-<p>1. A sub-mesh on face is selected. A pattern is created from the 2d \r
- elements bound to a face by mesher. Node coordinates are either "positions \r
- on face" computed by mesher, or coordinates got by node projection \r
- on a geometrical surface, according to your choice.</p>\r
-\r
-<p>2. A mesh where the main shape is a face, is selected. A pattern is \r
- created from all the 2d elements in a mesh. If all mesh elements are build \r
- by mesher, the user can select the way of getting nodes coordinates, else \r
- all nodes are projected on a face surface.</p>\r
-\r
-<table x-use-null-cells cellspacing="0" width="68.686%" class="whs15">\r
-<col class="whs16">\r
-<col class="whs17">\r
-\r
-<tr valign="top" class="whs8">\r
-<td width="50.224%" class="whs18">\r
-<p><img src="pics/a-patterntype.png" x-maintain-ratio="TRUE" width="306px" height="428px" border="0" class="img_whs19"></td>\r
-<td width="49.776%" class="whs20">\r
-<p><img src="pics/a-patterntype1.png" x-maintain-ratio="TRUE" width="306px" height="248px" border="0" class="img_whs21"></td></tr>\r
-</table>\r
-\r
-<p> </p>\r
-\r
-<h3>Mapping algorithm:</h3>\r
-\r
-<p class="whs22">The mapping algorithm is as follows:</p>\r
-\r
-<p class="whs22"> </p>\r
-\r
-<p class="whs2">1. Key-points are set in the order that they \r
- are encountered when walking along a pattern boundary so that elements \r
- are on the left. The first key-point is preserved.</p>\r
-\r
-<p class="whs2">2. Find geometrical vertices corresponding \r
- to key-points by vertices order in a face boundary; here, "Reverse \r
- order of key-points" flag is taken into account.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2"><img src="image95.gif" width="554px" height="279px" border="0" class="img_whs23"></p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">3. Boundary nodes of a pattern are mapped \r
- onto edges of a face: a node located between certain key-points on a pattern \r
- boundary is mapped on a geometrical edge limited by corresponding geometrical \r
- vertices. Node position on an edge reflects its distance from two key-points.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2"><img src="image96.gif" width="572px" height="233px" border="0" class="img_whs24"></p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">4. Coordinates of a non-boundary node in \r
- a parametric space of a face are defined as following. In a parametric \r
- space of a pattern, a node lays at the intersection of two iso-lines, \r
- each of which intersects a pattern boundary at least at two points. Knowing \r
- mapped positions of boundary nodes, we find where isoline-boundary intersection \r
- points are mapped to, and hence we can find mapped isolines direction \r
- and then, two node positions on two mapped isolines. The eventual mapped \r
- position of a node is found as an average of positions on mapped isolines.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2"><img src="image97.gif" width="606px" height="249px" border="0" class="img_whs25"></p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p> <span style="font-weight: bold;"><B>See \r
- Also</B></span> a sample TUI Script of a <a href="modifying_meshes.htm#bookmark13">Pattern \r
- Mapping</a><a href="modifying_meshes.htm#bookmark11"> </a>operation. </p>\r
-\r
-<p> </p>\r
-\r
-<script type="text/javascript" language="javascript1.2">\r
-<!--\r
-if (window.writeIntopicBar)\r
- writeIntopicBar(0);\r
-//-->\r
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-</body>\r
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+ writeIntopicBar(4);
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+</script>
+<h1>Pattern mapping</h1>
+
+<h3>About patterns</h3>
+
+<p><img src="i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> The pattern describes a mesh to generate: positions of
+ nodes within a geometrical domain and nodal connectivity of elements.
+ As well, a pattern specifies the so-called key-points, i.e. nodes that
+ will be located at geometrical vertices. Pattern description is stored
+ in <pattern_name>.smp file.</p>
+
+<p> </p>
+
+<p>The smp file contains 4 sections:</p>
+
+<p> </p>
+
+<p class="whs2">1. The first line holds the number of nodes
+ (N).</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2">2. The next N lines describe nodes coordinates.
+ Each line holds 2 coordinates of a node.</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2">3. A key-points line: indices of nodes to
+ be mapped on geometrical vertices. An index n refers to a node described
+ on an n-th line of section 2. The first node index is zero.</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2">4. The rest lines describe nodal connectivity
+ of elements, one line for an element. A line holds indices of nodes forming
+ an element. An index n refers to a node described on an n-th line of the
+ section 2. The first node index is zero. There must be 3 or 4 indices
+ on a line: only 2d elements are allowed.</p>
+
+<p class="whs2"> </p>
+
+<p>The 2D pattern must contain at least one element and at least one key-point.
+ All key-points must lay on boundaries.</p>
+
+<p> </p>
+
+<p>An example of a simple smp file and a preview of a pattern described
+ in this file:</p>
+
+<p> </p>
+
+<p><img src="image94.gif" width="626px" height="471px" border="0" class="img_whs3"></p>
+
+<p> </p>
+
+<p> </p>
+
+<h3>Application of pattern mapping</h3>
+
+<p class=TODO>To apply pattern mapping to a geometrical object:</p>
+
+<p class=TODO> </p>
+
+<p class="whs2">1. From the <span style="font-weight: bold;"><B>Modification
+ </B></span>menu choose the <span style="font-weight: bold;"><B>Pattern Mapping
+ </B></span>item or click <img src="image98.gif" width="22px" height="28px" border="0" class="img_whs4"> button in the toolbar. The following
+ dialog box shall appear:</p>
+
+<p class="whs2"> </p>
+
+<table x-use-null-cells cellspacing="0" width="64.066%" class="whs5">
+<col class="whs6">
+<col class="whs7">
+
+<tr valign="top" class="whs8">
+<td width="56.089%" class="whs9">
+<p class="whs10"><img src="pics/patternmapping1.png" x-maintain-ratio="TRUE" width="306px" height="632px" border="0" class="img_whs11"></td>
+<td width="43.911%" class="whs12">
+<p><img src="pics/patternmapping2.png" x-maintain-ratio="TRUE" width="306px" height="670px" border="0" class="img_whs13"></td></tr>
+</table>
+
+<p class="whs2"> </p>
+
+<p>To apply a pattern to a geometrical object, you should specify:</p>
+
+<p class="whs2">- a face having the number of vertices equal
+ to the number of key-points in the pattern; the number of key-points on
+ internal boundaries of a pattern must also be equal to the number of vertices
+ on internal boundaries of a face;</p>
+
+<p class="whs2">- a vertex to which the first key-point should
+ be mapped,</p>
+
+<p class="whs2">- reverse or not the order of key-points.
+ (The order of vertices of a face is counterclockwise looking from outside).</p>
+
+<p> </p>
+
+<p>Then you either load a .smp pattern file previously created manually
+ by clicking on the <img src="image108.gif" width="34px" height="34px" border="0" class="img_whs14"> button, or click on the <span style="font-weight: bold;"><B>New</B></span>
+ button for automatic generation.</p>
+
+<p>For an automatic generation you just specify a geometrical face having
+ a mesh built on it. Mesh nodes lying on face vertices become key-points.
+ Additionally, you may choose the way of getting nodes coordinates by <span
+ style="font-weight: bold;"><B>projecting nodes on the face</B></span> instead
+ of using "positions on face" generated by mesher (if there is
+ any). Faces having a seam edge can\92t be used for automatic pattern creation.</p>
+
+<p> </p>
+
+<p>When creating a pattern from an existing mesh, there are two possible
+ cases:</p>
+
+<p> </p>
+
+<p>1. A sub-mesh on face is selected. A pattern is created from the 2d
+ elements bound to a face by mesher. Node coordinates are either "positions
+ on face" computed by mesher, or coordinates got by node projection
+ on a geometrical surface, according to your choice.</p>
+
+<p>2. A mesh where the main shape is a face, is selected. A pattern is
+ created from all the 2d elements in a mesh. If all mesh elements are build
+ by mesher, the user can select the way of getting nodes coordinates, else
+ all nodes are projected on a face surface.</p>
+
+<table x-use-null-cells cellspacing="0" width="68.686%" class="whs15">
+<col class="whs16">
+<col class="whs17">
+
+<tr valign="top" class="whs8">
+<td width="50.224%" class="whs18">
+<p><img src="pics/a-patterntype.png" x-maintain-ratio="TRUE" width="306px" height="428px" border="0" class="img_whs19"></td>
+<td width="49.776%" class="whs20">
+<p><img src="pics/a-patterntype1.png" x-maintain-ratio="TRUE" width="306px" height="248px" border="0" class="img_whs21"></td></tr>
+</table>
+
+<p> </p>
+
+<h3>Mapping algorithm:</h3>
+
+<p class="whs22">The mapping algorithm is as follows:</p>
+
+<p class="whs22"> </p>
+
+<p class="whs2">1. Key-points are set in the order that they
+ are encountered when walking along a pattern boundary so that elements
+ are on the left. The first key-point is preserved.</p>
+
+<p class="whs2">2. Find geometrical vertices corresponding
+ to key-points by vertices order in a face boundary; here, "Reverse
+ order of key-points" flag is taken into account.</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2"><img src="image95.gif" width="554px" height="279px" border="0" class="img_whs23"></p>
+
+<p class="whs2"> </p>
+
+<p class="whs2">3. Boundary nodes of a pattern are mapped
+ onto edges of a face: a node located between certain key-points on a pattern
+ boundary is mapped on a geometrical edge limited by corresponding geometrical
+ vertices. Node position on an edge reflects its distance from two key-points.</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2"><img src="image96.gif" width="572px" height="233px" border="0" class="img_whs24"></p>
+
+<p class="whs2"> </p>
+
+<p class="whs2">4. Coordinates of a non-boundary node in
+ a parametric space of a face are defined as following. In a parametric
+ space of a pattern, a node lays at the intersection of two iso-lines,
+ each of which intersects a pattern boundary at least at two points. Knowing
+ mapped positions of boundary nodes, we find where isoline-boundary intersection
+ points are mapped to, and hence we can find mapped isolines direction
+ and then, two node positions on two mapped isolines. The eventual mapped
+ position of a node is found as an average of positions on mapped isolines.</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2"><img src="image97.gif" width="606px" height="249px" border="0" class="img_whs25"></p>
+
+<p class="whs2"> </p>
+
+<p> <span style="font-weight: bold;"><B>See
+ Also</B></span> a sample TUI Script of a <a href="modifying_meshes.htm#bookmark13">Pattern
+ Mapping</a><a href="modifying_meshes.htm#bookmark11"> </a>operation. </p>
+
+<p> </p>
+
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