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<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 &lt;pattern_name&gt;.smp file.</p>

<p>&nbsp;</p>

<p>The smp file contains 4 sections:</p>

<p>&nbsp;</p>

<p class="whs2">1. The first line holds the number of nodes 
 (N).</p>

<p class="whs2">&nbsp;</p>

<p class="whs2">2. The next N lines describe nodes coordinates. 
 Each line holds 2 coordinates of a node.</p>

<p class="whs2">&nbsp;</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">&nbsp;</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">&nbsp;</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>&nbsp;</p>

<p>An example of a simple smp file and a preview of a pattern described 
 in this file:</p>

<p>&nbsp;</p>

<p><img src="image94.gif" width="626px" height="471px" border="0" class="img_whs3"></p>

<p>&nbsp;</p>

<h3>Creating patterns</h3>

<p>The pattern description can be created manually or automatically. Manual 
 pattern creation implies creation of pattern file by hands. For an automatic 
 generation the user just specifies a geometrical face having a mesh built 
 on it. Mesh nodes lying on face vertices become key-points. Additionally, 
 the user may choose the way of getting nodes coordinates by projecting 
 nodes on the face instead of using &quot;positions on face&quot; generated 
 by mesher (if there are any). Faces having a seam edge can�t be used for 
 automatic pattern creation.</p>

<p>&nbsp;</p>

<p>When creating a pattern from an existing mesh, there are two possible 
 cases:</p>

<p>&nbsp;</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 &quot;positions 
 on face&quot; computed by mesher, or coordinates got by node projection 
 on a geometrical surface, according to your choice.</p>

<p>&nbsp;</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>

<p>&nbsp;</p>

<h3>Application of pattern mapping</h3>

<p class=TODO>To apply pattern mapping to a geometrical object:</p>

<p class=TODO>&nbsp;</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">&nbsp;</p>

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<p class="whs2">&nbsp;</p>

<p>To apply a pattern to a geometrical object, you should specify:</p>

<p>&nbsp;</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 class="whs2">&nbsp;</p>

<p class="whs2">&nbsp;</p>

<h3>Mapping algorithm:</h3>

<p class="whs10">The mapping algorithm is as follows:</p>

<p class="whs10">&nbsp;</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, &quot;Reverse 
 order of key-points&quot; flag is taken into account.</p>

<p class="whs2">&nbsp;</p>

<p class="whs2"><img src="image95.gif" width="554px" height="279px" border="0" class="img_whs11"></p>

<p class="whs2">&nbsp;</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">&nbsp;</p>

<p class="whs2"><img src="image96.gif" width="572px" height="233px" border="0" class="img_whs12"></p>

<p class="whs2">&nbsp;</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">&nbsp;</p>

<p class="whs2"><img src="image97.gif" width="606px" height="249px" border="0" class="img_whs13"></p>

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