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308 lines
11 KiB
HTML
Executable File
308 lines
11 KiB
HTML
Executable File
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<h1>Pattern mapping</h1>
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<h3>About patterns</h3>
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<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
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nodes within a geometrical domain and nodal connectivity of elements.
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As well, a pattern specifies the so-called key-points, i.e. nodes that
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will be located at geometrical vertices. Pattern description is stored
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in <pattern_name>.smp file.</p>
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<p> </p>
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<p>The smp file contains 4 sections:</p>
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<p> </p>
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<p class="whs2">1. The first line holds the number of nodes
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(N).</p>
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<p class="whs2"> </p>
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<p class="whs2">2. The next N lines describe nodes coordinates.
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Each line holds 2 coordinates of a node.</p>
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<p class="whs2"> </p>
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<p class="whs2">3. A key-points line: indices of nodes to
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be mapped on geometrical vertices. An index n refers to a node described
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on an n-th line of section 2. The first node index is zero.</p>
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<p class="whs2"> </p>
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<p class="whs2">4. The rest lines describe nodal connectivity
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of elements, one line for an element. A line holds indices of nodes forming
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an element. An index n refers to a node described on an n-th line of the
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section 2. The first node index is zero. There must be 3 or 4 indices
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on a line: only 2d elements are allowed.</p>
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<p class="whs2"> </p>
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<p>The 2D pattern must contain at least one element and at least one key-point.
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All key-points must lay on boundaries.</p>
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<p> </p>
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<p>An example of a simple smp file and a preview of a pattern described
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in this file:</p>
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<p> </p>
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<p><img src="image94.gif" width="626px" height="471px" border="0" class="img_whs3"></p>
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<p> </p>
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<h3>Creating patterns</h3>
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<p>The pattern description can be created manually or automatically. Manual
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pattern creation implies creation of pattern file by hands. For an automatic
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generation the user just specifies a geometrical face having a mesh built
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on it. Mesh nodes lying on face vertices become key-points. Additionally,
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the user may choose the way of getting nodes coordinates by projecting
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nodes on the face instead of using "positions on face" generated
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by mesher (if there are any). Faces having a seam edge can<61>t be used for
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automatic pattern creation.</p>
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<p> </p>
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<p>When creating a pattern from an existing mesh, there are two possible
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cases:</p>
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<p> </p>
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<p>1. A sub-mesh on face is selected. A pattern is created from the 2d
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elements bound to a face by mesher. Node coordinates are either "positions
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on face" computed by mesher, or coordinates got by node projection
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on a geometrical surface, according to your choice.</p>
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<p> </p>
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<p>2. A mesh where the main shape is a face, is selected. A pattern is
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created from all the 2d elements in a mesh. If all mesh elements are build
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by mesher, the user can select the way of getting nodes coordinates, else
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all nodes are projected on a face surface.</p>
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<p> </p>
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<h3>Application of pattern mapping</h3>
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<p class=TODO>To apply pattern mapping to a geometrical object:</p>
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<p class=TODO> </p>
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<p class="whs2">1. From the <span style="font-weight: bold;"><B>Modification
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</B></span>menu choose the <span style="font-weight: bold;"><B>Pattern Mapping
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</B></span>item or click <img src="image98.gif" width="22px" height="28px" border="0" class="img_whs4"> button in the toolbar. The following
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dialog box shall appear:</p>
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<p class="whs2"> </p>
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<!--(Table)=========================================================-->
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<table x-use-null-cells cellspacing="0" width="100%" class="whs5">
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<col class="whs6">
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<col class="whs6">
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<tr valign=top>
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<td width="50%" class="whs7">
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<p><img src="image81.jpg" width="232px" height="400px" border="0" class="img_whs8"></td>
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<td width="50%" class="whs9">
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<p><img src="image80.jpg" width="232px" height="400px" border="0" class="img_whs8"></td></tr>
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</table>
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<p class="whs2"> </p>
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<p>To apply a pattern to a geometrical object, you should specify:</p>
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<p> </p>
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<p class="whs2">- a face having the number of vertices equal
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to the number of key-points in the pattern; the number of key-points on
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internal boundaries of a pattern must also be equal to the number of vertices
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on internal boundaries of a face;</p>
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<p class="whs2">- a vertex to which the first key-point should
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be mapped,</p>
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<p class="whs2">- reverse or not the order of key-points.
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(The order of vertices of a face is counterclockwise looking from outside).</p>
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<p class="whs2"> </p>
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<p class="whs2"> </p>
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<h3>Mapping algorithm:</h3>
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<p class="whs10">The mapping algorithm is as follows:</p>
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<p class="whs10"> </p>
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<p class="whs2">1. Key-points are set in the order that they
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are encountered when walking along a pattern boundary so that elements
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are on the left. The first key-point is preserved.</p>
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<p class="whs2">2. Find geometrical vertices corresponding
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to key-points by vertices order in a face boundary; here, "Reverse
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order of key-points" flag is taken into account.</p>
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<p class="whs2"> </p>
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<p class="whs2"><img src="image95.gif" width="554px" height="279px" border="0" class="img_whs11"></p>
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<p class="whs2"> </p>
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<p class="whs2">3. Boundary nodes of a pattern are mapped
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onto edges of a face: a node located between certain key-points on a pattern
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boundary is mapped on a geometrical edge limited by corresponding geometrical
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vertices. Node position on an edge reflects its distance from two key-points.</p>
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<p class="whs2"> </p>
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<p class="whs2"><img src="image96.gif" width="572px" height="233px" border="0" class="img_whs12"></p>
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<p class="whs2"> </p>
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<p class="whs2">4. Coordinates of a non-boundary node in
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a parametric space of a face are defined as following. In a parametric
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space of a pattern, a node lays at the intersection of two iso-lines,
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each of which intersects a pattern boundary at least at two points. Knowing
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mapped positions of boundary nodes, we find where isoline-boundary intersection
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points are mapped to, and hence we can find mapped isolines direction
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and then, two node positions on two mapped isolines. The eventual mapped
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position of a node is found as an average of positions on mapped isolines.</p>
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<p class="whs2"> </p>
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<p class="whs2"><img src="image97.gif" width="606px" height="249px" border="0" class="img_whs13"></p>
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