smesh/doc/salome/gui/SMESH/pattern_mapping.htm

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<title>Pattern mapping</title>
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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<61>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>
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