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\page pattern_mapping_page Pattern mapping

<br><h2>About patterns</h2>

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.

The smp file contains 4 sections:
<ol>
<li>The first line holds the number of nodes (N).</li>

<li>The next N lines describe nodes coordinates. Each line holds 2
coordinates of a node.</li>

<li>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.</li>

<li>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.</li>
</ol>

The 2D pattern must contain at least one element and at least one
key-point. All key-points must lay on boundaries.

An example of a simple smp file and a preview of a pattern described
in this file:

\image html image94.gif

<br><h2>Application of pattern mapping</h2>

<em>To apply pattern mapping to a geometrical object:</em>

From the \b Modification menu choose the <b>Pattern Mapping</b> item or click 
<em>"Pattern mapping"</em> button in the toolbar.

\image html image98.png
<center><em>"Pattern mapping" button</em></center>

The following dialog box shall appear:

\image html patternmapping1.png

\image html patternmapping2.png

To apply a pattern to a geometrical object, you should specify:
<ul>
<li>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;</li>
<li>a vertex to which the first key-point should be mapped;</li>
<li>reverse or not the order of key-points. (The order of vertices of
a face is counterclockwise looking from outside).</li>
</ul>

Then you either load a .smp pattern file previously created manually
by clicking on the <em>"Load pattern"</em> button, or click on the \b
New button for automatic generation.
\n 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 <b>projecting nodes on the face</b> instead of using
"positions on face" generated by mesher (if there is any). Faces
having a seam edge can't be used for automatic pattern creation.

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

\image html a-patterntype.png

\image html a-patterntype1.png

<br><h2>Mapping algorithm</h2>

The mapping algorithm is as follows:
<ol>
<li>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.
</li>

<li>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.

\image html image95.gif
</li>

<li>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.

\image html image96.gif
</li>

<li>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.

\image html image97.gif
</li>
</ol>

<br><b>See Also</b> a sample TUI Script of a 
\ref tui_pattern_mapping "Pattern Mapping" operation.

*/