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135 lines
4.8 KiB
Plaintext
135 lines
4.8 KiB
Plaintext
/*!
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\page pattern_mapping_page Pattern mapping
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<br><h2>About patterns</h2>
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The pattern describes a mesh to generate: positions of nodes within a
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geometrical domain and nodal connectivity of elements. As well, a
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pattern specifies the so-called key-points, i.e. nodes that will be
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located at geometrical vertices. Pattern description is stored in
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\<pattern_name\>.smp file.
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The smp file contains 4 sections:
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<ol>
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<li>The first line holds the number of nodes (N).</li>
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<li>The next N lines describe nodes coordinates. Each line holds 2
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coordinates of a node.</li>
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<li>A key-points line: indices of nodes to be mapped on geometrical
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vertices. An index n refers to a node described on an n-th line of
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section 2. The first node index is zero.</li>
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<li>The rest lines describe nodal connectivity of elements, one line
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for an element. A line holds indices of nodes forming an element. An
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index n refers to a node described on an n-th line of the section
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2. The first node index is zero. There must be 3 or 4 indices on a
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line: only 2d elements are allowed.</li>
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</ol>
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The 2D pattern must contain at least one element and at least one
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key-point. All key-points must lay on boundaries.
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An example of a simple smp file and a preview of a pattern described
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in this file:
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\image html image94.gif
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<br><h2>Application of pattern mapping</h2>
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<em>To apply pattern mapping to a geometrical object:</em>
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From the \b Modification menu choose the <b>Pattern Mapping</b> item or click
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<em>"Pattern mapping"</em> button in the toolbar.
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\image html image98.gif
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<center><em>"Pattern mapping" button</em></center>
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The following dialog box shall appear:
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\image html patternmapping1.png
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\image html patternmapping2.png
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To apply a pattern to a geometrical object, you should specify:
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<ul>
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<li>a face having the number of vertices equal to the number of
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key-points in the pattern; the number of key-points on internal
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boundaries of a pattern must also be equal to the number of vertices
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on internal boundaries of a face;</li>
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<li>a vertex to which the first key-point should be mapped;</li>
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<li>reverse or not the order of key-points. (The order of vertices of
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a face is counterclockwise looking from outside).</li>
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</ul>
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Then you either load a .smp pattern file previously created manually
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by clicking on the <em>"Load pattern"</em> button, or click on the \b
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New button for automatic generation.
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\n For an automatic generation you just specify a geometrical face
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having a mesh built on it. Mesh nodes lying on face vertices become
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key-points. Additionally, you may choose the way of getting nodes
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coordinates by <b>projecting nodes on the face</b> instead of using
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"positions on face" generated by mesher (if there is any). Faces
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having a seam edge can?t be used for automatic pattern creation.
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When creating a pattern from an existing mesh, there are two possible
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cases:
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<ol>
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<li>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
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"positions on face" computed by mesher, or coordinates got by node
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projection on a geometrical surface, according to your choice.</li>
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<li>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
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build by mesher, the user can select the way of getting nodes
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coordinates, else all nodes are projected on a face surface.</li>
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</ol>
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\image html a-patterntype.png
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\image html a-patterntype1.png
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<br><h2>Mapping algorithm</h2>
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The mapping algorithm is as follows:
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<ol>
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<li>Key-points are set in the order that they are encountered when
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walking along a pattern boundary so that elements are on the left. The
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first key-point is preserved.
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</li>
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<li>Find geometrical vertices corresponding to key-points by vertices
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order in a face boundary; here, "Reverse order of key-points" flag is
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taken into account.
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\image html image95.gif
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</li>
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<li>Boundary nodes of a pattern are mapped onto edges of a face: a
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node located between certain key-points on a pattern boundary is
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mapped on a geometrical edge limited by corresponding geometrical
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vertices. Node position on an edge reflects its distance from two
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key-points.
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\image html image96.gif
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</li>
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<li>Coordinates of a non-boundary node in a parametric space of a face
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are defined as following. In a parametric space of a pattern, a node
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lays at the intersection of two iso-lines, each of which intersects a
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pattern boundary at least at two points. Knowing mapped positions of
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boundary nodes, we find where isoline-boundary intersection points are
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mapped to, and hence we can find mapped isolines direction and then,
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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
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isolines.
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\image html image97.gif
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</li>
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</ol>
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<br><b>See Also</b> a sample TUI Script of a
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\ref tui_pattern_mapping "Pattern Mapping" operation.
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*/ |