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232 lines
7.9 KiB
Plaintext
232 lines
7.9 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. A
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pattern also specifies the so-called key-points, i.e. the nodes that will be
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located at geometrical vertices. The 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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-# The first line indicates the total number of pattern nodes (N).
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-# The next N lines describe nodes coordinates. Each line contains 2
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node coordinates for a 2D pattern or 3 node coordinates for a 3D pattern.
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Note, that node coordinates of a 3D pattern can be defined only by
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relative values in range [0;1].
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-# The key-points line contains the indices of the nodes to be mapped on geometrical
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vertices (for a 2D pattern only). Index n refers to the node described
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on the n-th line of section 2. The index of the first node is
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zero. For a 3D pattern the key points are not specified.
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-# The remaining lines describe nodal connectivity of elements, one line
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for each element. Each line holds indices of nodes forming an element.
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Index n refers to the node described on the n-th line of section 2.
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The first node index is zero. There must be 3 or 4 indices on each
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line for a 2D pattern (only liner 2d elements are allowed) and 4, 5, 6 or 8
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indices for a 3D pattern (only linear 3d elements are allowed).
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A 2D pattern must contain at least one element and at least one
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key-point. All key-points must lie on boundaries.
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A 3D pattern must contain at least one element.
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An example of a simple 2D pattern smp file:
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\code
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!!! SALOME 2D mesh pattern file
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!!!
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!!! Nb of points:
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9
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200 0 !- 0
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100 0 !- 1
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0 0 !- 2
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0 -100 !- 3
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0 -200 !- 4
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100 -200 !- 5
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200 -200 !- 6
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200 -100 !- 7
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100 -100 !- 8
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!!! Indices of 4 key-points
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2 0 4 6
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!!! Indices of points of 6 elements
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0 1 8
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8 5 6 7
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2 3 8
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8 3 4 5
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8 7 0
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8 1 2
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\endcode
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The image below provides a preview of the above pattern:
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\image html pattern2d.png
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An example of a simple 3D pattern smp file:
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\code
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!!! SALOME 3D mesh pattern file
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!!!
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!!! Nb of points:
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9
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0 0 0 !- 0
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1 0 0 !- 1
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0 1 0 !- 2
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1 1 0 !- 3
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0 0 1 !- 4
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1 0 1 !- 5
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0 1 1 !- 6
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1 1 1 !- 7
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0.5 0.5 0.5 !- 8
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!!! Indices of points of 6 elements:
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0 1 5 4 8
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7 5 1 3 8
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3 2 6 7 8
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2 0 4 6 8
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0 2 3 1 8
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4 5 7 6 8
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\endcode
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<br><h2>Application of pattern mapping</h2>
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<em>To apply pattern mapping to a geometrical object or mesh elements:</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.png
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<center><em>"Pattern mapping" button</em></center>
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The following dialog box will appear:
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\n For a <b>2D pattern</b>
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\image html patternmapping1.png
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In this dialog you should specify:
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<ul>
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<li> \b Pattern, which can be loaded from .smp pattern file previously
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created manually or generated automatically from an existing mesh or
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sub-mesh.</li>
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<li> \b Face with 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 the pattern must also be equal to the number of vertices
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on internal boundaries of the face;</li>
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<li> \b Vertex to which the first key-point should be mapped;</li>
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</ul>
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Alternatively, it is possible to select <b>Refine selected mesh elements</b>
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check-box and apply the pattern to <ul>
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<li> <b>Mesh Face</b> instead of a geometric Face</li>
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<li> and select \b Node instead of vertex.</li>
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</ul>
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Additionally it is possible to: <ul>
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<li> <b>Reverse the order of key-points</b>. By default, the vertices of
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a face are ordered counterclockwise.</li>
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<li> Enable to <b> Create polygons near boundary</b> </li>
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<li> and <b>Create polyhedrons near boundary</b></li>
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</ul>
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\n For a <b>3D pattern</b>
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\image html patternmapping2.png
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In this dialog you should specify:
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<ul>
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<li> \b Pattern, which can be loaded from .smp pattern file previously
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created manually or generated automatically from an existing mesh or
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sub-mesh.</li>
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<li> A 3D block (Solid) object.</li>
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<li> Two vertices that specify the order of nodes in the resulting
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mesh.</li>
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</ul>
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Alternatively, it is possible to select <b>Refine selected mesh elements</b>
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check-box and apply the pattern to
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<ul>
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<li> One or several <b>Mesh volumes</b> instead of a geometric 3D object</li>
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<li> and select two \b Nodes instead of vertices.</li>
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</ul>
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Additionally it is possible to:
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<ul>
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<li> Enable to <b> Create polygons near boundary</b> </li>
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<li> and <b>Create polyhedrons near boundary</b></li>
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</ul>
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<br>
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<h3> Automatic Pattern Generation</h3>
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To generate a pattern automatically from an existing mesh or sub-mesh,
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click \b New button.
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The following dialog box will appear:
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\image html a-patterntype1.png
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In this dialog you should specify:
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<ul>
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<li> <b>Mesh or Sub-mesh</b>, which is a meshed geometrical face (for a
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2D pattern) or a meshed solid block (for a 3D pattern). Mesh nodes lying on
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the face vertices become key-points of the pattern. </li>
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<li> A custom <b>Pattern Name </b> </li>
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<li>Additionally, for a 2D pattern you may choose to
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<b>Project nodes on the face</b> to get node coordinates instead of using
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"positions on face" generated by the mesher (if there is any). The faces
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having a seam edge cannot be used for automatic pattern creation.</li>
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</ul>
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When a pattern is created from an existing mesh, two cases are possible:
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- A sub-mesh on a face/solid is selected. The pattern is created from the 2d/3d
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elements bound to the face/solid by the mesher. For a 2D pattern, the node coordinates are either
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"positions on face" computed by the mesher, or coordinates got by node
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projection on a geometrical surface, according to the user choice. For
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a 3D pattern, the node coordinates correspond to the nodes computed by
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the mesher.
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- A mesh, where the main shape is a face/solid, is selected. The pattern is
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created from all 2d/3d elements in a mesh. In addition, if all mesh
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elements of a 2D pattern are built by the mesher, the user can select
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how to get node coordinates, otherwise all nodes are projected on
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a face surface.
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<br><h2>Mapping algorithm</h2>
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The mapping algorithm for a 2D case is as follows:
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- The key-points are set counterclockwise in the order corresponding
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to their location on the pattern boundary. The first key-point is preserved.
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- The geometrical vertices corresponding to the key-points are found
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on face boundary. Here, "Reverse order of key-points" flag is set.
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\image html image95.gif
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- The boundary nodes of the pattern are mapped onto the edges of the face: a
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node located between two key-points on the pattern boundary is
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mapped on the geometrical edge limited by the corresponding geometrical
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vertices. The node position on the edge depends on its distance from the
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key-points.
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\image html image96.gif
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- The coordinates of a non-boundary node in the parametric space of the face
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are defined in the following way. In the parametric space of the
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pattern, the node lies at the intersection of two iso-lines. Both
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of them intersect the pattern boundary at two
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points at least. If the mapped positions of boundary nodes are known, it is
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possible to find, where the points at the intersection of iso-lines
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and boundaries are mapped. Then it is possible to find
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the direction of mapped iso-line section and, finally, the positions of
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two nodes on two mapped isolines. The eventual mapped
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position of the node is found as an average of the positions on mapped
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iso-lines.
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\image html image97.gif
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The 3D algorithm is similar.
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<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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*/
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