/*! \page pattern_mapping_page Pattern mapping

About patterns

The pattern describes a mesh to generate: positions of nodes within a geometrical domain and nodal connectivity of elements. A pattern also specifies the so-called key-points, i.e. the nodes that will be located at geometrical vertices. The pattern description is stored in \.smp file. The smp file contains 4 sections: -# The first line indicates the total number of pattern nodes (N). -# The next N lines describe nodes coordinates. Each line contains 2 node coordinates for a 2D pattern or 3 node coordinates for a 3D pattern. Note, that node coordinates of a 3D pattern can be defined only by relative values in range [0;1]. -# The key-points line contains the indices of the nodes to be mapped on geometrical vertices (for a 2D pattern only). Index n refers to the node described on the n-th line of section 2. The index of the first node is zero. For a 3D pattern the key points are not specified. -# The remaining lines describe nodal connectivity of elements, one line for each element. Each line holds indices of nodes forming an element. Index n refers to the node described on the n-th line of section 2. The first node index is zero. There must be 3 or 4 indices on each line for a 2D pattern (only liner 2d elements are allowed) and 4, 5, 6 or 8 indices for a 3D pattern (only linear 3d elements are allowed). A 2D pattern must contain at least one element and at least one key-point. All key-points must lie on boundaries. A 3D pattern must contain at least one element. An example of a simple 2D pattern smp file: \code !!! SALOME 2D mesh pattern file !!! !!! Nb of points: 9 200 0 !- 0 100 0 !- 1 0 0 !- 2 0 -100 !- 3 0 -200 !- 4 100 -200 !- 5 200 -200 !- 6 200 -100 !- 7 100 -100 !- 8 !!! Indices of 4 key-points 2 0 4 6 !!! Indices of points of 6 elements 0 1 8 8 5 6 7 2 3 8 8 3 4 5 8 7 0 8 1 2 \endcode The image below provides a preview of the above pattern: \image html pattern2d.png An example of a simple 3D pattern smp file: \code !!! SALOME 3D mesh pattern file !!! !!! Nb of points: 9 0 0 0 !- 0 1 0 0 !- 1 0 1 0 !- 2 1 1 0 !- 3 0 0 1 !- 4 1 0 1 !- 5 0 1 1 !- 6 1 1 1 !- 7 0.5 0.5 0.5 !- 8 !!! Indices of points of 6 elements: 0 1 5 4 8 7 5 1 3 8 3 2 6 7 8 2 0 4 6 8 0 2 3 1 8 4 5 7 6 8 \endcode

Application of pattern mapping

To apply pattern mapping to a geometrical object or mesh elements: From the \b Modification menu choose the Pattern Mapping item or click "Pattern mapping" button in the toolbar. \image html image98.png
"Pattern mapping" button
The following dialog box will appear: \n For a 2D pattern \image html patternmapping1.png In this dialog you should specify: Alternatively, it is possible to select Refine selected mesh elements check-box and apply the pattern to Additionally it is possible to: \n For a 3D pattern \image html patternmapping2.png In this dialog you should specify: Alternatively, it is possible to select Refine selected mesh elements check-box and apply the pattern to Additionally it is possible to:

Automatic Pattern Generation

To generate a pattern automatically from an existing mesh or sub-mesh, click \b New button. The following dialog box will appear: \image html a-patterntype1.png In this dialog you should specify: When a pattern is created from an existing mesh, two cases are possible: - A sub-mesh on a face/solid is selected. The pattern is created from the 2d/3d elements bound to the face/solid by the mesher. For a 2D pattern, the node coordinates are either "positions on face" computed by the mesher, or coordinates got by node projection on a geometrical surface, according to the user choice. For a 3D pattern, the node coordinates correspond to the nodes computed by the mesher. - A mesh, where the main shape is a face/solid, is selected. The pattern is created from all 2d/3d elements in a mesh. In addition, if all mesh elements of a 2D pattern are built by the mesher, the user can select how to get node coordinates, otherwise all nodes are projected on a face surface.

Mapping algorithm

The mapping algorithm for a 2D case is as follows: - The key-points are set counterclockwise in the order corresponding to their location on the pattern boundary. The first key-point is preserved. - The geometrical vertices corresponding to the key-points are found on face boundary. Here, "Reverse order of key-points" flag is set. \image html image95.gif - The boundary nodes of the pattern are mapped onto the edges of the face: a node located between two key-points on the pattern boundary is mapped on the geometrical edge limited by the corresponding geometrical vertices. The node position on the edge depends on its distance from the key-points. \image html image96.gif - The coordinates of a non-boundary node in the parametric space of the face are defined in the following way. In the parametric space of the pattern, the node lies at the intersection of two iso-lines. Both of them intersect the pattern boundary at two points at least. If the mapped positions of boundary nodes are known, it is possible to find, where the points at the intersection of iso-lines and boundaries are mapped. Then it is possible to find the direction of mapped iso-line section and, finally, the positions of two nodes on two mapped isolines. The eventual mapped position of the node is found as an average of the positions on mapped iso-lines. \image html image97.gif The 3D algorithm is similar. See Also a sample TUI Script of a \ref tui_pattern_mapping "Pattern Mapping" operation. */