/*! \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. 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 \.smp file. The smp file contains 4 sections: -# The first line holds the total number of the pattern nodes (N). -# The next N lines describe nodes coordinates. Each line holds 2 coordinates of a node for 2D pattern or 3 cordinates for 3D pattern. Note, that for 3D pattern only relateive values in range [0;1] are valid for coordinates of the nodes. -# A key-points line: indices of nodes to be mapped on geometrical vertices (for 2D pattern only). An index n refers to a node described on an n-th line of section 2. The first node index is zero. For 3D pattern key points are not specified. -# 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 for 2D pattern (only 2d elements are allowed) and 4, 5, 6 or 8 indices for 3D pattern (only 3d elements are allowed). The 2D pattern must contain at least one element and at least one key-point. All key-points must lay on boundaries. The 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 above described 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: 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 shall appear: \image html patternmapping1.png
2D Pattern Mapping dialog box
\image html patternmapping2.png
3D Pattern Mapping dialog box
To apply a pattern to a geometrical object, you should specify: -# For 2D pattern - 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; - A vertex to which the first key-point should be mapped; - Reverse or not the order of key-points. (The order of vertices of a face is counterclockwise looking from outside). -# For 3D pattern - 3D block (Solid) object; - Two vertices that specify the order of nodes in the resulting mesh. Then you either load a .smp pattern file previously created manually by clicking on the "Load pattern" button, or click on the \b New button for automatic generation of the pattern. For an automatic generation you just specify a geometrical face (for 2D) or solid (for 3d) having a mesh built on it. Mesh nodes lying on face vertices become key-points of 2D pattern. Additionally, for 2D pattern you may choose the way of getting nodes coordinates by projecting nodes on the face 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: - A sub-mesh on face/solid is selected. A pattern is created from the 2d/3d elements bound to a face/solid by mesher. For 2D pattern, node coordinates are either "positions on face" computed by mesher, or coordinates got by node projection on a geometrical surface, according to the user choice. For 3D pattern, nodes coordinates correspond to the nodes computed by mesher. - A mesh where the main shape is a face/solid, is selected. A pattern is created from all the 2d/3d elements in a mesh. In addition, for 2D pattern, 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. \image html a-patterntype.png
2D Pattern Creation dialog box
\image html a-patterntype1.png
3D Pattern Creation dialog box

Mapping algorithm

The mapping algorithm for 2D case is as follows: - 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. - 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 - 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 - 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 For 3D case the algorithm is similar. See Also a sample TUI Script of a \ref tui_pattern_mapping "Pattern Mapping" operation. */