<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
+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
\<pattern_name\>.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.
+-# 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 cordinates 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 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 2d elements are allowed) and 4, 5, 6 or 8
+indices for a 3D pattern (only 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:
8 1 2
\endcode
-The image below provides a preview of above described pattern:
+The image below provides a preview of the above pattern:
\image html pattern2d.png
\image html image98.png
<center><em>"Pattern mapping" button</em></center>
-The following dialog box shall appear:
+The following dialog box will appear:
+
+\n For a <b>2D pattern</b>
\image html patternmapping1.png
-<center><b> 2D Pattern Mapping dialog box</b></center>
+In this dialog you should specify:
+
+<ul>
+<li> \b Pattern, which can be loaded from .smp pattern file previously
+created manually or generated automatically from an existing mesh or submesh.</li>
+<li> \b Face with the number of vertices equal to the number of
+ key-points in the pattern; the number of key-points on internal
+ boundaries of the pattern must also be equal to the number of vertices
+ on internal boundaries of the face;</li>
+<li> \b Vertex to which the first key-point should be mapped;</li>
+Alternatively, it is possible to select <b>Refine selected mesh elements</b>
+checkbox and apply the pattern to
+<li> <b>Mesh Face</b> instead of a geometric Face</li>
+<li> and select \b Node instead of vertex.</li>
+
+Additionally it is possible to:
+<li> <b>Reverse the order of key-points</b> By default, the vertices of
+ a face are ordered counterclockwise.<li>
+<li> Enable to <b> Create polygons near boundary</b> </li>
+<li> and <b>Create polyhedrons near boundary</b><li>
+</ul>
+
+\n For a <b>3D pattern</b>
\image html patternmapping2.png
-<center><b> 3D Pattern Mapping dialog box</b></center>
+In this dialog you should specify:
+<ul>
+<li> \b Pattern, which can be loaded from .smp pattern file previously
+created manually or generated automatically from an existing mesh or submesh.</li>
+ <li> A 3D block (Solid) object;</li>
+ <li> Two vertices that specify the order of nodes in the resulting mesh.</li>
+Alternatively, it is possible to select <b>Refine selected mesh elements</b>
+checkbox and apply the pattern to
+<li> One or several <b>Mesh volumes</b> instead of a geometric 3D
+object</li>
+<li> and select two /b Nodes instead of vertices.</li>
+Additionally it is possible to:
+<li> Enable to <b> Create polygons near boundary</b> </li>
+<li> and <b>Create polyhedrons near boundary</b><li>
+</ul>
+
+\n Automatic Generation
+
+To generate a pattern automatically from an existing mesh or submesh,
+click \b New button.
+
+The following dialog box will appear:
-To apply a pattern to a geometrical object, you should specify:
+\image html a-patterntype1.png
--# 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 <em>"Load pattern"</em> 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
-<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:
-
-- 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.
+In this dialog you should specify:
-\image html a-patterntype.png
+<ul>
+<li> <b>Mesh or Submesh</b>, which is a meshed geometrical face (for a
+2D pattern) or a meshed solid (for a 3D pattern). Mesh nodes lying on
+the face vertices become key-points of the pattern. </li>
+<li> A custom <b>Pattern Name </b> </li>
+<li>Additionally, for a 2D pattern you may choose to
+<b>Project nodes on the face</b> to get node coordinates instead of using
+"positions on face" generated by the mesher (if there is any). The faces
+having a seam edge cannot be used for automatic pattern creation.</li>
+</ul>
-<center><b> 2D Pattern Creation dialog box</b></center>
+When a pattern is created from an existing mesh, two cases are possible:
-\image html a-patterntype1.png
+- 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.
-<center><b> 3D Pattern Creation dialog box</b></center>
<br><h2>Mapping algorithm</h2>
-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.
+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 cordinates 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 isolines
+ and boundaries are mapped. Then it is possible to find
+ the direction of mapped isolinesection and, filally, the poitions of
+ two nodes on two mapped isolines. The eventual mapped
+ position of the node is found as an average of the positions on mapped
+ isolines.
+\image html image97.gif
+
+The 3D algorithm is similar.
<b>See Also</b> a sample TUI Script of a
\ref tui_pattern_mapping "Pattern Mapping" operation.
