<b>Max Element Area</b> hypothesis is applied for meshing of faces
composing your geometrical object. Definition of this hypothesis
-consists of setting the <b>maximum area</b> of mesh elements,
+consists of setting the <b>maximum area</b> of mesh faces,
which will compose the mesh of these faces.
\image html a-maxelarea.png
\anchor length_from_edges_anchor
<h2>Length from Edges</h2>
-<b>Length from edges</b> hypothesis builds 2D mesh elements having a
-maximum linear size calculated as an average segment length for a wire
-of a given face.
+<b>Length from edges</b> hypothesis defines the maximum linear size of
+mesh faces as an average length of mesh edges approximating
+the meshed face boundary.
<b>See Also</b> a sample TUI Script of a
\ref tui_length_from_edges "Length from Edges" hypothesis operation.
\anchor hypo_quad_params_anchor
<h2>Quadrangle parameters</h2>
-\image html hypo_quad_params_dialog.png "Quadrangle parameters creation/edition dialog"
+\image html hypo_quad_params_dialog.png "Quadrangle parameters: Transition"
-<b>Quadrangle parameters</b> is a hypothesis for Quadrangle (Mapping).
+<b>Quadrangle parameters</b> is a hypothesis for \ref quad_ijk_algo_page.
-<b>Base vertex</b> parameter allows using Quadrangle (Mapping)
-algorithm for meshing of trilateral faces. In this case it is
-necessary to select the vertex, which will be used as the fourth edge
-(degenerated).
-
-\image html hypo_quad_params_1.png "A face built from 3 edges"
-
-\image html hypo_quad_params_res.png "The resulting mesh"
-
-This parameter can be also used to mesh a segment of a circular face.
-Please, consider that there is a limitation on the selection of the
-vertex for the faces built with the angle > 180 degrees (see the picture).
-
-\image html hypo_quad_params_2.png "3/4 of a circular face"
-
-In this case, selection of a wrong vertex for the <b>Base vertex</b>
-parameter will generate a wrong mesh. The picture below
-shows the good (left) and the bad (right) results of meshing.
-
-\image html hypo_quad_params_res_2.png "The resulting meshes"
-
-<b>Type</b> parameter is used on faces with a different number of
-segments on opposite sides to define the algorithm of transition
-between them. The following types are available:
+<b>Transition</b> tab is used to define the algorithm of transition
+between opposite sides of the face with a different number of
+segments on them. The following types of transition
+algorithms are available:
- <b>Standard</b> is the default case, when both triangles and quadrangles
are possible in the transition area along the finer meshed sides.
- <b>Quadrangle preference</b> forces building only quadrangles in the
transition area along the finer meshed sides. This hypothesis has a
restriction: the total quantity of segments on all
- four sides of the face must be even (divisible by 2).
+ four face sides must be even (divisible by 2).
\note This type corresponds to <b>Quadrangle Preference</b> additional hypothesis,
which is obsolete now.
- <b>Quadrangle preference (reversed)</b> works in the same way and
- <b>Reduced</b> type forces building only quadrangles and the transition
between the sides is made gradually, layer by layer. This type has
a limitation on the number of segments: one pair of opposite sides must have
- the same number of segments, the other pair must have an even difference
- between the numbers of segments on the sides. In addition, the number
- of rows between sides with different discretization
+ the same number of segments, the other pair must have an even total
+ number of segments. In addition, the number of rows
+ between sides with different discretization
should be enough for the transition. Following the fastest transition
pattern, three segments become one (see the image below), hence
the least number of face rows needed to reduce from Nmax segments
to Nmin segments is log<sub>3</sub>( Nmax / Nmin ). The number of
face rows is equal to the number of segments on each of equally
discretized sides.
- \image html reduce_three_to_one.png "The fastest transition pattern: 3 to 1"
+
+\image html reduce_three_to_one.png "The fastest transition pattern: 3 to 1"
+
+<b>Base vertex</b> tab allows using Quadrangle (Mapping)
+algorithm for meshing of trilateral faces. In this case it is
+necessary to select the vertex, which will be used as the forth
+degenerated side of quadrangle.
+
+\image html hypo_quad_params_dialog_vert.png "Quadrangle parameters: Base Vertex"
+
+\image html hypo_quad_params_1.png "A face built from 3 edges"
+
+\image html hypo_quad_params_res.png "The resulting mesh"
+
+This parameter can be also used to mesh a segment of a circular face.
+Please, consider that there is a limitation on the selection of the
+vertex for the faces built with the angle > 180 degrees (see the picture).
+
+\image html hypo_quad_params_2.png "3/4 of a circular face"
+
+In this case, selection of a wrong vertex for the <b>Base vertex</b>
+parameter will generate a wrong mesh. The picture below
+shows the good (left) and the bad (right) results of meshing.
+
+\image html hypo_quad_params_res_2.png "The resulting meshes"
+
+\image html hypo_quad_params_dialog_enf.png "Quadrangle parameters: Enforced nodes"
+
+<b>Enforced nodes</b> tab allows defining points, where the
+algorithm should create nodes. There are two ways to define positions
+of the enforced nodes.
+<ul>
+ <li>\b Vertices group allows to set up shapes whose vertices will
+ define positions of the enforced nodes. Only vertices successfully
+ projected to the meshed face and located close enough to the
+ meshed face will be used to create the enforced nodes.</li>
+ <li> \b Points group allows to explicitly define coordinates of
+ points used to create the enforced nodes. Only points successfully
+ projected to the meshed face and located close enough to the
+ meshed face will be used to create the enforced nodes.</li>
+</ul>
+\note <b>Enforced nodes</b> cannot be created at \b Reduced transition type.
+
+Let us see how the algorithm works:
+<ul>
+ <li> Initially positions of nodes are computed without taking into
+ account the enforced vertex (yellow point).</li>
+\image html hypo_quad_params_enfnodes_algo1.png "Initial mesh"
+
+ <li> Then the node closest to the enforced vertex is
+ detected. Extreme nodes of the row and column of the detected node
+ are used to create virtual edges (yellow lines) ending at the
+ enforced vertex. </li>
+\image html hypo_quad_params_enfnodes_algo2.png "Creation of virtual edges"
+
+ <li> Consequently, the meshed face is divided by the virtual
+ edges into four quadrilateral sub-domains each of which is meshed
+ as usually: the nodes of the row and column of the detected node are
+ moved to the virtual edges and the quadrilateral elements are
+ constructed.
+
+\image html hypo_quad_params_enfnodes_algo3.png "Final mesh"
+
+</ul>
+If there are several enforced vertices, the algorithm is applied
+recursively to the formed sub-domains.
<b>See Also</b> a sample TUI Script of a
\ref tui_quadrangle_parameters "Quadrangle Parameters" hypothesis.
