\image html hypo_quad_params_dialog.png "Quadrangle parameters creation/edition dialog"
-<b>Quadrangle parameters</b> is a hypothesis for Quadrangle (Mapping).
+<b>Quadrangle parameters</b> is a hypothesis for Quadrangle (Mapping) algorithm.
-<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 faces with a different number of
+segments on opposite sides. 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.
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 fourth edge
+(degenerated).
+
+\image html hypo_quad_params_dialog_vert.png "Base Vertex tab of Quadrangle parameters creation/edition dialog"
+
+\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 "Enforced nodes tab of Quadrangle parameters creation/edition dialog"
+
+<b>Enforced nodes</b> tab allows for 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>
+Algorithm of creation of the enforced nodes is following.
+
+\image html hypo_quad_params_enfnodes_algo.png "Steps of the algorithm of creation of the enforced nodes"
+<ol>
+ <li> Left image: Positions of nodes are computed without taking into
+ account the enforced vertex (yellow point).</li>
+ <li> Middle image: A 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>
+ <li> Right image: The meshed face is thus 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 detected node are
+ moved to the virtual edges and the quadrilateral elements are
+ constructed.
+</ol>
+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.
