smesh/doc/salome/gui/SMESH/input/2d_meshing_hypo.doc

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\page a2d_meshing_hypo_page 2D Meshing Hypotheses

<br>
<ul>
<li>\ref max_element_area_anchor "Max Element Area"</li>
<li>\ref length_from_edges_anchor "Length from Edges"</li>
<li>\ref hypo_quad_params_anchor "Quadrangle parameters"</li>
</ul>

<br>
\anchor max_element_area_anchor
<h2>Max Element Area</h2>

<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,
which will compose the mesh of these faces.

\image html a-maxelarea.png

\n

\image html max_el_area.png "In this example, Max. element area is very small compared to the 1D hypothesis"

<b>See Also</b> a sample TUI Script of a 
\ref tui_max_element_area "Maximum Element Area" hypothesis
operation. 

<br>
\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>See Also</b> a sample TUI Script of a 
\ref tui_length_from_edges "Length from Edges" hypothesis operation.

<br>
\anchor hypo_quad_params_anchor
<h2>Quadrangle parameters</h2>

\image html hypo_quad_params_dialog.png "Quadrangle parameters creation/edition dialog"

<b>Quadrangle parameters</b> is a hypothesis for Quadrangle (Mapping).

<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:

<ul>
<li><b>Standard</b> is the default case, when both triangles and quadrangles
    are possible in the transition area along the finer meshed sides.</li>
<li><b>Triangle preference</b> forces building only triangles in the
    transition area along the finer meshed sides.
    <i>This type corresponds to <b>Triangle Preference</b> additional
    hypothesis, which is obsolete now.</i></li>
<li><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).</li>
    <i>This type corresponds to <b>Quadrangle Preference</b>
    additional hypothesis, which is obsolete now.</i></li>
<li><b>Quadrangle preference (reversed)</b> works in the same way and
  with the same restriction as <b>Quadrangle preference</b>, but
  the transition area is located along the coarser meshed sides.</li>
<li><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, number
    of rows of faces between sides with different discretization
    should be enough for the transition. At the fastest transition
    pattern, tree 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 number of segments on each of equally
    discretized sides.
\image html reduce_three_to_one.png "The fastest transition pattern: 3 to 1"
</li>
</ul>

<b>See Also</b> a sample TUI Script of a 
\ref tui_quadrangle_parameters "Quadrangle Parameters" hypothesis.

<br>
*/