smesh/doc/salome/gui/SMESH/input/1d_meshing_hypo.doc

/*!

\page a1d_meshing_hypo_page 1D Meshing Hypotheses

<br>
<ul>
<li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
<li>\ref average_length_anchor "Average Length"</li>
<li>\ref max_length_anchor "Max Size"</li>
<li>\ref deflection_1d_anchor "Deflection 1D"</li>
<li>\ref number_of_segments_anchor "Number of segments"</li>
<li>\ref start_and_end_length_anchor "Start and end length"</li>
<li>\ref automatic_length_anchor "Automatic Length"</li>
<li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
</ul>

<br>
\anchor arithmetic_1d_anchor
<h2>Arithmetic 1D hypothesis</h2>

<b>Arithmetic 1D</b> hypothesis allows to split edges into segments with a
length that changes in arithmetic progression (Lk = Lk-1 + d)
beginning from a given starting length and up to a given end length.

The direction of the splitting is defined by the orientation of the underlying geometrical edge. 
<b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made 
in the direction opposing to their orientation. This list box is enabled only if the geometry object 
is selected for the meshing. In this case the user can select edges to be reversed either directly 
picking them in the 3D viewer or by selecting the edges or groups of edges in the Object browser.

\image html a-arithmetic1d.png

\image html b-ithmetic1d.png "Arithmetic 1D hypothesis - the size of mesh elements gradually increases"

<b>See Also</b> a sample TUI Script of a 
\ref tui_1d_arithmetic "Defining Arithmetic 1D hypothesis" operation.  

<br>
\anchor deflection_1d_anchor
<h2>Deflection 1D hypothesis</h2>

<b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
composing your geometrical object. It uses only one parameter: the
value of deflection.  
\n A geometrical edge is divided into equal segments. The maximum
distance between a point on the edge within a segment and the line
connecting the ends of the segment should not exceed the specified
value of deflection . Then mesh nodes are constructed at end segment
locations and 1D mesh elements are constructed on segments.

\image html a-deflection1d.png

\image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"

<b>See Also</b> a sample TUI Script of a 
\ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.

<br>
\anchor average_length_anchor
<h2>Average Length hypothesis</h2>

<b>Average Length</b> hypothesis can be applied for meshing of edges
composing your geometrical object. Definition of this hypothesis
consists of setting the \b length of segments, which will split these
edges, and the \b precision of rounding. The points on the edges
generated by these segments will represent nodes of your mesh.
Later these nodes will be used for meshing of the faces abutting to
these edges.

The \b precision parameter is used to allow rounding a number of
segments, calculated from the edge length and average length of
segment, to the lower integer, if this value outstands from it in
bounds of the precision. Otherwise, the number of segments is rounded
to the higher integer. Use value 0.5 to provide rounding to the
nearest integer, 1.0 for the lower integer, 0.0 for the higher
integer. Default value is 1e-07.

\image html image41.gif

\image html a-averagelength.png

\image html b-erage_length.png "Average length hypothesis - all 1D mesh elements are roughly equal"

<b>See Also</b> a sample TUI Script of a 
\ref tui_average_length "Defining Average Length" hypothesis
operation.

<br>\anchor max_length_anchor
<h2>Max Size</h2>
<b>Max Size</b> hypothesis allows splitting geometrical edges into
segments not longer than the given length. Definition of this hypothesis
consists of setting the maximal allowed \b length of segments.
<b>Use preestimated length</b> check box lets you specify \b length
automatically calculated basing on size of your geometrical object,
namely as diagonal of bounding box divided by ten. The divider can be
changed via "Ratio Bounding Box Diagonal / Max Size"
preference parameter.
<b>Use preestimated length</b> check box is enabled only if the
geometrical object has been selected before hypothesis definition.

\image html a-maxsize1d.png

<br>
\anchor number_of_segments_anchor
<h2>Number of segments hypothesis</h2>

<b>Number of segments</b> hypothesis can be applied for meshing of edges
composing your geometrical object. Definition of this hypothesis
consists of setting the number of segments, which will split these
edges. In other words your edges will be split into a definite number
of segments with approximately the same length. The points on the
edges generated by these segments will represent nodes of your
mesh. Later these nodes will be used for meshing of the faces abutting
to these edges.

The direction of the splitting is defined by the orientation of the underlying geometrical edge. 
<b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made 
in the direction opposing to their orientation. This list box is enabled only if the geometry object 
is selected for the meshing. In this case the user can select edges to be reversed either directly 
picking them in the 3D viewer or by selecting the edges or groups of edges in the Object browser.

\image html image46.gif

You can set the type of distribution for this hypothesis in the
<b>Hypothesis Construction</b> dialog bog :

\image html a-nbsegments1.png

<br><b>Equidistant Distribution</b> - all segments will have the same
length, you define only the <b>Number of Segments</b>.

<br><b>Scale Distribution</b> - length of segments gradually changes depending on the <b>Scale Factor</b>, which is a ratio of the first segment length to the last segment length.

\image html a-nbsegments2.png

<br><b>Distribution with Table Density</b> - you input a number of
pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1,  and the module computes the
formula, which will rule the change of length of segments and shows
the curve in the plot. You can select the <b>Conversion mode</b> from
\b Exponent and <b>Cut negative</b>.

\image html distributionwithtabledensity.png

<br><b>Distribution with Analytic Density</b> - you input the formula,
which will rule the change of length of segments and the module shows
the curve in the plot.

\image html distributionwithanalyticdensity.png

<b>See Also</b> a sample TUI Script of a 
\ref tui_deflection_1d "Defining Number of Segments" hypothesis
operation.

<br>
\anchor start_and_end_length_anchor
<h2>Start and End Length hypothesis</h2>

<b>Start and End Length</b> hypothesis allows to divide a geometrical edge
into segments so that the first and the last segments have a specified
length. The length medium segments changes with automatically chosen
geometric progression. Then mesh nodes are
constructed at segment ends location and 1D mesh elements are
constructed on them.

The direction of the splitting is defined by the orientation of the underlying geometrical edge. 
<b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made 
in the direction opposing to their orientation. This list box is enabled only if the geometry object 
is selected for the meshing. In this case the user can select edges to be reversed either directly 
picking them in the 3D viewer or by selecting the edges or groups of edges in the Object browser.

\image html a-startendlength.png

\image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"

<b>See Also</b> a sample TUI Script of a 
\ref tui_start_and_end_length "Defining Start and End Length"
hypothesis operation.

<br>
\anchor automatic_length_anchor
<h2>Automatic Length</h2>

This hypothesis is automatically applied when you select <b>Assign a
set of hypotheses</b> option in Create Mesh menu.

\image html automaticlength.png

The dialog box prompts you to define the quality of the future mesh by
only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
low number of elements) to 1 (extremely fine mesh, great number of
elements). Compare one and the same object (sphere) meshed with
minimum and maximum value of this parameter.

\image html image147.gif "Example of a very rough mesh. Automatic Length works for 0."

\image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."

<br>
\anchor fixed_points_1d_anchor
<h2>Fixed points 1D hypothesis</h2>

<b>Fixed points 1D</b> hypothesis allows to split edges into segments
using set of fixed points given by normalized parameters on edge and
set of numbers of segments for splitting each sub-segment between
fixed points. Optionally it is possible to set flag
<b>Same Nb. Segments for all intervals</b> and
only one value for mentioned number of segments.

The direction of the splitting is defined by the orientation of the
underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
specify the edges for which the splitting should be made in the
direction opposing to their orientation. This list box is enabled only
if the geometry object is selected for the meshing. In this case the
user can select edges to be reversed either directly picking them in
the 3D viewer or by selecting the edges or groups of edges in the
Object browser.

Using of this hypothesis for quadrangle face where main mesh is
created using <b>Quadrangle(Mapping)</b> and <b>NumberOfSegments</b>
hypothesises. Creation hypothesis <b>FixedPoint_1D</b> for submesh on
one edge:

\image html hypo_fixedpnt_dlg.png

Resulting 2D mesh:

\image html mesh_fixedpnt.png

<b>See Also</b> a sample TUI Script of a
\ref tui_fixed_points "Defining Fixed Points" hypothesis operation.

*/