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 by directly
-picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
+The splitting direction is defined by the orientation of the
+underlying geometrical edge.
+<b>Reverse Edges</b> list box allows specifying the edges, for which
+the splitting should be made in the direction opposite to their
+orientation. This list box is usable only if a geometry object is
+selected for meshing. In this case it is possible to 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. Use \b
+Add button to add the selected edges to the list.
\image html a-arithmetic1d.png
<b>Geometric Progression</b> hypothesis allows splitting edges into
segments with a length that changes in geometric progression (Lk =
-Lk-1 * d) starting from a given <b>Start Length</b> and <b>Common Ratio</b>.
+Lk-1 * d) starting from a given <b>Start Length</b> and with a given
+<b>Common Ratio</b>.
The splitting direction is defined by the orientation of the
underlying geometrical edge.
orientation. This list box is usable only if a geometry object is
selected for meshing. In this case it is possible to 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.
+selecting the edges or groups of edges in the Object Browser. Use \b
+Add button to add the selected edges to the list.
\image html a-geometric1d.png
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.
+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 it is
+possible to select edges to be reversed either by directly picking them
+in the 3D viewer or by selecting the edges or groups of edges in the
+Object Browser.
\image html image46.gif
<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>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.<br>
+Length of segments changes in geometric progression with the common
+ratio (A) depending on the <b>Scale Factor</b> (S) and <b>Number of
+Segments</b> (N) as follows: <code> A = S**(1/(N-1))</code>. For an
+edge of length L, length of the first segment is
+<code>L * (1 - A)/(1 - A**N)</code>.
-<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
+\image html a-nbsegments2.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.
+in the plot the density function curve in red and the node
+distribution as blue crosses.
\image html distributionwithanalyticdensity.png
+<br>
+\anchor analyticdensity_anchor
+The node distribution is computed so that to have the density function
+integral on the range between two nodes equal for all segments.
+\image html analyticdensity.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
+in the plot the density function curve in red and the node
+distribution as blue crosses. The node distribution is computed in the
+same way as for
+\ref analyticdensity_anchor "Distribution with Analytic Density". You
+can select the <b>Conversion mode</b> from\b Exponent and <b>Cut
+negative</b>.
+
+\image html distributionwithtabledensity.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>
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.
+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 it is
+possible to select edges to be reversed either by 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
\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
+elements).
+
+\image html automaticlength.png
+
+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."
