<br>
<ul>
+<li>\ref adaptive_1d_anchor "Adaptive"</li>
<li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
+<li>\ref geometric_1d_anchor "Geometric Progression"</li>
<li>\ref average_length_anchor "Local Length"</li>
<li>\ref max_length_anchor "Max Size"</li>
<li>\ref deflection_1d_anchor "Deflection 1D"</li>
<li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
</ul>
+<br>
+\anchor adaptive_1d_anchor
+<h2>Adaptive hypothesis</h2>
+
+<b>Adaptive</b> hypothesis allows to split edges into segments with a
+length that depends on the curvature of edges and faces and is limited by <b>Min. Size</b>
+and <b>Max Size</b>. The length of a segment also depends on the lengths
+of adjacent segments (that can't differ more than twice) and on the
+distance to close geometrical entities (edges and faces) to avoid
+creation of narrow 2D elements.
+
+\image html adaptive1d.png
+
+- <b>Min size</b> parameter limits the minimal segment size.
+- <b>Max size</b> parameter defines the length of segments on straight edges.
+- \b Deflection parameter gives maximal distance of a segment from a curved edge.
+
+\image html adaptive1d_sample_mesh.png "Adaptive hypothesis and Netgen 2D algorithm - the size of mesh segments reflects the size of geometrical features"
+
+<b>See Also</b> a \ref tui_1d_adaptive "sample TUI Script" that uses Adaptive hypothesis.
+
<br>
\anchor arithmetic_1d_anchor
<h2>Arithmetic 1D hypothesis</h2>
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.
+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
\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.
+\ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
+
+<br>
+\anchor geometric_1d_anchor
+<h2>Geometric Progression hypothesis</h2>
+
+<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 with a given
+<b>Common Ratio</b>.
+
+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-geometric1d.png
+
+<b>See Also</b> a sample TUI Script of a
+\ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
<br>
\anchor deflection_1d_anchor
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.
+<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>.
-\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
+\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."
if the geometrical object is selected for meshing. In this case it is
possible to select the edges to be reversed either directly picking them in
the 3D viewer or selecting the edges or groups of edges in the
-Object browser.
+Object Browser.
\image html mesh_fixedpnt.png "Example of a submesh on the edge built using Fixed points 1D hypothesis"
