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-/*!
-
-\page a1d_meshing_hypo_page 1D Meshing Hypotheses
-
-Basic 1D hypothesis specifies:
-
-- how \ref a1d_algos_anchor "Wire Discretization" should divide the edge;
-- how \ref a1d_algos_anchor "Composite Side Discretization" should divide the group of C1-continuous edges.
-
-
-1D hypotheses can be categorized by type of nodes distribution as follows:
-
-- Uniform distribution:
-
- - \ref average_length_anchor "Local Length"
- - \ref max_length_anchor "Max Size"
- - \ref number_of_segments_anchor "Number of Segments" with Equidistant distribution
- - \ref automatic_length_anchor "Automatic Length"
-
-- Constantly increasing or decreasing length of segments:
-
- - \ref arithmetic_1d_anchor "Arithmetic Progression"
- - \ref geometric_1d_anchor "Geometric Progression"
- - \ref start_and_end_length_anchor "Start and end length"
- - \ref number_of_segments_anchor "Number of Segments" with Scale distribution
-
-- Distribution depending on curvature:
-
- - \ref adaptive_1d_anchor "Adaptive"
- - \ref deflection_1d_anchor "Deflection"
-
-- Arbitrary distribution:
-
- - \ref fixed_points_1d_anchor "Fixed Points"
- - \ref number_of_segments_anchor "Number of Segments" with
- \ref analyticdensity_anchor "Analytic Density Distribution" or Table Density Distribution
-
-
-
-
-\anchor adaptive_1d_anchor
-Adaptive hypothesis
-
-Adaptive hypothesis allows to split edges into segments with a
-length that depends on the curvature of edges and faces and is limited by Min. Size
-and Max Size. 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
-
-- Min size parameter limits the minimal segment size.
-- Max size 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"
-
-See Also a \ref tui_1d_adaptive "sample TUI Script" that uses Adaptive hypothesis.
-
-
-\anchor arithmetic_1d_anchor
-Arithmetic Progression hypothesis
-
-Arithmetic Progression 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 splitting direction is defined by the orientation of the
-underlying geometrical edge.
-Reverse Edges 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.
-
-\ref reversed_edges_helper_anchor "Helper" group assists you in
-defining Reversed Edges parameter.
-
-
-\image html a-arithmetic1d.png
-
-\image html b-ithmetic1d.png "Arithmetic Progression hypothesis - the size of mesh elements gradually increases"
-
-See Also a sample TUI Script of a
-\ref tui_1d_arithmetic "Defining Arithmetic Progression and Geometric Progression hypothesis" operation.
-
-
-\anchor geometric_1d_anchor
-Geometric Progression hypothesis
-
-Geometric Progression hypothesis allows splitting edges into
-segments with a length that changes in geometric progression (Lk =
-Lk-1 * d) starting from a given Start Length and with a given
-Common Ratio.
-
-The splitting direction is defined by the orientation of the
-underlying geometrical edge.
-Reverse Edges 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.
-
-\ref reversed_edges_helper_anchor "Helper" group assists you in
-defining Reversed Edges parameter.
-
-\image html a-geometric1d.png
-
-See Also a sample TUI Script of a
-\ref tui_1d_arithmetic "Defining Arithmetic Progression and Geometric Progression hypothesis" operation.
-
-
-\anchor deflection_1d_anchor
-Deflection hypothesis
-
-Deflection hypothesis can be applied for meshing curvilinear edges
-composing your geometrical object. It defines only one parameter: the
-value of deflection (or chord error).
-
-A geometrical edge is divided into segments of length depending on
-edge curvature. The more curved the edge, the shorter the
-segment. Nodes on the edge are placed so that the maximum distance
-between the edge and a segment approximating a part of edge between
-two nodes should not exceed the value of deflection.
-
-\image html a-deflection1d.png
-
-\image html b-flection1d.png "Deflection hypothesis - useful for meshing curvilinear edges"
-
-See Also a sample TUI Script of a
-\ref tui_deflection_1d "Defining Deflection hypothesis" operation.
-
-
-\anchor average_length_anchor
-Local Length hypothesis
-
-Local Length 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 approximate these
-edges, and the \b precision of rounding.
-
-The \b precision parameter is used to round a number of segments,
-calculated by dividing the edge length by the specified \b length of
-segment, to the higher integer if the \a remainder exceeds the \b precision
-and to the lower integer otherwise.
-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.
-
-For example: if edge length is 10.0 and the segment \b length
-is 3.0 then their division gives 10./3. = 3.33(3) and the \a remainder is 0.33(3).
-If \b precision is less than 0.33(3) then the edge is divided into 3 segments.
-If \b precision is more than 0.33(3) then the edge is divided into 4 segments.
-
-
-\image html image41.gif
-
-\image html a-averagelength.png
-
-\image html b-erage_length.png "Local Length hypothesis - all 1D mesh segments are equal"
-
-See Also a sample TUI Script of a
-\ref tui_average_length "Defining Local Length" hypothesis
-operation.
-
-
\anchor max_length_anchor
-Max Size
-Max Size 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.
-Use preestimated length check box lets you use \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 \ref diagonal_size_ratio_pref "Ratio Bounding Box Diagonal / Max Size"
-preference parameter.
-Use preestimated length check box is enabled only if the
-geometrical object has been selected before hypothesis definition.
-
-\image html a-maxsize1d.png
-
-
-\anchor number_of_segments_anchor
-Number of Segments hypothesis
-
-Number of Segments hypothesis can be applied for approximating
-edges by a definite number of mesh segments with length depending on
-the selected type of distribution of nodes. The default number of
-segments can be set via
-\ref nb_segments_pref "Automatic Parameters / Default Number of Segments"
-preference parameter.
-
-The direction of the splitting is defined by the orientation of the
-underlying geometrical edge. Reverse Edges 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.
-
-\ref reversed_edges_helper_anchor "Helper" group assists you in
-defining Reversed Edges parameter.
-
-You can set the type of node distribution for this hypothesis in the
-Hypothesis Construction dialog bog :
-
-\image html a-nbsegments1.png
-
-
Equidistant Distribution - all segments will have the same
-length, you define only the Number of Segments.
-
-
Scale Distribution - length of segments gradually changes
-depending on the Scale Factor, which is a ratio of the first
-segment length to the last segment length.
-Length of segments changes in geometric progression with the common
-ratio (A) depending on the Scale Factor (S) and Number of
-Segments (N) as follows: A = S**(1/(N-1))
. For an
-edge of length L, length of the first segment is
-L * (1 - A)/(1 - A**N)
.
-
-
-\image html a-nbsegments2.png
-
-
Distribution with Analytic Density - you input the formula,
-which will rule the change of length of segments and the module shows
-in the plot the density function curve in red and the node
-distribution as blue crosses.
-
-\image html distributionwithanalyticdensity.png
-
-
-\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
-
-
Distribution with Table Density - you input a number of
-pairs t - F(t), 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 Conversion mode from \b Exponent and Cut
-negative.
-
-\image html distributionwithtabledensity.png
-
-See Also a sample TUI Script of a
-\ref tui_deflection_1d "Defining Number of Segments" hypothesis
-operation.
-
-\note The plot functionality is available only if GUI module is built with Plot 2D Viewer (option SALOME_USE_PLOT2DVIEWER is ON when building GUI module).
-
-
-\anchor start_and_end_length_anchor
-Start and End Length hypothesis
-
-Start and End Length hypothesis allows to divide a geometrical edge
-into segments so that the first and the last segments have a specified
-length. The length of medium segments changes with automatically chosen
-geometric progression.
-
-The direction of the splitting is defined by the orientation of the
-underlying geometrical edge. Reverse Edges 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.
-
-\ref reversed_edges_helper_anchor "Helper" group assists you in
-defining Reversed Edges parameter.
-
-
-\image html a-startendlength.png
-
-\image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
-
-See Also a sample TUI Script of a
-\ref tui_start_and_end_length "Defining Start and End Length"
-hypothesis operation.
-
-
-\anchor automatic_length_anchor
-Automatic Length
-
-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 segments) to 1 (extremely fine mesh, great number of
-segments).
-
-\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 rough mesh at Automatic Length Fineness of 0."
-
-\image html image148.gif "Example of a fine mesh at Automatic Length Fineness of 1."
-
-
-\anchor fixed_points_1d_anchor
-Fixed Points hypothesis
-
-Fixed Points hypothesis allows splitting edges through a
-set of points parametrized on the edge (from 1 to 0) and a number of
-segments for each interval limited by the points.
-
-\image html hypo_fixedpnt_dlg.png
-
-It is possible to check in Same Nb. Segments for all intervals
-option and to define one value for all intervals.
-
-The splitting direction is defined by the orientation of the
-underlying geometrical edge. Reverse Edges list box allows to
-specify the edges for which the splitting should be made in the
-direction opposite to their orientation. This list box is enabled only
-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.
-
-\ref reversed_edges_helper_anchor "Helper" group assists in
-defining Reversed Edges parameter.
-
-
-\image html mesh_fixedpnt.png "Example of a sub-mesh on the edge built using Fixed Points hypothesis"
-
-See Also a sample TUI Script of a
-\ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
-
-\anchor reversed_edges_helper_anchor
-Reversed Edges Helper
-
-\image html rev_edges_helper_dlg.png
-
-\b Helper group assists in defining Reversed Edges
-parameter of the hypotheses depending on edge direction.
-
-Show whole geometry check-box allows seeing the whole
-geometrical model in the 3D Viewer, which can help to understand the
-location of a set of edges within the model.
-
-Propagation chains group allows defining Reversed Edges
-for splitting opposite edges of quadrilateral faces in a logically
-uniform direction. When this group is activated, the list is filled
-with propagation chains found within the shape on which a hypothesis
-is assigned. When a chain is selected in the list its edges are shown
-in the Viewer with arrows, which enables choosing a common direction
-for all chain edges. \b Reverse button inverts the common direction of
-chain edges. \b Add button is active if some edges of a chain have a
-different direction, so you can click \b Add button to add them
-to Reversed Edges list.
-
-\image html propagation_chain.png "The whole geometry and a propagation chain"
-
-\note Alternatively, uniform direction of edges of one propagation
-chain can be achieved by
-\ref constructing_submeshes_page "definition of a sub-mesh" on one
-edge of the chain and assigning a
-\ref propagation_anchor "Propagation" additional hypothesis.
-Orientation of this edge (and hence of all the rest edges of the chain) can be
-controlled by using Reversed Edges field.
-
-*/