/*! \page a1d_meshing_hypo_page 1D Meshing Hypotheses Basic 1D hypothesis specifies: 1D hypotheses can be categorized by type of nodes distribution as follows:
\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.
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Arithmetic 1D hypothesis

Arithmetic 1D 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 1D hypothesis - the size of mesh elements gradually increases" See Also a sample TUI Script of a \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
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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 1D and Geometric Progression hypothesis" operation.
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Deflection 1D hypothesis

Deflection 1D 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 1D hypothesis - useful for meshing curvilinear edges" See Also a sample TUI Script of a \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
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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.
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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 "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 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 builded with Plot 2D Viewer (set option SALOME_USE_PLOT2DVIEWER to ON when building GUI module).
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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.
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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."
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Fixed points 1D hypothesis

Fixed points 1D 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 1D 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. */