/*! \page a1d_meshing_hypo_page 1D Meshing Hypotheses

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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. \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. \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 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" 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 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 "Local Length hypothesis - all 1D mesh elements are roughly 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 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. Use preestimated length check box is enabled only if the geometrical object has been selected before hypothesis definition. \image html a-maxsize1d.png
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Number of segments hypothesis

Number of segments 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. "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. \image html image46.gif You can set the type of 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.
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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. 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. "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. \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 elements) to 1 (extremely fine mesh, great number of 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." \image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."
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Fixed points 1D hypothesis

Fixed points 1D hypothesis allows splitting edges through a set of points parameterized 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. \image html mesh_fixedpnt.png "Example of a submesh 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. */