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368 lines
15 KiB
Plaintext
368 lines
15 KiB
Plaintext
/*!
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\page a1d_meshing_hypo_page 1D Meshing Hypotheses
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Basic 1D hypothesis specifies:
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<ul>
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<li>how \ref a1d_algos_anchor "Wire Discretization" should divide the edge;</li>
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<li>how \ref a1d_algos_anchor "Composite Side Discretization" should divide the group of C1-continuous edges.</li>
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</ul>
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1D hypotheses can be categorized by type of nodes distribution as follows:
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<ul>
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<li>Uniform distribution:
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<ul>
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<li>\ref average_length_anchor "Local Length"</li>
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<li>\ref max_length_anchor "Max Size"</li>
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<li>\ref number_of_segments_anchor "Number of segments" with Equidistant distribution</li>
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<li>\ref automatic_length_anchor "Automatic Length"</li>
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</ul></li>
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<li>Constantly increasing or decreasing length of segments:
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<ul>
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<li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
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<li>\ref geometric_1d_anchor "Geometric Progression"</li>
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<li>\ref start_and_end_length_anchor "Start and end length"</li>
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<li>\ref number_of_segments_anchor "Number of segments" with Scale distribution</li>
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</ul></li>
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<li>Distribution depending on curvature:
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<ul>
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<li>\ref adaptive_1d_anchor "Adaptive"</li>
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<li>\ref deflection_1d_anchor "Deflection 1D"</li>
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</ul></li>
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<li>Arbitrary distribution:
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<ul>
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<li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
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<li>\ref number_of_segments_anchor "Number of segments" with
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\ref analyticdensity_anchor "Analytic Density Distribution" or Table Density Distribution</li>
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</ul></li>
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</ul>
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<br>
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\anchor adaptive_1d_anchor
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<h2>Adaptive hypothesis</h2>
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<b>Adaptive</b> hypothesis allows to split edges into segments with a
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length that depends on the curvature of edges and faces and is limited by <b>Min. Size</b>
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and <b>Max Size</b>. The length of a segment also depends on the lengths
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of adjacent segments (that can't differ more than twice) and on the
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distance to close geometrical entities (edges and faces) to avoid
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creation of narrow 2D elements.
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\image html adaptive1d.png
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- <b>Min size</b> parameter limits the minimal segment size.
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- <b>Max size</b> parameter defines the length of segments on straight edges.
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- \b Deflection parameter gives maximal distance of a segment from a curved edge.
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\image html adaptive1d_sample_mesh.png "Adaptive hypothesis and Netgen 2D algorithm - the size of mesh segments reflects the size of geometrical features"
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<b>See Also</b> a \ref tui_1d_adaptive "sample TUI Script" that uses Adaptive hypothesis.
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<br>
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\anchor arithmetic_1d_anchor
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<h2>Arithmetic 1D hypothesis</h2>
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<b>Arithmetic 1D</b> hypothesis allows to split edges into segments with a
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length that changes in arithmetic progression (Lk = Lk-1 + d)
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beginning from a given starting length and up to a given end length.
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The splitting direction is defined by the orientation of the
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underlying geometrical edge.
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<b>Reverse Edges</b> list box allows specifying the edges, for which
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the splitting should be made in the direction opposite to their
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orientation. This list box is usable only if a geometry object is
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selected for meshing. In this case it is possible to select edges to
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be reversed either directly picking them in the 3D viewer or by
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selecting the edges or groups of edges in the Object Browser. Use \b
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Add button to add the selected edges to the list.
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\ref reversed_edges_helper_anchor "Helper" group assists you in
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defining <b>Reversed Edges</b> parameter.
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\image html a-arithmetic1d.png
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\image html b-ithmetic1d.png "Arithmetic 1D hypothesis - the size of mesh elements gradually increases"
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<b>See Also</b> a sample TUI Script of a
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\ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
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<br>
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\anchor geometric_1d_anchor
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<h2>Geometric Progression hypothesis</h2>
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<b>Geometric Progression</b> hypothesis allows splitting edges into
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segments with a length that changes in geometric progression (Lk =
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Lk-1 * d) starting from a given <b>Start Length</b> and with a given
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<b>Common Ratio</b>.
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The splitting direction is defined by the orientation of the
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underlying geometrical edge.
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<b>Reverse Edges</b> list box allows specifying the edges, for which
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the splitting should be made in the direction opposite to their
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orientation. This list box is usable only if a geometry object is
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selected for meshing. In this case it is possible to select edges to
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be reversed either directly picking them in the 3D viewer or by
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selecting the edges or groups of edges in the Object Browser. Use \b
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Add button to add the selected edges to the list.
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\ref reversed_edges_helper_anchor "Helper" group assists you in
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defining <b>Reversed Edges</b> parameter.
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\image html a-geometric1d.png
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<b>See Also</b> a sample TUI Script of a
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\ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
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<br>
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\anchor deflection_1d_anchor
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<h2>Deflection 1D hypothesis</h2>
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<b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
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composing your geometrical object. It defines only one parameter: the
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value of deflection (or chord error).
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A geometrical edge is divided into segments of length depending on
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edge curvature. The more curved the edge, the shorter the
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segment. Nodes on the edge are placed so that the maximum distance
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between the edge and a segment approximating a part of edge between
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two nodes should not exceed the value of deflection.
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\image html a-deflection1d.png
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\image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"
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<b>See Also</b> a sample TUI Script of a
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\ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
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<br>
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\anchor average_length_anchor
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<h2>Local Length hypothesis</h2>
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<b>Local Length</b> hypothesis can be applied for meshing of edges
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composing your geometrical object. Definition of this hypothesis
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consists of setting the \b length of segments, which will approximate these
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edges, and the \b precision of rounding.
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The \b precision parameter is used to round a <em>number of segments</em>,
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calculated by dividing the <em>edge length</em> by the specified \b length of
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segment, to the higher integer if the \a remainder exceeds the \b precision
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and to the lower integer otherwise. <br>
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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.
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For example: if <em>edge length</em> is 10.0 and the segment \b length
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is 3.0 then their division gives 10./3. = 3.33(3) and the \a remainder is 0.33(3).
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If \b precision is less than 0.33(3) then the edge is divided into 3 segments.
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If \b precision is more than 0.33(3) then the edge is divided into 4 segments.
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\image html image41.gif
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\image html a-averagelength.png
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\image html b-erage_length.png "Local Length hypothesis - all 1D mesh segments are equal"
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<b>See Also</b> a sample TUI Script of a
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\ref tui_average_length "Defining Local Length" hypothesis
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operation.
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<br>\anchor max_length_anchor
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<h2>Max Size</h2>
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<b>Max Size</b> hypothesis allows splitting geometrical edges into
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segments not longer than the given length. Definition of this hypothesis
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consists of setting the maximal allowed \b length of segments.
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<b>Use preestimated length</b> check box lets you use \b length
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automatically calculated basing on size of your geometrical object,
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namely as diagonal of bounding box divided by ten. The divider can be
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changed via "Ratio Bounding Box Diagonal / Max Size"
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preference parameter.
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<b>Use preestimated length</b> check box is enabled only if the
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geometrical object has been selected before hypothesis definition.
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\image html a-maxsize1d.png
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<br>
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\anchor number_of_segments_anchor
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<h2>Number of segments hypothesis</h2>
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<b>Number of segments</b> hypothesis can be applied for approximating
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edges by a definite number of mesh segments with length depending on
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the selected type of distribution of nodes.
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The direction of the splitting is defined by the orientation of the
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underlying geometrical edge. <b>Reverse Edges</b> list box allows to
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specify the edges for which the splitting should be made in the
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direction opposing to their orientation. This list box is enabled only
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if the geometry object is selected for the meshing. In this case it is
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possible to select edges to be reversed either by directly picking them
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in the 3D viewer or by selecting the edges or groups of edges in the
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Object Browser.
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\ref reversed_edges_helper_anchor "Helper" group assists you in
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defining <b>Reversed Edges</b> parameter.
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You can set the type of node distribution for this hypothesis in the
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<b>Hypothesis Construction</b> dialog bog :
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\image html a-nbsegments1.png
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<br><b>Equidistant Distribution</b> - all segments will have the same
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length, you define only the <b>Number of Segments</b>.
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<br><b>Scale Distribution</b> - length of segments gradually changes
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depending on the <b>Scale Factor</b>, which is a ratio of the first
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segment length to the last segment length.<br>
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Length of segments changes in geometric progression with the common
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ratio (A) depending on the <b>Scale Factor</b> (S) and <b>Number of
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Segments</b> (N) as follows: <code> A = S**(1/(N-1))</code>. For an
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edge of length L, length of the first segment is
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<code>L * (1 - A)/(1 - A**N)</code>.
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\image html a-nbsegments2.png
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<br><b>Distribution with Analytic Density</b> - you input the formula,
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which will rule the change of length of segments and the module shows
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in the plot the density function curve in red and the node
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distribution as blue crosses.
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\image html distributionwithanalyticdensity.png
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<br>
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\anchor analyticdensity_anchor
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The node distribution is computed so that to have the density function
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integral on the range between two nodes equal for all segments.
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\image html analyticdensity.png
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<br><b>Distribution with Table Density</b> - you input a number of
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pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
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formula, which will rule the change of length of segments and shows
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in the plot the density function curve in red and the node
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distribution as blue crosses. The node distribution is computed in the
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same way as for
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\ref analyticdensity_anchor "Distribution with Analytic Density". You
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can select the <b>Conversion mode</b> from \b Exponent and <b>Cut
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negative</b>.
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\image html distributionwithtabledensity.png
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<b>See Also</b> a sample TUI Script of a
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\ref tui_deflection_1d "Defining Number of Segments" hypothesis
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operation.
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\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).
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<br>
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\anchor start_and_end_length_anchor
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<h2>Start and End Length hypothesis</h2>
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<b>Start and End Length</b> hypothesis allows to divide a geometrical edge
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into segments so that the first and the last segments have a specified
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length. The length of medium segments changes with automatically chosen
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geometric progression.
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The direction of the splitting is defined by the orientation of the
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underlying geometrical edge. <b>Reverse Edges</b> list box allows to
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specify the edges, for which the splitting should be made in the
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direction opposing to their orientation. This list box is enabled only
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if the geometry object is selected for the meshing. In this case it is
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possible to select edges to be reversed either by directly picking them
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in the 3D viewer or by selecting the edges or groups of edges in the
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Object Browser.
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\ref reversed_edges_helper_anchor "Helper" group assists you in
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defining <b>Reversed Edges</b> parameter.
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\image html a-startendlength.png
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\image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
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<b>See Also</b> a sample TUI Script of a
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\ref tui_start_and_end_length "Defining Start and End Length"
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hypothesis operation.
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<br>
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\anchor automatic_length_anchor
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<h2>Automatic Length</h2>
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The dialog box prompts you to define the quality of the future mesh by
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only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
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low number of segments) to 1 (extremely fine mesh, great number of
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segments).
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\image html automaticlength.png
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Compare one and the same object (sphere) meshed with
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minimum and maximum value of this parameter.
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\image html image147.gif "Example of a rough mesh at Automatic Length Fineness of 0."
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\image html image148.gif "Example of a fine mesh at Automatic Length Fineness of 1."
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<br>
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\anchor fixed_points_1d_anchor
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<h2>Fixed points 1D hypothesis</h2>
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<b>Fixed points 1D</b> hypothesis allows splitting edges through a
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set of points parametrized on the edge (from 1 to 0) and a number of
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segments for each interval limited by the points.
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\image html hypo_fixedpnt_dlg.png
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It is possible to check in <b>Same Nb. Segments for all intervals</b>
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option and to define one value for all intervals.
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The splitting direction is defined by the orientation of the
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underlying geometrical edge. <b>Reverse Edges</b> list box allows to
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specify the edges for which the splitting should be made in the
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direction opposite to their orientation. This list box is enabled only
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if the geometrical object is selected for meshing. In this case it is
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possible to select the edges to be reversed either directly picking them in
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the 3D viewer or selecting the edges or groups of edges in the
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Object Browser.
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\ref reversed_edges_helper_anchor "Helper" group assists in
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defining <b>Reversed Edges</b> parameter.
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\image html mesh_fixedpnt.png "Example of a sub-mesh on the edge built using Fixed points 1D hypothesis"
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<b>See Also</b> a sample TUI Script of a
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\ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
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\anchor reversed_edges_helper_anchor
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<h2>Reversed Edges Helper</h2>
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\image html rev_edges_helper_dlg.png
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\b Helper group assists in defining <b>Reversed Edges</b>
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parameter of the hypotheses depending on edge direction.
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<b>Show whole geometry</b> check-box allows seeing the whole
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geometrical model in the 3D Viewer, which can help to understand the
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location of a set of edges within the model.
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<b>Propagation chains</b> group allows defining <b>Reversed Edges</b>
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for splitting opposite edges of quadrilateral faces in a logically
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uniform direction. When this group is activated, the list is filled
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with propagation chains found within the shape on which a hypothesis
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is assigned. When a chain is selected in the list its edges are shown
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in the Viewer with arrows, which enables choosing a common direction
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for all chain edges. \b Reverse button inverts the common direction of
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chain edges. \b Add button is active if some edges of a chain have a
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different direction, so you can click \b Add button to add them
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to <b>Reversed Edges</b> list.
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\image html propagation_chain.png "The whole geometry and a propagation chain"
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\note Alternatively, uniform direction of edges of one propagation
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chain can be achieved by
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\ref constructing_submeshes_page "definition of a sub-mesh" on one
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edge of the chain and assigning a
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\ref propagation_anchor "Propagation" additional hypothesis.
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Orientation of this edge (and hence of all the rest edges of the chain) can be
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controlled by using <b>Reversed Edges</b> field.
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*/
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