3 \page a1d_meshing_hypo_page 1D Meshing Hypotheses
7 <li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
8 <li>\ref average_length_anchor "Average Length"</li>
9 <li>\ref deflection_1d_anchor "Deflection 1D"</li>
10 <li>\ref number_of_segments_anchor "Number of segments"</li>
11 <li>\ref start_and_end_length_anchor "Start and end length"</li>
12 <li>\ref automatic_length_anchor "Automatic Length"</li>
16 \anchor arithmetic_1d_anchor
17 <h2>Arithmetic 1D hypothesis</h2>
19 <b>Arithmetic 1D</b> hypothesis allows to split edges into segments with a
20 length that changes in arithmetic progression (Lk = Lk-1 + d)
21 beginning from a given starting length and up to a given end length.
23 \image html a-arithmetic1d.png
25 \image html b-ithmetic1d.png
27 <b>See Also</b> a sample TUI Script of a
28 \ref tui_1d_arithmetic "Defining Arithmetic 1D hypothesis" operation.
31 \anchor deflection_1d_anchor
32 <h2>Deflection 1D hypothesis</h2>
34 <b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
35 composing your geometrical object. It uses only one parameter: the
37 \n A geometrical edge is divided into equal segments. The maximum
38 distance between a point on the edge within a segment and the line
39 connecting the ends of the segment should not exceed the specified
40 value of deflection . Then mesh nodes are constructed at end segment
41 locations and 1D mesh elements are constructed on segments.
43 \image html a-deflection1d.png
45 \image html b-flection1d.png
47 <b>See Also</b> a sample TUI Script of a
48 \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
51 \anchor average_length_anchor
52 <h2>Average Length hypothesis</h2>
54 <b>Average Length</b> hypothesis can be applied for meshing of edges
55 composing your geometrical object. Definition of this hypothesis
56 consists of setting the \b length of segments, which will split these
57 edges, and the \b precision of rounding. The points on the edges
58 generated by these segments will represent nodes of your mesh.
59 Later these nodes will be used for meshing of the faces abutting to
62 The \b precision parameter is used to allow rounding a number of
63 segments, calculated from the edge length and average length of
64 segment, to the lower integer, if this value outstands from it in
65 bounds of the precision. Otherwise, the number of segments is rounded
66 to the higher integer. Use value 0.5 to provide rounding to the
67 nearest integer, 1.0 for the lower integer, 0.0 for the higher
68 integer. Default value is 1e-07.
70 \image html image41.gif
72 \image html a-averagelength.png
74 \image html b-erage_length.png
76 <b>See Also</b> a sample TUI Script of a
77 \ref tui_average_length "Defining Average Length" hypothesis
81 \anchor number_of_segments_anchor
82 <h2>Number of segments hypothesis</h2>
84 <b>Number of segments</b> hypothesis can be applied for meshing of edges
85 composing your geometrical object. Definition of this hypothesis
86 consists of setting the number of segments, which will split these
87 edges. In other words your edges will be split into a definite number
88 of segments with approximately the same length. The points on the
89 edges generated by these segments will represent nodes of your
90 mesh. Later these nodes will be used for meshing of the faces abutting
93 \image html image46.gif
95 You can set the type of distribution for this hypothesis in the
96 <b>Hypothesis Construction</b> dialog bog :
98 \image html a-nbsegments1.png
100 <br><b>Equidistant Distribution</b> - all segments will have the same
101 length, you define only the <b>Number of Segments</b>.
103 \image html b-mberofsegments.png
105 <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.
107 \image html a-nbsegments2.png
109 <br><b>Distribution with Table Density</b> - you input a number of
110 pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
111 formula, which will rule the change of length of segments and shows
112 the curve in the plot. You can select the <b>Conversion mode</b> from
113 \b Exponent and <b>Cut negative</b>.
115 \image html distributionwithtabledensity.png
117 <br><b>Distribution with Analytic Density</b> - you input the formula,
118 which will rule the change of length of segments and the module shows
119 the curve in the plot.
121 \image html distributionwithanalyticdensity.png
123 <b>See Also</b> a sample TUI Script of a
124 \ref tui_deflection_1d "Defining Number of Segments" hypothesis
128 \anchor start_and_end_length_anchor
129 <h2>Start and End Length hypothesis</h2>
131 <b>Start and End Length</b> hypothesis allows to divide a geometrical edge
132 into segments so that the first and the last segments have a specified
133 length. The length of each but the first segment differs from length
134 of the previous one by a constant factor. Then mesh nodes are
135 constructed at segment ends location and 1D mesh elements are
138 \image html a-startendlength.png
140 \image html b-art_end_length.png
142 <b>See Also</b> a sample TUI Script of a
143 \ref tui_start_and_end_length "Defining Start and End Length"
144 hypothesis operation.
147 \anchor automatic_length_anchor
148 <h2>Automatic Length</h2>
150 This hypothesis is automatically applied when you select <b>Assign a
151 set of hypotheses</b> option in Create Mesh menu.
153 \image html automaticlength.png
155 The dialog box prompts you to define the quality of the future mesh by
156 only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
157 low number of elements) to 1 (extremely fine mesh, great number of
158 elements). Compare one and the same object (sphere) meshed with
159 minimum and maximum value of this parameter.
161 \image html image147.gif
163 \image html image148.gif