3 \page a1d_meshing_hypo_page 1D Meshing Hypotheses
7 <li>\ref adaptive_1d_anchor "Adaptive"</li>
8 <li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
9 <li>\ref geometric_1d_anchor "Geometric Progression"</li>
10 <li>\ref average_length_anchor "Local Length"</li>
11 <li>\ref max_length_anchor "Max Size"</li>
12 <li>\ref deflection_1d_anchor "Deflection 1D"</li>
13 <li>\ref number_of_segments_anchor "Number of segments"</li>
14 <li>\ref start_and_end_length_anchor "Start and end length"</li>
15 <li>\ref automatic_length_anchor "Automatic Length"</li>
16 <li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
20 \anchor adaptive_1d_anchor
21 <h2>Adaptive hypothesis</h2>
23 <b>Adaptive</b> hypothesis allows to split edges into segments with a
24 length that depends on the curvature of edges and faces and is limited by <b>Min. Size</b>
25 and <b>Max Size</b>. The length of a segment also depends on the lengths
26 of adjacent segments (that can't differ more than twice) and on the
27 distance to close geometrical entities (edges and faces) to avoid
28 creation of narrow 2D elements.
30 \image html adaptive1d.png
32 - <b>Min size</b> parameter limits the minimal segment size.
33 - <b>Max size</b> parameter defines the length of segments on straight edges.
34 - \b Deflection parameter gives maximal distance of a segment from a curved edge.
36 \image html adaptive1d_sample_mesh.png "Adaptive hypothesis and Netgen 2D algorithm - the size of mesh segments reflects the size of geometrical features"
38 <b>See Also</b> a \ref tui_1d_adaptive "sample TUI Script" that uses Adaptive hypothesis.
41 \anchor arithmetic_1d_anchor
42 <h2>Arithmetic 1D hypothesis</h2>
44 <b>Arithmetic 1D</b> hypothesis allows to split edges into segments with a
45 length that changes in arithmetic progression (Lk = Lk-1 + d)
46 beginning from a given starting length and up to a given end length.
48 The splitting direction is defined by the orientation of the
49 underlying geometrical edge.
50 <b>Reverse Edges</b> list box allows specifying the edges, for which
51 the splitting should be made in the direction opposite to their
52 orientation. This list box is usable only if a geometry object is
53 selected for meshing. In this case it is possible to select edges to
54 be reversed either directly picking them in the 3D viewer or by
55 selecting the edges or groups of edges in the Object Browser. Use \b
56 Add button to add the selected edges to the list.
58 \image html a-arithmetic1d.png
60 \image html b-ithmetic1d.png "Arithmetic 1D hypothesis - the size of mesh elements gradually increases"
62 <b>See Also</b> a sample TUI Script of a
63 \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
66 \anchor geometric_1d_anchor
67 <h2>Geometric Progression hypothesis</h2>
69 <b>Geometric Progression</b> hypothesis allows splitting edges into
70 segments with a length that changes in geometric progression (Lk =
71 Lk-1 * d) starting from a given <b>Start Length</b> and with a given
74 The splitting direction is defined by the orientation of the
75 underlying geometrical edge.
76 <b>Reverse Edges</b> list box allows specifying the edges, for which
77 the splitting should be made in the direction opposite to their
78 orientation. This list box is usable only if a geometry object is
79 selected for meshing. In this case it is possible to select edges to
80 be reversed either directly picking them in the 3D viewer or by
81 selecting the edges or groups of edges in the Object Browser. Use \b
82 Add button to add the selected edges to the list.
84 \image html a-geometric1d.png
86 <b>See Also</b> a sample TUI Script of a
87 \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
90 \anchor deflection_1d_anchor
91 <h2>Deflection 1D hypothesis</h2>
93 <b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
94 composing your geometrical object. It uses only one parameter: the
96 \n A geometrical edge is divided into equal segments. The maximum
97 distance between a point on the edge within a segment and the line
98 connecting the ends of the segment should not exceed the specified
99 value of deflection . Then mesh nodes are constructed at end segment
100 locations and 1D mesh elements are constructed on segments.
102 \image html a-deflection1d.png
104 \image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"
106 <b>See Also</b> a sample TUI Script of a
107 \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
110 \anchor average_length_anchor
111 <h2>Local Length hypothesis</h2>
113 <b>Local Length</b> hypothesis can be applied for meshing of edges
114 composing your geometrical object. Definition of this hypothesis
115 consists of setting the \b length of segments, which will split these
116 edges, and the \b precision of rounding. The points on the edges
117 generated by these segments will represent nodes of your mesh.
118 Later these nodes will be used for meshing of the faces abutting to
121 The \b precision parameter is used to allow rounding a number of
122 segments, calculated from the edge length and average length of
123 segment, to the lower integer, if this value outstands from it in
124 bounds of the precision. Otherwise, the number of segments is rounded
125 to the higher integer. Use value 0.5 to provide rounding to the
126 nearest integer, 1.0 for the lower integer, 0.0 for the higher
127 integer. Default value is 1e-07.
129 \image html image41.gif
131 \image html a-averagelength.png
133 \image html b-erage_length.png "Local Length hypothesis - all 1D mesh elements are roughly equal"
135 <b>See Also</b> a sample TUI Script of a
136 \ref tui_average_length "Defining Local Length" hypothesis
139 <br>\anchor max_length_anchor
141 <b>Max Size</b> hypothesis allows splitting geometrical edges into
142 segments not longer than the given length. Definition of this hypothesis
143 consists of setting the maximal allowed \b length of segments.
144 <b>Use preestimated length</b> check box lets you specify \b length
145 automatically calculated basing on size of your geometrical object,
146 namely as diagonal of bounding box divided by ten. The divider can be
147 changed via "Ratio Bounding Box Diagonal / Max Size"
148 preference parameter.
149 <b>Use preestimated length</b> check box is enabled only if the
150 geometrical object has been selected before hypothesis definition.
152 \image html a-maxsize1d.png
155 \anchor number_of_segments_anchor
156 <h2>Number of segments hypothesis</h2>
158 <b>Number of segments</b> hypothesis can be applied for meshing of edges
159 composing your geometrical object. Definition of this hypothesis
160 consists of setting the number of segments, which will split these
161 edges. In other words your edges will be split into a definite number
162 of segments with approximately the same length. The points on the
163 edges generated by these segments will represent nodes of your
164 mesh. Later these nodes will be used for meshing of the faces abutting
167 The direction of the splitting is defined by the orientation of the
168 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
169 specify the edges for which the splitting should be made in the
170 direction opposing to their orientation. This list box is enabled only
171 if the geometry object is selected for the meshing. In this case the
172 user can select edges to be reversed either by directly picking them
173 in the 3D viewer or by selecting the edges or groups of edges in the
176 \image html image46.gif
178 You can set the type of distribution for this hypothesis in the
179 <b>Hypothesis Construction</b> dialog bog :
181 \image html a-nbsegments1.png
183 <br><b>Equidistant Distribution</b> - all segments will have the same
184 length, you define only the <b>Number of Segments</b>.
186 <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.
188 \image html a-nbsegments2.png
190 <br><b>Distribution with Table Density</b> - you input a number of
191 pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
192 formula, which will rule the change of length of segments and shows
193 the curve in the plot. You can select the <b>Conversion mode</b> from
194 \b Exponent and <b>Cut negative</b>.
196 \image html distributionwithtabledensity.png
198 <br><b>Distribution with Analytic Density</b> - you input the formula,
199 which will rule the change of length of segments and the module shows
200 the curve in the plot.
202 \image html distributionwithanalyticdensity.png
204 <b>See Also</b> a sample TUI Script of a
205 \ref tui_deflection_1d "Defining Number of Segments" hypothesis
209 \anchor start_and_end_length_anchor
210 <h2>Start and End Length hypothesis</h2>
212 <b>Start and End Length</b> hypothesis allows to divide a geometrical edge
213 into segments so that the first and the last segments have a specified
214 length. The length of medium segments changes with automatically chosen
215 geometric progression. Then mesh nodes are
216 constructed at segment ends location and 1D mesh elements are
219 The direction of the splitting is defined by the orientation of the
220 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
221 specify the edges for which the splitting should be made in the
222 direction opposing to their orientation. This list box is enabled only
223 if the geometry object is selected for the meshing. In this case the
224 user can select edges to be reversed either by directly picking them
225 in the 3D viewer or by selecting the edges or groups of edges in the
228 \image html a-startendlength.png
230 \image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
232 <b>See Also</b> a sample TUI Script of a
233 \ref tui_start_and_end_length "Defining Start and End Length"
234 hypothesis operation.
237 \anchor automatic_length_anchor
238 <h2>Automatic Length</h2>
240 This hypothesis is automatically applied when you select <b>Assign a
241 set of hypotheses</b> option in Create Mesh menu.
243 \image html automaticlength.png
245 The dialog box prompts you to define the quality of the future mesh by
246 only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
247 low number of elements) to 1 (extremely fine mesh, great number of
248 elements). Compare one and the same object (sphere) meshed with
249 minimum and maximum value of this parameter.
251 \image html image147.gif "Example of a very rough mesh. Automatic Length works for 0."
253 \image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."
256 \anchor fixed_points_1d_anchor
257 <h2>Fixed points 1D hypothesis</h2>
259 <b>Fixed points 1D</b> hypothesis allows splitting edges through a
260 set of points parameterized on the edge (from 1 to 0) and a number of segments for each
261 interval limited by the points.
263 \image html hypo_fixedpnt_dlg.png
265 It is possible to check in <b>Same Nb. Segments for all intervals</b>
266 option and to define one value for all intervals.
268 The splitting direction is defined by the orientation of the
269 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
270 specify the edges for which the splitting should be made in the
271 direction opposite to their orientation. This list box is enabled only
272 if the geometrical object is selected for meshing. In this case it is
273 possible to select the edges to be reversed either directly picking them in
274 the 3D viewer or selecting the edges or groups of edges in the
277 \image html mesh_fixedpnt.png "Example of a submesh on the edge built using Fixed points 1D hypothesis"
279 <b>See Also</b> a sample TUI Script of a
280 \ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
