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 <b>Common Ratio</b>.
73 The splitting direction is defined by the orientation of the
74 underlying geometrical edge.
75 <b>Reverse Edges</b> list box allows specifying the edges, for which
76 the splitting should be made in the direction opposite to their
77 orientation. This list box is usable only if a geometry object is
78 selected for meshing. In this case it is possible to select edges to
79 be reversed either directly picking them in the 3D viewer or by
80 selecting the edges or groups of edges in the Object Browser. Use \b
81 Add button to add the selected edges to the list.
83 \image html a-geometric1d.png
85 <b>See Also</b> a sample TUI Script of a
86 \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
89 \anchor deflection_1d_anchor
90 <h2>Deflection 1D hypothesis</h2>
92 <b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
93 composing your geometrical object. It uses only one parameter: the
95 \n A geometrical edge is divided into equal segments. The maximum
96 distance between a point on the edge within a segment and the line
97 connecting the ends of the segment should not exceed the specified
98 value of deflection . Then mesh nodes are constructed at end segment
99 locations and 1D mesh elements are constructed on segments.
101 \image html a-deflection1d.png
103 \image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"
105 <b>See Also</b> a sample TUI Script of a
106 \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
109 \anchor average_length_anchor
110 <h2>Local Length hypothesis</h2>
112 <b>Local Length</b> hypothesis can be applied for meshing of edges
113 composing your geometrical object. Definition of this hypothesis
114 consists of setting the \b length of segments, which will split these
115 edges, and the \b precision of rounding. The points on the edges
116 generated by these segments will represent nodes of your mesh.
117 Later these nodes will be used for meshing of the faces abutting to
120 The \b precision parameter is used to allow rounding a number of
121 segments, calculated from the edge length and average length of
122 segment, to the lower integer, if this value outstands from it in
123 bounds of the precision. Otherwise, the number of segments is rounded
124 to the higher integer. Use value 0.5 to provide rounding to the
125 nearest integer, 1.0 for the lower integer, 0.0 for the higher
126 integer. Default value is 1e-07.
128 \image html image41.gif
130 \image html a-averagelength.png
132 \image html b-erage_length.png "Local Length hypothesis - all 1D mesh elements are roughly equal"
134 <b>See Also</b> a sample TUI Script of a
135 \ref tui_average_length "Defining Local Length" hypothesis
138 <br>\anchor max_length_anchor
140 <b>Max Size</b> hypothesis allows splitting geometrical edges into
141 segments not longer than the given length. Definition of this hypothesis
142 consists of setting the maximal allowed \b length of segments.
143 <b>Use preestimated length</b> check box lets you specify \b length
144 automatically calculated basing on size of your geometrical object,
145 namely as diagonal of bounding box divided by ten. The divider can be
146 changed via "Ratio Bounding Box Diagonal / Max Size"
147 preference parameter.
148 <b>Use preestimated length</b> check box is enabled only if the
149 geometrical object has been selected before hypothesis definition.
151 \image html a-maxsize1d.png
154 \anchor number_of_segments_anchor
155 <h2>Number of segments hypothesis</h2>
157 <b>Number of segments</b> hypothesis can be applied for meshing of edges
158 composing your geometrical object. Definition of this hypothesis
159 consists of setting the number of segments, which will split these
160 edges. In other words your edges will be split into a definite number
161 of segments with approximately the same length. The points on the
162 edges generated by these segments will represent nodes of your
163 mesh. Later these nodes will be used for meshing of the faces abutting
166 The direction of the splitting is defined by the orientation of the
167 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
168 specify the edges for which the splitting should be made in the
169 direction opposing to their orientation. This list box is enabled only
170 if the geometry object is selected for the meshing. In this case the
171 user can select edges to be reversed either by directly picking them
172 in the 3D viewer or by selecting the edges or groups of edges in the
175 \image html image46.gif
177 You can set the type of distribution for this hypothesis in the
178 <b>Hypothesis Construction</b> dialog bog :
180 \image html a-nbsegments1.png
182 <br><b>Equidistant Distribution</b> - all segments will have the same
183 length, you define only the <b>Number of Segments</b>.
185 <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.
187 \image html a-nbsegments2.png
189 <br><b>Distribution with Table Density</b> - you input a number of
190 pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
191 formula, which will rule the change of length of segments and shows
192 the curve in the plot. You can select the <b>Conversion mode</b> from
193 \b Exponent and <b>Cut negative</b>.
195 \image html distributionwithtabledensity.png
197 <br><b>Distribution with Analytic Density</b> - you input the formula,
198 which will rule the change of length of segments and the module shows
199 the curve in the plot.
201 \image html distributionwithanalyticdensity.png
203 <b>See Also</b> a sample TUI Script of a
204 \ref tui_deflection_1d "Defining Number of Segments" hypothesis
208 \anchor start_and_end_length_anchor
209 <h2>Start and End Length hypothesis</h2>
211 <b>Start and End Length</b> hypothesis allows to divide a geometrical edge
212 into segments so that the first and the last segments have a specified
213 length. The length of medium segments changes with automatically chosen
214 geometric progression. Then mesh nodes are
215 constructed at segment ends location and 1D mesh elements are
218 The direction of the splitting is defined by the orientation of the
219 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
220 specify the edges for which the splitting should be made in the
221 direction opposing to their orientation. This list box is enabled only
222 if the geometry object is selected for the meshing. In this case the
223 user can select edges to be reversed either by directly picking them
224 in the 3D viewer or by selecting the edges or groups of edges in the
227 \image html a-startendlength.png
229 \image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
231 <b>See Also</b> a sample TUI Script of a
232 \ref tui_start_and_end_length "Defining Start and End Length"
233 hypothesis operation.
236 \anchor automatic_length_anchor
237 <h2>Automatic Length</h2>
239 This hypothesis is automatically applied when you select <b>Assign a
240 set of hypotheses</b> option in Create Mesh menu.
242 \image html automaticlength.png
244 The dialog box prompts you to define the quality of the future mesh by
245 only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
246 low number of elements) to 1 (extremely fine mesh, great number of
247 elements). Compare one and the same object (sphere) meshed with
248 minimum and maximum value of this parameter.
250 \image html image147.gif "Example of a very rough mesh. Automatic Length works for 0."
252 \image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."
255 \anchor fixed_points_1d_anchor
256 <h2>Fixed points 1D hypothesis</h2>
258 <b>Fixed points 1D</b> hypothesis allows splitting edges through a
259 set of points parameterized on the edge (from 1 to 0) and a number of segments for each
260 interval limited by the points.
262 \image html hypo_fixedpnt_dlg.png
264 It is possible to check in <b>Same Nb. Segments for all intervals</b>
265 option and to define one value for all intervals.
267 The splitting direction is defined by the orientation of the
268 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
269 specify the edges for which the splitting should be made in the
270 direction opposite to their orientation. This list box is enabled only
271 if the geometrical object is selected for meshing. In this case it is
272 possible to select the edges to be reversed either directly picking them in
273 the 3D viewer or selecting the edges or groups of edges in the
276 \image html mesh_fixedpnt.png "Example of a submesh on the edge built using Fixed points 1D hypothesis"
278 <b>See Also</b> a sample TUI Script of a
279 \ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
