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 average_length_anchor "Local Length"</li>
10 <li>\ref max_length_anchor "Max Size"</li>
11 <li>\ref deflection_1d_anchor "Deflection 1D"</li>
12 <li>\ref number_of_segments_anchor "Number of segments"</li>
13 <li>\ref start_and_end_length_anchor "Start and end length"</li>
14 <li>\ref automatic_length_anchor "Automatic Length"</li>
15 <li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
19 \anchor adaptive_1d_anchor
20 <h2>Adaptive hypothesis</h2>
22 <b>Adaptive</b> hypothesis allows to split edges into segments with a
23 length that depends on curvature of edges and faces and is limited
24 from up and down. In addition length of a segment depends on lengths
25 of adjacent segments (that can't differ more than twice) and on
26 distance to close geometrical entities (edges and faces) to avoid
27 creation of narrow 2D elements.
29 \image html adaptive1d.png
31 <b>Min size</b> parameter limits minimal segment size. <b>Max size</b>
32 parameter defines length of segments on stright edges. \b Deflection
33 parameter gives maximal distance of a segment from a curved edge.
35 \image html adaptive1d_sample_mesh.png "A geometry and a mesh generated on this geometry using Adaptive hypothesis and Netgen 2D algorithm - the size of mesh segments reflects size of geometrical features"
37 <b>See Also</b> a \ref tui_1d_adaptive "sample TUI Script" that
38 creates the mesh of the above image.
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 direction of the splitting is defined by the orientation of the underlying geometrical edge.
49 <b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made
50 in the direction opposing to their orientation. This list box is enabled only if the geometry object
51 is selected for the meshing. In this case the user can select edges to be reversed either directly
52 picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
54 \image html a-arithmetic1d.png
56 \image html b-ithmetic1d.png "Arithmetic 1D hypothesis - the size of mesh elements gradually increases"
58 <b>See Also</b> a sample TUI Script of a
59 \ref tui_1d_arithmetic "Defining Arithmetic 1D hypothesis" operation.
62 \anchor deflection_1d_anchor
63 <h2>Deflection 1D hypothesis</h2>
65 <b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
66 composing your geometrical object. It uses only one parameter: the
68 \n A geometrical edge is divided into equal segments. The maximum
69 distance between a point on the edge within a segment and the line
70 connecting the ends of the segment should not exceed the specified
71 value of deflection . Then mesh nodes are constructed at end segment
72 locations and 1D mesh elements are constructed on segments.
74 \image html a-deflection1d.png
76 \image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"
78 <b>See Also</b> a sample TUI Script of a
79 \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
82 \anchor average_length_anchor
83 <h2>Local Length hypothesis</h2>
85 <b>Local Length</b> hypothesis can be applied for meshing of edges
86 composing your geometrical object. Definition of this hypothesis
87 consists of setting the \b length of segments, which will split these
88 edges, and the \b precision of rounding. The points on the edges
89 generated by these segments will represent nodes of your mesh.
90 Later these nodes will be used for meshing of the faces abutting to
93 The \b precision parameter is used to allow rounding a number of
94 segments, calculated from the edge length and average length of
95 segment, to the lower integer, if this value outstands from it in
96 bounds of the precision. Otherwise, the number of segments is rounded
97 to the higher integer. Use value 0.5 to provide rounding to the
98 nearest integer, 1.0 for the lower integer, 0.0 for the higher
99 integer. Default value is 1e-07.
101 \image html image41.gif
103 \image html a-averagelength.png
105 \image html b-erage_length.png "Local Length hypothesis - all 1D mesh elements are roughly equal"
107 <b>See Also</b> a sample TUI Script of a
108 \ref tui_average_length "Defining Local Length" hypothesis
111 <br>\anchor max_length_anchor
113 <b>Max Size</b> hypothesis allows splitting geometrical edges into
114 segments not longer than the given length. Definition of this hypothesis
115 consists of setting the maximal allowed \b length of segments.
116 <b>Use preestimated length</b> check box lets you specify \b length
117 automatically calculated basing on size of your geometrical object,
118 namely as diagonal of bounding box divided by ten. The divider can be
119 changed via "Ratio Bounding Box Diagonal / Max Size"
120 preference parameter.
121 <b>Use preestimated length</b> check box is enabled only if the
122 geometrical object has been selected before hypothesis definition.
124 \image html a-maxsize1d.png
127 \anchor number_of_segments_anchor
128 <h2>Number of segments hypothesis</h2>
130 <b>Number of segments</b> hypothesis can be applied for meshing of edges
131 composing your geometrical object. Definition of this hypothesis
132 consists of setting the number of segments, which will split these
133 edges. In other words your edges will be split into a definite number
134 of segments with approximately the same length. The points on the
135 edges generated by these segments will represent nodes of your
136 mesh. Later these nodes will be used for meshing of the faces abutting
139 The direction of the splitting is defined by the orientation of the underlying geometrical edge.
140 <b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made
141 in the direction opposing to their orientation. This list box is enabled only if the geometry object
142 is selected for the meshing. In this case the user can select edges to be reversed either directly
143 picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
145 \image html image46.gif
147 You can set the type of distribution for this hypothesis in the
148 <b>Hypothesis Construction</b> dialog bog :
150 \image html a-nbsegments1.png
152 <br><b>Equidistant Distribution</b> - all segments will have the same
153 length, you define only the <b>Number of Segments</b>.
155 <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.
157 \image html a-nbsegments2.png
159 <br><b>Distribution with Table Density</b> - you input a number of
160 pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
161 formula, which will rule the change of length of segments and shows
162 the curve in the plot. You can select the <b>Conversion mode</b> from
163 \b Exponent and <b>Cut negative</b>.
165 \image html distributionwithtabledensity.png
167 <br><b>Distribution with Analytic Density</b> - you input the formula,
168 which will rule the change of length of segments and the module shows
169 the curve in the plot.
171 \image html distributionwithanalyticdensity.png
173 <b>See Also</b> a sample TUI Script of a
174 \ref tui_deflection_1d "Defining Number of Segments" hypothesis
178 \anchor start_and_end_length_anchor
179 <h2>Start and End Length hypothesis</h2>
181 <b>Start and End Length</b> hypothesis allows to divide a geometrical edge
182 into segments so that the first and the last segments have a specified
183 length. The length of medium segments changes with automatically chosen
184 geometric progression. Then mesh nodes are
185 constructed at segment ends location and 1D mesh elements are
188 The direction of the splitting is defined by the orientation of the underlying geometrical edge.
189 <b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made
190 in the direction opposing to their orientation. This list box is enabled only if the geometry object
191 is selected for the meshing. In this case the user can select edges to be reversed either directly
192 picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
194 \image html a-startendlength.png
196 \image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
198 <b>See Also</b> a sample TUI Script of a
199 \ref tui_start_and_end_length "Defining Start and End Length"
200 hypothesis operation.
203 \anchor automatic_length_anchor
204 <h2>Automatic Length</h2>
206 This hypothesis is automatically applied when you select <b>Assign a
207 set of hypotheses</b> option in Create Mesh menu.
209 \image html automaticlength.png
211 The dialog box prompts you to define the quality of the future mesh by
212 only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
213 low number of elements) to 1 (extremely fine mesh, great number of
214 elements). Compare one and the same object (sphere) meshed with
215 minimum and maximum value of this parameter.
217 \image html image147.gif "Example of a very rough mesh. Automatic Length works for 0."
219 \image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."
222 \anchor fixed_points_1d_anchor
223 <h2>Fixed points 1D hypothesis</h2>
225 <b>Fixed points 1D</b> hypothesis allows splitting edges through a
226 set of points parameterized on the edge (from 1 to 0) and a number of segments for each
227 interval limited by the points.
229 \image html hypo_fixedpnt_dlg.png
231 It is possible to check in <b>Same Nb. Segments for all intervals</b>
232 option and to define one value for all intervals.
234 The splitting direction is defined by the orientation of the
235 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
236 specify the edges for which the splitting should be made in the
237 direction opposite to their orientation. This list box is enabled only
238 if the geometrical object is selected for meshing. In this case it is
239 possible to select the edges to be reversed either directly picking them in
240 the 3D viewer or selecting the edges or groups of edges in the
243 \image html mesh_fixedpnt.png "Example of a submesh on the edge built using Fixed points 1D hypothesis"
245 <b>See Also</b> a sample TUI Script of a
246 \ref tui_fixed_points "Defining Fixed Points" hypothesis operation.