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 creates 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 by 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 and Geometric Progression hypothesis" operation.
62 \anchor geometric_1d_anchor
63 <h2>Geometric Progression hypothesis</h2>
65 <b>Geometric Progression</b> hypothesis allows splitting edges into
66 segments with a length that changes in geometric progression (Lk =
67 Lk-1 * d) starting from a given <b>Start Length</b> and <b>Common Ratio</b>.
69 The splitting direction is defined by the orientation of the
70 underlying geometrical edge.
71 <b>Reverse Edges</b> list box allows specifying the edges, for which the splitting should be made in the
72 direction opposite to their orientation. This list box is filled after a geometry object is selected for meshing. In this case it is possible to select edges to be reversed either directly picking them in
73 the 3D viewer or by selecting the edges or groups of edges in the
76 \image html a-geometric1d.png
78 <b>See Also</b> a sample TUI Script of a
79 \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
82 \anchor deflection_1d_anchor
83 <h2>Deflection 1D hypothesis</h2>
85 <b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
86 composing your geometrical object. It uses only one parameter: the
88 \n A geometrical edge is divided into equal segments. The maximum
89 distance between a point on the edge within a segment and the line
90 connecting the ends of the segment should not exceed the specified
91 value of deflection . Then mesh nodes are constructed at end segment
92 locations and 1D mesh elements are constructed on segments.
94 \image html a-deflection1d.png
96 \image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"
98 <b>See Also</b> a sample TUI Script of a
99 \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
102 \anchor average_length_anchor
103 <h2>Local Length hypothesis</h2>
105 <b>Local Length</b> hypothesis can be applied for meshing of edges
106 composing your geometrical object. Definition of this hypothesis
107 consists of setting the \b length of segments, which will split these
108 edges, and the \b precision of rounding. The points on the edges
109 generated by these segments will represent nodes of your mesh.
110 Later these nodes will be used for meshing of the faces abutting to
113 The \b precision parameter is used to allow rounding a number of
114 segments, calculated from the edge length and average length of
115 segment, to the lower integer, if this value outstands from it in
116 bounds of the precision. Otherwise, the number of segments is rounded
117 to the higher integer. Use value 0.5 to provide rounding to the
118 nearest integer, 1.0 for the lower integer, 0.0 for the higher
119 integer. Default value is 1e-07.
121 \image html image41.gif
123 \image html a-averagelength.png
125 \image html b-erage_length.png "Local Length hypothesis - all 1D mesh elements are roughly equal"
127 <b>See Also</b> a sample TUI Script of a
128 \ref tui_average_length "Defining Local Length" hypothesis
131 <br>\anchor max_length_anchor
133 <b>Max Size</b> hypothesis allows splitting geometrical edges into
134 segments not longer than the given length. Definition of this hypothesis
135 consists of setting the maximal allowed \b length of segments.
136 <b>Use preestimated length</b> check box lets you specify \b length
137 automatically calculated basing on size of your geometrical object,
138 namely as diagonal of bounding box divided by ten. The divider can be
139 changed via "Ratio Bounding Box Diagonal / Max Size"
140 preference parameter.
141 <b>Use preestimated length</b> check box is enabled only if the
142 geometrical object has been selected before hypothesis definition.
144 \image html a-maxsize1d.png
147 \anchor number_of_segments_anchor
148 <h2>Number of segments hypothesis</h2>
150 <b>Number of segments</b> hypothesis can be applied for meshing of edges
151 composing your geometrical object. Definition of this hypothesis
152 consists of setting the number of segments, which will split these
153 edges. In other words your edges will be split into a definite number
154 of segments with approximately the same length. The points on the
155 edges generated by these segments will represent nodes of your
156 mesh. Later these nodes will be used for meshing of the faces abutting
159 The direction of the splitting is defined by the orientation of the underlying geometrical edge.
160 <b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made
161 in the direction opposing to their orientation. This list box is enabled only if the geometry object
162 is selected for the meshing. In this case the user can select edges to be reversed either directly
163 picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
165 \image html image46.gif
167 You can set the type of distribution for this hypothesis in the
168 <b>Hypothesis Construction</b> dialog bog :
170 \image html a-nbsegments1.png
172 <br><b>Equidistant Distribution</b> - all segments will have the same
173 length, you define only the <b>Number of Segments</b>.
175 <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.
177 \image html a-nbsegments2.png
179 <br><b>Distribution with Table Density</b> - you input a number of
180 pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
181 formula, which will rule the change of length of segments and shows
182 the curve in the plot. You can select the <b>Conversion mode</b> from
183 \b Exponent and <b>Cut negative</b>.
185 \image html distributionwithtabledensity.png
187 <br><b>Distribution with Analytic Density</b> - you input the formula,
188 which will rule the change of length of segments and the module shows
189 the curve in the plot.
191 \image html distributionwithanalyticdensity.png
193 <b>See Also</b> a sample TUI Script of a
194 \ref tui_deflection_1d "Defining Number of Segments" hypothesis
198 \anchor start_and_end_length_anchor
199 <h2>Start and End Length hypothesis</h2>
201 <b>Start and End Length</b> hypothesis allows to divide a geometrical edge
202 into segments so that the first and the last segments have a specified
203 length. The length of medium segments changes with automatically chosen
204 geometric progression. Then mesh nodes are
205 constructed at segment ends location and 1D mesh elements are
208 The direction of the splitting is defined by the orientation of the underlying geometrical edge.
209 <b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made
210 in the direction opposing to their orientation. This list box is enabled only if the geometry object
211 is selected for the meshing. In this case the user can select edges to be reversed either directly
212 picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
214 \image html a-startendlength.png
216 \image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
218 <b>See Also</b> a sample TUI Script of a
219 \ref tui_start_and_end_length "Defining Start and End Length"
220 hypothesis operation.
223 \anchor automatic_length_anchor
224 <h2>Automatic Length</h2>
226 This hypothesis is automatically applied when you select <b>Assign a
227 set of hypotheses</b> option in Create Mesh menu.
229 \image html automaticlength.png
231 The dialog box prompts you to define the quality of the future mesh by
232 only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
233 low number of elements) to 1 (extremely fine mesh, great number of
234 elements). Compare one and the same object (sphere) meshed with
235 minimum and maximum value of this parameter.
237 \image html image147.gif "Example of a very rough mesh. Automatic Length works for 0."
239 \image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."
242 \anchor fixed_points_1d_anchor
243 <h2>Fixed points 1D hypothesis</h2>
245 <b>Fixed points 1D</b> hypothesis allows splitting edges through a
246 set of points parameterized on the edge (from 1 to 0) and a number of segments for each
247 interval limited by the points.
249 \image html hypo_fixedpnt_dlg.png
251 It is possible to check in <b>Same Nb. Segments for all intervals</b>
252 option and to define one value for all intervals.
254 The splitting direction is defined by the orientation of the
255 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
256 specify the edges for which the splitting should be made in the
257 direction opposite to their orientation. This list box is enabled only
258 if the geometrical object is selected for meshing. In this case it is
259 possible to select the edges to be reversed either directly picking them in
260 the 3D viewer or selecting the edges or groups of edges in the
263 \image html mesh_fixedpnt.png "Example of a submesh on the edge built using Fixed points 1D hypothesis"
265 <b>See Also</b> a sample TUI Script of a
266 \ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
