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 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 and Geometric Progression hypothesis" operation.
62 \anchor geometric_1d_anchor
63 <h2>Geometric Progression hypothesis</h2>
65 <b>Geometric Progression</b> hypothesis allows to split edges into
66 segments with a length that changes in geometric progression (Lk =
67 Lk-1 * d) beginning from a given starting length and with a given
70 The direction of the splitting is defined by the orientation of the
71 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
72 specify the edges for which the splitting should be made in the
73 direction opposing to their orientation. This list box is enabled only
74 if the geometry object is selected for the meshing. In this case the
75 user can select edges to be reversed either directly picking them in
76 the 3D viewer or by selecting the edges or groups of edges in the
79 \image html a-geometric1d.png
81 <b>See Also</b> a sample TUI Script of a
82 \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
85 \anchor deflection_1d_anchor
86 <h2>Deflection 1D hypothesis</h2>
88 <b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
89 composing your geometrical object. It uses only one parameter: the
91 \n A geometrical edge is divided into equal segments. The maximum
92 distance between a point on the edge within a segment and the line
93 connecting the ends of the segment should not exceed the specified
94 value of deflection . Then mesh nodes are constructed at end segment
95 locations and 1D mesh elements are constructed on segments.
97 \image html a-deflection1d.png
99 \image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"
101 <b>See Also</b> a sample TUI Script of a
102 \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
105 \anchor average_length_anchor
106 <h2>Local Length hypothesis</h2>
108 <b>Local Length</b> hypothesis can be applied for meshing of edges
109 composing your geometrical object. Definition of this hypothesis
110 consists of setting the \b length of segments, which will split these
111 edges, and the \b precision of rounding. The points on the edges
112 generated by these segments will represent nodes of your mesh.
113 Later these nodes will be used for meshing of the faces abutting to
116 The \b precision parameter is used to allow rounding a number of
117 segments, calculated from the edge length and average length of
118 segment, to the lower integer, if this value outstands from it in
119 bounds of the precision. Otherwise, the number of segments is rounded
120 to the higher integer. Use value 0.5 to provide rounding to the
121 nearest integer, 1.0 for the lower integer, 0.0 for the higher
122 integer. Default value is 1e-07.
124 \image html image41.gif
126 \image html a-averagelength.png
128 \image html b-erage_length.png "Local Length hypothesis - all 1D mesh elements are roughly equal"
130 <b>See Also</b> a sample TUI Script of a
131 \ref tui_average_length "Defining Local Length" hypothesis
134 <br>\anchor max_length_anchor
136 <b>Max Size</b> hypothesis allows splitting geometrical edges into
137 segments not longer than the given length. Definition of this hypothesis
138 consists of setting the maximal allowed \b length of segments.
139 <b>Use preestimated length</b> check box lets you specify \b length
140 automatically calculated basing on size of your geometrical object,
141 namely as diagonal of bounding box divided by ten. The divider can be
142 changed via "Ratio Bounding Box Diagonal / Max Size"
143 preference parameter.
144 <b>Use preestimated length</b> check box is enabled only if the
145 geometrical object has been selected before hypothesis definition.
147 \image html a-maxsize1d.png
150 \anchor number_of_segments_anchor
151 <h2>Number of segments hypothesis</h2>
153 <b>Number of segments</b> hypothesis can be applied for meshing of edges
154 composing your geometrical object. Definition of this hypothesis
155 consists of setting the number of segments, which will split these
156 edges. In other words your edges will be split into a definite number
157 of segments with approximately the same length. The points on the
158 edges generated by these segments will represent nodes of your
159 mesh. Later these nodes will be used for meshing of the faces abutting
162 The direction of the splitting is defined by the orientation of the underlying geometrical edge.
163 <b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made
164 in the direction opposing to their orientation. This list box is enabled only if the geometry object
165 is selected for the meshing. In this case the user can select edges to be reversed either directly
166 picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
168 \image html image46.gif
170 You can set the type of distribution for this hypothesis in the
171 <b>Hypothesis Construction</b> dialog bog :
173 \image html a-nbsegments1.png
175 <br><b>Equidistant Distribution</b> - all segments will have the same
176 length, you define only the <b>Number of Segments</b>.
178 <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.
180 \image html a-nbsegments2.png
182 <br><b>Distribution with Table Density</b> - you input a number of
183 pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
184 formula, which will rule the change of length of segments and shows
185 the curve in the plot. You can select the <b>Conversion mode</b> from
186 \b Exponent and <b>Cut negative</b>.
188 \image html distributionwithtabledensity.png
190 <br><b>Distribution with Analytic Density</b> - you input the formula,
191 which will rule the change of length of segments and the module shows
192 the curve in the plot.
194 \image html distributionwithanalyticdensity.png
196 <b>See Also</b> a sample TUI Script of a
197 \ref tui_deflection_1d "Defining Number of Segments" hypothesis
201 \anchor start_and_end_length_anchor
202 <h2>Start and End Length hypothesis</h2>
204 <b>Start and End Length</b> hypothesis allows to divide a geometrical edge
205 into segments so that the first and the last segments have a specified
206 length. The length of medium segments changes with automatically chosen
207 geometric progression. Then mesh nodes are
208 constructed at segment ends location and 1D mesh elements are
211 The direction of the splitting is defined by the orientation of the underlying geometrical edge.
212 <b>"Reverse Edges"</b> list box allows to specify the edges for which the splitting should be made
213 in the direction opposing to their orientation. This list box is enabled only if the geometry object
214 is selected for the meshing. In this case the user can select edges to be reversed either directly
215 picking them in the 3D viewer or by selecting the edges or groups of edges in the Object Browser.
217 \image html a-startendlength.png
219 \image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
221 <b>See Also</b> a sample TUI Script of a
222 \ref tui_start_and_end_length "Defining Start and End Length"
223 hypothesis operation.
226 \anchor automatic_length_anchor
227 <h2>Automatic Length</h2>
229 This hypothesis is automatically applied when you select <b>Assign a
230 set of hypotheses</b> option in Create Mesh menu.
232 \image html automaticlength.png
234 The dialog box prompts you to define the quality of the future mesh by
235 only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
236 low number of elements) to 1 (extremely fine mesh, great number of
237 elements). Compare one and the same object (sphere) meshed with
238 minimum and maximum value of this parameter.
240 \image html image147.gif "Example of a very rough mesh. Automatic Length works for 0."
242 \image html image148.gif "Example of a very fine mesh. Automatic Length works for 1."
245 \anchor fixed_points_1d_anchor
246 <h2>Fixed points 1D hypothesis</h2>
248 <b>Fixed points 1D</b> hypothesis allows splitting edges through a
249 set of points parameterized on the edge (from 1 to 0) and a number of segments for each
250 interval limited by the points.
252 \image html hypo_fixedpnt_dlg.png
254 It is possible to check in <b>Same Nb. Segments for all intervals</b>
255 option and to define one value for all intervals.
257 The splitting direction is defined by the orientation of the
258 underlying geometrical edge. <b>"Reverse Edges"</b> list box allows to
259 specify the edges for which the splitting should be made in the
260 direction opposite to their orientation. This list box is enabled only
261 if the geometrical object is selected for meshing. In this case it is
262 possible to select the edges to be reversed either directly picking them in
263 the 3D viewer or selecting the edges or groups of edges in the
266 \image html mesh_fixedpnt.png "Example of a submesh on the edge built using Fixed points 1D hypothesis"
268 <b>See Also</b> a sample TUI Script of a
269 \ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
