3 \page a1d_meshing_hypo_page 1D Meshing Hypotheses
5 Basic 1D hypothesis specifies:
7 <li>how \ref a1d_algos_anchor "Wire Discretization" should divide the edge;</li>
8 <li>how \ref a1d_algos_anchor "Composite Side Discretization" should divide the group of C1-continuous edges.</li>
11 1D hypotheses can be categorized by type of nodes distribution as follows:
13 <li>Uniform distribution:
15 <li>\ref average_length_anchor "Local Length"</li>
16 <li>\ref max_length_anchor "Max Size"</li>
17 <li>\ref number_of_segments_anchor "Number of segments" with Equidistant distribution</li>
18 <li>\ref automatic_length_anchor "Automatic Length"</li>
20 <li>Constantly increasing or decreasing length of segments:
22 <li>\ref arithmetic_1d_anchor "Arithmetic 1D"</li>
23 <li>\ref geometric_1d_anchor "Geometric Progression"</li>
24 <li>\ref start_and_end_length_anchor "Start and end length"</li>
25 <li>\ref number_of_segments_anchor "Number of segments" with Scale distribution</li>
27 <li>Distribution depending on curvature:
29 <li>\ref adaptive_1d_anchor "Adaptive"</li>
30 <li>\ref deflection_1d_anchor "Deflection 1D"</li>
32 <li>Arbitrary distribution:
34 <li>\ref fixed_points_1d_anchor "Fixed points 1D"</li>
35 <li>\ref number_of_segments_anchor "Number of segments" with
36 \ref analyticdensity_anchor "Analytic Density Distribution" or Table Density Distribution</li>
41 \anchor adaptive_1d_anchor
42 <h2>Adaptive hypothesis</h2>
44 <b>Adaptive</b> hypothesis allows to split edges into segments with a
45 length that depends on the curvature of edges and faces and is limited by <b>Min. Size</b>
46 and <b>Max Size</b>. The length of a segment also depends on the lengths
47 of adjacent segments (that can't differ more than twice) and on the
48 distance to close geometrical entities (edges and faces) to avoid
49 creation of narrow 2D elements.
51 \image html adaptive1d.png
53 - <b>Min size</b> parameter limits the minimal segment size.
54 - <b>Max size</b> parameter defines the length of segments on straight edges.
55 - \b Deflection parameter gives maximal distance of a segment from a curved edge.
57 \image html adaptive1d_sample_mesh.png "Adaptive hypothesis and Netgen 2D algorithm - the size of mesh segments reflects the size of geometrical features"
59 <b>See Also</b> a \ref tui_1d_adaptive "sample TUI Script" that uses Adaptive hypothesis.
62 \anchor arithmetic_1d_anchor
63 <h2>Arithmetic 1D hypothesis</h2>
65 <b>Arithmetic 1D</b> hypothesis allows to split edges into segments with a
66 length that changes in arithmetic progression (Lk = Lk-1 + d)
67 beginning from a given starting length and up to a given end length.
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
72 the splitting should be made in the direction opposite to their
73 orientation. This list box is usable only if a geometry object is
74 selected for meshing. In this case it is possible to select edges to
75 be reversed either directly picking them in the 3D viewer or by
76 selecting the edges or groups of edges in the Object Browser. Use \b
77 Add button to add the selected edges to the list.
79 \ref reversed_edges_helper_anchor "Helper" group assists you in
80 defining <b>Reversed Edges</b> parameter.
83 \image html a-arithmetic1d.png
85 \image html b-ithmetic1d.png "Arithmetic 1D hypothesis - the size of mesh elements gradually increases"
87 <b>See Also</b> a sample TUI Script of a
88 \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
91 \anchor geometric_1d_anchor
92 <h2>Geometric Progression hypothesis</h2>
94 <b>Geometric Progression</b> hypothesis allows splitting edges into
95 segments with a length that changes in geometric progression (Lk =
96 Lk-1 * d) starting from a given <b>Start Length</b> and with a given
99 The splitting direction is defined by the orientation of the
100 underlying geometrical edge.
101 <b>Reverse Edges</b> list box allows specifying the edges, for which
102 the splitting should be made in the direction opposite to their
103 orientation. This list box is usable only if a geometry object is
104 selected for meshing. In this case it is possible to select edges to
105 be reversed either directly picking them in the 3D viewer or by
106 selecting the edges or groups of edges in the Object Browser. Use \b
107 Add button to add the selected edges to the list.
109 \ref reversed_edges_helper_anchor "Helper" group assists you in
110 defining <b>Reversed Edges</b> parameter.
112 \image html a-geometric1d.png
114 <b>See Also</b> a sample TUI Script of a
115 \ref tui_1d_arithmetic "Defining Arithmetic 1D and Geometric Progression hypothesis" operation.
118 \anchor deflection_1d_anchor
119 <h2>Deflection 1D hypothesis</h2>
121 <b>Deflection 1D</b> hypothesis can be applied for meshing curvilinear edges
122 composing your geometrical object. It defines only one parameter: the
123 value of deflection (or chord error).
125 A geometrical edge is divided into segments of length depending on
126 edge curvature. The more curved the edge, the shorter the
127 segment. Nodes on the edge are placed so that the maximum distance
128 between the edge and a segment approximating a part of edge between
129 two nodes should not exceed the value of deflection.
131 \image html a-deflection1d.png
133 \image html b-flection1d.png "Deflection 1D hypothesis - useful for meshing curvilinear edges"
135 <b>See Also</b> a sample TUI Script of a
136 \ref tui_deflection_1d "Defining Deflection 1D hypothesis" operation.
139 \anchor average_length_anchor
140 <h2>Local Length hypothesis</h2>
142 <b>Local Length</b> hypothesis can be applied for meshing of edges
143 composing your geometrical object. Definition of this hypothesis
144 consists of setting the \b length of segments, which will approximate these
145 edges, and the \b precision of rounding.
147 The \b precision parameter is used to round a <em>number of segments</em>,
148 calculated by dividing the <em>edge length</em> by the specified \b length of
149 segment, to the higher integer if the \a remainder exceeds the \b precision
150 and to the lower integer otherwise. <br>
151 Use value 0.5 to provide rounding to the nearest integer, 1.0 for the lower integer, 0.0 for the higher integer. Default value is 1e-07.
153 For example: if <em>edge length</em> is 10.0 and the segment \b length
154 is 3.0 then their division gives 10./3. = 3.33(3) and the \a remainder is 0.33(3).
155 If \b precision is less than 0.33(3) then the edge is divided into 3 segments.
156 If \b precision is more than 0.33(3) then the edge is divided into 4 segments.
159 \image html image41.gif
161 \image html a-averagelength.png
163 \image html b-erage_length.png "Local Length hypothesis - all 1D mesh segments are equal"
165 <b>See Also</b> a sample TUI Script of a
166 \ref tui_average_length "Defining Local Length" hypothesis
169 <br>\anchor max_length_anchor
171 <b>Max Size</b> hypothesis allows splitting geometrical edges into
172 segments not longer than the given length. Definition of this hypothesis
173 consists of setting the maximal allowed \b length of segments.
174 <b>Use preestimated length</b> check box lets you use \b length
175 automatically calculated basing on size of your geometrical object,
176 namely as diagonal of bounding box divided by ten. The divider can be
177 changed via "Ratio Bounding Box Diagonal / Max Size"
178 preference parameter.
179 <b>Use preestimated length</b> check box is enabled only if the
180 geometrical object has been selected before hypothesis definition.
182 \image html a-maxsize1d.png
185 \anchor number_of_segments_anchor
186 <h2>Number of segments hypothesis</h2>
188 <b>Number of segments</b> hypothesis can be applied for approximating
189 edges by a definite number of mesh segments with length depending on
190 the selected type of distribution of nodes.
192 The direction of the splitting is defined by the orientation of the
193 underlying geometrical edge. <b>Reverse Edges</b> list box allows to
194 specify the edges for which the splitting should be made in the
195 direction opposing to their orientation. This list box is enabled only
196 if the geometry object is selected for the meshing. In this case it is
197 possible to select edges to be reversed either by directly picking them
198 in the 3D viewer or by selecting the edges or groups of edges in the
201 \ref reversed_edges_helper_anchor "Helper" group assists you in
202 defining <b>Reversed Edges</b> parameter.
204 You can set the type of node distribution for this hypothesis in the
205 <b>Hypothesis Construction</b> dialog bog :
207 \image html a-nbsegments1.png
209 <br><b>Equidistant Distribution</b> - all segments will have the same
210 length, you define only the <b>Number of Segments</b>.
212 <br><b>Scale Distribution</b> - length of segments gradually changes
213 depending on the <b>Scale Factor</b>, which is a ratio of the first
214 segment length to the last segment length.<br>
215 Length of segments changes in geometric progression with the common
216 ratio (A) depending on the <b>Scale Factor</b> (S) and <b>Number of
217 Segments</b> (N) as follows: <code> A = S**(1/(N-1))</code>. For an
218 edge of length L, length of the first segment is
219 <code>L * (1 - A)/(1 - A**N)</code>.
222 \image html a-nbsegments2.png
224 <br><b>Distribution with Analytic Density</b> - you input the formula,
225 which will rule the change of length of segments and the module shows
226 in the plot the density function curve in red and the node
227 distribution as blue crosses.
229 \image html distributionwithanalyticdensity.png
232 \anchor analyticdensity_anchor
233 The node distribution is computed so that to have the density function
234 integral on the range between two nodes equal for all segments.
235 \image html analyticdensity.png
237 <br><b>Distribution with Table Density</b> - you input a number of
238 pairs <b>t - F(t)</b>, where \b t ranges from 0 to 1, and the module computes the
239 formula, which will rule the change of length of segments and shows
240 in the plot the density function curve in red and the node
241 distribution as blue crosses. The node distribution is computed in the
243 \ref analyticdensity_anchor "Distribution with Analytic Density". You
244 can select the <b>Conversion mode</b> from\b Exponent and <b>Cut
247 \image html distributionwithtabledensity.png
249 <b>See Also</b> a sample TUI Script of a
250 \ref tui_deflection_1d "Defining Number of Segments" hypothesis
253 \note The plot functionality is available only if GUI module is builded with Plot 2D Viewer (set option SALOME_USE_PLOT2DVIEWER to ON when building GUI module).
256 \anchor start_and_end_length_anchor
257 <h2>Start and End Length hypothesis</h2>
259 <b>Start and End Length</b> hypothesis allows to divide a geometrical edge
260 into segments so that the first and the last segments have a specified
261 length. The length of medium segments changes with automatically chosen
262 geometric progression.
264 The direction of the splitting is defined by the orientation of the
265 underlying geometrical edge. <b>Reverse Edges</b> list box allows to
266 specify the edges, for which the splitting should be made in the
267 direction opposing to their orientation. This list box is enabled only
268 if the geometry object is selected for the meshing. In this case it is
269 possible to select edges to be reversed either by directly picking them
270 in the 3D viewer or by selecting the edges or groups of edges in the
273 \ref reversed_edges_helper_anchor "Helper" group assists you in
274 defining <b>Reversed Edges</b> parameter.
277 \image html a-startendlength.png
279 \image html b-art_end_length.png "The lengths of the first and the last segment are strictly defined"
281 <b>See Also</b> a sample TUI Script of a
282 \ref tui_start_and_end_length "Defining Start and End Length"
283 hypothesis operation.
286 \anchor automatic_length_anchor
287 <h2>Automatic Length</h2>
289 The dialog box prompts you to define the quality of the future mesh by
290 only one parameter, which is \b Fineness, ranging from 0 (coarse mesh,
291 low number of segments) to 1 (extremely fine mesh, great number of
294 \image html automaticlength.png
296 Compare one and the same object (sphere) meshed with
297 minimum and maximum value of this parameter.
299 \image html image147.gif "Example of a rough mesh at Automatic Length Fineness of 0."
301 \image html image148.gif "Example of a fine mesh at Automatic Length Fineness of 1."
304 \anchor fixed_points_1d_anchor
305 <h2>Fixed points 1D hypothesis</h2>
307 <b>Fixed points 1D</b> hypothesis allows splitting edges through a
308 set of points parametrized on the edge (from 1 to 0) and a number of
309 segments for each interval limited by the points.
311 \image html hypo_fixedpnt_dlg.png
313 It is possible to check in <b>Same Nb. Segments for all intervals</b>
314 option and to define one value for all intervals.
316 The splitting direction is defined by the orientation of the
317 underlying geometrical edge. <b>Reverse Edges</b> list box allows to
318 specify the edges for which the splitting should be made in the
319 direction opposite to their orientation. This list box is enabled only
320 if the geometrical object is selected for meshing. In this case it is
321 possible to select the edges to be reversed either directly picking them in
322 the 3D viewer or selecting the edges or groups of edges in the
325 \ref reversed_edges_helper_anchor "Helper" group assists in
326 defining <b>Reversed Edges</b> parameter.
329 \image html mesh_fixedpnt.png "Example of a sub-mesh on the edge built using Fixed points 1D hypothesis"
331 <b>See Also</b> a sample TUI Script of a
332 \ref tui_fixed_points "Defining Fixed Points" hypothesis operation.
334 \anchor reversed_edges_helper_anchor
335 <h2>Reversed Edges Helper</h2>
337 \image html rev_edges_helper_dlg.png
339 \b Helper group assists in defining <b>Reversed Edges</b>
340 parameter of the hypotheses depending on edge direction.
342 <b>Show whole geometry</b> check-box allows seeing the whole
343 geometrical model in the 3D Viewer, which can help to understand the
344 location of a set of edges within the model.
346 <b>Propagation chains</b> group allows defining <b>Reversed Edges</b>
347 for splitting opposite edges of quadrilateral faces
348 in a logically uniform direction. When this group is
349 activated, the list is filled with propagation chains found within the
350 model. When a chain is selected in the list its edges are
351 shown in the Viewer with arrows, which enables choosing a common
352 direction for all chain edges. \b Reverse button inverts the common
353 direction of chain edges. If \b Add button is active, some
354 edges of a chain have a different direction, so you can click \b Add
355 button to add them to <b>Reversed Edges</b> list.
357 \image html propagation_chain.png "The whole geometry and a propagation chain"