3 \page blsurf_hypo_page BLSURF Parameters hypothesis
5 \n BLSURF Parameters hypothesis works only with <b>BLSURF</b> 2d
6 algorithm. This algorithm is a commercial software.
8 <h1>General parameters</h1>
10 \image html blsurf_parameters.png
13 <li><b>Name</b> - allows defining the name of the hypothesis (BLSURF
14 Parameters_n by default).</li>
16 <li><b>Physical Mesh</b> - can be set to None, Custom or Size Map
18 <li>if set to "Custom", allows user input in the
19 in <b>User size</b>, <b>Max Physical Size</b> and <b>Min Physical
21 <li>if set to "Size Map", behaves like "Custom" mode and takes into account the custom elements sizes given in the Size Map tab.</li>
25 <li><b>User size</b> - defines the size of the generated mesh elements. </li>
27 <li><b>Max Physical Size</b> - defines the upper limit of mesh element size. </li>
29 <li><b>Min Physical Size</b> - defines the lower limit of mesh element size. </li>
31 <li><b>Geometrical mesh</b> - if set to "Custom", allows user input in
32 <b>Angle Mesh S</b>, <b>Angle Mesh C</b> and
33 <b>Gradation</b> fields. These fields control
34 computation of the element size, so called <i>geometrical size</i>, conform to
35 the surface geometry considering local curvatures. \n
36 If both the <b>User size</b> and the <i>geometrical size</i> are defined, the
37 eventual element size correspond to the least of the two. </li>
39 <li><b>Angle Mesh S</b> - maximum angle between the mesh face and the
40 tangent to the geometrical surface at each mesh node, in degrees. </li>
42 <li><b>Angle Mesh C</b> - maximum angle between the mesh edge and the
43 tangent to the geometrical curve at each mesh node, in degrees. </li>
45 <li><b>Max Geometrical Size</b> - defines the upper limit of the <i>geometrical size</i>.</li>
47 <li><b>Min Geometrical Size</b> - defines the lower limit of the <i>geometrical size</i>.</li>
49 <li><b>Gradation</b> - maximum ratio between the lengths of
50 two adjacent edges. </li>
52 <li><b>Allow Quadrangles</b> - if checked, allows the creation of quadrilateral elements.</li>
54 <li><b>Patch independent</b> - if checked, geometrical
55 edges are not respected and all geometrical faces are meshed as one
58 <h1>Advanced parameters</h1>
60 \image html blsurf_parameters_advanced.png
62 <li><b>Topology</b> - allows creation of a conform mesh on a shell of
65 <li>"From CAD" means that mesh conformity is assured by conformity
67 <li>"Pre-process" and "Pre-process++" allow the BLSURF software to
68 pre-process the geometrical model to eventually produce a conform
72 <li><b>Verbosity level</b> - Defines the percentage of "verbosity" of
75 <li><b>Add option</b> - provides the choice of multiple advanced
76 options, which appear, if selected, in a table where it is possible to
77 input the value of the option and to edit it later.</li>
79 <li><b>Clear option</b> - removes the option selected in the table.
84 The following options are commonly usable. The notion of <i>diag</i>
85 used in the descriptions means
86 the diagonal of the bounding box of the geometrical object to mesh.
89 <li><b>topo_eps1</b> (real) - is the tolerance level inside a CAD
90 patch. By default is equal to <i>diag</i> � 10-4. This tolerance is used to
91 identify nodes to merge within one geometrical face when \b Topology
92 option is to pre-process. Default is <i>diag</i>/10.0.</li>
94 <li><b>topo_eps2</b> (real) - is the tolerance level between two CAD
95 patches. By default is equal to <i>diag</i> � 10-4. This tolerance is used to
96 identify nodes to merge over different geometrical faces when
97 \b Topology option is to pre-process. Default is <i>diag</i>/10.0.</li>
99 <li>\b LSS (real) - is an abbreviation for "length of sub-segment". It is
100 a maximal allowed length of a mesh edge. Default is 0.5.</li>
102 <li>\b frontal (integer)
104 <li> 1 - the mesh generator inserts points with an advancing front method.</li>
105 <li> 0 - it inserts them with an algebraic method (on internal edges). This method is
106 slightly faster but generates less regular meshes. </li>
110 \anchor blsurf_hinterpol_flag
111 <li>\b hinterpol_flag (integer) - determines the computation of an
112 interpolated value <i>v</i> between two points <i>P1</i> and <i>P2</i> on a
113 curve. Let <i>h1</i> be the value at point <i>P1,</i> <i>h2</i> be the value at point
114 <i>P2,</i> and <i>t</i> be a parameter varying from 0 to 1 when moving from <i>P1
117 <li>0 - the interpolation is linear: <i>v = h1 + t (h2 - h1 )</i></li>
118 <li>1 - the interpolation is geometric: <i>v = h1 * pow( h2/h1, t)</i></li>
119 <li>2 - the interpolation is sinusoidal: <i>v = (h1+h2)/2 +
120 (h1-h2)/2*cos(PI*t)</i></li>
124 \anchor blsurf_hmean_flag
125 <li>\b hmean_flag (integer) - determines the computation of the average of several
127 <li>-1 - the minimum is computed.</li>
128 <li>0 or 2 - the arithmetic average computed.
129 <li>1 - the geometric average is computed.</li>
133 <li>\b CheckAdjacentEdges, \b CheckCloseEdges and \b CheckWellDefined
134 (integers) - gives the number of calls of equally named subroutines the
135 purpose of which is to improve the mesh of domains having narrow
136 parts. At each iteration,\b CheckCloseEdges decreases the sizes of the
137 edges when two boundary curves are neighboring,\b CheckAdjacentEdges
138 balances the sizes of adjacent edges, and \b CheckWellDefined checks if
139 the parametric domain is well defined. Default values are 0.</li>
142 <li>\b CoefRectangle (real)- defines the relative thickness of the rectangles
143 used by subroutine \b CheckCloseEdges (see above). Default is 0.25.</li>
145 <li>\b eps_collapse (real) - if more than 0.0, BLSURF removes
146 curves whose lengths are less than \b eps_collapse. To obtain an
147 approximate value of the length of a curve, it is arbitrarily
148 split into 20 edges. Default is 0.0.</li>
150 <li>\b eps_ends (real) - is used to detect the curves whose lengths are very
151 small, which sometimes constitutes an error. A message is printed
152 if<i> fabs(P2-P1) < eps_ends</i>, where <i>P1</i> and <i>P2</i> are the
153 extremities of a curve. Default is <i>diag</i>/500.0.</li>
155 <li>\b prefix (char) - is a prefix of the files generated by
156 BLSURF. Default is "x".</li>
158 <li>\b refs (integer) - reference of a surface, used when exporting
159 files. Default is 1.</li>
163 The following advanced options are not documented and you can use them
165 \n\n Integer variables:
167 <li> addsurf_ivertex</li>
168 <li> background </li>
170 <li> communication </li>
172 <li> export_flag </li>
176 <li> intermedfile </li>
180 <li> pardom_flag </li>
183 <li> surforient </li>
185 <li> topo_collapse </li>
189 <li> addsurf_angle </li>
192 <li> addsurf_FG </li>
194 <li> addsurf_PA </li>
195 <li> angle_compcurv </li>
196 <li> angle_ridge </li>
197 <li> eps_pardom </li>
201 <li> export_format </li>
202 <li> export_option </li>
203 <li> import_option </li>
206 <h1>Custom size map</h1>
208 \image html blsurf_parameters_sizemap1.png
210 User sizes can be defined on faces, edges or vertices.
212 <li>The faces, edges and vertices can belong to the meshed geometrical
213 object or to its sub-shapes (created using <b>Explode</b> command).</li>
214 <li>Groups of faces, edges and vertices are also handled.</li>
215 <li>It is possible to attribute the same size to several geometries using multi-selection.</li>
216 <li>The sizes are constant values or python functions.</li>
217 <li>In case of a python function, the following rules must be respected:
219 <li>The name of the function is f.</li>
220 <li>If geometry is a face or a group of faces, the function is f(u,v).</li>
221 <li>If geometry is an edge or a group of edges, the function is f(t).</li>
222 <li>If geometry is a vertex or a group of vertices, the function is f().</li>
223 <li>The function must return a double.</li>
227 \anchor blsurf_attractor
228 <h2>Advanced maps</h2>
230 \image html blsurf_parameters_sizemap2.png
232 Specific size maps, called attractors can be defined on faces. They allow to define the size of the mesh elements on a face so that the mesh is the finest on the attractor shape and becomes coarser when getting far from this shape.
233 The selected attractor can be either a Vertex or an Edge. The attractor doesn't have to be a sub-shape of the shape to mesh.
235 Furthermore you can choose to keep the size constant until a certain distance from a shape. This option can be combined or not with the "attractor" size map described above.
237 If the two options are combined the size will remain constant until the distant specified in "constant over" and grow then as prescribed by the attractor function. Else the growing is only controled by the standard arguments of BLSURF (gradation ...).
239 \image html blsurf_attractors2.png "Example of mesh created using attractors, the attractors here are the side edges and the size grow from the side of the surface towards the apex"
241 \image html blsurf_const_size_near_shape2.png "Example of size map with constant size option, the size is kept constant on the left side of the surface until a certain distance"
243 Remark : The validation of the hypothesis might take a few seconds if attractors are defined or the "constant size" option is used because a map of distances has to be built on the whole surface for each face where such an hypothesis has been defined.
245 <br><b>See Also</b> a sample TUI Script of the \ref tui_blsurf "creation of a BLSurf hypothesis", including size map.
247 \anchor blsurf_sizemap_computation
248 <h2>Computation of the physical size</h2>
250 The physical size is obtained by querying sizemap functions associated to the input CAD object for surfaces, curves and points.
251 Each function can either return a value h (which is then trimmed
252 between the two bounds hphymin and hphymax), or "no answer" (by not
253 assigning a value to h), thus providing great flexibility in the
254 specification of the sizes. The computation depends on whether point P is internal to a surface, internal to a curve, or at the end of several curves:
256 <li> If point P is internal to a surface, the CAD surface size function is queried. If no answer is returned, one interpolates with the values at the vertices of the discretized interface curves.</li>
257 <li> If point P is internal to a curve, the CAD curve size function is queried first. If no answer is returned, the surface size function is queried for every adjacent surface and the mean value of the returned values is computed. If no answer is returned, sizes h1 and h2 at both ends of the curve are considered (see next item) and the interpolated value is computed.</li>
258 <li> If point P is at the extremity of several curves, the CAD point size function is queried first. If no answer is returned, the curve size function is queried for every adjacent curve and the mean value of the returned values is computed. If no answer is returned, the surface size function is queried for every adjacent surface and the mean value of the returned values is computed. If there is still no answer returned, the default value hphydef is kept.</li>
260 In order to compute the mean of several values, the arithmetic mean is used by default, but this can be modified by the parameter \ref blsurf_hmean_flag "hmean flag". In the same way, in order to interpolate two values, a linear interpolation is used by default, but this can be modified by \ref blsurf_hinterpol_flag "hinterpol flag".
262 \anchor blsurf_attractor_computation
263 <h2>Computation of attractors</h2>
265 The size grow exponentially following the equation : h(d) = User size + (h_start - User Size) * exp( -(d / R)^2 ).
269 <li>h_start is the desired size on the given attractor shape</li>
270 <li>d is the distance of the current point from the attractor shape. The distance is the geodesic distance (i.e. calculated by following the surface to be meshed) </li>
271 <li>R is called the distance of influence and allows controlling the growth rate of the mesh </li>
273 Warning : The formula is respected only if it doesn't imply a gradation bigger than the one set in the "Arguments" tab. So it's better to set it to its maximum value : 2.5.
275 <h1>Custom enforced vertices</h1>
277 \image html blsurf_parameters_enforced_vertices.png
279 It is possible to define some enforced vertices to BLSurf algorithm
280 without creating any vertices by CAD algorithms.
282 <li>The enforced vertex is the projection of a point defined by its
283 (x,y,z) coordinates on the selected face.</li>
284 <li>It is possible to define several enforced vertices on a face or a group of faces.</li>
285 <li>If the projected point is on the boundary or outside of the face, it will be ignored.</li>
288 <br><b>See Also</b> a sample TUI Script of the \ref tui_blsurf "creation of a BLSurf hypothesis", including enforced vertices.
292 Currently BLSURF plugin has the following limitations.
294 <li>The created mesh will contain inverted elements if it is based on a shape,
295 consisting of more than one face (box, cone, torus...) and if
296 the option "Allow Quadrangles (Test)" has been checked before
299 <li>SIGFPE exception is raised at the attempt to compute the mesh
300 based on a box when the option "Patch independent" is checked.</li>
302 <li>BLSURF algorithm cannot be used as a local algorithm (on
303 sub-meshes) or as a provider of a low-level
304 mesh for some 3D algorithms, because the BLSURF mesher (and
305 consequently plugin) does not provide the information on node
306 parameters on edges (U) and faces (U,V). For example the
307 following combinations of algorithms are impossible:
309 <li> global MEFISTO or Quadrangle(mapping) + local BLSURF;</li>
310 <li> BLSURF + Projection 2D from faces meshed by BLSURF;</li>
311 <li> local BLSURF + Extrusion 3D;</li>