\page blsurf_hypo_page BLSURF Parameters hypothesis
\anchor blsurf_top
-\n BLSURF Parameters hypothesis works only with <b>BLSURF</b> 2d
-algorithm. This algorithm is a commercial software.
-\n To get a licence, visit http://www.distene.com/corp/eval-distene.html
-
-<ol>
-<li>\ref blsurf_general_parameters "General parameters"</li>
-<li>\ref blsurf_advanced_parameters "Advanced parameters"</li>
-<li>\ref blsurf_local_size "Local size"</li>
-<ol>
-<li type="a">\ref blsurf_sizemap_computation "Computation of the physical size"</li>
-<li type="a">\ref blsurf_attractor "Advanced maps"</li>
-<li type="a">\ref blsurf_attractor_computation "Computation of attractors"</li>
-</ol>
-<li>\ref blsurf_enforced_elements "Enforced vertices"</li>
-<li>\ref blsurf_limitations "Limitations"</li>
-</ol>
-
-\anchor blsurf_general_parameters
-<h1>General parameters</h1>
+BLSURF Parameters hypothesis works only with \b DISTENE \b BLSurf 2d
+algorithm. This algorithm is a commercial software. To obtain a
+licence, visit http://www.distene.com/corp/eval-distene.html
+
+\tableofcontents
+
+\section blsurf_general_parameters General parameters
\image html blsurf_parameters.png
-<ul>
-<li><b>Name</b> - allows defining the name of the hypothesis (BLSURF
-Parameters_n by default).</li>
+- <b>Name</b> - allows defining the name of the hypothesis (BLSURF
+Parameters_n by default).
+
+- <b>Physical Mesh</b> - can be set to <em>None</em>, <em>Custom</em>
+ or <em>Size Map</em>
-<li><b>Physical Mesh</b> - can be set to None, Custom or Size Map
- <ul>
- <li>if set to "Custom", allows user input in the
-in <b>User size</b>, <b>Max Physical Size</b> and <b>Min Physical
-Size</b> fields.</li>
- <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>
-</ul>
-</li>
+ - if set to <em>Custom</em>, allows user input in the in <b>User size</b>,
+ <b>Max Physical Size</b> and <b>Min Physical Size</b> fields.
-<li><b>User size</b> - defines the size of the generated mesh elements. </li>
+ - if set to <em>Size Map</em>, behaves like <em>Custom</em> mode and takes into
+ account the custom elements sizes given in the Size Map tab.
-<li><b>Max Physical Size</b> - defines the upper limit of mesh element size. </li>
+- <b>User size</b> - defines the size of the generated mesh elements.
-<li><b>Min Physical Size</b> - defines the lower limit of mesh element size. </li>
+- <b>Max Physical Size</b> - defines the upper limit of mesh element size.
-<li><b>Geometrical mesh</b> - if set to "Custom", allows user input in
- <b>Angle Mesh S</b>, <b>Angle Mesh C</b> and
-<b>Gradation</b> fields. These fields control
-computation of the element size, so called <i>geometrical size</i>, conform to
-the surface geometry considering local curvatures. \n
-If both the <b>User size</b> and the <i>geometrical size</i> are defined, the
- eventual element size correspond to the least of the two. </li>
+- <b>Min Physical Size</b> - defines the lower limit of mesh element size.
-<li><b>Angle Mesh S</b> - maximum angle between the mesh face and the
-tangent to the geometrical surface at each mesh node, in degrees. </li>
+- <b>Geometrical mesh</b> - if set to <em>Custom</em>, allows user input in
+<b>Angle Mesh S</b>, <b>Angle Mesh C</b> and <b>Gradation</b>
+fields. These fields control computation of the element size, so
+called <i>geometrical size</i>, conform to the surface geometry
+considering local curvatures. If both the <b>User size</b> and the
+<i>geometrical size</i> are defined, the eventual element size
+corresponds to the least of the two.
-<li><b>Angle Mesh C</b> - maximum angle between the mesh edge and the
-tangent to the geometrical curve at each mesh node, in degrees. </li>
+- <b>Angle Mesh S</b> - maximum angle between the mesh face and the
+tangent to the geometrical surface at each mesh node, in degrees.
-<li><b>Max Geometrical Size</b> - defines the upper limit of the <i>geometrical size</i>.</li>
+- <b>Angle Mesh C</b> - maximum angle between the mesh edge and the
+tangent to the geometrical curve at each mesh node, in degrees.
-<li><b>Min Geometrical Size</b> - defines the lower limit of the <i>geometrical size</i>.</li>
+- <b>Max Geometrical Size</b> - defines the upper limit of the
+ <i>geometrical size</i>.
-<li><b>Gradation</b> - maximum ratio between the lengths of
-two adjacent edges. </li>
+- <b>Min Geometrical Size</b> - defines the lower limit of the
+ <i>geometrical size</i>.
-<li><b>Allow Quadrangles</b> - if checked, allows the creation of quadrilateral elements.</li>
+- <b>Gradation</b> - maximum ratio between the lengths of two adjacent
+ edges.
-<li><b>Patch independent</b> - if checked, geometrical
-edges are not respected and all geometrical faces are meshed as one
-hyper-face.</li>
-</ul>
+- <b>Allow Quadrangles</b> - if checked, allows the creation of
+ quadrilateral elements.
+
+- <b>Patch independent</b> - if checked, geometrical edges are not
+respected and all geometrical faces are meshed as one hyper-face.
\ref blsurf_top "Back to top"
-\anchor blsurf_advanced_parameters
-<h1>Advanced parameters</h1>
+\section blsurf_advanced_parameters Advanced parameters
-The notion of <i>diag</i> used in the descriptions means the diagonal of the bounding box of the
-geometrical object to mesh.
+The notion of <i>diag</i> used in the descriptions means the diagonal
+of the bounding box of the geometrical object to mesh.
\image html blsurf_parameters_advanced.png
-<li><b>Verbosity level</b> - Defines the percentage of "verbosity" of
-BLSURF [0-100].</li>
+- <b>Verbosity level</b> - defines the percentage of "verbosity" of
+BLSURF [0-100].
+
+- <b>Topology</b> - allows creation of a conform mesh on a shell of
+not sewed faces. The following choices are allowed:
-<li><b>Topology</b> - allows creation of a conform mesh on a shell of
-not sewed faces.
-<ul>
- <li>"From CAD" means that mesh conformity is assured by conformity
- of a shape.</li>
- <li>"Pre-process" and "Pre-process++" allow the BLSURF software to
+ - <em>"From CAD"</em> means that mesh conformity is assured by conformity
+ of a shape.
+
+ - <em>"Pre-process"</em> and <em>"Pre-process++"</em> allow the BLSURF software to
pre-process the geometrical model to eventually produce a conform
- mesh. </li>
- <li>"PreCAD" is an auxiliary CAD pre-processing module which has
+ mesh.
+
+ - <em>"PreCAD"</em> is an auxiliary CAD pre-processing module which has
two main goals:
- <ul>
- <li> Complete missing or inadequate CAD descriptions.</li>
- <li> Perform topology reconstruction and specific geometry
- enhancement for mesh generation.</li>
- </ul>
- This module requires a specific licence.
- \n
- The following PreCAD options are the most significant and important ones:
- <ul>
- <li><b>Merge Edges</b> - allows PreCAD to optimize the geometry by merging some
- edges. This option is 0 by default.</li>
- <li><b>Remove nano edges</b> - allows PreCAD to optimize the geometry by removing
- the nano edges whenever possible. This option is 0 by default.</li>
- <li><b>Nano edge length</b> - gives the length below which an edge is considered as nano
- for the topology processing. See also the \b remove_nano_edges option. If unset, PreCAD
- default value is \f$\mathrm{diag} \times 10^{-5}\f$.</li>
- <li><b>Discard input topology</b> - computes the CAD topology from scratch,
- without considering the toplogical information contained in the original CAD
- (Useful for iges files). This option is 0 by default.</li>
- </ul>
- </li>
-</ul>
-
-<li><b>ExportGMF</b> - saves the computed mesh into a GMF file (.mesh or .meshb).</li>
-
-<li><b>Add option</b> - provides the choice of multiple PreCAD and BLSURF
-advanced options, which appear, if selected, in a table where it is
-possible to input the value of the option and to edit it later.</li>
-<li><b>Clear option</b> - removes the option selected in the table.</li>
+ - Complete missing or inadequate CAD descriptions.
+
+ - Perform topology reconstruction and specific geometry
+ enhancement for mesh generation.
+
+ \n This module requires a specific licence. The following PreCAD
+ options are the most significant and important ones:
-</ul>
+ - <b>Merge Edges</b> - allows PreCAD to optimize the geometry by merging some
+ edges. This option is 0 by default.
-\n
-The following BLSURF options are commonly usable.
+ - <b>Remove nano edges</b> - allows PreCAD to optimize the geometry by removing
+ the nano edges whenever possible. This option is 0 by default.
-<ul>
-<li>\b topo_eps1 (real) - is the tolerance level inside a CAD
+ - <b>Nano edge length</b> - gives the length below which an edge is considered as nano
+ for the topology processing. See also the \b remove_nano_edges option. If unset, PreCAD
+ default value is \f$\mathrm{diag} \times 10^{-5}\f$.
+
+ - <b>Discard input topology</b> - computes the CAD topology from scratch,
+ without considering the topological information contained in the original CAD
+ (useful for iges files). This option is 0 by default.
+
+- <b>ExportGMF</b> - saves the computed mesh into a GMF file (.mesh or .meshb).
+
+- <b>Add option</b> - provides the choice of multiple PreCAD and BLSURF
+advanced options, which appear, if selected, in a table where it is
+possible to input the value of the option and edit it later.
+
+- <b>Clear option</b> - removes the option selected in the table.
+
+The following BLSURF options are commonly usable:
+
+- \b topo_eps1 (real) - is the tolerance level inside a CAD
patch. By default is equal to \f$\mathrm{diag} \times 10^{-4}\f$. This tolerance is used to
identify nodes to merge within one geometrical face when \b Topology
-option is to pre-process.</li>
+option is to pre-process.
-<li>\b topo_eps2 (real) - is the tolerance level between two CAD
+- \b topo_eps2 (real) - is the tolerance level between two CAD
patches. By default is equal to \f$\mathrm{diag} \times 10^{-4}\f$. This tolerance is used to
identify nodes to merge over different geometrical faces when
-\b Topology option is to pre-process.</li>
+\b Topology option is to pre-process.
+
+- \b LSS (real) - is an abbreviation for "length of sub-segment". It is
+a maximal allowed length of a mesh edge. Default is \f$0.5\f$.
+
+- \b frontal (integer)
+
+ - 1 - the mesh generator inserts points with an advancing front method.
-<li>\b LSS (real) - is an abbreviation for "length of sub-segment". It is
-a maximal allowed length of a mesh edge. Default is \f$0.5\f$.</li>
+ - 0 - it inserts them with an algebraic method (on internal edges). This method is
+ slightly faster but generates less regular meshes.
-<li>\b frontal (integer)
-<ul>
-<li> 1 - the mesh generator inserts points with an advancing front method.</li>
-<li> 0 - it inserts them with an algebraic method (on internal edges). This method is
-slightly faster but generates less regular meshes. </li>
-</ul>
-Default is 0.</li>
+ \n Default is 0.
-\anchor blsurf_hinterpol_flag
-<li>\b hinterpol_flag (integer) - determines the computation of an
+- \anchor blsurf_hinterpol_flag \b hinterpol_flag (integer) - determines the computation of an
interpolated value <i>v</i> between two points <i>P1</i> and <i>P2</i> on a
curve. Let <i>h1</i> be the value at point <i>P1,</i> <i>h2</i> be the value at point
<i>P2,</i> and <i>t</i> be a parameter varying from 0 to 1 when moving from <i>P1
to</i> <i>P2</i>.
-<ul>
-<li>0 - the interpolation is linear: \f$v = h1 + t (h2 - h1 )\f$</li>
-<li>1 - the interpolation is geometric: \f$v = h1 \times \left( \frac{h1}{h2} \right)^{t}\f$</li>
-<li>2 - the interpolation is sinusoidal: \f$v = \frac{h1+h2}{2} + \frac{h1-h2}{2 \cdot \cos(\pi \cdot t)}\f$</li>
-</ul>
-Default is 0.</li>
-
-\anchor blsurf_hmean_flag
-<li>\b hmean_flag (integer) - determines the computation of the average of several
-values:<ul>
-<li>-1 - the minimum is computed.</li>
-<li>0 or 2 - the arithmetic average is computed.
-<li>1 - the geometric average is computed.</li>
-</ul>
-Default is 0.</li>
-
-<li>\b CheckAdjacentEdges, \b CheckCloseEdges and \b CheckWellDefined
-(integers) - gives the number of calls of equally named subroutines the
+
+ - 0 - the interpolation is linear: \f$v = h1 + t (h2 - h1 )\f$
+
+ - 1 - the interpolation is geometric: \f$v = h1 \times \left( \frac{h1}{h2} \right)^{t}\f$
+
+ - 2 - the interpolation is sinusoidal: \f$v = \frac{h1+h2}{2} + \frac{h1-h2}{2 \cdot \cos(\pi \cdot t)}\f$
+
+ \n Default is 0.
+
+- \anchor blsurf_hmean_flag \b hmean_flag (integer) - determines the computation of the average of several
+values:
+
+ - -1 - the minimum is computed.
+
+ - 0 or 2 - the arithmetic average is computed.
+
+ - 1 - the geometric average is computed.
+
+ \n Default is 0.
+
+- \b CheckAdjacentEdges, \b CheckCloseEdges and \b CheckWellDefined
+(integers) - give the number of calls of equally named subroutines the
purpose of which is to improve the mesh of domains having narrow
parts. At each iteration,\b CheckCloseEdges decreases the sizes of the
edges when two boundary curves are neighboring,\b CheckAdjacentEdges
balances the sizes of adjacent edges, and \b CheckWellDefined checks if
-the parametric domain is well defined. Default values are 0.</li>
+the parametric domain is well defined. Default values are 0.
+- \b CoefRectangle (real)- defines the relative thickness of the rectangles
+used by subroutine \b CheckCloseEdges (see above). Default is 0.25.
-<li>\b CoefRectangle (real)- defines the relative thickness of the rectangles
-used by subroutine \b CheckCloseEdges (see above). Default is 0.25.</li>
-
-<li>\b eps_collapse (real) - if more than 0.0, BLSURF removes
+- \b eps_collapse (real) - if more than 0.0, BLSURF removes
curves whose lengths are less than \b eps_collapse. To obtain an
approximate value of the length of a curve, it is arbitrarily
-split into 20 edges. Default is 0.0.</li>
+split into 20 edges. Default is 0.0.
-<li>\b eps_ends (real) - is used to detect the curves whose lengths are very
-small, which sometimes constitutes an error. A message is printed
+- \b eps_ends (real) - is used to detect the curves whose lengths are very
+small, that sometimes constitutes an error. A message is printed
if \f$\left|P2-P1\right| < eps\_ends\f$, where <i>P1</i> and <i>P2</i> are the
-extremities of a curve. Default is \f$\frac{\mathrm{diag}}{500.0}\f$.</li>
+extremities of a curve. Default is \f$\frac{\mathrm{diag}}{500.0}\f$.
-<li>\b prefix (char) - is a prefix of the files generated by
-BLSURF. Default is "x".</li>
+- \b prefix (char) - is a prefix of the files generated by
+BLSURF. Default is "x".
-<li>\b refs (integer) - reference of a surface, used when exporting
-files. Default is 1.</li>
-</ul>
+- \b refs (integer) - reference of a surface, used when exporting
+files. Default is 1.
-\n
The following PreCAD options are commonly usable.
-<ul>
-<li>\b closed_geometry (int) - describes whether the working geometry
+
+- \b closed_geometry (int) - describes whether the working geometry
should be closed or not. When activated, this option helps PreCAD to process
-the dirtiest geometries. By default this option is 0.</li>
-<li>\b debug (int) - If debug = 1 PreCAD will be very verbose and will output
+the dirtiest geometries. By default this option is 0.
+
+- \b debug (int) - If debug = 1 PreCAD will be very verbose and will output
some intermediate files in the working directory. By default this
-option is 0.</li>
-<li>\b eps_nano_relative (real) - the same as \b eps_nano, but relatively to
-the diagonal of the box bounding the geometry. By default this option is \f$10^{-5}\f$.</li>
-<li>\b eps_sewing (real) - tolerance of the assembly. It rarely requires to be tuned.
-By default this option is \f$\mathrm{diag} \times 5 \cdot 10^{-4}\f$.</li>
-<li>\b eps_sewing_relative (real) - the same as \b eps_nano but relatively to
-the diagonal of the box bounding the geometry. By default this option is \f$5 \cdot 10^{-4}\f$.</li>
-<li>\b manifold_geometry (int) - describes whether the working geometry should be manifold or not.
+option is 0.
+
+- \b eps_nano_relative (real) - the same as \b eps_nano, but relatively to
+the diagonal of the box bounding the geometry. By default this option is \f$10^{-5}\f$.
+
+- \b eps_sewing (real) - tolerance of the assembly. It rarely requires to be tuned.
+By default this option is \f$\mathrm{diag} \times 5 \cdot 10^{-4}\f$.
+
+- \b eps_sewing_relative (real) - the same as \b eps_nano but relatively to
+the diagonal of the box bounding the geometry. By default this option
+is \f$5 \cdot 10^{-4}\f$.
+
+- \b manifold_geometry (int) - describes whether the working geometry should be manifold or not.
When activated, this option helps PreCAD to process the dirtiest
-geometries. By default this option is 0.</li>
-<li>\b create_tag_collision (int) - creates new tags from original ones in case
+geometries. By default this option is 0.
+
+- \b create_tag_collision (int) - creates new tags from original ones in case
of collision (entity merge or association for example). By default
-this option is 0.</li>
-<li>\b periodic_tolerance (real) - defines the maximum distance error accepted between
-two sets of periodic entities. By default this option is \f$\mathrm{diag} \times 10^{-5}\f$.</li>
-<li>\b periodic_tolerance_relative (real) - the same as \b
-periodic_tolerance but in a relative unit. Bu default this option is \f$10^{-5}\f$.</li>
-<li>\b periodic_split_tolerance (real) - This periodicity processing related option defines
+this option is 0.
+
+- \b periodic_tolerance (real) - defines the maximum distance error accepted between
+two sets of periodic entities. By default this option is \f$\mathrm{diag} \times 10^{-5}\f$.
+
+- \b periodic_tolerance_relative (real) - the same as \b periodic_tolerance but in a relative unit.
+By default this option is \f$10^{-5}\f$.
+
+- \b periodic_split_tolerance (real) - This periodicity processing related option defines
the minimum distance between a CAD point and an imprinted point. It allows to indirectly
control the number of created points and small edges. By default this
-option is \f$\mathrm{diag} \times 10^{-4}\f$.</li>
-<li>\b periodic_split_tolerance_relative (real - the same as \b
+option is \f$\mathrm{diag} \times 10^{-4}\f$.
+
+- \b periodic_split_tolerance_relative (real - the same as \b
periodic_split_tolerance but in a relative unit. By default this
-option is \f$10^{-4}\f$.</li>
-</ul>
+option is \f$10^{-4}\f$.
-\n
The following advanced options are not documented and you can use them
at your own risk.
-\n\n Integer variables:
-<ul>
-<li> addsurf_ivertex</li>
-<li> anisotropic </li>
-<li> background </li>
-<li> coiter </li>
-<li> communication </li>
-<li> decim </li>
-<li> export_flag </li>
-<li> file_h </li>
-<li> gridnu </li>
-<li> gridnv </li>
-<li> intermedfile </li>
-<li> memory </li>
-<li> normals </li>
-<li> optim </li>
-<li> pardom_flag </li>
-<li> pinch </li>
-<li> rigid </li>
-<li> surforient </li>
-<li> tconf </li>
-<li> topo_collapse </li>
-</ul>
-Real variables:
-<ul>
-<li> addsurf_angle </li>
-<li> addsurf_R </li>
-<li> addsurf_H </li>
-<li> addsurf_FG </li>
-<li> addsurf_r </li>
-<li> addsurf_PA </li>
-<li> angle_compcurv </li>
-<li> angle_ridge </li>
-<li> anisotropic_ratio</li>
-<li> eps_pardom </li>
-</ul>
-String variables:
-<ul>
-<li> export_format </li>
-<li> export_option </li>
-<li> import_option </li>
-</ul>
+
+- Integer variables:
+ - addsurf_ivertex
+ - anisotropic
+ - background
+ - coiter
+ - communication
+ - decim
+ - export_flag
+ - file_h
+ - gridnu
+ - gridnv
+ - intermedfile
+ - memory
+ - normals
+ - optim
+ - pardom_flag
+ - pinch
+ - rigid
+ - surforient
+ - tconf
+ - topo_collapse
+- Real variables:
+ - addsurf_angle
+ - addsurf_R
+ - addsurf_H
+ - addsurf_FG
+ - addsurf_r
+ - addsurf_PA
+ - angle_compcurv
+ - angle_ridge
+ - anisotropic_ratio
+ - eps_pardom
+- String variables:
+ - export_format
+ - export_option
+ - import_option
\ref blsurf_top "Back to top"
-\anchor blsurf_local_size
-<h1>Local size</h1>
-
-Local sizes can be defined on faces, edges or vertices.
-<ul>
-<li>The faces, edges and vertices can belong to the meshed geometrical
-object or to its sub-shapes (created using <b>Explode</b> command).</li>
-<li>Groups of faces, edges and vertices are also handled.</li>
-<li>It is possible to attribute the same size to several geometries using multi-selection.</li>
-<li>The sizes are constant values or python functions.</li>
-<li>In case of a python function, the following rules must be respected:
-<ul>
-<li>The name of the function is f.</li>
-<li>If geometry is a face or a group of faces, the function is f(u,v).</li>
-<li>If geometry is an edge or a group of edges, the function is f(t).</li>
-<li>If geometry is a vertex or a group of vertices, the function is f().</li>
-<li>The function must return a double.</li>
-</ul></li>
-</ul>
+\section blsurf_local_size Local size
+
+Local sizes can be defined on faces, edges or vertices:
+
+- The faces, edges and vertices can belong to the meshed geometrical
+object or to its sub-shapes (created using <b>Explode</b> command).
+
+- Groups of faces, edges and vertices are also handled.
+
+- It is possible to attribute the same size to several geometries using multi-selection.
+
+- The sizes are constant values or python functions.
+
+- In case of a python function, the following rules must be respected:
+
+ - The name of the function is f.
+
+ - If geometry is a face or a group of faces, the function is f(u,v).
+
+ - If geometry is an edge or a group of edges, the function is f(t).
+
+ - If geometry is a vertex or a group of vertices, the function is f().
+
+ - The function must return a double.
3 different types of size maps can be defined:
-<ol>
-<li type="a">\ref blsurf_sizemap_computation "Computation of the physical size"</li>
-<li type="a">\ref blsurf_attractor "Advanced maps"</li>
-<li type="a">\ref blsurf_attractor_computation "Computation of attractors"</li>
-</ol>
+
+-# \ref blsurf_sizemap_computation "Computation of the physical size"
+-# \ref blsurf_attractor "Advanced maps"
+-# \ref blsurf_attractor_computation "Computation of attractors"
\ref blsurf_top "Back to top"
-\anchor blsurf_sizemap_computation
-<h2>Computation of the physical size</h2>
+\subsection blsurf_sizemap_computation Computation of the physical size
+
\image html blsurf_parameters_sizemap1.png
-The physical size is obtained by querying sizemap functions associated to the input CAD object for surfaces, curves and points.
+The physical size is obtained by querying sizemap functions associated
+to the input CAD object for surfaces, curves and points.
Each function can either return a value h (which is then trimmed
between the two bounds hphymin and hphymax), or "no answer" (by not
assigning a value to h), thus providing great flexibility in the
-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:
-<ul>
-<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>
-<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>
-<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>
-</ul>
-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".
-
-\ref blsurf_local_size "Back to \"Local size\"" \n
+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:
+
+- 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.
+
+- 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.
+
+- 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.
+
+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".
+
+\ref blsurf_local_size "Back to \"Local size\""\n
\ref blsurf_top "Back to top"
-\anchor blsurf_attractor
-<h2>Advanced maps</h2>
-\n
+\subsection blsurf_attractor Advanced maps
+
\image html blsurf_parameters_sizemap2.png
-\n
+
More specific size maps can be defined on faces.
-<ul>
-<li> <i> Attractors </i> allow to define the size of the mesh elements
+- <i> Attractors </i> 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.
-<ul>
-<li> The selected attractor can be a Vertex, an Edge, a Wire or a
-Compound mixing several entities of those types.</li>
-<li> The attractor doesn't have to be a sub-shape of the shape to mesh.</li>
-<li> The size will grow exponentially (see the formula below) but is
-bounded by gradation, \n so if you want the formula to be strictly
-respected, you should set the <i>gradation</i>
-to its maximum (2.5) in the <i>arguments</i> tab.
-</ul>
-\n
-<li> Furthermore you can choose to <i> keep the size constant </i>
+
+ - The selected attractor can be a Vertex, an Edge, a Wire or a
+ Compound mixing several entities of those types.
+
+ - The attractor doesn't have to be a sub-shape of the shape to mesh.
+
+ - The size will grow exponentially (see the formula below) but is
+ bounded by gradation, \n so if you want the formula to be strictly
+ respected, you should set the <i>gradation</i>
+ to its maximum (2.5) in the <i>arguments</i> tab.
+
+- Furthermore you can choose to <i> keep the size constant </i>
until a certain distance from a shape. This option can be combined or
not with an <i>attractor</i> size map described above.
-<ul>
-<li> If the two options are combined the size will remain constant
-until the distance specified in "constant over" and grow then as
-prescribed by the attractor function.</li>
-<li> Else the growing is only controled by the standard arguments of
-BLSURF (gradation ...).</li>
-</ul>
-</ul>
+
+ - If the two options are combined the size will remain constant
+ until the distance 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 ...).
\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"
-Remark : The validation of the hypothesis might take a few seconds if
+\note 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 a hypothesis has been defined.
-<br><b>See Also</b> a sample TUI Script of the \ref tui_blsurf "creation of a BLSurf hypothesis", including size map.
+\sa Sample TUI Script of the \ref tui_blsurf "creation of a BLSurf hypothesis", including size map.
-\ref blsurf_local_size "Back to \"Local size\"" \n
+\ref blsurf_local_size "Back to \"Local size\""\n
\ref blsurf_top "Back to top"
-\anchor blsurf_attractor_computation
-<h2>Computation of attractors</h2>
-\n
+\subsection blsurf_attractor_computation Computation of attractors
+
The size grows exponentially following the equation :
\f$h(d) = \mathrm{User Size} + (\mathrm{h\_start} - \mathrm{User Size}) \times e ^ { - \left( \frac{d}{R} \right) ^ {2} }\f$
-\n
+
Where :
-<ul>
-<li>h_start is the desired size on the given attractor shape</li>
-<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>
-<li>R is called the distance of influence and allows controlling the growth rate of the mesh </li>
-</ul>
+
+- h_start is the desired size on the given attractor shape
+
+- 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)
+
+- R is called the distance of influence and allows controlling the growth rate of the mesh
\image html blsurf_attractors2.png "Example of mesh created using attractors, the attractors here are the side edges and the size grows from the side of the surface towards the apex"
-\ref blsurf_local_size "Back to \"Local size\"" \n
+\ref blsurf_local_size "Back to \"Local size\""\n
\ref blsurf_top "Back to top"
-\anchor blsurf_enforced_elements
-<h1>Enforced vertices</h1>
+\section blsurf_enforced_elements Enforced vertices
\image html blsurf_parameters_enforced_vertices.png
It is possible to define some enforced vertices to BLSurf algorithm.
An enforced vertex is defined on a Face or a Compound by
-<ul>
-<li> selecting an existing Vertex or Compound,</li>
-<li> or creating a new vertex given its coordinates.</li>
-</ul>
+
+- selecting an existing Vertex or Compound,
+
+- or creating a new vertex given its coordinates.
+
The enforced vertex is the projection of a point defined by its
(x,y,z) coordinates on the selected face.
-<ul>
-<li>It is possible to define several enforced vertices on a face or a group of faces.</li>
-<li>If the projected point is on the boundary or outside of the face, it will be ignored.</li>
-<li>If a group name is specified, the enforced nodes will be added in the group. If the group does not exist it will be created.
-</ul>
-<br><b>See Also</b> a sample TUI Script of the \ref tui_blsurf "creation of a BLSurf hypothesis", including enforced vertices.
+- It is possible to define several enforced vertices on a face or a group of faces.
+
+- If the projected point is on the boundary or outside of the face, it will be ignored.
+
+- If a group name is specified, the enforced nodes will be added in the group. If the group does not exist it will be created.
+
+\sa Sample TUI Script of the \ref tui_blsurf "creation of a BLSurf hypothesis", including enforced vertices.
\ref blsurf_top "Back to top"
-\anchor blsurf_limitations
-<h1>Limitations</h1>
+\section blsurf_limitations Limitations
Currently BLSURF plugin has the following limitations.
-<ul>
- <li>BLSURF algorithm cannot be used as a local algorithm (on
- sub-meshes) or as a provider of a low-level
- mesh for some 3D algorithms, because the BLSURF mesher (and
- consequently plugin) does not provide the information on node
- parameters on edges (U) and faces (U,V). For example the
- following combinations of algorithms are impossible:
- <ul>
- <li> global MEFISTO or Quadrangle(mapping) + local BLSURF;</li>
- <li> BLSURF + Projection 2D from faces meshed by BLSURF;</li>
- <li> local BLSURF + Extrusion 3D;</li>
- </ul>
- </li>
-</ul>
+- BLSURF algorithm cannot be used as a local algorithm (on
+sub-meshes) or as a provider of a low-level
+mesh for some 3D algorithms, because the BLSURF mesher (and
+consequently plugin) does not provide the information on node
+parameters on edges (U) and faces (U,V). For example the
+following combinations of algorithms are impossible:
+
+ - global MEFISTO or Quadrangle(mapping) + local BLSURF;
+
+ - BLSURF + Projection 2D from faces meshed by BLSURF;
+
+ - local BLSURF + Extrusion 3D;
+
\ref blsurf_top "Back to top"
*/
