/*!

\page blsurf_hypo_page BLSURF Parameters hypothesis

\n BLSURF Parameters hypothesis works only with <b>BLSURF</b> 2d
algorithm. This algorithm is a commercial software.

<h1>General parameters</h1>

\image html blsurf_parameters.png

<ul>
<li><b>Name</b> - allows defining the name of the hypothesis (BLSURF
Parameters_n by default).</li>

<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>

<li><b>User size</b> - defines the size of the generated mesh elements. </li>

<li><b>Max Physical Size</b> - defines the upper limit of mesh element size. </li>

<li><b>Min Physical Size</b> - defines the lower limit of mesh element size. </li>

<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>

<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>

<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>

<li><b>Max Geometrical Size</b> - defines the upper limit of the <i>geometrical size</i>.</li>

<li><b>Min Geometrical Size</b> - defines the lower limit of the <i>geometrical size</i>.</li>

<li><b>Gradation</b> - maximum ratio between the lengths of
two adjacent edges. </li>

<li><b>Allow Quadrangles</b> - if checked, allows the creation of quadrilateral elements.</li>

<li><b>Patch independent</b> - if checked, geometrical
edges are not respected and all geometrical faces are meshed as one
hyper-face.</li>

<h1>Advanced parameters</h1>

\image html blsurf_parameters_advanced.png

<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
  pre-process the geometrical model to eventually produce a conform
  mesh. </li>
</ul>

<li><b>Verbosity level</b> - Defines the percentage of "verbosity" of
BLSURF [0-100].</li>

<li><b>Add option</b> - provides the choice of multiple 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.

</ul>

\n
The following options are commonly usable. The notion of <i>diag</i>
used in the descriptions means
the diagonal of the bounding box of the geometrical object to mesh.

<ul>
<li><b>topo_eps1</b> (real) - is the tolerance level inside a CAD
patch. By default is equal to <i>diag</i> � 10-4. This tolerance is used to
identify nodes to merge within one geometrical face when \b Topology
option is to pre-process. Default is <i>diag</i>/10.0.</li>

<li><b>topo_eps2</b> (real) - is the tolerance level between two CAD
patches. By default is equal to <i>diag</i> � 10-4. This tolerance is used to
identify nodes to merge over different geometrical faces when
\b Topology option is to pre-process. Default is <i>diag</i>/10.0.</li>

<li>\b LSS (real) - is an abbreviation for "length of sub-segment". It is
a maximal allowed length of a mesh edge. Default is 0.5.</li>

<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>

\anchor blsurf_hinterpol_flag
<li>\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: <i>v = h1 + t (h2 - h1 )</i></li>
<li>1 - the interpolation is geometric: <i>v = h1 * pow( h2/h1, t)</i></li>
<li>2 - the interpolation is sinusoidal: <i>v = (h1+h2)/2 +
(h1-h2)/2*cos(PI*t)</i></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 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
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>


<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
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>

<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
if<i> fabs(P2-P1) < eps_ends</i>, where <i>P1</i> and <i>P2</i> are the
extremities of a curve. Default is <i>diag</i>/500.0.</li>

<li>\b prefix (char) - is a prefix of the files generated by
BLSURF. Default is "x".</li>

<li>\b refs (integer) - reference of a surface, used when exporting
files. Default is 1.</li>
</ul>

\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>    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>    eps_pardom     </li>
</ul>
String variables:
<ul>
<li>    export_format  </li>
<li>    export_option  </li>
<li>    import_option  </li>  
</ul>

<h1>Custom size map</h1>

\image html blsurf_parameters_sizemap1.png 

User 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>

\anchor blsurf_sizemap_computation
<h2>Computation of the physical size</h2>
\n
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".

\anchor blsurf_attractor
<h2>Advanced maps</h2>
\n
\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
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>
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>

\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"
\n
\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"
\n
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 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.

\anchor blsurf_attractor_computation
<h2>Computation of attractors</h2>
\n
The size grows exponentially following the equation : h(d) = User size + (h_start - User Size) * exp( -(d / R)^2  ).
\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>

<h1>Custom enforced vertices</h1>

\image html blsurf_parameters_enforced_vertices.png

It is possible to define some enforced vertices to BLSurf algorithm
without creating any vertices by CAD algorithms.
<ul>
<li>The enforced vertex is the projection of a point defined by its
(x,y,z) coordinates on the selected face.</li>
<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>
</ul>

<br><b>See Also</b> a sample TUI Script of the \ref tui_blsurf "creation of a BLSurf hypothesis", including enforced vertices.

<h1>Limitations</h1>

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>

*/