BLSURF Parameters hypothesis

BLSURF Parameters hypothesis works only with BLSURF 2d algorithm. This algorithm is a commercial software.

General parameters

• Name - allows defining the name of the hypothesis (BLSURF Parameters_n by default).

• Physical Mesh - can be set to None, Custom or Size Map

  • if set to "Custom", allows user input in the in User size, Max Physical Size and Min Physical Size fields.
  • if set to "Size Map", behaves like "Custom" mode and takes into account the custom elements sizes given in the Size Map tab.

• User size - defines the size of the generated mesh elements.

• Max Physical Size - defines the upper limit of mesh element size.

• Min Physical Size - defines the lower limit of mesh element size.

• Geometrical mesh - if set to "Custom", allows user input in Angle Mesh S, Angle Mesh C and Gradation fields. These fields control computation of the element size, so called geometrical size, conform to the surface geometry considering local curvatures.
  If both the User size and the geometrical size are defined, the eventual element size correspond to the least of the two.

• Angle Mesh S - maximum angle between the mesh face and the tangent to the geometrical surface at each mesh node, in degrees.

• Angle Mesh C - maximum angle between the mesh edge and the tangent to the geometrical curve at each mesh node, in degrees.

• Max Geometrical Size - defines the upper limit of the geometrical size.

• Min Geometrical Size - defines the lower limit of the geometrical size.

• Gradation - maximum ratio between the lengths of two adjacent edges.

• Allow Quadrangles - if checked, allows the creation of quadrilateral elements.

• Patch independent - if checked, geometrical edges are not respected and all geometrical faces are meshed as one hyper-face.

  Advanced parameters

  

• Topology - allows creation of a conform mesh on a shell of not sewed faces.

  • "From CAD" means that mesh conformity is assured by conformity of a shape.
  • "Pre-process" and "Pre-process++" allow the BLSURF software to pre-process the geometrical model to eventually produce a conform mesh.

• Verbosity level - Defines the percentage of "verbosity" of BLSURF [0-100].

• Add option - 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.

• Clear option - removes the option selected in the table.

The following options are commonly usable. The notion of diag used in the descriptions means the diagonal of the bounding box of the geometrical object to mesh.

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

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

• LSS (real) - is an abbreviation for "length of sub-segment". It is a maximal allowed length of a mesh edge. Default is 0.5.

• frontal (integer)

  • 1 - the mesh generator inserts points with an advancing front method.
  • 0 - it inserts them with an algebraic method (on internal edges). This method is slightly faster but generates less regular meshes.

  Default is 0.

• hinterpol_flag (integer) - determines the computation of an interpolated value v between two points P1 and P2 on a curve. Let h1 be the value at point P1, h2 be the value at point P2, and t be a parameter varying from 0 to 1 when moving from P1 to P2 .

  • 0 - the interpolation is linear: v = h1 + t (h2 - h1 )
  • 1 - the interpolation is geometric: v = h1 * pow( h2/h1, t)
  • 2 - the interpolation is sinusoidal: v = (h1+h2)/2 + (h1-h2)/2*cos(PI*t)

  Default is 0.

• hmean_flag (integer) - determines the computation of the average of several values:

  • -1 - the minimum is computed.
  • 0 or 2 - the arithmetic average computed.
  • 1 - the geometric average is computed.

  Default is 0.

• CheckAdjacentEdges, CheckCloseEdges and 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,CheckCloseEdges decreases the sizes of the edges when two boundary curves are neighboring,CheckAdjacentEdges balances the sizes of adjacent edges, and CheckWellDefined checks if the parametric domain is well defined. Default values are 0.

• CoefRectangle (real)- defines the relative thickness of the rectangles used by subroutine CheckCloseEdges (see above). Default is 0.25.

• eps_collapse (real) - if more than 0.0, BLSURF removes curves whose lengths are less than eps_collapse. To obtain an approximate value of the length of a curve, it is arbitrarily split into 20 edges. Default is 0.0.

• eps_ends (real) - is used to detect the curves whose lengths are very small, which sometimes constitutes an error. A message is printed if fabs(P2-P1) < eps_ends, where P1 and P2 are the extremities of a curve. Default is diag/500.0.

• prefix (char) - is a prefix of the files generated by BLSURF. Default is "x".

• refs (integer) - reference of a surface, used when exporting files. Default is 1.

The following advanced options are not documented and you can use them at your own risk.

Integer variables:

• addsurf_ivertex
• 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
• eps_pardom

String variables:

• export_format
• export_option
• import_option

Custom size map

User 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 Explode 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.

Computation of the physical size

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:

• 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 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 hinterpol flag.

Advanced maps

More specific size maps can be defined on faces.

• Attractors 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.
  • 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,
    so if you want the formula to be strictly respected, you should set the gradation to its maximum (2.5) in the arguments tab.
  
  
• Furthermore you can choose to keep the size constant until a certain distance from a shape. This option can be combined or not with an attractor size map described above.
  • 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 ...).

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"

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 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.

See Also a sample TUI Script of the creation of a BLSurf hypothesis, including size map.

Computation of attractors

The size grows exponentially following the equation : h(d) = User size + (h_start - User Size) * exp( -(d / R)^2 ).
Where :

• 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

Custom enforced vertices

It is possible to define some enforced vertices to BLSurf algorithm without creating any vertices by CAD algorithms.

• The enforced vertex is the projection of a point defined by its (x,y,z) coordinates on the selected face.
• 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.

See Also a sample TUI Script of the creation of a BLSurf hypothesis, including enforced vertices.

Limitations

Currently BLSURF plugin has the following limitations.

• 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;