====== 3D Meshers (Volumes) ======


===== Transfinite Mesher =====

Metafor possesses a simple transfinite mesher, which is able to mesh hexahedra (object with 6 sides, such as a cube). For more complex geometries, it is necessary to divide it into hexaedra or use external meshers ([[doc:user:general:glossaire#Samcef]], [[http://tetgen.berlios.de/|TetGen]], ...) and import the mesh in Metafor (see [[doc:user:geometry:import:tuto2]]).

__Preliminary note:__ To mesh a ''[[doc:user:geometry:user:volumes|Volume]]'', all its ''[[doc:user:geometry:user:faces|Sides]]'' and ''[[doc:user:geometry:user:courbes|Curves]]'' must be meshed first !

{{ doc:user:mesh-3d-1.gif |Volume hexaédrique}}

==== With auto-detection ====

Auto-detection is possible if the ''[[doc:user:geometry:user:peaux|Skin]]'' has 12 edges, each of which possesses only one line.

  TransfiniteMesher3D(volumeset(number)).execute(type)

| ''number'' | number of the ''[[doc:user:geometry:user:volumes|Volume]] to mesh''                         |
| ''type''   | = ''True'' if mesh elements must be generated (''CELL_HEXA'')\\ = ''False''  if only nodes must be generated (useful to debug only)      |

In this case, the ''[[doc:user:geometry:user:peaux|Skin]]'' must be defined with the orientation shown below:

{{ doc:user:mesh-3d-2.gif |Définition de la skin du domaine pour l'autodétection}}

which means that

  skin = add(Skin(1)); 
  for i in [1,2,3,4,5,6]:
     skin.push(sideset(i))

where the number used in the ''push'' function are the number of the ''[[doc:user:geometry:user:faces|Sides]]'' included in the ''[[doc:user:geometry:user:peaux|Skin]]''.


==== Without auto-detection ====

This case is the most general, and can be applied to any ''[[doc:user:geometry:user:peaux|Skin]]'' with the shape of a hexaedron. The definition of the skin must no longer be as the above figure shows, which means the sides can be "pushed" in the skin in any order.

The mesher needs a set of 12 sets of ''[[doc:user:geometry:user:courbes|Curves]]'', where each of these sets defines an edge of the hexaedron.

  mat = ((mat11, ..., mat1nbmax), ..., (mat121, ..., mat12nbmax))
  TransfiniteMesher3D(volumeset(number)).execute2(mat, type)

where ''number'' is the number of the hexahedral ''[[doc:user:geometry:user:volumes|Volume]]''to mesh, and ''mat'' is a Python tuple with 12 components. Each component is a tuple which contains the number of the curves which constitute each edge. Each of these 12 edges can be made of a different number of curves.

These 12 tuples must be ordered as shown below:

{{ doc:user:mesh-3d-3.gif |Ordre des lignes dans le tuple python}}

__Example:__

{{ doc:user:mesh3d-4.jpg |Maillage manuel - géométrie initiale}}

The hexahedral domain above can be meshed with the command:

  TransfiniteMesher3D(volumeset(1)).execute2( ((103,101,102),2,3,4,5,6,7,8,10,11,12,13) )
or
  TransfiniteMesher3D(volumeset(1)).execute2( (5,11,(103,101,102),10,7,12,3,13,8,6,2,4) )
or
  TransfiniteMesher3D(volumeset(1)).execute2( (6,12,2,11,8,13,4,10,5,7,3,(101,102,103)) )
or
  ...

leading to:

{{ doc:user:mesh3d-5.jpg |Maillage résultant}}

==== Transfinite 3D mesher with non-uniform mesh elements distribution ====

This is done with the commands:

  MesherTFI3D =TransfiniteMesher3D(volumeset(number))
  MesherTFI3D.setEnableDistribution()
  MesherTFI3D.execute(type, tri) ou MesherTFI3D.execute2(mat, type)        

when one if the edges is already discretized using a mesh elements distribution.

__Note__ : By default, the parameter ''setEnableDistribution'' is set to ''True''.

===== Mesher by extrusion =====

This method can be used, but could be improved upon: density non-constant along the extrusion direction, improvement of meshing speed, giving the extruded nodes as groups (internal ones, external surface, ...). For now on, a ''[[doc:user:geometry:user:faces|Side]]'', a ''[[doc:user:geometry:user:peaux|Skin]]'' or a ''[[doc:user:geometry:user:selections|Group]]'' can be extruded along any direction, with any number of elements.

The geometry associated to the extrusion can also be created (only for a ''[[doc:user:geometry:user:faces|Side]]''). For a ''[[doc:user:geometry:user:peaux|Skin]]'' or a ''Group'', we can create the ''[[doc:user:geometry:user:points|Points]]'' and ''[[doc:user:geometry:user:Courbes|Curves]]'' associated by extrusion to the ''[[doc:user:geometry:user:points|Points]]'' and ''[[doc:user:geometry:user:Courbes|Curves]]'' of the object.

=== Example ====

Extrusion of a circle pierced by a square (see ''apps.qs.extruMesher3d'' and ''apps.qs.extruMesher3dTx'' or ''apps.qs.extruMesher3dTorsion'' ''apps.qs.extruMesher3dDist03'' for modified extrusions).

{{commit:2006:extru2_000.jpg?200|Extrusion d'un cercle troué}}
{{:doc:user:geometry:mesh:extrusionmeshertx.jpg?150|setXfct(fctX) }}
{{:doc:user:geometry:mesh:extrusionmesherrot.jpg?150|setAnglefct(fctAngle)}}
{{:doc:user:geometry:mesh:extrusionmesherDist.png?100|setNbOfLayers(10,0.3)}}

The definition and meshing of the circle can be seen in the the file. To extrude the result (''[[doc:user:geometry:user:faces|Side]]'' #1):

  mesher = ExtrusionMesher3D(sideset(1), groupset(1))
  mesher.setFillGroup(True)
  mesher.setDirection(0.0,0.0,1.0)
  mesher.setLength(length)
  mesher.setNbOfLayers(nLayers, dist = 1.0)
  mesher.setAnglefct(fctAngle)	
  mesher.setXfct(fctX)	
  mesher.setYfct(fctY)
  mesher.execute()
  grpNo = mesher.getLastLayer(no)

| Group 1          | all the mesh element refer to this group (the ''FieldApplicator'' is applied to this group) |
| setFillGroup()   | fills Group 1 with the nodes of the mesh                                          |
| setDirection     | direction of the extrusion (by default = ''z'')                                              |
| setLength        | length of the extrusion |

| setNbOfLayers    | nLayers : number of extruded elements                                          |
|                  | dist  : ratio between the length of the last and first element (default : dist = 1.0) |
| setAnglefct(fctAngle)	| Application of a rotation of slices around extrusion vector (direction 'z' but starting from origin!!!) | 
| fctAngle | One parameter defining rotation of slices function in degrees (t) - t=[0,1] ATTENTION : fctAngle(0) = 0 |
| setXfct(fctX)	| Application of a modification of the generatrice direction in X Direction | 
| setYfct(fctY)	| Application of a modification of the generatrice direction in Y Direction | 
| fctX/fctY | One parameter defining modification of generatrice : fct(t) - ATTENTION t=[0,Length] and fctX/fctY(0) = 0 |
| execute          | execute the extrusion                                                               |
| getLastLayer(no) | returns the group grpNo (number ''no'') which contains the nodes of the last layer  |


:!: When meshing in 2D, the wires must be defined "area to the left" :!:


=== Example 2 ====

In a same way, a planar face meshed with triangles can be extruded in 3D to be meshed with prisms (see ''apps.monosMeca.monoTrac3dPenta'').

{{ commit:2007:cube_prismes.jpg?200 |Maillage d'un cube en prismes}}


==== Creation of the geometry ====


=== General case: Extrusion of a''Side'', a ''Skin'' or a ''Group'' ===

After the extrusion of a ''[[doc:user:geometry:user:faces|Side]]'', a ''[[doc:user:geometry:user:peaux|Skin]]'' or a ''[[doc:user:geometry:user:selections|Group]]'', the geometry can also be extruded from a ''[[doc:user:geometry:user:faces|Side]]'' with the function:
  mesher.createGeometryOn(Side, NoGObject, geometry)
Geometrical objects are created and numbered starting from NoGObject.

The function ''createLineAbove'' can create only one ''[[doc:user:geometry:user:Courbes|Line]]'' corresponding to the extrusion of a ''[[doc:user:geometry:user:Points|Point]]'' :

  line = createLineAbove(pt1, NumLine, NumPtOnTop, geometry)

| line       | ''[[doc:user:geometry:user:Courbes|Line]]'' created (numbered: NumLine)             |
| pt1        | reference ''[[doc:user:geometry:user:Points|Point]]''                             |
| NumPtOnTop | number of the ''[[doc:user:geometry:user:Points|Point]]'' situated at the other line extremity |


=== Particular case : extrusion of a Side ===

To create a geometry after the extrusion of a ''[[doc:user:geometry:user:faces|Side]]'', this function is used:
  mesher.createGeometry(NoGObject, geometry)
:!: To use this function, the target to extrude must be of type ''[[doc:user:geometry:user:faces|Side]]'' :!:

Geometrical objects are created and numbered starting from NoGObject.


=== Récupération des objets géométrique ===

The retrieval of the created geometrical objetcs is done with the functions:

  Vol1  = mesher.getVolumeOnTop(side1)
  side  = mesher.getSideOnTop(curveOrSide)
  curve = mesher.getCurveOnTop(pointOrCurve)
  point = mesher.getPointOnTop(ptref)

| Vol1  | ''[[doc:user:geometry:user:volumes|Volume]]'' created from ''Side 1'', the one which is extruded.
| side  | ''[[doc:user:geometry:user:faces|Side]]'' created from the object ''curveOrSide'' (which corresponds to a ''[[doc:user:geometry:user:Courbes|Curve]]'' or a ''[[doc:user:geometry:user:faces|Side]]'' of the extruded object). \\ If : ''curveOrSide'' = ''[[doc:user:geometry:user:courbes|Curve]]'' -> the returned ''Side'' is tangent to the extrusion direction. \\ If: ''curveOrSide'' = ''[[doc:user:geometry:user:faces|Side]]''     -> the extrusion direction is a vector which is normal to the returned ''Side'' |
| curve | ''[[doc:user:geometry:user:Courbes|Curve]]'' created from ''pointOrCurve'' (which corresponds to a ''[[doc:user:geometry:user:Points|Point]]'' or a ''[[doc:user:geometry:user:Courbes|Curve]]'' of the extruded object) \\ If : ''pointOrCurve'' = ''[[doc:user:geometry:user:Points|Point]]'' -> the returned ''Curve'' is tangent to the extrusion direction. \\ If: ''pointOrCurve'' = ''[[doc:user:geometry:user:Courbes|Curve]]''     -> the extrusion direction is a vector which is normal to the returned ''Curve''|
| point | ''[[doc:user:geometry:user:Points|Point]]'' created from ''ptref'' (''[[doc:user:geometry:user:Points|Point]]'' of the extruded object) |

The geometry is created in the test cases ''apps.welding.welding'' and ''aspCrushing.tests.threeD.smoothStripRoughTool''.

<important note>
CAREFUL, after creating the geometry, the ''Volume'', returned by the function ''mesher.getVolumeOnTop(side)'' must be added with the ''push'' command to the ''FieldApplicator'' in place of the group (groupset(1) of the constructor of the object ''ExtrusionMesher3D''). In the case where only one layer of elements is found in the extrusion direction, the group (groupset(1) of the constructor of the object ''ExtrusionMesher3D'') must be added with the ''push'' command in the ''FieldApplicator'', whichever the extruded entity (''[[doc:user:geometry:user:faces|Side]]'', ''[[doc:user:geometry:user:peaux|Skin]]'' or ''[[doc:user:geometry:user:selections|Group]]''). 
</note>


===== Mesher by extrusion of revolution =====

Axisymmetric extrusion of a meshed side.
The extrusion can be open ($0 < \mbox{angle} < 360^\circ$) or close ($\mbox{angle} = 360^\circ$).

To this day, no reconstruction of the extruded geometry exists. ''Groups'' should be used to set boundary conditions. 

  mesher = RevolutionExtrusionMesher3D(gobject, group, axe, angle=180.0)
  setAngle(angle)
  mesher.setNbOfLayers(10)
  mesher.execute()

| gobject          | Meshed 2D geometrical entity                                                            |
| group            | Group father of the 3D mesh elements                                                    |
| axe              | Line which defines the revolution axis                                                  |
| setAngle         | Angle of the extrusion (in degrees 0.0 < angle <= 360.0 - default = 180.0)              |
| setNbOfLayers    | number of extruded elements                                                             |
| setFillGroup     | fill the reference group with all nodes (base & generated)                              |
| execute          | executes the extrusion                                                                  |
| getLastLayer     | return the group of the last layer (if not closed extrusion)                            |

==== Example ====

{{:commit:2012:revolutionextusion1.png?200|}} {{:commit:2012:revolutionextrusion2.png?200|}} {{:commit:2012:revolutionextrusion3.png?200|}}