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sup_gmsh.py

#@ MODIF sup_gmsh Utilitai  DATE 08/11/2005   AUTEUR ASSIRE A.ASSIRE 
# -*- coding: iso-8859-1 -*-
#            CONFIGURATION MANAGEMENT OF EDF VERSION
# ======================================================================
# COPYRIGHT (C) 1991 - 2004  EDF R&D                  WWW.CODE-ASTER.ORG
# THIS PROGRAM IS FREE SOFTWARE; YOU CAN REDISTRIBUTE IT AND/OR MODIFY
# IT UNDER THE TERMS OF THE GNU GENERAL PUBLIC LICENSE AS PUBLISHED BY
# THE FREE SOFTWARE FOUNDATION; EITHER VERSION 2 OF THE LICENSE, OR
# (AT YOUR OPTION) ANY LATER VERSION.
#
# THIS PROGRAM IS DISTRIBUTED IN THE HOPE THAT IT WILL BE USEFUL, BUT
# WITHOUT ANY WARRANTY; WITHOUT EVEN THE IMPLIED WARRANTY OF
# MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. SEE THE GNU
# GENERAL PUBLIC LICENSE FOR MORE DETAILS.
#
# YOU SHOULD HAVE RECEIVED A COPY OF THE GNU GENERAL PUBLIC LICENSE
# ALONG WITH THIS PROGRAM; IF NOT, WRITE TO EDF R&D CODE_ASTER,
#    1 AVENUE DU GENERAL DE GAULLE, 92141 CLAMART CEDEX, FRANCE.
# ======================================================================

import os.path, string, os, copy
from Numeric import *

try :
  from Cata.cata import *
  from Accas import _F
except :
  print 'Fonctionnalites Aster indisponibles'


_CARAC = {
  'prec' : 1.E-8
  }


def Class_search(class_name, target_class) :

  """
    Check that class_name inherits from target_class
    (run recursively through the inheritance lists)
  """

  if class_name == target_class : return 1

  for cl in class_name.__bases__ :
    if Class_search(cl, target_class) : return 1
  return 0


def Progress(L,**para) :

  """
    Compute the unknown parameters for a geometric progression :
      r = ratio
      N = number of elements
      h = initial size

    So that :
      L = Sum(i=0:N-1, h(i)) where h(i+1) = h(i)*r, h(0)=h

    Usage :
      Progress(L,r=...,N=...) -> h
      Progress(L,r=...,h=...) -> N
      Progress(L,h=...,N=...) -> r

  """

  prec = 1.E-4

 # Calcul de N
  if 'N' not in para.keys() :
    r = float(para['r'])
    h = float(para['h'])
    N = log(1+(r-1)*L/h)/log(r)
    N = int(N+0.5)
    return N

 # Calcul de h
  elif 'h' not in para.keys() :
    r = float(para['r'])
    N = int(para['N']+0.5)
    h = L*(r-1)/(r**N-1)
    return h

 # Calcul de r
  elif 'r' not in para.keys() :
    h = float(para['h'])
    N = int(para['N']+0.5)
    a = L/h
    if N > a :
      x = 0
    else :
      x = a**(1./(N-1))

    for i in xrange(100) :
      res = x**N - a*x + a-1
      if abs(res) < prec*(x-1)*a :
        return x
      dx = res/(a-N*x**(N-1))
      x = x+dx

    raise 'Solution failure'

  else :
    raise 'Unknown parameters'



def Is_Geometric(object) :

  """
    return true if the object inherits of the Geometric class
  """

  return Class_search(object.__class__, Geometric)



# --------------------------------------------------------------------------------------

00121 class Geometric :

  """
    GENERIC CLASS FOR GEOMETRICAL OBJECTS

    private attribute
     parameters  : dictionnary of the attributes (except relation and parameters itself)
                   see __getattr__ and __setattr__


    Attributes
     num         : index among gmsh objects
     md          : mesh descriptor
     mesh        : related mesh object
     relation    : model object in case of coincidence
     type        : type of the object (None, Point, Line, Circle, Surface, Volume)

    Public methods
     Is_point : return true is the object inherits of the Point class

     Is_line  : return true is the object inherits of the Line class

     Is_surface : return true is the object inherits of the Surface class

     Is_volume : return true is the object inherits of the Volume class

     Base_class : return the name of the base class : Point, Line, Surface
                     or Volume

     Is_same_dimension : return true is both objects are of the same dimension
                         (point, line, surface or volume)
       in -> object to compare to self

     Duplicate   : duplicate an object and base its mesh_descriptor
                   on the mesh_descriptor of the model

     Coincide    : assert that an object is coincident with a model one
                   All the attributes are then automatically read from
                   the model object (see __setattr__ and __getattr__).
       in -> model object

    Private method

     Root :
       Provides the root object of an object, ie the object itself if there is no relation
       or the deepest model in case of relation.

     Geometric_coincide : check if a geometrical coincidence is possible
                          return information about the coincidence, false else.
       in -> model object

     Deep_coincide : proceed recursively to ensure coincidence of the relevant sub-objects
       in -> model object
       in -> correspond (information returned by Geometric_coincide)

     __setattr__ : distinguish two sets of attributes
                    relation (to express a relation with a model object in case of coincidence)
                    all the other attributes which are stored in the dictionnary parameters
                    instead of the usual __dict__ if there is no relation (see Coincide)
                    and in the model object if there is a coincidence

     __getattr__ : if the object is related (relation <> None) the attribute is read
                   in the model object. Else, it is read in the current object, actually
                   in the dictionnary parameters (see __setattr__)

     Thanks to these two overloaded methods, the access to the attributes is usual if
     there is no relation whereas the attributes of the model object are accessed
     transparently if there is a relation.

     __cmp__ :
       The comparison of two objects involves possible coincidence. It is no more the object ids
       that are compared but the object roots (.relation if any).

     Gmsh  : produce the source code for Gmsh
       in -> mesh

     Gmsh_send : send a line code to the gmsh interpreter
       in -> line_code (string)

     Intermediate_meshing : produce the source code for the intermediate objects
       in -> mesh

     Object meshing : produce the source code for the current object
       var -> object number (modified if several objects are created)

  """

  def __init__(self) :
    self.relation    = None
    self.parameters  = {}
    self.num         = 0
    self.md          = Mesh_Descriptor()

    types = {}
    types[Geometric]   = 'Geometric'
    types[Point]       = 'Point'
    types[Line]        = 'Line'
    types[Circle]      = 'Circle'
    types[Surface]     = 'Surface'
    types[Volume]      = 'Volume'
    types[LineLoop]    = 'LineLoop'
    types[SurfaceLoop] = 'SurfaceLoop'
    try :
      self.type = types[self.__class__]
    except KeyError :
      raise 'Unknown object type'


  def Is_point(self) :
    return Class_search(self.__class__, Point)

  def Is_line(self) :
    return Class_search(self.__class__, Line)

  def Is_surface(self) :
    return Class_search(self.__class__, Surface)

  def Is_volume(self) :
    return Class_search(self.__class__, Volume)

  def Base_class(self) :
    if self.Is_volume()  : return 'Volume'
    if self.Is_surface() : return 'Surface'
    if self.Is_line()    : return 'Line'
    if self.Is_point()   : return 'Point'

  def Is_same_dimension(self, obj) :

    return (
      (self.Is_point()    and  obj.Is_point()   ) or
      (self.Is_line()     and  obj.Is_line()    ) or
      (self.Is_surface()  and  obj.Is_surface() ) or
      (self.Is_volume()   and  obj.Is_volume()  )
      )


  def __setattr__(self, attr, value) :

    if attr in ['relation','parameters'] :
      self.__dict__[attr] = value
    else :
      if self.relation :
        setattr(self.relation,attr,value)
      else :
        self.parameters[attr] = value


  def __getattr__(self,attr) :

    if self.relation :
      return (getattr(self.relation,attr))
    else :
      if attr in self.parameters.keys() :
        return self.parameters[attr]
      else :
        raise AttributeError,attr


  def Root(self) :

    o = self
    while o.relation : o = o.relation
    return o


  def __cmp__(self,obj) :

    if self.Root() is obj.Root() :
      return 0
    else :
      return -1


  def Geometric_coincide(self,obj) : return 0

  def Deep_coincide(self,obj,correspond) : pass

  def Coincide(self, obj) :

    if self == obj : return       # in that way recursive loops cannot exist

    if self.relation :            # the root is put in coincidence, not the object itself
      self.Root().Coincide(obj)
      return

    if not self.Is_same_dimension(obj) :
      raise 'Coincidence impossible : objects are not of the same dimension'

    correspond = self.Geometric_coincide(obj)
    if not correspond :
      raise 'The objects are not geometrically coincident'

    self.Deep_coincide(obj,correspond)
    self.relation = obj


  def Duplicate(self) :

    return copy.deepcopy(self)    # special deepcopy for the Mesh_Descriptor


  def Gmsh(self,mesh) :

    if self.num : return              # already meshed object
    self.mesh = mesh                  # Storing the mesh
    self.Intermediate_meshing(mesh)   # creation of the intermediate objects
    num = mesh.num+1                  # New object number
    self.Object_meshing(num)          # object meshing (with current number num)
    mesh.num = num                    # Updating the current gmsh pointer
    self.num = num                    # Storing the current object number


  def Gmsh_send(self, line_code) :

    self.mesh.command.append(line_code)


  def Intermediate_meshing(self,mesh) :
    pass


  def Object_meshing(self,num) :
    raise "Creation of the Gmsh source not implemented"




# -------------------- POINT OBJECTS ---------------------


00351 class Point(Geometric) :

  """
    POINT OBJECT

    Public methods
     __init__ :
       in -> coordinates (the 3rd is zero by default)

     Size  : set the size of the neighbouring elements
       in -> size

     Attractor : define the point as an attractor
       in -> scale_x : size amplification factor in the x-direction
       in -> scale_y : size amplification factor in the y-direction
       in -> distance: influence distance for the perturbation

     Translate : translation of the point
       in -> x,y,z translation vector (default : z=0)

    Attributes
     coor : coordinates
     size : neighbouring element size
     attractor : parameters of the attractor
  """

  def __init__(self,x,y,z=0) :

    Geometric.__init__(self)
    self.coor = array([x,y,z], Float)
    self.attractor = None


  def Geometric_coincide(self,obj) :

    global _CARAC
    prec = _CARAC['prec']

    d = VectorNorm(self.coor - obj.coor)
    if d < prec*self.md.size :
      return 1
    else :
      return None


  def Size(self,h) :

    self.md.size = float(h)


  def Attractor(self, scale_x, scale_y, distance) :

    self.attractor = (float(scale_x), float(scale_y), float(distance))


  def Translate(self,x,y,z=0) :

    tran = array([x,y,z]).astype(Float)
    self.coor = self.coor + tran


  def Object_meshing(self,num) :

    ch = (
        'Point(' + `num` + ') = {'
      + `self.coor[0]` + ', '
      + `self.coor[1]` + ', '
      + `self.coor[2]` + ', '
      + `self.md.size` + '};'
      )
    self.Gmsh_send(ch)

    if self.attractor :
      ch = (
        'Attractor Point{' + `num` + '} = {'
        + `self.attractor[0]`+','
        + `self.attractor[1]`+','
        + `1./self.attractor[2]` + '};'
        )
      self.Gmsh_send(ch)



# -------------------- LINE OBJECTS ----------------------


00437 class Line(Geometric) :

  """
    LINE OBJECT


    Public methods

     Attractor : define the point as an attractor
       in -> scale_x : size amplification factor in the x-direction
       in -> scale_y : size amplification factor in the y-direction
       in -> distance: influence distance for the perturbation

  """


  def __init__(self,*points) :

    Geometric.__init__(self)

    if len(points) <=1 :
      raise "There should be at least two points"

    for point in points :
      if not point.Is_point() :
        raise "Arguments should be points"

    self.points = list(points)
    self.attractor = None


  def Geometric_coincide(self,obj) :

    nb_points = len(self.points)
    if nb_points <> len(obj.points) :
      raise 'To coincide, lines should have the same number of points'

   # same order of points
    info = range(nb_points)
    for i in range(nb_points) :
      p1 = self.points[i]
      p2 = obj.points[info[i]]
      if not p1.Geometric_coincide(p2) :
        break
    else :
      return info

   # reverse order of points
    info.reverse()
    for i in range(nb_points) :
      p1 = self.points[i]
      p2 = obj.points[info[i]]
      if not p1.Geometric_coincide(p2) :
        break
    else :
      return info

    return None


  def Deep_coincide(self,obj,info) :

    for i in range(len(info)) :
      p1 = self.points[i]
      p2 = obj.points[info[i]]
      p1.Coincide(p2)



  def Translate(self,x,y,z=0) :

    for point in self.points :
      point.Translate(x,y,z)


  def Transfinite(self,number,progression = 1) :

    self.md.number      = int(number)
    self.md.progression = float(progression)


  def Attractor(self,scale_x, scale_y, distance) :

    self.attractor = (float(scale_x), float(scale_y), float(distance))


  def __rmul__(self,base) :

    if len(self.points) > 2 :
      raise "Support (right argument) should be a straight line"

    if self.points[0] in base.points :
      supp_orig = 0
      supp_extr = 1
    elif self.points[1] in base.points :
      supp_orig = 1
      supp_extr = 0
    else :
      raise "No common point"

    if self.points[supp_orig] == base.points[0] :
      base_orig = 0
      base_extr = -1
    else :
      base_orig = -1
      base_extr = 0

  # Translation vector
    ce = self.points[supp_extr].coor
    co = self.points[supp_orig].coor
    tran = ce-co

  # Definition of the edge opposite to the base
    opp_base = base.Duplicate()
    opp_base.Translate(tran[0],tran[1],tran[2])
    opp_base.points[base_orig] = self.points[supp_extr]

  # Definition of the edge opposite to the support
    opp_supp = self.Duplicate()
    opp_supp.points[0] = base.points[base_extr]
    opp_supp.points[1] = opp_base.points[base_extr]

    surf = Surface(base,self,opp_base,opp_supp)

    if len(base.points) > 2 : surf.Ruled()

    return surf


  def Intermediate_meshing(self,mesh) :

    for point in self.points :
      point.Gmsh(mesh)


  def Object_meshing(self,num) :

    ch = self.type + '(' + `num` + ') = {'
    for point in self.points :
      ch = ch + `point.num` + ','
    ch = ch[:-1] + '};'
    self.Gmsh_send(ch)

    if self.md.transfinite :
      ch = (
          'Transfinite Line{' + `num` + '} = ' +
          `self.md.number+1` +
          ' Using Progression ' + `self.md.progression` + ';'
          )
      self.Gmsh_send(ch)

    if self.attractor :
      ch = (
        'Attractor Line{' + `num` + '} = {'
        + `self.attractor[0]`+','
        + `self.attractor[1]`+','
        + `1./self.attractor[2]` + '};'
        )
      self.Gmsh_send(ch)



class Circle(Line) : pass

# The class inherits everything from Line but its name (to tell Gmsh
# that it is a circle).



def Curve(l_x,l_y,l_z=None) :

  if not l_z :
    l_z = [0.] * len(l_x)

  l_P = []
  for x,y,z in map(None,l_x,l_y,l_z) :
    l_P.append(Point(x,y,z))

  line = apply(Line,l_P)
  return line





# -------------------- SURFACE OBJECTS ---------------------


00625 class Surface(Geometric) :

  """
    SURFACE OBJECT (inherit from the Geometric class)

    Public methods
     __init__ :
       in -> lines : external bounday of the surface (lines should be connected)

     Holes : set the internal holes (surfaces)
       in -> holes : list of holes

     Boundary : checks that the boundary is a closed loop and returns the orientation of the edges

     Summit : returns the summit list sorted according to the orientation (see Boundary method)

     Ruled : declare the surface is a ruled one

     Translate : translate the surface
       in -> x,y,z translation vector (default : z=0)

     Recombine : recombine the surface (try to mesh with quadrangles instead of triangles)

     Transfinite : Declare the mesh to be transfinite


    Attributes
     lines : list of external boundary lines
     holes : list of internal holes (surfaces)
     ruled : indicates (false or true) if the surface is a ruled surface
     loops : list of boundary (external and internal) loops (computed when meshing)
  """


  def __init__(self,*lines) :

    Geometric.__init__(self)
    self.lines = list(lines)
    self.holes = []
    self.ruled = 0

  # Check Assumptions
    for line in lines :
      if not line.Is_line() :
        raise "Arguments should be lines : " + repr(line)
    if lines == 0 : raise "There should be at least one line"
    self.Boundary()


  def Boundary(self) :

  # checking the boundary is a loop
    orie = []
    tmp  = list(self.lines) + [self.lines[0]]
    for i in range(len(self.lines)) :
      lb = tmp[i]
      la = tmp[i+1]
      if lb.points[-1] in [la.points[0], la.points[-1]] :
        orie.append(1)
      elif lb.points[0] in [la.points[0], la.points[-1]] :
        orie.append(-1)
      else :
        raise "This is not a loop"

  # checking the boundary is closed
    if orie[0]  ==  1 : pi = self.lines[0].points[0]
    if orie[0]  == -1 : pi = self.lines[0].points[-1]
    if orie[-1] ==  1 : pf = self.lines[-1].points[-1]
    if orie[-1] == -1 : pf = self.lines[-1].points[0]
    if pi <> pf : raise "The loop is not closed"

    return orie


  def Summit(self) :

    summits = []
    for line, orie in map(None,self.lines,self.Boundary()) :
      if orie == 1 :
        summits.append(line.points[0])
      else :
        summits.append(line.points[-1])
    return summits


  def Holes(self,*holes) :

    for hole in holes :
      if not hole.Is_surface() :
        raise "Holes should be surfaces"
    self.holes = list(holes)


00718   def Geometric_coincide(self,obj) :

    """
      return (line_order, hole_order) :
        line_order : list of the coupled lines ith line of self with line_order[i]th line of obj
        hole_order : same as line_order but with the internal holes
    """

    if len(self.lines) <> len(obj.lines) :
      raise 'To coincide, surfaces should have the same number of border lines'

    if len(self.holes) <> len(obj.holes) :
      raise 'To coincide, surfaces should have the same number of internal holes'

   # Coincidence of the surface holes
    hole_order = []
    nb_holes = len(self.holes)
    for hole_1 in self.holes :
      for i in xrange(nb_holes) :
        if i in hole_order :
          continue
        hole_2 = obj.holes[i]
        if hole_1.Geometric_coincide(hole_2) :
          hole_order.append(i)
          break
      else :
        return None

   # Coincidence of the external boundary lines
    line_order = []
    nb_lines = len(self.lines)
    for line_1 in self.lines :
      for i in xrange(nb_lines) :
        if i in line_order :
          continue
        line_2 = obj.lines[i]
        if line_1.Geometric_coincide(line_2) :
          line_order.append(i)
          break
      else :
        return None

    return (line_order, hole_order)


  def Deep_coincide(self,obj,info) :

    line_order = info[0]
    hole_order = info[1]

    for i,j in map(None,xrange(len(line_order)),line_order) :
      l1 = self.lines[i]
      l2 = obj.lines[j]
      l1.Coincide(l2)

    for i,j in map(None,xrange(len(hole_order)),hole_order) :
      h1 = self.holes[i]
      h2 = obj.holes[j]
      h1.Coincide(h2)



  def Ruled(self) :

    self.ruled = 1

    if len(self.lines) not in [3,4] :
      raise "Ruled surfaces require 3 or 4 edges"

    if self.holes :
      raise "Holes are forbidden for ruled surfaces"


  def Translate(self,x,y,z=0) :

    l_points = []
    for surf in [self] + self.holes :
      for line in surf.lines :
        for point in line.points :
          if point not in l_points : l_points.append(point)

    for point in l_points :
      point.Translate(x,y,z)


  def Recombine(self,val=1) :

    self.md.recombine = val


  def Transfinite(self) :

    self.Ruled()

    if len(self.lines) == 4 :
      self.Recombine()

    self.md.transfinite = 1

    for line in self.lines :
      if not line.md.transfinite :
        raise "Transfinite surfaces require transfinite edges"

    if (
      self.lines[0].md.number <> self.lines[2].md.number or
      self.lines[1].md.number <> self.lines[3].md.number
    ) :
      raise "Coupled edges should have the same number of elements"



  def Intermediate_meshing(self,mesh) :

    self.loops = []
    for surf in [self]+self.holes :
      loop = LineLoop(surf)
      self.loops.append(loop)
      loop.Gmsh(mesh)


  def Object_meshing(self,num) :

  # Creation of the surface
    if self.ruled :
      ch = 'Ruled Surface(' + `num` + ') = {'
    else :
      ch = 'Plane Surface(' + `num` + ') = {'
    for loop in self.loops :
      ch = ch + `loop.num` + ','
    ch = ch[:-1] + '};'
    self.Gmsh_send(ch)

  # Declaration of transfinite surface
    if self.md.transfinite :
      ch = 'Transfinite Surface {' + `num` + '} = {'
      for summit in self.Summit() :
        ch = ch + `summit.num` + ','
      ch = ch[:-1] + '};'
      self.Gmsh_send(ch)

  # Recombine elements if requested
    if self.md.recombine :
      self.Gmsh_send('Recombine Surface {' + `num` + '} ;')



class LineLoop(Geometric) :    # Used only during the meshing phase


  def __init__(self,surface) :

    Geometric.__init__(self)
    self.surface = surface


  def Intermediate_meshing(self,mesh) :

    for line in self.surface.lines :
      line.Gmsh(mesh)


  def Object_meshing(self,num) :

    ch = 'Line Loop(' + `num` + ') = {'
    for line,orie in map(None,self.surface.lines,self.surface.Boundary()) :
      ch = ch + `orie*line.num` + ','
    ch = ch[:-1] +  '};'
    self.Gmsh_send(ch)




00890 class Volume(Geometric) :


  """
    VOLUME OBJECT (inherit from the Geometric class)

    Public methods
     __init__ :
       in -> surfaces : external bounday of the volume (surfaces should be connected)

     Edge : returns the list of edges

     Holes : set the internal holes (surfaces)
       in -> holes : list of holes

     Transfinite : Declare the mesh to be transfinite (force the surfaces to be transfinite too)

     Translate : translate the surface
       in -> x,y,z translation vector (default : z=0)


    Attributes
     surfaces : list of external boundary surfaces
     holes : list of internal holes (volumes)
     loops : list of boundary (external and internal) loops (computed when meshing)


    Private methods :

     Boundary : checks that the boundary is a closed loop and returns the orientation of the edges

  """


  def __init__(self,*surfaces) :

    Geometric.__init__(self)
    self.surfaces = list(surfaces)
    self.holes = []
    self.ruled = 0

  # Check Assumptions
    for surface in surfaces :
      if not surface.Is_surface() :
        raise "Arguments should be surfaces : " + repr(surface)
    if len(surfaces) < 2 : raise "There should be at least two surfaces"
    self.Boundary()


  def Boundary(self) :

    edges = []
    for surface in self.surfaces :
      edges = edges + surface.lines

  # each edge has to appear twice in the list of edges
    for edge in edges :
      if edges.count(edge) <> 2 :
        raise "The surface loop is not closed : each edge should appear twice"


  def Edge(self) :

    edges = []
    for surface in self.surfaces :
      for line in surface.lines :
        if line not in edges : edges.append(line)
    return edges


  def Holes(self,*holes) :

    for hole in holes :
      if not hole.Is_volume() :
        raise "Holes should be volumes"
    self.holes = list(holes)


00968   def Geometric_coincide(self,obj) :

    """
      return (surface_order, hole_order) :
        surface_order : list of the coupled surfaces ith surface of self with surface_order[i]th surface of obj
        hole_order    : same as surface_order but with the internal holes
    """

    if len(self.surfaces) <> len(obj.surfaces) :
      raise 'To coincide, volumes should have the same number of border surfaces'

    if len(self.holes) <> len(obj.holes) :
      raise 'To coincide, volumes should have the same number of internal holes'

   # Coincidence of the surface holes
    hole_order = []
    nb_holes = len(self.holes)
    for hole_1 in self.holes :
      for i in xrange(nb_holes) :
        if i in hole_order :
          continue
        hole_2 = obj.holes[i]
        if hole_1.Geometric_coincide(hole_2) :
          hole_order.append(i)
          break
      else :
        return None

   # Coincidence of the external boundary lines
    surface_order = []
    nb_surfaces = len(self.surfaces)
    for surface_1 in self.surfaces :
      for i in xrange(nb_surfaces) :
        if i in surface_order :
          continue
        line_2 = obj.surfaces[i]
        if surface_1.Geometric_coincide(surface_2) :
          surface_order.append(i)
          break
      else :
        return None

    return (surface_order, hole_order)


  def Deep_coincide(self,obj,info) :

    surface_order = info[0]
    hole_order    = info[1]

    for i,j in map(None,xrange(len(surface_order)),surface_order) :
      l1 = self.surfaces[i]
      l2 = obj.surfaces[j]
      l1.Coincide(l2)

    for i,j in map(None,xrange(len(hole_order)),hole_order) :
      h1 = self.holes[i]
      h2 = obj.holes[j]
      h1.Coincide(h2)


  def Transfinite(self) :

    if len(self.surfaces) == 5 :
      raise "Not implemented"

    if len(self.surfaces) not in [5,6] :
      raise "Transfinite volumes require 5 or 6 faces"

    if self.holes :
      raise "Holes are forbidden for transfinite volumes"

    self.md.transfinite = 1

    for surface in self.surfaces :
      if not surface.md.transfinite :
        surface.Transfinite() # attention : ce n'est pas vrai dans le cas des prismes

# ATTENTION : ICI, IL FAUDRAIT VERIFIER QUE LES SURFACES PEUVENT ETRE MISES EN VIS A VIS



  def Translate(self,x,y,z=0) :

    l_points = []
    for volu in [self] + self.holes :
      for surf in volu.surfaces :
        for line in surf.lines :
          for point in line.points :
            if point not in l_points : l_points.append(point)

    for point in l_points :
      point.Translate(x,y,z)



  def Intermediate_meshing(self,mesh) :

    self.loops = []
    for volume in [self]+self.holes :
      loop = SurfaceLoop(volume)
      self.loops.append(loop)
      loop.Gmsh(mesh)


  def Object_meshing(self,num) :

  # Creation of the volume
    ch = 'Volume(' + `num` + ') = {'
    for loop in self.loops :
      ch = ch + `loop.num` + ','
    ch = ch[:-1] + '};'
    self.Gmsh_send(ch)

  # Declaration of transfinite surface
    if self.md.transfinite :

      bottom_summits = self.surfaces[0].Summit()
      edges = self.Edge()
      top_summits = []
      for summit in bottom_summits :
        for edge in edges :
          if summit == edge.points[0] and edge.points[-1] not in bottom_summits :
            top_summits.append(edge.points[-1])
            break
          elif summit == edge.points[-1] and edge.points[0] not in bottom_summits :
            top_summits.append(edge.points[0])
            break

      ch = 'Transfinite Volume {' + `num` + '} = {'
      for summit in bottom_summits + top_summits :
        ch = ch + `summit.num` + ','
      ch = ch[:-1] + '};'
      self.Gmsh_send(ch)



class SurfaceLoop(Geometric) :    # Used only during the meshing phase


  def __init__(self,volume) :

    Geometric.__init__(self)
    self.volume = volume


  def Intermediate_meshing(self,mesh) :

    for surface in self.volume.surfaces :
      surface.Gmsh(mesh)


  def Object_meshing(self,num) :

    ch = 'Surface Loop(' + `num` + ') = {'
    for surface in self.volume.surfaces :
      ch = ch + `surface.num` + ','
    ch = ch[:-1] +  '};'
    self.Gmsh_send(ch)




# ------------------- GEOMETRICAL TRANSFORMATION --------------

def VectorProduct(u,v) :

  return array([u[1]*v[2]-u[2]*v[1],u[2]*v[0]-u[0]*v[2],u[0]*v[1]-u[1]*v[0]])


def VectorNorm(u) :

  return sqrt(dot(u,u))


class Rotation :

  def __init__(self,A,C,B) :

    self.C = c
    self.a = A-C
    n = VectorProduct(self.a,B-C)
    self.n = n / VectorNorm(n)


  def Proj(self,M) :

    lbd = dot(M-self.C,self.n)
    H = self.C + lbd*self.n
    return H


def Scaling_P2(p,t) : return (1.-p)*t*t+p*t

def Scaling_P3(p,t) :
  q = 1./p
  a = p+q-2
  b = 3-2*p-q
  return a*t**3 + b*t*t +p*t


# -------------------- MESHING OPERATIONS ---------------------

01171 class Mesh_Descriptor :

  """
    Attributes
      relation     Another mesh descriptor provides the mesh parameters
      parameters   dictionnary of the mesh parameters
                        size         Point size
                        transfinite  Transfinite mesh (0 or 1)
                        number       Number of elements along a line (transfinite)
                        progression  Progression of element size (transfinite)
                        recombine    Recombine mesh or not

     Specific access :
       md.parameter_name = xxx -> the relation is destroyed (set to None)
       xxx = md.parameter_name -> if there is a relation, the effective
                                  parameter is looked for recursively

     Deep copying : a relation is set to the model instead of a true copy
  """

  List_Attr = ['size','transfinite','number','progression','recombine']


  def __init__(self) :

    self.relation = None
    self.parameters = {
      'size'       :  1.  ,     # Point size
      'transfinite':  0   ,     # Transfinite mesh (0 or 1)
      'recombine'  :  0         # Recombine mesh or not
      }


  def __setattr__(self, attr, value) :

    if attr in Mesh_Descriptor.List_Attr :
      self.relation = None
      self.parameters[attr] = value

      if attr == 'number' :
        self.transfinite = 1

    else :
      self.__dict__[attr] = value


  def __getattr__(self,attr) :

    if self.relation :
      return (getattr(self.relation,attr))
    else :
      if attr in self.parameters.keys() :
        return self.parameters[attr]
      else :
        raise AttributeError


  def __deepcopy__(self,visit) :

    md = copy.copy(self)
    md.parameters = copy.copy(self.parameters)
    md.relation = self
    return md



01237 class Mesh :

  """

  """


  def __init__(self, algo = 2, order = 1, gmsh='gmsh') :

    self.num_ph  = 0
    self.num     = 0
    self.order   = order
    self.command = ['Mesh.Algorithm = ' + repr(algo) + ' ;']
    self.command += ['Mesh.ElementOrder = ' + repr(order) + ' ;']
    self.physicals = {}
    self.gmsh    = gmsh


  def Physical(self, name, *l_lobj) :

  # Checking the name
    if type(name) <> type(' ') :
      raise 'First argument should be the name of the physical'
    if name in self.physicals.keys() :
      raise 'Physical '+name+' already exists'

  # treating the case of list of lists parameters
    l_obj = []
    for l in l_lobj :
      if type(l) == type([]) :
        l_obj = l_obj + l
      else :
        l_obj.append(l)

  # Checking all objects are geometric
    for obj in l_obj :
      if not Is_Geometric(obj) :
        raise "Non geometrical object : " + repr(obj) + " Physical = " + name

    cl = l_obj[0].Base_class()
  # Checking all objects are of the same dimension
  #  ref_dim = l_obj[0]
  #  for obj in l_obj[1:] :
  #    if not ref_dim.Is_same_dimension(obj) :
  #      raise "All objects are not of the same dimension : " + repr(obj)

  # Creation of the objects if necessary
    for obj in l_obj :
      obj.Gmsh(self)

  # Creation of the physical
    self.num_ph= self.num_ph + 1
    ch = name + '=' + `self.num_ph` + ';'
    self.command.append(ch)
    ch = 'Physical ' + cl + '(' + name + ') = {'
    for obj in l_obj :
      ch = ch + `obj.num` + ','
    ch = ch[:-1] + '};'
    self.command.append(ch)

  # Name of the physical
    name_gmsh = 'GM'+`self.num_ph`
    self.physicals[name] = name_gmsh


  def Save(self, file = 'fort.geo') :

    if os.path.isfile(file) :
      os.remove(file)

    f = open(file,'w')
    f.write(string.joinfields(self.command,'\n'))
    f.close()


  def View(self) :

    self.Save('fort.geo')
#    os.system('gmsh fort.geo')
    os.system(self.gmsh + ' fort.geo')
    os.remove('fort.geo')


  def Create(self, file = 'fort.19') :

    self.Save()
    os.system(self.gmsh + ' -3 fort.geo')
    try: os.remove(file)
    except: pass
    os.rename('fort.msh',file)


  def Name(self, MA, CREA_GROUP_NO) :

    l_gma = []
    l_mcf =  []
    for gma in self.physicals.keys() :
      l_gma.append(self.physicals[gma])
      l_mcf.append(_F(GROUP_MA = self.physicals[gma],NOM=gma))

    DEFI_GROUP(reuse = MA,
      MAILLAGE = MA,
      CREA_GROUP_MA = tuple(l_mcf),
      )

    SMESH_02 = CREA_MAILLAGE(
      MAILLAGE = MA,
      DETR_GROUP_MA = _F(GROUP_MA = tuple(l_gma)),
      )

    DETRUIRE(CONCEPT = _F(NOM = MA), INFO=1)

    if CREA_GROUP_NO == 'OUI' :
      DEFI_GROUP(reuse = SMESH_02,
        MAILLAGE = SMESH_02,
        CREA_GROUP_NO = _F(TOUT_GROUP_MA = 'OUI'),
        )

    else :
#    Traitement des GROUP_NO qui sont des points
      info_gno = SMESH_02.LIST_GROUP_NO()
      l_gno = []
      for gno in info_gno :
        if gno[1] == 1 : l_gno.append(gno[0])

      l_gma = []
      for gma in self.physicals.keys() :
        nom_gmsh = self.physicals[gma]
        if nom_gmsh in l_gno :
          l_gma.append(gma)

      if l_gma :
        DEFI_GROUP(reuse = SMESH_02,
          MAILLAGE = SMESH_02,
          CREA_GROUP_NO = _F(GROUP_MA = tuple(l_gma)),
          )

    return SMESH_02



01378   def LIRE_GMSH(self,
    UNITE_GMSH     = 19,
    UNITE_MAILLAGE = 20,
    MODI_QUAD      = 'NON',
    CREA_GROUP_NO  = 'OUI'
    ) :

    """
      Lecture du maillage (format Aster) a partir de sa definition
      (format sup_gmsh)
      UNITE_GMSH     = Numero d'unite logique pour le fichier msh
      UNITE_MAILLAGE = Numero d'unite logique pour le fichier mail
      MODI_QUAD      = 'OUI' si line->quad, 'NON' sinon
      CREA_GROUP_NO  = 'OUI' si on cree les group_no, 'NON' sinon
    """

    nom_gmsh = 'fort.' + repr(UNITE_GMSH)
    self.Create(nom_gmsh)

    PRE_GMSH(UNITE_GMSH=UNITE_GMSH, UNITE_MAILLAGE=UNITE_MAILLAGE)

    SMESH_00 = LIRE_MAILLAGE(UNITE = UNITE_MAILLAGE)
    DEFI_FICHIER(ACTION='LIBERER',UNITE = UNITE_GMSH)
    DEFI_FICHIER(ACTION='LIBERER',UNITE = UNITE_MAILLAGE)

    if MODI_QUAD == 'OUI' and self.order == 2 :
      raise 'The finite elements are already of second order'

    if MODI_QUAD == 'OUI' and self.order <> 2 :
      SMESH_01 = CREA_MAILLAGE(
        MAILLAGE = SMESH_00,
        LINE_QUAD = _F(TOUT = 'OUI')
        )
      DETRUIRE(CONCEPT=_F(NOM=SMESH_00), INFO=1)
      SMESH_00 = SMESH_01

    SMESH_00 = self.Name(SMESH_00,CREA_GROUP_NO)

    return SMESH_00

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