# Source code for mesh

```
#
##
## This file is part of pyFormex 1.0.7 (Mon Jun 17 12:20:39 CEST 2019)
## pyFormex is a tool for generating, manipulating and transforming 3D
## geometrical models by sequences of mathematical operations.
## Home page: http://pyformex.org
## Project page: http://savannah.nongnu.org/projects/pyformex/
## Copyright 2004-2019 (C) Benedict Verhegghe (benedict.verhegghe@ugent.be)
## Distributed under the GNU General Public License version 3 or later.
##
## 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 3 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, see http://www.gnu.org/licenses/.
##
#
## 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, see http://www.gnu.org/licenses/.
##
"""
Finite element meshes in pyFormex.
This module defines the Mesh class, which can be used to describe discrete
geometrical models like those used in Finite Element models.
It also contains some useful functions to create such models.
"""
from __future__ import absolute_import, division, print_function
import numpy as np
import pyformex as pf
from pyformex import utils
from pyformex import arraytools as at
from pyformex.coords import *
from pyformex.formex import Formex
from pyformex.connectivity import Connectivity
from pyformex.elements import ElementType, Elems
from pyformex.geometry import Geometry
##############################################################
# TODO: replace Connectivity with Elems wherever needed
[docs]class Mesh(Geometry):
"""
A Mesh is a discrete geometrical model defined by nodes and elements.
The Mesh class is one of the two basic geometrical models in pyFormex,
the other one being the :class:`Formex`. Both classes have a lot in
common: they represent a collection of geometrical entities of the same
type (e.g., lines, or triangles, ...). The geometrical entities are
also called 'elements', and the number of elements in the Mesh is
:meth:`nelems`. The :term:`plexitude` (the number of points in an
element) of a Mesh is found from :meth:`nplex`. Each point has
``ndim=3`` coordinates. While in a :class:`Formex` all these points
are stored in an array with shape (nelems, nplex, 3), the :class:`Mesh`
stores the information in two arrays: the coordinates of all the points
are gathered in a single twodimensional array with shape (ncoords,3).
The individual geometrical elements are then described by indices into
that array: we call that the connectivity, with shape (nelems, nplex).
This model has some advantages over the :class:`Formex` data model:
- a more compact storage, because coordinates of coinciding points
require only be stored once (and we usually call the points
:term:`node` s);
- the single storage of coinciding points represents the notion
of connections between elements (a :class:`Formex` to the contrary
is always a loose collection of elements);
- connectivity related algorithms are generally faster;
- the connectivity info also allows easy identification of geometric
subentities (entities of a lower :term:`level`, like the border
lines of a surface).
The downside is that geometry generating and replicating algorithms are
often far more complex and possibly slower.
In pyFormex we therefore mostly use the Formex data model when creating,
copying and replicating geometry, but when we come to the point of needing
connectivity related algorithms or exporting the geometry to file (and to
other programs), a Mesh data model usually becomes more appropriate.
A :class:`Formex can be converted into a Mesh with the :meth:`Formex.toMesh`
method, while the :meth:`Mesh.toFormex` method performs the inverse
conversion.
Parameters
----------
coords: :class:`~coords.Coords` or other object.
Usually, a 2-dim Coords object holding the coordinates of all the
nodes used in the Mesh geometry.
See details below for different initialization methods.
elems: :class:`~connectivity.Connectivity` (nelems,nplex)
A Connectivity object, defining the elements of the geometry
by indices into the ``coords`` Coords array. All values in elems
should be in the range 0 <= value < ncoords.
prop: int :term:`array_like`, optional
1-dim int array with non-negative element property numbers.
If provided, :meth:`setProp` will be called to assign the
specified properties.
eltype: str or :class:`~elements.ElementType`, optional
The element type of the geometric entities (elements).
This is only needed if the element type has not yet been
set in the ``elems`` Connectivity. See below.
A Mesh object can be initialized in many different ways, depending on
the values passed for the ``coords`` and ``elems`` arguments.
- Coords, Connectivity: This is the most obvious case:
``coords`` is a 2-dim :class:`~coords.Coords` object holding
the coordinates of all the nodes in the Mesh,
and ``elems`` is a :class:`~connectivity.Connectivity` object
describing the geometric elements by indices into the ``coords``.
- Coords, : If A Coords is passed as first argument, but no ``elems``,
the result is a Mesh of points, with plexitude 1. The Connectivity
will be constructed automatically.
- object with ``toMesh``, : As a convenience, if another object is
provided that has a ``toMesh`` method and ``elems`` is not provided,
the result of the ``toMesh`` method will be used to initialize
both ``coords`` and ``elems``.
- None: If neither ``coords`` nor ``elems`` are specified, but ``eltype``
is, a unit sized single element Mesh of the specified
:class:`~elements.ElementType` is created.
- Specifying no parameters at all creates an empty Mesh, without any data.
Setting the element type can also be done in different ways. If ``elems``
is a Connectivity, it will normally already have a element type.
If not, it can be done by passing it in the ``eltype`` parameter.
In case you pass a simple array or list in the ``elems`` parameter,
an element type is required.
Finally, the user can specify an eltype to override the one in the
Connectivity. It should however match the plexitude of the connectivity
data.
``eltype`` should be one of the :class:`~elements.ElementType`
instances or the name of such an instance.
If required but not provided, the pyFormex default is used, which is
based on the plexitude: 1 = point, 2 = line segment,
3 = triangle, 4 or more is a polygon.
A properly initialized Mesh has the following attributes:
Attributes
----------
coords: :class:`~coords.Coords` (ncoords,3)
A 2-dim Coords object holding the coordinates of all the nodes used
to describe the Mesh geometry.
elems: :class:`~connectivity.Connectivity` (nelems,nplex)
A Connectivity object, defining the elements of the geometry
by indices into the :attr:`coords` Coords array. All values in elems
should be in the range ``0 <= value < ncoords``.
The Connectivity also stores the element type of the Mesh.
prop: int array, optional
Element property numbers. See :attr:`geometry.Geometry.prop`.
attrib: :class:`~attributes.Attributes`
An Attributes object. See :attr:`geometry.Geometry.attrib`.
fields: OrderedDict
The Fields defined on the Mesh. See :attr:`geometry.Geometry.fields`.
Note
----
The `coords`` attribute of a Mesh can hold points that are not used
or needed to describe the Geometry. They do not influence the result
of Mesh operations, but only use up some memory. If their number becomes
large, you may want to free up that memory by calling the
:meth:`compact` method. Also, before exporting a Mesh (e.g. to a
numerical simulation program), you may want to compact the Mesh first.
Examples
--------
Create a Mesh with four points and two triangle elements of type 'tri3'.
>>> coords = Coords('0123')
>>> elems = [[0,1,2], [0,2,3]]
>>> M = Mesh(coords,elems,eltype='tri3')
>>> print(M.report())
Mesh: nnodes: 4, nelems: 2, nplex: 3, level: 2, eltype: tri3
BBox: [ 0. 0. 0.], [ 1. 1. 0.]
Size: [ 1. 1. 0.]
Area: 1.0
Coords: [[ 0. 0. 0.]
[ 1. 0. 0.]
[ 1. 1. 0.]
[ 0. 1. 0.]]
Elems: [[0 1 2]
[0 2 3]]
>>> M.nelems(), M.ncoords(), M.nplex(), M.level(), M.elName()
(2, 4, 3, 2, 'tri3')
And here is a line Mesh converted from of a Formex:
>>> M1 = Formex('l:11').toMesh()
>>> print(M1.report())
Mesh: nnodes: 3, nelems: 2, nplex: 2, level: 1, eltype: line2
BBox: [ 0. 0. 0.], [ 2. 0. 0.]
Size: [ 2. 0. 0.]
Length: 2.0
Coords: [[ 0. 0. 0.]
[ 1. 0. 0.]
[ 2. 0. 0.]]
Elems: [[0 1]
[1 2]]
Indexing returns the full coordinate set of the element(s):
>>> M1[0]
Coords([[ 0., 0., 0.],
[ 1., 0., 0.]])
The Mesh class inherits from :class:`Geometry` and therefore has
all the coordinate transform methods defined there readily
available:
>>> M2 = M1.rotate(90)
>>> print(M2.coords)
[[ 0. 0. 0.]
[ 0. 1. 0.]
[ 0. 2. 0.]]
"""
###################################################################
## DEVELOPERS: ATTENTION
##
## The Mesh class is intended to be subclassable: TriSurface is an
## example of a class derived from Mesh.
## Therefore, all methods returning a Mesh and also operating correctly
## on a subclass, should use self.__class__ to return the proper class.
## The self.__class__ initiator should be called with the 'prop' and
## 'eltype' arguments, using keyword arguments, because only the first
## two arguments ('coords', 'elems') are guaranteed.
## See the copy() method for an example.
###################################################################
# TODO: remove this when docstring for __getitem__ has been moved above
_special_members_ = ['__getitem__']
_exclude_members_ = ['matchLowerEntitiesMesh', 'matchFaces']
fieldtypes = ['node', 'elemc', 'elemn']
def __init__(self, coords=None, elems=None, prop=None, eltype=None):
"""
Initialize a new Mesh.
"""
Geometry.__init__(self)
self.coords = self.elems = self.prop = None
self.ndim = -1
self.nodes = self.edges = self.faces = self.cells = None
self.elem_edges = self.eadj = None
self.conn = self.econn = self.fconn = None
if coords is None:
if eltype is None:
# Create an empty Mesh object
return
else:
# Create unit Mesh of specified type
el = ElementType.get(eltype)
coords = el.vertices
elems = el.getElement()
if elems is None:
# A single object was specified instead of (coords,elems) pair
try:
# initialize from a single object
if isinstance(coords, Coords):
M = Mesh(coords, arange(coords.ncoords()))
elif isinstance(coords, Mesh):
M = coords
else:
M = coords.toMesh()
coords, elems = M.coords, M.elems
except:
raise ValueError("No `elems` specified and the first argument can not be converted to a Mesh.")
try:
self.coords = Coords(coords)
if self.coords.ndim != 2:
raise ValueError("\nExpected 2D coordinate array, got %s" % self.coords.ndim)
self.elems = Connectivity(elems,eltype=eltype)
if self.elems.size > 0 and (
self.elems.max() >= self.coords.shape[0] or
self.elems.min() < 0):
raise ValueError("\nInvalid connectivity data: some node number(s) not in coords array (min=%s, max=%s, ncoords=%s)" % (self.elems.min(), self.elems.max(), self.coords.shape[0]))
except:
raise
self.eltype = eltype # This sanitizes the eltype
self.setProp(prop)
def _set_coords(self, coords):
"""
Replace the current coords with new ones.
Parameters
----------
coords: Coords
A Coords with same shape as self.coords.
Returns
-------
Mesh
A Mesh (or subclass) instance with same connectivity, eltype
and properties as the current, but with possible changes in the
coordinates of the nodes.
"""
if isinstance(coords, Coords) and coords.shape == self.coords.shape:
M = self.__class__(coords, self.elems, prop=self.prop, eltype=self.elType())
M.attrib(**self.attrib)
return M
else:
raise ValueError("Invalid reinitialization of %s coords" % self.__class__)
@property
def eltype(self):
"""
Return the element type of the Mesh.
Returns
-------
:class:`elements.ElementType`
The eltype attribute of the :attr:`elems` attribute.
Examples
--------
>>> M = Mesh(eltype='tri3')
>>> M.eltype
Tri3
>>> M.eltype = 'line3'
>>> M.eltype
Line3
>>> print(M)
Mesh: nnodes: 3, nelems: 1, nplex: 3, level: 1, eltype: line3
BBox: [ 0. 0. 0.], [ 1. 1. 0.]
Size: [ 1. 1. 0.]
Length: 1.0
One cannot set an element type with nonmatching plexitude:
>>> M.eltype = 'quad4'
>>> M.eltype
'plex3'
"""
return self.elems.eltype
@eltype.setter
def eltype(self,eltype):
"""
Set the eltype from a character string.
Parameters
----------
eltype: str or :class:`~elements.ElementType`, optional
The element type to be set in the ``elems`` Connectivity.
It is either one of the ElementType instances defined in
elements.py, or the name of such an instance.
The plexitude of the ElementType should match the plexitude
of the Mesh.
Note
----
Setting the eltype sanitizes the eltype stored in the elems attribute
and promotes the elems attribute to Elems class.
"""
if eltype is None and hasattr(self.elems, 'eltype'):
eltype = self.elems.eltype
try:
self.elems = Elems(self.elems,eltype)
except:
# We need this in intermediary states of a Mesh.convert,
# where element types are used that are not (yet) defined.
self.elems.eltype = 'plex%d' % self.nplex()
[docs] def setEltype(self, eltype=None):
"""
Set the eltype from a character string.
Parameters
----------
eltype: str or :class:`~elements.ElementType`, optional
The element type to be set in the ``elems`` Connectivity.
It is either one of the ElementType instances defined in
elements.py, or the name of such an instance.
The plexitude of the ElementType should match the plexitude
of the Mesh.
Returns
-------
Mesh
The Mesh itself with possibly changed eltype.
Examples
--------
>>> Mesh(eltype='tri3').setEltype('line3').eltype
Line3
"""
self.eltype = eltype
return self
# TODO: deprecate this in favor of self.eltype
[docs] def elType(self):
"""
Return the element type of the Mesh.
Returns
-------
:class:`~elements.ElementType`
The ElementType of the Mesh.
See Also
--------
elName: returns the name of the ElementType.
Examples
--------
>>> Formex('4:0123').toMesh().elType()
Quad4
"""
return self.elems.eltype
# TODO: deprecate this in favor of self.eltype.name
[docs] def elName(self):
"""
Return the element name of the Mesh.
Returns
-------
str
The name of the ElementType of the Mesh.
See Also
--------
elType: returns the ElementType instance
Examples
--------
>>> Formex('4:0123').toMesh().elName()
'quad4'
"""
return self.elType().name()
[docs] def setNormals(self, normals=None):
"""
Set/Remove the normals of the mesh.
Parameters
----------
normals: float :term:`array_like`
A float array of shape (ncoords,3) or (nelems,nplex,3).
If provided, this will set these normals for use in
rendering, overriding the automatically computed ones.
If None, this will clear any previously set user normals.
"""
from pyformex import geomtools as gt
if normals is None:
pass
elif pf.isString(normals):
if normals == 'auto':
normals = gt.polygonNormals(self.coords[self.elems])
elif normals == 'avg':
normals = gt.averageNormals(self.coords, self.elems)
else:
normals = checkArray(normals, (self.nelems(), self.nplex(), 3), 'f')
self.normals = normals
# This docstring is shown in the refman because __getitem__
# is in _special_members_; it might be better to add this docstring
# to the Mesh docstring.
[docs] def __getitem__(self, i):
"""
Return element i of the Mesh.
This allows addressing element i of Mesh M as M[i].
Parameters
----------
i: :term:`index`
The index of the element(s) to return. This can be a single
element number, a slice, or an array with a list of numbers.
Returns
-------
Coords
A Coords with a shape (nplex, 3), or if multiple elements are
requested, a shape (nelements, nplex, 3), holding the
coordinates of all points of the requested elements.
Notes
-----
This is normally used in an expression as ``M[i]``, which will
return the element i. Then ``M[i][j]`` will return the coordinates
of node j of element i.
"""
return self.coords[self.elems[i]]
def __setstate__(self, state):
"""
Set the object from serialized state.
This allows to read back old pyFormex Project files where the Mesh
class did not set element type yet.
"""
elems = state['elems']
if 'eltype' in state:
if state['eltype'] is not None:
# We acknowledge this eltype, even if it is also stored
# in elems. This makes the restore also work for older projects
# where eltype was not in elems.
elems.eltype = ElementType.get(state['eltype'])
# Do not store the eltype in the Mesh anymore
del state['eltype']
else:
# No eltype in Mesh
if hasattr(elems, 'eltype'):
# eltype in elems: leave as it is
pass
else:
# Try to set elems eltype from plexitude
try:
elems.eltype = ElementType.get(nplex=elems.nplex())
except:
raise ValueError("I can not restore a Mesh without eltype")
self.__dict__.update(state)
[docs] def ndim(self):
"""
Returns the dimensionality of the global coordinate space.
Currently, this always returns 3.
"""
return 3
[docs] def level(self):
"""
Return the level of the elements in the Mesh.
Returns
-------
int
The dimensionality of the elements: 0 (point), 1(line),
2 (surface), 3 (volume).
"""
return self.elType().ndim
[docs] def nelems(self):
"""
Return the number of elements in the Mesh. This is the first
dimension of the :attr:`elems` array.
"""
return self.elems.shape[0]
[docs] def nplex(self):
"""
Return the plexitude of the elements in the Mesh. This is the
second dimension of the :attr:`elems` array.
"""
return self.elems.shape[1]
[docs] def ncoords(self):
"""
Return the number of nodes in the Mesh. This is the first
dimension of the :attr:`~mesh.Mesh.coords` array.
"""
return self.coords.shape[0]
nnodes = ncoords
npoints = ncoords
[docs] def shape(self):
"""
Return the shape of the :attr:`elems` array.
"""
return self.elems.shape
[docs] def nedges(self):
"""
Return the number of edges.
Returns
-------
int
The number of rows that would be returned by :meth:`getEdges`,
without actually constructing the edges.
Notes
-----
This is the total number of edges for all elements.
Edges shared by multiple elements are counted multiple times.
"""
try:
return self.nelems() * self.elType().nedges()
except:
return 0
[docs] def info(self):
"""
Return short info about the Mesh.
Returns
-------
str
A string with info about the shape of the
:attr:`~mesh.Mesh.coords` and :attr:`elems` attributes.
"""
return "coords" + str(self.coords.shape) + "; elems" + str(self.elems.shape)
#TODO: We need an option here to let numpy print the full tables.
[docs] def report(self, full=True):
"""
Create a report on the Mesh shape and size.
The report always contains the number of nodes, number of elements,
plexitude, dimensionality, element type, bbox and size.
If full==True(default), it also contains the nodal coordinate
list and element connectivity table. Because the latter can be rather
bulky, they can be switched off.
Note
----
NumPy normally limits the printed output. You will have to change
numpy settings to actually print the full arrays.
"""
bb = self.bbox()
s = """Mesh: nnodes: %s, nelems: %s, nplex: %s, level: %s, eltype: %s
BBox: %s, %s
Size: %s""" % (self.ncoords(), self.nelems(), self.nplex(), self.level(), self.elName(), bb[0], bb[1], bb[1]-bb[0])
if self.level() == 1:
s += "\n Length: %s" % self.length()
elif self.level() == 2:
s += "\n Area: %s" % self.area()
elif self.level() == 3:
s += "\n Volume: %s" % self.volume()
if full:
s += '\n' + at.stringar(" Coords: ", self.coords) + \
'\n' + at.stringar(" Elems: ", self.elems)
return s
def __str__(self):
"""
Format a Mesh in a string.
This creates a detailed string representation of a Mesh,
containing the report() and the lists of nodes and elements.
"""
return self.report(False)
[docs] def shallowCopy(self, prop=None):
"""
Return a shallow copy.
Parameters
----------
prop: int :term:`array_like`, optional
1-dim int array with non-negative element property numbers.
Returns
-------
Mesh
A shallow copy of the Mesh, using the same data arrays
for ``coords`` and ``elems``. If ``prop`` was provided,
the new Mesh can have other property numbers.
This is a convenient method to use the same Mesh
with different property attributes.
"""
if prop is None:
prop = self.prop
return self.__class__(self.coords, self.elems, prop=prop)
[docs] def toFormex(self):
"""
Convert a Mesh to a Formex.
Returns
-------
Formex
A Formex equivalent with the calling Mesh. The Formex inherits
the element property numbers and eltype from the Mesh.
Drawing attributes and Fields are not transfered though.
Examples
--------
>>> M = Mesh([[0,0,0],[1,0,0]],[[0,1],[1,0]],eltype='line2')
>>> M.toFormex()
Formex([[[ 0., 0., 0.],
[ 1., 0., 0.]],
<BLANKLINE>
[[ 1., 0., 0.],
[ 0., 0., 0.]]])
"""
return Formex(self.coords[self.elems], self.prop, self.elName())
[docs] def toMesh(self):
"""
Convert to a Mesh.
Returns
-------
Mesh
The Mesh itself. This is provided as a convenience for use
in functions that need to work on different Geometry types.
"""
return self
[docs] def toSurface(self):
"""
Convert a Mesh to a TriSurface.
Only Meshes of level 2 (surface) and 3 (volume) can be converted to a
TriSurface. For a level 3 Mesh, the border Mesh is taken first.
A level 2 Mesh is converted to element type 'tri3' and then to a
TriSurface.
Returns
-------
:class:`TriSurface`
A TriSurface corresponding with the input Mesh. If that has
eltype 'tri3', the resulting TriSurface is fully equivalent.
Otherwise, a triangular approximation is returned.
Raises
------
ValueError
If the Mesh can not be converted to a TriSurface.
"""
from pyformex.trisurface import TriSurface
if self.level() == 3:
obj = self.getBorderMesh()
elif self.level() == 2:
obj = self
else:
raise ValueError("Can not convert a Mesh of level %s to a Surface" % self.level())
obj = obj.convert('tri3')
return TriSurface(obj)
[docs] def toCurve(self, connect=False):
"""
Convert a Mesh to a Curve.
If the element type is one of 'line*' types, the Mesh is converted
to a Curve. The type of the returned Curve is dependent on the
element type of the Mesh:
- 'line2': :class:`PolyLine`,
- 'line3': :class:`BezierSpline` (degree 2),
- 'line4': :class:`BezierSpline` (degree 3)
If connect is False, this is equivalent to ::
self.toFormex().toCurve()
Any other type will raise an exception.
"""
if self.elName() in ['line2', 'line3', 'line4']:
if connect:
elems = self.elems.chained()
if len(elems)!=1:
# BV: We should return all connected parts
raise ValueError("Can not convert a Mesh to a single continuos curve")
else:
elems=elems[0]
closed = elems[-1, -1] == elems[0, 0]
# BV: This should be done without conversion to Formex
return Mesh(self.coords, elems, eltype=self.elType()).toFormex().toCurve(closed=closed)
else:
closed = self.elems[-1, -1] == self.elems[0, 0]
return self.toFormex().toCurve(closed=closed)
else:
raise ValueError("Can not convert a Mesh of type '%s' to a curve" % self.elName())
[docs] def centroids(self):
"""
Return the centroids of all elements of the Mesh.
The centroid of an element is the point with coordinates
equal to the average of those of all nodes of the element.
Returns
-------
Coords
A Coords object with shape (:meth:`nelems`, 3), holding the
centroids of all the elements in the Mesh.
Examples
--------
>>> rectangle(L=3,W=2,nl=3,nw=2).centroids()
Coords([[ 0.5, 0.5, 0. ],
[ 1.5, 0.5, 0. ],
[ 2.5, 0.5, 0. ],
[ 0.5, 1.5, 0. ],
[ 1.5, 1.5, 0. ],
[ 2.5, 1.5, 0. ]])
"""
return self.coords[self.elems].mean(axis=1)
[docs] def bboxes(self):
"""
Returns the bboxes of all elements in the Mesh.
Returns
-------
float array (nelems,2,3).
An array with the minimal and maximal values of the
coordinates of the nodes of each element, stored along
the 1-axis.
"""
return self.coords[self.elems].bboxes()
#######################################################################
## Entity selection and mesh traversal ##
[docs] def getLowerEntities(self, level=-1, unique=False):
"""
Get the entities of a lower dimensionality.
Parameters
----------
level: int
The :term:`level` of the entities to return. If negative,
it is a value relative to the level of the caller. If non-negative,
it specifies the absolute level. Thus, for a Mesh with a 3D
element type, getLowerEntities(-1) returns the faces, while for a
2D element type, it returns the edges.
For both meshes however, getLowerEntities(+1) returns the edges.
unique: bool, optional
If True, return only the unique entities.
Returns
-------
:class:`~connectivity.Connectivity`
A Connectivity defining the lower entities of the specified
level in terms of the nodes of the Mesh.
By default, all entities for all elements are returned and
entities shared by multiple elements will appear multiple times.
With ``unique=True`` only the unique ones are returned.
The return value may be an empty table, if the element type does
not have the requested entities (e.g. 'quad4' Mesh does not
have entities of level 3).
If the targeted entity level is outside the range 0..3, the return
value is None.
See Also
--------
level: return the dimensionality of the Mesh
:meth:`connectivity.Connectivity.insertLevel`: returns two tables:
elems vs. lower entities, lower enitites vs. nodes.
Examples
--------
Mesh with one 'quad4' element and 4 nodes.
>>> M = Mesh(eltype='quad4')
The element defined in function of the nodes.
>>> print(M.elems)
[[0 1 2 3]]
The edges of the element defined in function of the nodes.
>>> print(M.getLowerEntities(-1))
[[0 1]
[1 2]
[2 3]
[3 0]]
And finally, the nodes themselves: not very useful, but works.
>>> print(M.getLowerEntities(-2))
[[0]
[1]
[2]
[3]]
"""
sel = self.elType().getEntities(level)
ent = self.elems.selectNodes(sel)
ent.eltype = sel.eltype
if unique:
utils.warn("depr_mesh_getlowerentities_unique")
ent = ent.removeDuplicate()
return ent
[docs] @utils.deprecated("The use of Mesh.getElems() is deprecated: use Mesh.elems instead.")
def getElems(self):
"""Get the elems table.
Returns
-------
:class:`~elements.Elems`
The element connectivity table (the :attr:`elems` attribute).
Notes
-----
This is deprecated. Use the :attr:`elems` attribute instead.
"""
return self.elems
[docs] def getNodes(self):
"""Return the set of unique node numbers in the Mesh.
Returns
-------
int array
The sorted node numbers that are actually used in the connectivity
table.
For a compacted Mesh, it is equal to ``arange(self.nelems)``.
"""
return unique(self.elems)
[docs] def getPoints(self):
"""Return the nodal coordinates of the Mesh.
Returns
-------
:class:`~coords.Coords`
The coordinates of the nodes that are actually used in
the connectivity table. For a compacted Mesh, it is equal to
the coords attribute.
"""
return self.coords[self.getNodes()]
[docs] def getEdges(self):
"""Return the unique edges of all the elements in the Mesh.
Returns
------
:class:`~elements.Elems`
A connectivity table defining the unique element edges in function
of the nodes.
This is like ``self.getLowerEntities(1,unique=True)``, but
the result is stored internally in the Mesh object so that
it does not need recomputation on a next call.
"""
if self.edges is None:
self.edges = self.elems.insertLevel(1)[1]
return self.edges
[docs] def getFaces(self):
"""Return the unique faces of all the elements in the Mesh.
Returns
-------
:class:`~elements.Elems`
A connectivity table defining all the element faces in function
of the nodes.
This is like ``self.getLowerEntities(2,unique=True)``, but
the result is stored internally in the Mesh object so that
it does not need recomputation on a next call.
"""
if self.faces is None:
self.faces = self.elems.insertLevel(2)[1]
return self.faces
# TODO: Can this anyhow be different from self.elems or None?
# Is there any purpose then on storing it?
[docs] def getCells(self):
"""Return the cells of the elements.
This is a convenient function to create a table with the element
cells. It is equivalent to ``self.getLowerEntities(3,unique=True)``,
but this also stores the result internally so that future
requests can return it without the need for computing it again.
"""
if self.cells is None:
self.cells = self.elems.insertLevel(3)[1]
return self.cells
[docs] def edgeMesh(self):
"""Return a Mesh with the unique edges of the elements.
This can only be used with a Mesh of level >= 1.
"""
return Mesh(self.coords, self.getEdges())
[docs] def faceMesh(self):
"""Return a Mesh with the unique faces of the elements.
This can only be used with a Mesh of level >= 2.
"""
return Mesh(self.coords, self.getFaces())
[docs] def getElemEdges(self):
"""Defines the elements in function of its edges.
Returns
-------
:class:`~elements.Elems`
A connectivity table with the elements defined in
function of the edges.
Notes
-----
As a side effect, this also stores the definition of the edges
and the returned element to edge connectivity in the attributes
`edges`, resp. `elem_edges`.
"""
if self.elem_edges is None:
self.elem_edges, self.edges = self.elems.insertLevel(1)
return self.elem_edges
[docs] def getFreeEntities(self, level=-1, return_indices=False):
"""Return the free entities of the specified level.
Parameters
----------
level: int
The :term:`level` of the entities to return. If negative,
it is a value relative to the level of the caller. If non-negative,
it specifies the absolute level.
return_indices: bool
If True, also returns an index array (nentities,2) for inverse
lookup of the higher entity (column 0) and its local
lower entity number (column 1).
Returns
-------
:class:`~elements.Elems`
A connectivity table with the free entities of the
specified level of the Mesh. Free entities are entities
that are only connected to a single element.
See Also
--------
getFreeEntitiesMesh: return the free entities as a Mesh
getBorder: return the free entities of the first lower level
Examples
--------
>>> M = Formex('3:.12.34').toMesh()
>>> print(M.report())
Mesh: nnodes: 4, nelems: 2, nplex: 3, level: 2, eltype: tri3
BBox: [ 0. 0. 0.], [ 1. 1. 0.]
Size: [ 1. 1. 0.]
Area: 1.0
Coords: [[ 0. 0. 0.]
[ 1. 0. 0.]
[ 0. 1. 0.]
[ 1. 1. 0.]]
Elems: [[0 1 3]
[3 2 0]]
>>> M.getFreeEntities(1)
Elems([[0, 1],
[1, 3],
[3, 2],
[2, 0]], eltype=Line2)
>>> M.getFreeEntities(1,True)[1]
array([[0, 0],
[0, 1],
[1, 0],
[1, 1]])
"""
hi, lo = self.elems.insertLevel(level)
if hi.size == 0:
if return_indices:
return Connectivity(), []
else:
return Connectivity()
hiinv = hi.inverse()
ncon = (hiinv>=0).sum(axis=1)
isbrd = (ncon<=1) # < 1 should not occur
brd = lo[isbrd]
if not return_indices:
return brd
# also return indices where the border elements come from
binv = hiinv[isbrd]
enr = binv[binv >= 0] # element number
a = hi[enr]
b = arange(lo.shape[0])[isbrd].reshape(-1, 1)
fnr = where(a==b)[1] # local border part number
return brd, column_stack([enr, fnr])
[docs] def getFreeEntitiesMesh(self, level=-1, compact=True):
"""Return a Mesh with lower entities.
Parameters
----------
level: int
The :term:`level` of the entities to return. If negative,
it is a value relative to the level of the caller. If non-negative,
it specifies the absolute level.
compact: bool
If True (default), the returned Mesh will be compacted. If False,
the returned Mesh will contain all the nodes present in the
input Mesh.
Returns
-------
:class:`Mesh`
A Mesh containing the lower entities of the specified
level. If the Mesh has property numbers, the lower entities inherit
the property of the element to which they belong.
See Also
--------
getFreeEdgesMesh: return a Mesh with the free entities of the level 1
getBorderMesh: return the free entities Mesh of the first lower level
"""
if self.prop is None:
M = Mesh(self.coords, self.getFreeEntities(level=level))
else:
brd, indices = self.getFreeEntities(return_indices=True, level=level)
enr = indices[:, 0]
M = Mesh(self.coords, brd, prop=self.prop[enr])
if compact:
M = M.compact()
return M
[docs] def getFreeEdgesMesh(self, compact=True):
"""Return a Mesh with the free edges.
Parameters
----------
compact: bool
If True (default), the returned Mesh will be compacted. If False,
the returned Mesh will contain all the nodes present in the
input Mesh.
Returns
-------
:class:`Mesh`
A Mesh containing the free edges of the input Mesh.
If the input Mesh has property numbers, the edge elements inherit
the property of the element to which they belong.
See Also
--------
getFreeEntitiesMesh: return the free entities Mesh of any lower level
getBorderMesh: return the free entities Mesh of level -1
"""
return self.getFreeEntitiesMesh(level=1, compact=compact)
[docs] def getBorder(self, return_indices=False):
"""Return the border of the Mesh.
Border entities are the free entities of the first lower level.
Parameters
----------
return_indices: bool
If True, also returns an index array (nentities,2) for inverse
lookup of the higher entity (column 0) and its local
lower entity number (column 1).
Returns
-------
:class:`~elements.Elems`
A connectivity table with the border entities of the
specified level of the Mesh. Free entities are entities
that are only connected to a single element.
See Also
--------
getFreeEntities: return the free entities of any lower level
getBorderMesh: return the border as a Mesh
Notes
-----
This is a convenient shorthand for ::
self.getFreeEntities(level=-1,return_indices=return_indices)
"""
return self.getFreeEntities(level=-1, return_indices=return_indices)
[docs] def getBorderMesh(self, compact=True):
"""Return a Mesh representing the border.
Parameters
----------
compact: bool
If True (default), the returned Mesh will be compacted. If False,
the returned Mesh will contain all the nodes present in the
input Mesh.
Returns
-------
:class:`Mesh`
A Mesh containing the border of the input Mesh. The level of the
Mesh is one less than that of the input Mesh.
If the input Mesh has property numbers, the border elements inherit
the property of the element to which they belong.
Notes
-----
This is a convenient shorthand for ::
self.getFreeEntitiesMesh(level=-1,compact=compact)
"""
return self.getFreeEntitiesMesh(level=-1, compact=compact)
borderMesh = getBorderMesh
[docs] def getBorderElems(self):
"""Find the elements that are touching the border of the Mesh.
Returns
-------
int array
A list of the numbers of the elements that fully contain at
least one of the elements of the border Mesh.
Thus, in a volume Mesh, elements only touching the border
by a vertex or an edge are not considered border elements.
"""
brd, ind = self.getBorder(True)
return unique(ind[:, 0])
[docs] def getBorderNodes(self):
"""Find the nodes that are on the border of the Mesh.
Returns
-------
int array
A list of the numbers of the nodes that are on the
border of the Mesh.
"""
brd = self.getBorder()
return unique(brd)
[docs] def peel(self, nodal=False):
"""Remove the border elements from a Mesh.
Parameters
----------
nodal: bool
If True, all elements connected to a border node are removed.
The default will only remove the elements returned by
:meth:`getBorderElems`.
Returns
-------
Mesh
A Mesh with the border elements removed.
"""
if nodal:
brd=self.connectedTo(self.getBorderNodes())
else:
brd=self.getBorderElems()
return self.cselect(brd)
# TODO: the level parameter here seems useless: how does one know
# the indices of the lower level entities??
[docs] @utils.warning("mesh_connectedTo")
def connectedTo(self, entities, level=0):
"""Find the elements connected to specific lower entities.
Parameters
----------
entities: int or int :term:`array_like`.
The indices of the lower entities to which connection should
exist.
level: int
The :term:`level` of the entities to which connection should
exist. If negative, it is a value relative to the level of the
caller. If non-negative, it specifies the absolute level.
Default is 0 (nodes).
Returns
-------
int array
A list of the numbers of the elements that contain at
least one of the specified lower entities.
"""
if level == 0:
elems = self.elems
else:
elems, lo = self.elems.insertLevel(level)
return elems.connectedTo(entities)
@utils.deprecated("mesh_notConnectedTo")
def notConnectedTo(self, nodes):
pass
[docs] def adjacentTo(self, elements, level=0):
"""Find the elements adjacent to the specified elements.
Adjacent elements are elements that share some lower entity.
Parameters
----------
elements: int or int :term:`array_like`
Element numbers to find the adjacent elements for.
level: int
The :term:`level` of the entities used to define adjacency.
If negative, it is a value relative to the level of the
caller. If non-negative, it specifies the absolute level.
Default is 0 (nodes).
Returns
-------
int array
A list of the numbers of all the elements in the Mesh that are
adjacent to any of the specified elements.
"""
if level == 0:
elems = self.elems
else:
elems = self.elems.insertLevel(level)[0]
return np.unique(elems.adjacentElements(elements))
[docs] def reachableFrom(self, elements, level=0):
"""Select the elements reachable from the specified elements.
Elements are reachable if one can travel from one of the origin
elements to the target, by only following the specified level
of connections.
Parameters
----------
elements: int or int :term:`array_like`
Element number(s) from where to start the walk.
level: int
The :term:`level` of the entities used to define connections.
If negative, it is a value relative to the level of the
caller. If non-negative, it specifies the absolute level.
Default is 0 (nodes).
Returns
-------
int array
A list of the numbers of all the elements in the Mesh reachable
from any of the specified elements by walking over entities of the
specified level. The list will include the original set of elements.
"""
return where(self.frontWalk(startat=elements, level=level, frontinc=0, partinc=1, maxval=1) == 0)[0]
#############################################################################
# Adjacency #
[docs] def adjacency(self, level=0, diflevel=-1):
"""Create an element adjacency table.
Two elements are said to be adjacent if they share a lower
entity of the specified level.
Parameters
----------
level: int
Hierarchic level of the geometric items connecting two elements:
0 = node, 1 = edge, 2 = face. Only values of a lower hierarchy than
the level of the Mesh itself make sense. Default is to consider
nodes as the connection between elements.
diflevel: int, optional
If >= level, and smaller than the level of the Mesh itself,
elements that have a connection of this level are removed.
Thus, in a Mesh with volume elements, self.adjacency(0,1) gives the
adjacency of elements by a node but not by an edge.
Returns
-------
adj: :class:`~adjacency.Adjacency`
An Adjaceny table specifying for each element its neighbours
connected by the specified geometrical subitems.
"""
if diflevel > level:
return self.adjacency(level).symdiff(self.adjacency(diflevel))
if level == 0:
elems = self.elems
else:
elems = self.elems.insertLevel(level)[0]
return elems.adjacency()
[docs] def frontWalk(self, level=0, startat=0, frontinc=1, partinc=1, maxval=-1):
"""Visit all elements using a frontal walk.
In a frontal walk a forward step is executed simultanuously from all
the elements in the current front. The elements thus reached become
the new front. An element can be reached from the current element if
both are connected by a lower entity of the specified level. Default
level is 'point'.
Parameters
----------
level: int
Hierarchy of the geometric items connecting two elements:
0 = node, 1 = edge, 2 = face. Only values of a lower hierarchy than
the elements of the Mesh itself make sense. There are no
connections on the upper level.
startat: int or list of ints
Initial element number(s) in the front.
frontinc: int
Increment for the front number on each frontal step.
partinc: int
Increment for the front number when the front gets empty and
a new part is started.
maxval: int
Maximum frontal value. If negative (default) the walk will
continue until all elements have been reached. If non-negative,
walking will stop as soon as the frontal value reaches this
maximum.
Returns
-------
int array
An array of ints specifying for each element in which step
the element was reached by the walker.
See Also
--------
:meth:`adjacency.Adjacency.frontWalk`
Examples
--------
>>> M = Mesh(eltype='quad4').subdivide(5,2)
>>> print(M.frontWalk())
[0 1 2 3 4 1 1 2 3 4]
"""
return self.adjacency(level).frontWalk(startat=startat, frontinc=frontinc, partinc=partinc, maxval=maxval)
[docs] def maskedEdgeFrontWalk(self, mask=None, startat=0, frontinc=1, partinc=1, maxval=-1):
"""Perform a front walk over masked edge connections.
This is like frontWalk(level=1), but allows to specify a mask to
select the edges that are used as connectors between elements.
Parameters:
- `mask`: Either None or a boolean array or index flagging the nodes
which are to be considered connectors between elements. If None,
all nodes are considered connections.
The remainder of the parameters are like in
:meth:`adjacency.Adjacency.frontWalk`.
"""
if self.level() != 1:
hi, lo = self.elems.insertLevel(1)
else:
hi = self.elems
adj = hi.adjacency(mask=mask)
return adj.frontWalk(startat=startat, frontinc=frontinc, partinc=partinc, maxval=maxval)
# BV: DO WE NEED THE nparts ?
[docs] def partitionByConnection(self, level=0, startat=0, sort='number', nparts=-1):
"""
Detect the connected parts of a Mesh.
The Mesh is partitioned in parts in which all elements are
connected. Two elements are connected if it is possible to draw a
continuous line from a point in one element to a point in
the other element without leaving the Mesh.
Parameters:
- `sort`: str. Weighted sorting method. It can assume values
'number' (default), 'length', 'area', 'volume'.
- `nparts`: is the equivalent of parameter `maxval` in
:meth:`frontWalk`.
Maximum frontal value. If negative (default) the walk will
continue until all elements have been reached. If non-negative,
walking will stop as soon as the frontal value reaches this
maximum.
The remainder of the parameters are like in
:meth:`frontWalk`.
The partitioning is returned as a integer array having a value
for each element corresponding to the part number it belongs to.
By default the parts are sorted in decreasing order of the number
of elements. If you specify nparts, you may wish to switch off the
sorting by specifying sort=''.
"""
p = self.frontWalk(level=level, startat=startat, frontinc=0, partinc=1, maxval=nparts)
if sort=='number':
p = sortSubsets(p)
if sort=='length':
p = sortSubsets(p, self.lengths())
if sort=='area':
p = sortSubsets(p, self.areas())
if sort=='volume':
p = sortSubsets(p, self.volumes())
return p
[docs] def splitByConnection(self, level=0, startat=0, sort='number'):
"""Split the Mesh into connected parts.
The parameters `level` and `startat` are like in
:meth:`frontWalk`.
The parameter `sort` is like in
:meth:`partitionByConnection`.
Returns a list of Meshes that each form a connected part.
By default the parts are sorted in decreasing order of the number
of elements.
"""
p = self.partitionByConnection(level=level, startat=startat, sort=sort)
return self.splitProp(p)
[docs] def largestByConnection(self, level=0):
"""Return the largest connected part of the Mesh.
This is equivalent with, but more efficient than ::
self.splitByConnection(level)[0]
"""
p = self.partitionByConnection(level=level)
return self.clip(p==0)
[docs] def growSelection(self, sel, mode='node', nsteps=1):
"""Grow a selection of a surface.
`p` is a single element number or a list of numbers.
The return value is a list of element numbers obtained by
growing the front `nsteps` times.
The `mode` argument specifies how a single frontal step is done:
- 'node' : include all elements that have a node in common,
- 'edge' : include all elements that have an edge in common.
"""
level = {'node': 0, 'edge': 1}[mode]
p = self.frontWalk(level=level, startat=sel, maxval=nsteps)
return where(p>=0)[0]
[docs] def partitionByAngle(self, **kargs):
"""Partition a level-2 Mesh by the angle between adjacent elements.
The Mesh is partitioned in parts bounded by the sharp edges in the
surface. The arguments and return value are the same as in
:meth:`trisurface.TriSurface.partitionByAngle`.
For eltypes other than 'tri3',
a conversion to 'tri3' is done before computing the partitions.
"""
if self.elName() == 'tri3':
p = self.toSurface().partitionByAngle(**kargs)
else:
S = self.copy().setProp(arange(self.nelems())).toSurface()
p = S.partitionByAngle(**kargs)
j = unique(S.prop, return_index=True)[1]
p = p[j]
return p
###########################################################################
#
# IDEA: Should we move these up to Connectivity ?
# That would also avoid some possible problems
# with storing conn and econn
#
[docs] def nodeConnections(self):
"""Find and store the elems connected to nodes."""
if self.conn is None:
self.conn = self.elems.inverse()
return self.conn
[docs] def nNodeConnected(self):
"""Find the number of elems connected to nodes."""
return (self.nodeConnections() >=0).sum(axis=-1)
[docs] def edgeConnections(self):
"""Find and store the elems connected to edges."""
if self.econn is None:
self.econn = self.getElemEdges().inverse()
return self.econn
[docs] def nEdgeConnected(self):
"""Find the number of elems connected to edges."""
return (self.edgeConnections() >=0).sum(axis=-1)
#
# Are these really needed? better use adjacency(level)
#
#
[docs] def nodeAdjacency(self):
"""Find the elems adjacent to each elem via one or more nodes."""
return self.elems.adjacency()
[docs] def nNodeAdjacent(self):
"""Find the number of elems which are adjacent by node to each elem."""
return (self.nodeAdjacency() >=0).sum(axis=-1)
[docs] def edgeAdjacency(self):
"""Find the elems adjacent to elems via an edge."""
return self.getElemEdges().adjacency()
[docs] def nEdgeAdjacent(self):
"""Find the number of adjacent elems."""
return (self.edgeAdjacency() >=0).sum(axis=-1)
[docs] def nonManifoldNodes(self):
"""Return the non-manifold nodes of a Mesh.
Non-manifold nodes are nodes where subparts of a mesh of level >= 2
are connected by a node but not by an edge.
Returns an integer array with a sorted list of non-manifold node
numbers. Possibly empty (always if the dimensionality of the Mesh
is lower than 2).
"""
if self.level() < 2:
return []
ML = self.splitByConnection(1, sort='')
nm = [intersect1d(Mi.elems, Mj.elems) for Mi, Mj in combinations(ML, 2)]
return unique(concat(nm))
# TODO: Explain how this is sorted
[docs] def nonManifoldEdges(self):
"""Return the non-manifold edges of a Mesh.
Non-manifold edges are edges where subparts of a mesh of level 3
are connected by an edge but not by an face.
Returns an integer array with a sorted list of non-manifold edge
numbers. Possibly empty (always if the dimensionality of the Mesh
is lower than 3).
As a side effect, this constructs the list of edges in the object.
The definition of the nonManifold edges in terms of the nodes can
thus be got from ::
self.edges[self.nonManifoldEdges()]
"""
if self.level() < 3:
return []
elems = self.getElemEdges()
p = self.partitionByConnection(2, sort='')
eL = [elems[p==i] for i in unique(p)]
nm = [intersect1d(ei, ej) for ei, ej in combinations(eL, 2)]
return unique(concat(nm))
[docs] def nonManifoldEdgeNodes(self):
"""Return the non-manifold edge nodes of a Mesh.
Non-manifold edges are edges where subparts of a mesh of level 3
are connected by an edge but not by an face.
Returns an integer array with a sorted list of numbers of nodes
on the non-manifold edges.
Possibly empty (always if the dimensionality of the Mesh
is lower than 3).
"""
if self.level() < 3:
return []
ML = self.splitByConnection(2, sort='')
nm = [intersect1d(Mi.elems, Mj.elems) for Mi, Mj in combinations(ML, 2)]
return unique(concat(nm))
[docs] def fuse(self, parts=None, nodes=None, **kargs):
"""Fuse the nodes of a Meshes.
Nodes that are within the tolerance limits of each other
are merged into a single node.
Parameters:
- `parts`: int :term:`array_like` with length equal to number of elements.
If specified, it will be used to split the Mesh into parts (see
:func:`splitProp`) and do the fuse operation per part.
Elements for which the value of `nparts` is negative will not
be involved in the fuse operations.
- `nodes`: int :term:: a list of node numbers. If specified,
only these nodes will be involved in the fuse operation. This
option can not be used together with the `parts` option.
- Extra arguments for tuning the fuse operation are passed to the
:meth:`coords.Coords:fuse` method.
"""
if parts is None:
if nodes is None:
coords, index = self.coords.fuse(**kargs)
else:
keep = at.complement(nodes, self.nnodes())
coords, fusindex = self.coords[nodes].fuse(**kargs)
coords = Coords.concatenate([self.coords[keep], coords])
index = -ones(self.nnodes(), dtype=Int)
index[keep] = arange(len(keep), dtype=Int)
index[nodes] = len(keep) + fusindex
return self.__class__(coords, index[self.elems], prop=self.prop, eltype=self.elType())
else:
parts = checkArray(parts, (self.nelems(),), 'i')
ML = self.splitProp(parts)
if parts.min() >= 0:
n = (unique(parts) < 0).sum()
else:
n = 0
ML = ML[:n] + [M.fuse(**kargs) for M in ML[n:]]
return Mesh.concatenate(ML, fuse=False)
[docs] def matchCoords(self, coords, **kargs):
"""Match nodes of coords with nodes of self.
coords can be a Coords or a Mesh object
This is a convenience function equivalent to ::
self.coords.match(mesh.coords,**kargs)
or ::
self.coords.match(coords,**kargs)
See also :meth:`coords.Coords.match`
"""
if not(isinstance(coords, Coords)):
coords=coords.coords
return self.coords.match(coords, **kargs)
[docs] def matchCentroids(self, mesh, **kargs):
"""Match elems of Mesh with elems of self.
self and Mesh are same eltype meshes
and are both without duplicates.
Elems are matched by their centroids.
"""
c = Mesh(self.centroids(), arange(self.nelems()))
mc = Mesh(mesh.centroids(), arange(mesh.nelems()))
return c.matchCoords(mc, **kargs)
# BV: I'm not sure that we need this. Looks like it can or should
# be replaced with a method applied on the BorderMesh
#~ FI It has been tested on quad4-quad4, hex8-quad4, tet4-tri3
def matchLowerEntitiesMesh(self, mesh, level=-1):
"""_Match lower entity of mesh with the lower entity of self.
self and Mesh can be same eltype meshes or different eltype but of the
same hierarchical type (i.e. hex8-quad4 or tet4 - tri3)
and are both without duplicates.
Returns the indices array of the elems of self that matches
the lower entity of mesh, and the matched lower entity number
"""
if level < 0:
level = m1.elType().ndim + level
sel = self.elType().getEntities(level)
hi, lo = self.elems.insertLevel(sel)
hiinv = hi.inverse()
fm = Mesh(self.coords, lo)
sel1 = mesh.elType().getEntities(level)
mesh = Mesh(mesh.coords, mesh.elems.insertLevel(sel1)[1])
c = fm.matchCentroids(mesh)
hiinv = hiinv[c]
hpos = findFirst(c, hi).reshape(hi.shape)
enr = unique(hiinv[hiinv >= 0]) # element number
fnr=column_stack(where(hpos!=-1)) # face number
return enr, fnr
def matchFaces(self, mesh):
"""_Match faces of mesh with faces of self.
self and Mesh can be same eltype meshes or different eltype but of the
same hierarchical type (i.e. hex8-quad4 or tet4 - tri3)
and are both without duplicates.
eturns the indices array of the elems of self that matches
the faces of mesh, and the matched face number
"""
enr, fnr = self.matchLowerEntitiesMesh(mesh, level=2)
return enr, fnr
[docs] def compact(self, return_index=False):
"""Remove unconnected nodes and renumber the mesh.
Returns a mesh where all nodes that are not used in any
element have been removed, and the nodes are renumbered to
a compacter scheme.
If return_index is True, also returns an index specifying the
index of the new nodes in the old node scheme.
Examples
--------
>>> x = Coords([[i] for i in arange(5)])
>>> M = Mesh(x,[[0,2],[1,4],[4,2]])
>>> M,ind = M.compact(True)
>>> print(M.coords)
[[ 0. 0. 0.]
[ 1. 0. 0.]
[ 2. 0. 0.]
[ 4. 0. 0.]]
>>> print(M.elems)
[[0 2]
[1 3]
[3 2]]
>>> M = Mesh(x,[[0,2],[1,3],[3,2]])
>>> M = M.compact()
>>> print(M.coords)
[[ 0. 0. 0.]
[ 1. 0. 0.]
[ 2. 0. 0.]
[ 3. 0. 0.]]
>>> print(M.elems)
[[0 2]
[1 3]
[3 2]]
>>> print(ind)
[0 1 2 4]
>>> M = M.cselect([0,1,2])
>>> M.coords.shape, M.elems.shape
((4, 3), (0, 2))
>>> M = M.compact()
>>> M.coords.shape, M.elems.shape
((0, 3), (0, 2))
"""
if self.nelems() == 0:
ret = self.__class__(Coords(), self.elems)
nodes = array([], dtype=Int)
else:
elems, nodes = self.elems.renumber()
if elems is self.elems:
# node numbering is compact
if self.coords.shape[0] > len(nodes):
# remove extraneous nodes
self.coords = self.coords[:len(nodes)]
# numbering has not been changed, safe to use same object
ret = self
else:
# numbering has been changed, return new object
coords = self.coords[nodes]
ret = self.__class__(coords, elems, prop=self.prop, eltype=self.elType())
if return_index:
return ret, nodes
else:
return ret
def _select(self, selected, compact=True):
"""Return a Mesh only holding the selected elements.
This is the low level select method. The normal user interface
is via the Geometry.select method.
"""
selected = checkArray1D(selected)
M = self.__class__(self.coords, self.elems[selected], eltype=self.elType())
if self.prop is not None:
M.setProp(self.prop[selected])
if compact:
M = M.compact()
return M
[docs] def avgNodes(self, nodsel, wts=None):
"""Create average nodes from the existing nodes of a mesh.
`nodsel` is a local node selector as in :meth:`selectNodes`
Returns the (weighted) average coordinates of the points in the
selector as `(nelems*nnod,3)` array of coordinates, where
nnod is the length of the node selector.
`wts` is a 1-D array of weights to be attributed to the points.
Its length should be equal to that of nodsel.
"""
elems = self.elems.selectNodes(nodsel)
return self.coords[elems].average(wts=wts, axis=1)
# The following is equivalent to avgNodes(self,nodsel,wts=None)
# But is probably more efficient
[docs] def meanNodes(self, nodsel):
"""Create nodes from the existing nodes of a mesh.
`nodsel` is a local node selector as in :meth:`selectNodes`
Returns the mean coordinates of the points in the selector as
`(nelems*nnod,3)` array of coordinates, where nnod is the length
of the node selector.
"""
elems = self.elems.selectNodes(nodsel)
return self.coords[elems].mean(axis=1)
[docs] def addNodes(self, newcoords, eltype=None):
"""Add new nodes to elements.
`newcoords` is an `(nelems,nnod,3)` or`(nelems*nnod,3)` array of
coordinates. Each element gets exactly `nnod` extra nodes from this
array. The result is a Mesh with plexitude `self.nplex() + nnod`.
"""
newcoords = newcoords.reshape(-1, 3)
newnodes = arange(newcoords.shape[0]).reshape(self.elems.shape[0], -1) + self.coords.shape[0]
elems = Connectivity(concatenate([self.elems, newnodes], axis=-1))
coords = Coords.concatenate([self.coords, newcoords])
return Mesh(coords, elems, self.prop, eltype)
[docs] def addMeanNodes(self, nodsel, eltype=None):
"""Add new nodes to elements by averaging existing ones.
`nodsel` is a local node selector as in :meth:`selectNodes`
Returns a Mesh where the mean coordinates of the points in the
selector are added to each element, thus increasing the plexitude
by the length of the items in the selector.
The new element type should be set to correct value.
"""
newcoords = self.meanNodes(nodsel)
return self.addNodes(newcoords, eltype)
[docs] def selectNodes(self, nodsel, eltype=None):
"""Return a mesh with subsets of the original nodes.
`nodsel` is an object that can be converted to a 1-dim or 2-dim
array. Examples are a tuple of local node numbers, or a list
of such tuples all having the same length.
Each row of `nodsel` holds a list of local node numbers that
should be retained in the new connectivity table.
"""
elems = self.elems.selectNodes(nodsel)
prop = self.prop
if prop is not None:
prop = column_stack([prop]*len(nodsel)).reshape(-1)
return Mesh(self.coords, elems, prop=prop, eltype=eltype)
@utils.deprecated_by('Mesh.withProp', 'Mesh.selectProp')
def withProp(self, val):
return self.selectProp(val, compact=False)
@utils.deprecated_by('Mesh.withoutProp', 'Mesh.cselectProp')
def withoutProp(self, val):
return self.cselectProp(val, compact=False)
[docs] def hits(self, entities, level):
"""Count the lower entities from a list connected to the elements.
`entities`: a single number or a list/array of entities
`level`: 0 or 1 or 2 if entities are nodes or edges or faces, respectively.
The numbering of the entities corresponds to self.insertLevel(level).
Returns an (nelems,) shaped int array with the number of the
entities from the list that are contained in each of the elements.
This method can be used in selector expressions like::
self.select(self.hits(entities,level) > 0)
"""
hi = self.elems.insertLevel(level)[0]
return hi.hits(nodes=entities)
[docs] def splitRandom(self, n, compact=True):
"""Split a Mesh in n parts, distributing the elements randomly.
Returns a list of n Mesh objects, constituting together the same
Mesh as the original. The elements are randomly distributed over
the subMeshes.
By default, the Meshes are compacted. Compaction may be switched
off for efficiency reasons.
"""
sel = random.randint(0, n, (self.nelems()))
return [self.select(sel==i, compact=compact) for i in range(n) if i in sel]
###########################################################################
## simple mesh transformations ##
[docs] def reverse(self, sel=None):
"""Return a Mesh where the elements have been reversed.
Reversing an element has the following meaning:
- for 1D elements: reverse the traversal direction,
- for 2D elements: reverse the direction of the positive normal,
- for 3D elements: reverse inside and outside directions of the
element's border surface. This also changes the sign of the
elementt's volume.
The :meth:`reflect` method by default calls this method to undo
the element reversal caused by the reflection operation.
Parameters:
-`sel`: a selector (index or True/False array)
"""
utils.warn('warn_mesh_reverse')
# TODO: These can be merged
if sel is None:
if hasattr(self.elType(), 'reversed'):
elems = self.elems[:, self.elType().reversed]
else:
elems = self.elems[:, ::-1]
else:
elems = self.elems.copy()
elsel = elems[sel]
if hasattr(self.elType(), 'reversed'):
elsel = elsel[:, self.elType().reversed]
else:
elsel = elsel[:, ::-1]
elems[sel] = elsel
return self.__class__(self.coords, elems, prop=self.prop, eltype=self.elType())
[docs] def reflect(self, dir=0, pos=0.0, reverse=True, **kargs):
"""Reflect the coordinates in one of the coordinate directions.
Parameters:
- `dir`: int: direction of the reflection (default 0)
- `pos`: float: offset of the mirror plane from origin (default 0.0)
- `reverse`: boolean: if True, the :meth:`reverse` method is
called after the reflection to undo the element reversal caused
by the reflection of its coordinates. This will in most cases have
the desired effect. If not however, the user can set this to False
to skip the element reversal.
"""
if reverse is None:
reverse = True
utils.warn("warn_mesh_reflect")
M = Geometry.reflect(self, dir=dir, pos=pos)
if reverse:
M = M.reverse()
return M
[docs] def convert(self, totype, fuse=False, verbose=False):
"""Convert a Mesh to another element type.
Converting a Mesh from one element type to another can only be
done if both element types are of the same dimensionality.
Thus, 3D elements can only be converted to 3D elements.
The conversion is done by splitting the elements in smaller parts
and/or by adding new nodes to the elements.
Not all conversions between elements of the same dimensionality
are possible. The possible conversion strategies are implemented
in a table. New strategies may be added however.
The return value is a Mesh of the requested element type, representing
the same geometry (possibly approximatively) as the original mesh.
If the requested conversion is not implemented, an error is raised.
.. warning:: Conversion strategies that add new nodes may produce
double nodes at the common border of elements. The :meth:`fuse`
method can be used to merge such coincident nodes. Specifying
fuse=True will also enforce the fusing. This option become the
default in future.
"""
#
# totype is a string !
#
if verbose:
print("Convert Mesh from %s to %s" % (self.elName(), totype))
if totype == self.elName():
return self
strategy = self.elType().conversions.get(totype, None)
while not isinstance(strategy, list):
# This allows for aliases in the conversion database
strategy = self.elType().conversions.get(strategy, None)
if strategy is None:
raise ValueError("Don't know how to convert %s -> %s" % (self.elName(), totype))
# 'r' and 'v' steps can only be the first and only step
steptype, stepdata = strategy[0]
if steptype == 'r':
# Randomly convert elements to one of the types in list
return self.convertRandom(stepdata)
elif steptype == 'v':
return self.convert(stepdata).convert(totype)
# Execute a strategy
mesh = self
totype = totype.split('-')[0]
for step in strategy:
steptype, stepdata = step
if steptype == 'a':
mesh = mesh.addMeanNodes(stepdata, totype)
elif steptype == 's':
mesh = mesh.selectNodes(stepdata, totype)
elif steptype == 'x':
mesh = globals()[stepdata](mesh)
else:
raise ValueError("Unknown conversion step type '%s'" % steptype)
if fuse:
mesh = mesh.fuse()
return mesh
[docs] def convertRandom(self, choices):
"""Convert choosing randomly between choices
Returns a Mesh obtained by converting the current Mesh by a
randomly selected method from the available conversion type
for the current element type.
"""
ml = self.splitRandom(len(choices), compact=False)
ml = [m.convert(c) for m, c in zip(ml, choices)]
prop = self.prop
if prop is not None:
prop = concatenate([m.prop for m in ml])
elems = concatenate([m.elems for m in ml], axis=0)
eltype = {m.elName() for m in ml}
if len(eltype) > 1:
raise RuntimeError("Invalid choices for random conversions")
eltype = eltype.pop()
return Mesh(self.coords, elems, prop, eltype)
## TODO:
## - mesh_wts and mesh_els functions should be moved to elements.py
[docs] def subdivide(self, *ndiv, **kargs):
"""Subdivide the elements of a Mesh.
Note
----
This only works for some element types: 'line2', 'tri3', 'quad4',
'hex8'.
Parameters:
- `ndiv`: specifies the number (and place) of divisions (seeds)
along the edges of the elements. Accepted type and value depend
on the element type of the Mesh. Currently implemented:
- 'tri3': ndiv is a single int value specifying the number of
divisions (of equal size) for each edge.
- 'quad4': ndiv is a sequence of two int values nx,ny, specifying
the number of divisions along the first, resp. second
parametric direction of the element
- 'hex8': ndiv is a sequence of three int values nx,ny,nz specifying
the number of divisions along the first, resp. second and the third
parametric direction of the element
- `fuse`: bool, if True (default), the resulting Mesh is completely
fused. If False, the Mesh is only fused over each individual
element of the original Mesh.
Returns a Mesh where each element is replaced by a number of
smaller elements of the same type.
.. note:: This is currently only implemented for Meshes of type 'tri3'
and 'quad4' and 'hex8' and for the derived class 'TriSurface'.
"""
elname = self.elName()
try:
mesh_wts = globals()[elname+'_wts']
mesh_els = globals()[elname+'_els']
except:
raise ValueError("Can not subdivide element of type '%s'" % elname)
wts = mesh_wts(*ndiv)
lndiv = [nd if at.isInt(nd) else len(nd)-1 for nd in ndiv]
els = mesh_els(*lndiv)
X = self.coords[self.elems]
U = dot(wts, X).transpose([1, 0, 2]).reshape(-1, 3)
e = concatenate([els+i*wts.shape[0] for i in range(self.nelems())])
M = self.__class__(U, e, eltype=self.elType())
if self.prop is not None:
M.setProp(at.repeatValues(self.prop, prod(lndiv)))
if kargs.get('fuse', True):
M = M.fuse()
return M
@utils.warning('mesh_reduce_degenerate')
def reduceDegenerate(self, *arg, **kargs):
return self.splitDegenerate(**kargs)
[docs] def splitDegenerate(self, reduce=True, return_indices=False):
"""Split a Mesh in non-degenerate and degenerate elements.
Splits a Mesh in non-degenerate elements and degenerate elements,
and tries to reduce degenerate elements to lower plexitude elements.
Parameters
----------
reduce: bool or :class:`~elements.ElementType` name
If True, the degenerate elements will be tested against
known degeneration patterns, and the matching elements will be
transformed to non-degenerate elements of a lower plexitude.
If a string, it is an element name and only transforms to this
element type will be considered.
If False, no reduction of the degenerate elements will be
attempted.
return_indices: bool, optional
If True, also returns the element indices in the original
Mesh for all of the elements in the derived Meshes.
Returns
-------
ML: list of Mesh objects
The list of Meshes resulting from the split operation. The first
holds the non-degenerate elements of the original Mesh. The last
holds the remaining degenerate elements.
The intermediate Meshes, if any, hold elements of a lower plexitude
than the original.
Warning
-------
The Meshes that hold reduced elements may still contain degenerate
elements for the new element type
Examples
--------
>>> M = Mesh(np.zeros((4,3)),
... [[0,0,0,0],
... [0,0,0,1],
... [0,0,1,2],
... [0,1,2,3],
... [1,2,3,3],
... [2,3,3,3],
... ],eltype='quad4')
>>> M.elems.listDegenerate()
array([0, 1, 2, 4, 5])
>>> for Mi in M.splitDegenerate(): print(Mi)
Mesh: nnodes: 4, nelems: 1, nplex: 4, level: 2, eltype: quad4
BBox: [ 0. 0. 0.], [ 0. 0. 0.]
Size: [ 0. 0. 0.]
Area: 0.0
Mesh: nnodes: 4, nelems: 5, nplex: 3, level: 2, eltype: tri3
BBox: [ 0. 0. 0.], [ 0. 0. 0.]
Size: [ 0. 0. 0.]
Area: 0.0
>>> conn,ind = M.splitDegenerate(return_indices=True)
>>> print(ind[0],ind[1])
[3] [0 1 2 5 4]
>>> print(conn[1].elems)
[[0 0 0]
[0 0 1]
[0 1 2]
[2 3 3]
[1 2 3]]
"""
if reduce is False:
deg = self.elems.testDegenerate()
ML = [self.select(~deg, compact=False),
self.select(deg, compact=False)]
if return_indices:
ind = [np.where(~deg)[0], np.where(deg)[0]]
else:
target = None if reduce is True else reduce
conn, ind = self.elems.reduceDegenerate(target, return_indices=True)
ML = [Mesh(self.coords, e) for e in conn]
if self.prop is not None:
ML = [M.setProp(self.prop[i]) for M, i in zip(ML, ind)]
if return_indices:
return ML, ind
else:
return ML
[docs] def removeDegenerate(self):
"""Remove the degenerate elements from a Mesh.
Returns
-------
Mesh
A Mesh with all degenerate elements removed.
"""
deg = self.elems.testDegenerate()
return self.select(~deg, compact=False)
[docs] def removeDuplicate(self, permutations='all'):
"""Remove the duplicate elements from a Mesh.
Duplicate elements are elements that consist of the same nodes.
Parameters
----------
permutations: str
Defines which permutations of the nodes are allowed while still
considering the elements duplicates. Possible values are:
- 'none': no permutations are allowed: the node list of the elements
must have the same value at every position in order to be considered
duplicates;
- 'roll': rolling is allowed. Node lists that can be transformed into
each other by rolling are considered equal;
- 'all': any permutation of the same set of nodes will be considered
a duplicate element. This is the default.
Returns
-------
Mesh
A Mesh with all duplicate elements removed.
"""
return self.select(at.uniqueRows(self.elems, permutations))
[docs] def renumber(self, order='elems'):
"""Renumber the nodes of a Mesh in the specified order.
Parameters
----------
order: int :term:`array_like` or str
If an array, it is an index with length equal to the number of
nodes. It should be a permutation of ``arange(self.nnodes())``.
The index specifies the node number that should come at this
position. Thus, the order values are the old node numbers on
the new node number positions.
``order`` can also be a predefined string that will generate the
node index automatically:
- 'elems': the nodes are number in order of their appearance in the
Mesh connectivity.
- 'random': the nodes are numbered randomly.
- 'front': the nodes are numbered in order of their frontwalk.
Returns
-------
Mesh
A Mesh equivalent with the input, but with the nodes numbered
differently.
"""
if order == 'elems':
order = renumberIndex(self.elems)
elif order == 'random':
order = arange(self.nnodes())
random.shuffle(order)
elif order == 'front':
adj = self.elems.adjacency('n')
p = adj.frontWalk()
order = p.argsort()
newnrs = inverseUniqueIndex(order)
return self.__class__(self.coords[order], newnrs[self.elems], prop=self.prop, eltype=self.elType())
[docs] def reorder(self, order='nodes'):
"""Reorder the elements of a Mesh.
Parameters
----------
order: :term:`array_like` or str
If an array, it is a permutation of the numbers in
``arange(self.nelems())``, specifying the requested order of
the elements.
``order`` can also be one of the following predefined strings:
- 'nodes': order the elements in increasing node number order.
- 'random': number the elements in a random order.
- 'reverse': number the elements in reverse order.
Returns
-------
Mesh
A Mesh equivalent with self but with the elements ordered as
specified.
"""
order = self.elems.reorder(order)
if self.prop is None:
prop = None
else:
prop = self.prop[order]
return self.__class__(self.coords, self.elems[order], prop=prop, eltype=self.elType())
#
# Should we create some general 'masked mesh' class?
#
[docs] def connectedElements(self, startat, mask, level=0):
"""Return the elements reachable from startat.
Finds the elements which can be reached from startat by walking along
a mask (a subset of elements). Walking is possible over nodes, edges
or faces, as specified in level.
Parameters
----------
startat: int or :term:`array_like`, int.
The starting element number(s).
level: int
Specifies how elements can be reached: via node (0), edge (1)
or face (2).
mask: :term:`array_like`, bool or int.
Flags the elements that are considered walkable. It is an int array
with the walkable element numbers, or a bool array flagging the
these elements with a value True.
"""
startat = asarray(startat).reshape(-1)
if len(intersect1d(startat, arange(self.nelems()))) < len(startat):
raise ValueError("wrong elem index found in startat, outside range 0 - %d" % self.nelems())
mask = asarray(mask)
if mask.dtype == bool:
if len(mask)!=self.nelems():
raise ValueError("if it is an array of boolean mask should have all elements %d, got %d" % (self.nelems(), len(mask)))
mask = where(mask)[0]
if len(intersect1d(mask, arange(self.nelems()))) < len(mask):
raise ValueError("wrong elem index found in mask, outside range 0 - %d" % self.nelems())
startat = intersect1d(startat, mask)
if len(startat) == 0:
return []
startat = findFirst(mask, startat)
return mask[self.select(mask).reachableFrom(startat, level=level)]
##############################################################
#
# Connection, Extrusion, Sweep, Revolution
#
[docs] def connect(self, coordslist, div=1, degree=1, loop=False, eltype=None):
"""Connect a sequence of topologically congruent Meshes into a hypermesh.
Parameters:
- `coordslist`: either a list of Coords objects, or a list of
Mesh objects or a single Mesh object.
If Mesh objects are given, they should (all) have the same element
type as `self`. Their connectivity tables will not be used though.
They will only serve to construct a list of Coords objects by
taking the `coords` attribute of each of the Meshes. If only a single
Mesh was specified, `self.coords` will be added as the first Coords
object in the list.
All Coords objects in the coordslist (either specified or
constructed from the Mesh objects), should have the exact same
shape as `self.coords`. The number of Coords items in the list should
be a multiple of `degree`, plus 1.
Each of the Coords in the final coordslist is combined with the
connectivity table, element type and property numbers of `self` to
produce a list of toplogically congruent meshes.
The return value is the hypermesh obtained by connecting
each consecutive slice of (degree+1) of these meshes. The hypermesh
has a dimensionality that is one higher than the original Mesh (i.e.
points become lines, lines become surfaces, surfaces become volumes).
The resulting elements will be of the given `degree` in the
direction of the connection.
Notice that unless a single Mesh was specified as coordslist, the
coords of `self` are not used. In many cases however `self` or
`self.coords` will be one of the items in the specified `coordslist`.
- `degree`: degree of the connection. Currently only degree 1 and 2
are supported.
- If degree is 1, every Coords from the `coordslist`
is connected with hyperelements of a linear degree in the
connection direction.
- If degree is 2, quadratic hyperelements are
created from one Coords item and the next two in the list.
Note that all Coords items should contain the same number of nodes,
even for higher order elements where the intermediate planes
contain less nodes.
Currently, degree=2 is not allowed when `coordslist` is specified
as a single Mesh.
- `loop`: if True, the connections with loop around the list and
connect back to the first. This is accomplished by adding the first
Coords item back at the end of the list.
- `div`: This should only be used for degree==1.
With this parameter the generated connections can be further
subdivided along the connection direction. `div` is either a
single input for :func:`~arraytools.smartSeed`,
or a list thereof.
In the latter case, the length of the list should be one less
than the length of the `coordslist`. Each pair of consecutive
items from the coordinate list will be connected using the
seeds generated by the corresponding value from `div`, passed to
:func:`~arraytools.smartSeed`.
Notice that if seed
values are specified directly as a list of floats, the list
should start with a value 0.0 and end with 1.0.
- `eltype`: the element type of the constructed hypermesh. Normally,
this is set automatically from the base element type and the
connection degree. If a different element type is specified,
a final conversion to the requested element type is attempted.
"""
if isinstance(coordslist, list):
if isinstance(coordslist[0], Mesh):
if sum([c.elType() != self.elType() for c in coordslist]):
raise ValueError("All Meshes in the list should have same element type")
clist = [c.coords for c in coordslist]
else:
clist = coordslist
elif isinstance(coordslist, Mesh):
clist = [self.coords, coordslist.coords]
if degree == 2:
raise ValueError("This only works for linear connection")
## BV: Any reason why this would not work??
## xm = 0.5 * (clist[0]+clist[1])
## clist.insert(1, xm)
else:
raise ValueError("Invalid coordslist argument")
if sum([c.shape != self.coords.shape for c in clist]):
raise ValueError("Incompatible shape in coordslist")
# implement loop parameter
if loop:
clist.append(clist[0])
if (len(clist)-1) % degree != 0:
raise ValueError("Invalid length of coordslist (%s) for degree %s." % (len(clist), degree))
# set divisions
if degree > 1:
div = 1
if not isinstance(div, list) or isFloat(div[0]):
div=[div]
# now we should have list of: ints, tuples or floatlists
div = [at.smartSeed(divi)[1:] for divi in div]
# check length
nsteps = (len(clist)-1) // degree
if len(div) == 1:
div = div * nsteps
elif len(div)!=nsteps:
raise ValueError("A list of div seeds must have a length equal to (len(clist)-1)//degree) = %s" % nsteps)
# For higher order non-lagrangian elements the procedure could be
# optimized by first compacting the coords and elems.
# Instead we opted for the simpler method of adding the maximum
# number of nodes, and then selecting the used ones.
# A final compact() throws out the unused points.
# Concatenate the coordinates
if degree == 1:
# We do not have a 2nd degree interpolation yet
x = [Coords.interpolate(xi, xj, d).reshape(-1, 3) for xi, xj, d in zip(clist[:-1], clist[1:], div)]
clist = clist[:1] + x
x = Coords.concatenate(clist)
# Create the connectivity table
nnod = self.ncoords()
nrep = (x.shape[0]//nnod - 1) // degree
## print("NREP %s" % nrep)
e = self.elems.extrude(nnod, degree).replic(nrep, nnod*degree)
# Create the Mesh
M = Mesh(x, e).setProp(self.prop)
# convert to proper eltype
if eltype:
M = M.convert(eltype)
return M
[docs] def extrude(self, div, dir=0, length=1., degree=1, eltype=None):
"""Extrude a Mesh along a straight line.
The Mesh is extruded over a given length in the given direction.
Parameters
----------
div: smartseed
Specifies how the extruded direction will be subdivided in
elements. It can be anything that is acceptable as input for
:func:`~arraytools.smartSeed`.
dir: int (0,1,2) or float :term:`array_like` (3,)
The direction of the extrusion: either a global axis
number or a direction vector.
length: float
The length of the extrusion, measured along the direction ``dir``.
Returns
-------
Mesh
A Mesh obtained by extruding the input Mesh over the
given ``length`` in direction ``dir``, subdividing this
length according to the seeds generated
by ``smartSeed(div)``.
Examples
--------
>>> M = Mesh(Formex(origin())).extrude(3,0,3)
>>> print(M)
Mesh: nnodes: 4, nelems: 3, nplex: 2, level: 1, eltype: line2
BBox: [ 0. 0. 0.], [ 3. 0. 0.]
Size: [ 3. 0. 0.]
Length: 3.0
"""
if isFloat(dir):
# Probably old style extrude parameters?
utils.warn("warn_mesh_extrude")
t = at.smartSeed(div)
if degree > 1:
t2 = 0.5 * (t[:-1] + t[1:])
t = concatenate([t[:1], column_stack([t2, t[1:]]).ravel()])
x0 = self.coords
x1 = x0.trl(dir, length)
dx = x1-x0
x = [x0 + ti*dx for ti in t]
return self.connect(x, degree=degree, eltype=eltype)
[docs] def revolve(self, n, axis=0, angle=360., around=None, loop=False, eltype=None):
"""Revolve a Mesh around an axis.
Returns a new Mesh obtained by revolving the given Mesh
over an angle around an axis in n steps, while extruding
the mesh from one step to the next.
This extrudes points into lines, lines into surfaces and surfaces
into volumes.
"""
angles = arange(n+1) * angle / n
seq = [self.coords.rotate(angle=a, axis=axis, around=around) for a in angles]
return self.connect(seq, loop=loop, eltype=eltype)
[docs] def sweep(self, path, eltype=None, **kargs):
"""Sweep a mesh along a path, creating an extrusion
Parameters:
- `path`: Curve object. The path over which to sweep the Mesh.
- `eltype`: string. Name of the element type on the
returned Meshes.
- `**kargs`: keyword arguments that are passed to
:meth:`curve.Curve.sweep2`, with the same meaning.
Usually, you will need to at least set the `normal` parameter.
Returns a Mesh obtained by sweeping the given Mesh over a path.
The returned Mesh has double plexitude of the original.
If `path` is a closed Curve connect back to the first.
This operation is similar to the extrude() method, but the path
can be any 3D curve.
"""
loop = path.closed
seq = path.sweep2(self.coords, **kargs)
return self.connect(seq, eltype=eltype, loop=loop)
[docs] def smooth(self, iterations=1, lamb=0.5, k=0.1, edg=True, exclnod=[], exclelem=[], weight=None):
"""Return a smoothed mesh.
Smoothing algorithm based on lowpass filters.
If edg is True, the algorithm tries to smooth the
outer border of the mesh seperately to reduce mesh shrinkage.
Higher values of k can reduce shrinkage even more
(up to a point where the mesh expands),
but will result in less smoothing per iteration.
- `exclnod`: It contains a list of node indices to exclude from the smoothing.
If exclnod is 'border', all nodes on the border of the mesh will
be unchanged, and the smoothing will only act inside.
If exclnod is 'inner', only the nodes on the border of the mesh will
take part to the smoothing.
- `exclelem`: It contains a list of elements to exclude from the smoothing.
The nodes of these elements will not take part to the smoothing.
If exclnod and exclelem are used at the same time the union of them
will be exluded from smoothing.
-`weight` : it is a string that can assume 2 values `inversedistance` and
`distance`. It allows to specify the weight of the adjancent points according
to their distance to the point
"""
if self.elType().ndim == 1:
if edg == True:
raise ValueError("Cannot use edg=True with a line mesh")
if iterations < 1:
return self
if lamb*k == 1:
raise ValueError("Cannot assign values of lamb and k which result in lamb*k==1")
mu = -lamb/(1-k*lamb)
adj = self.getEdges().adjacency(kind='n')
incl = resize(True, self.ncoords())
if exclnod == 'border':
exclnod = unique(self.getBorder())
k = 0. # k can be zero because it cannot shrink
edg = False # there is no border edge
if exclnod == 'inner':
exclnod = delete(arange(self.ncoords()), unique(self.getBorder()))
exclelemnod = unique(self.elems[exclelem])
exclude=array(unique(concatenate([exclnod, exclelemnod])), dtype = int)
incl[exclude] = False
if edg:
externals = resize(False, self.ncoords())
expoints = unique(self.getFreeEntities())
if len(expoints) not in [0, self.ncoords()]:
externals[expoints] = True
a = adj[externals].ravel()
inpoints = delete(arange(self.ncoords()), expoints)
a[findFirst(inpoints, a) != -1] = -2
adj[externals] = a.reshape(adj[externals].shape)
else:
print('Failed to recognize external points.\nShrinkage may be considerable.')
w = ones(adj.shape, dtype=float)
if weight == 'inversedistance':
dist = length(self.coords[adj]-self.coords.reshape(-1, 1, 3))
w[dist!=0] /= dist[dist!=0]
if weight == 'distance':
w = length(self.coords[adj]-self.coords.reshape(-1, 1, 3))
w[adj<0] = 0.
w /= w.sum(-1).reshape(-1, 1)
w = w.reshape(adj.shape[0], adj.shape[1], 1)
c = self.coords.copy()
for i in range(iterations):
c[incl] = (1.-lamb)*c[incl] + lamb*(w[incl] *c[adj][incl]).sum(1)
c[incl] = (1.-mu)*c[incl] + mu*(w[incl] *c[adj][incl]).sum(1)
return self.__class__(c, self.elems, prop=self.prop, eltype=self.elType())
def __add__(self, other):
"""Return the sum of two Meshes.
The sum of the Meshes is simply the concatenation thereof.
It allows us to write simple expressions as M1+M2 to concatenate
the Meshes M1 and M2. Both meshes should be of the same plexitude
and have the same eltype.
The result will be of the same class as self (either a Mesh or a
subclass thereof).
"""
return self.concatenate([self, other])
[docs] @classmethod
def concatenate(clas, meshes, fuse=True, **kargs):
"""Concatenate a list of meshes of the same plexitude and eltype
All Meshes in the list should have the same plexitude.
Meshes with plexitude are ignored though, to allow empty
Meshes to be added in.
Merging of the nodes can be tuned by specifying extra arguments
that will be passed to :meth:`coords.Coords:fuse`.
If any of the meshes has property numbers, the resulting mesh will
inherit the properties. In that case, any meshes without properties
will be assigned property 0.
If all meshes are without properties, so will be the result.
This is a class method, and should be invoked as follows::
Mesh.concatenate([mesh0,mesh1,mesh2])
"""
def _force_prop(m):
if m.prop is None:
return zeros(m.nelems(), dtype=Int)
else:
return m.prop
meshes = [m for m in meshes if m.nplex() > 0]
nplex = {m.nplex() for m in meshes}
if len(nplex) > 1:
raise ValueError("Cannot concatenate meshes with different plexitude: %s" % str(nplex))
eltype = {m.elType() for m in meshes}
if len(eltype) > 1:
raise ValueError("Cannot concatenate meshes with different eltype: %s" % [m.elName() for m in meshes])
# Keep the available props
prop = [m.prop for m in meshes if m.prop is not None]
if len(prop) == 0:
prop = None
elif len(prop) < len(meshes):
prop = concatenate([_force_prop(m) for m in meshes])
else:
prop = concatenate(prop)
coords, elems = mergeMeshes(meshes, fuse=fuse, **kargs)
elems = concatenate(elems, axis=0)
return clas(coords, elems, prop=prop, eltype=eltype.pop())
# Test and clipping functions
[docs] def test(self, nodes='all', dir=0, min=None, max=None, atol=0.):
"""Flag elements having nodal coordinates between min and max.
This function is very convenient in clipping a Mesh in a specified
direction. It returns a 1D integer array flagging (with a value 1 or
True) the elements having nodal coordinates in the required range.
Use where(result) to get a list of element numbers passing the test.
Or directly use clip() or cclip() to create the clipped Mesh
The test plane can be defined in two ways, depending on the value of dir.
If dir == 0, 1 or 2, it specifies a global axis and min and max are
the minimum and maximum values for the coordinates along that axis.
Default is the 0 (or x) direction.
Else, dir should be compaitble with a (3,) shaped array and specifies
the direction of the normal on the planes. In this case, min and max
are points and should also evaluate to (3,) shaped arrays.
nodes specifies which nodes are taken into account in the comparisons.
It should be one of the following:
- a single (integer) point number (< the number of points in the Formex)
- a list of point numbers
- one of the special strings: 'all', 'any', 'none'
The default ('all') will flag all the elements that have all their
nodes between the planes x=min and x=max, i.e. the elements that
fall completely between these planes. One of the two clipping planes
may be left unspecified.
"""
if min is None and max is None:
raise ValueError("At least one of min or max have to be specified.")
if pf.isString(nodes):
nod = arange(self.nplex())
else:
nod = nodes
# Perform the test on the selected nodes
X = self.coords[self.elems][:, nod]
T = X.test(dir=dir, min=min, max=max, atol=atol)
if len(T.shape) > 1:
# We have results for more than 1 node per element
if nodes == 'any':
T = T.any(axis=1)
elif nodes == 'none':
T = ~T.any(axis=1)
else:
T = T.all(axis=1)
return asarray(T)
[docs] def clipAtPlane(self, p, n, nodes='any', side='+'):
"""Return the Mesh clipped at plane (p,n).
This is a convenience function returning the part of the Mesh
at one side of the plane (p,n)
"""
if side == '-':
n = -n
return self.clip(self.test(nodes=nodes, dir=n, min=p))
[docs] def intersectionWithLines(self, approximated=True, **kargs):
"""Return the intersections of a level-2 Mesh with lines.
The Mesh is intersected with lines. The arguments and return values are
the same as in :meth:`trisurface.TriSurface.intersectionWithLines`,
except for the `approximated`.
For a Mesh with eltype 'tri3', the intersections are exact. For other
eltypes, if `approximated` is True a conversion to 'tri3' is done before
computing the intersections. This may produce an exact result,
an approximate result or no result (if the conversion fails).
Of course the user can create his own approximation to a 'tri3'
surface first, before calling this method.
"""
if self.elName() == 'tri3':
p, i = self.toSurface().intersectionWithLines(**kargs)
else:
if approximated:
S = self.copy().setProp(list(range(self.nelems()))).toSurface()
p, i = S.intersectionWithLines(**kargs)
i[:, 2] = S.prop[i[:, 2]]
else:
raise ValueError('Exact intersectionWithLines not implemented for %s mesh'%self.elName())
return p, i
[docs] def levelVolumes(self):
"""Return the level volumes of all elements in a Mesh.
The level volume of an element is defined as:
- the length of the element if the Mesh is of level 1,
- the area of the element if the Mesh is of level 2,
- the (signed) volume of the element if the Mesh is of level 3.
The level volumes can be computed directly for Meshes of eltypes
'line2', 'tri3' and 'tet4' and will produce accurate results.
All other Mesh types are converted to one of these before computing
the level volumes. Conversion may result in approximation of the
results. If conversion can not be performed, None is returned.
If succesful, returns an (nelems,) float array with the level
volumes of the elements.
Returns None if the Mesh level is 0, or the conversion to the
level's base element was unsuccesful.
Note that for level-3 Meshes, negative volumes will be returned
for elements having a reversed node ordering.
"""
from pyformex.geomtools import levelVolumes
base_elem = {
1: 'line2',
2: 'tri3',
3: 'tet4'
}
try:
base = base_elem[self.level()]
except:
return None
if self.elName() == base:
M = self
else:
try:
M = self.shallowCopy(prop=arange(self.nelems())).convert(base)
except:
print("CONVERSION TO %s FAILED!" % base)
return None
V = levelVolumes(M.coords[M.elems])
if V is not None and M != self:
V = array([V[where(M.prop==i)[0]].sum() for i in range(self.nelems())])
return V
[docs] def lengths(self):
"""Return the length of all elements in a level-1 Mesh.
For a Mesh with eltype 'line2', the lengths are exact. For other
eltypes, a conversion to 'line2' is done before computing the lengths.
This may produce an exact result, an approximated result or no result
(if the conversion fails).
If succesful, returns an (nelems,) float array with the lengths.
Returns None if the Mesh level is not 1, or the conversion to 'line2'
does not succeed.
"""
if self.level() == 1:
return self.levelVolumes()
else:
return None
[docs] def areas(self):
"""Return the area of all elements in a level-2 Mesh.
For a Mesh with eltype 'tri3', the areas are exact. For other
eltypes, a conversion to 'tri3' is done before computing the areas.
This may produce an exact result, an approximate result or no result
(if the conversion fails).
If succesful, returns an (nelems,) float array with the areas.
Returns None if the Mesh level is not 2, or the conversion to 'tri3'
does not succeed.
"""
if self.level() == 2:
return self.levelVolumes()
else:
return None
[docs] def volumes(self):
"""Return the signed volume of all the mesh elements
For a 'tet4' tetraeder Mesh, the volume of the elements is calculated
as 1/3 * surface of base * height.
For other Mesh types the volumes are calculated by first splitting
the elements into tetraeder elements.
The return value is an array of float values with length equal to the
number of elements.
If the Mesh conversion to tetraeder does not succeed, the return
value is None.
"""
if self.level() == 3:
return self.levelVolumes()
else:
return None
[docs] def length(self):
"""Return the total length of a Mesh.
Returns the sum of self.lengths(), or 0.0 if the self.lengths()
returned None.
"""
try:
return self.lengths().sum()
except:
return 0.0
[docs] def area(self):
"""Return the total area of a Mesh.
Returns the sum of self.areas(), or 0.0 if the self.areas()
returned None.
"""
try:
return self.areas().sum()
except:
return 0.0
[docs] def volume(self):
"""Return the total volume of a Mesh.
For a Mesh of level < 3, a value 0.0 is returned.
For a Mesh of level 3, the volume is computed by converting its
border to a surface and taking the volume inside that surface.
It is equivalent with ::
self.toSurface().volume()
This is far more efficient than `self.volumes().sum()`.
"""
if self.level() == 3:
return self.toSurface().volume()
else:
return 0.0
[docs] def fixVolumes(self):
"""Reverse the elements with negative volume.
Elements with negative volume may result from incorrect
local node numbering. This method will reverse all elements
in a Mesh of dimensionality 3, provide the volumes of these
elements can be computed.
"""
return self.reverse(self.volumes() < 0.)
##########################################
## Deprecated ##
@utils.deprecated_by('Mesh.nodalToElement', 'Field.convert')
def nodalToElement(self, val):
return val[self.elems].mean(axis=1)
@utils.deprecated_by('Mesh.getLowerEntitiesSelector', 'Element.getEntities')
def getLowerEntitiesSelector(self, level=-1):
return self.elType().getEntities(level)
# 20190514
@utils.deprecated_by('Mesh.setType','Mesh.setEltype or Mesh.eltype assignment')
def setType(self, eltype):
return self.setEltype(eltype)
##########################################
## Allow drawing ##
def actor(self, **kargs):
if self.nelems() == 0:
return None
from pyformex.opengl.drawable import GeomActor
return GeomActor(self, **kargs)
######################## Functions #####################
[docs]def mergeNodes(nodes, fuse=True, **kargs):
"""Merge all the nodes of a list of node sets.
Merging the nodes creates a single Coords object containing all nodes,
and the indices to find the points of the original node sets in the
merged set.
Parameters:
- `nodes`: a list of Coords objects, all having the same shape, except
possibly for their first dimension
- `fuse`: if True (default), coincident (or very close) points will
be fused to a single point
- `**kargs`: keyword arguments that are passed to the fuse operation
Returns:
- a Coords with the coordinates of all (unique) nodes,
- a list of indices translating the old node numbers to the new. These
numbers refer to the serialized Coords.
The merging operation can be tuned by specifying extra arguments
that will be passed to :meth:`coords.Coords.fuse`.
"""
coords = Coords(concatenate([x for x in nodes], axis=0))
if fuse:
coords, index = coords.fuse(**kargs)
else:
index = arange(coords.shape[0])
n = array([0] + [x.npoints() for x in nodes]).cumsum()
ind = [index[f:t] for f, t in zip(n[:-1], n[1:])]
return coords, ind
[docs]def mergeMeshes(meshes, fuse=True, **kargs):
"""Merge all the nodes of a list of Meshes.
Each item in meshes is a Mesh instance.
The return value is a tuple with:
- the coordinates of all unique nodes,
- a list of elems corresponding to the input list,
but with numbers referring to the new coordinates.
The merging operation can be tuned by specifying extra arguments
that will be passed to :meth:`coords.Coords:fuse`.
Setting fuse=False will merely concatenate all the mesh.coords, but
not fuse them.
"""
coords = [m.coords for m in meshes]
elems = [m.elems for m in meshes]
coords, index = mergeNodes(coords, fuse, **kargs)
return coords, [Connectivity(i[e], eltype=e.eltype) for i, e in zip(index, elems)]
[docs]def line2_wts(seed0):
"""Create weights for line2 subdivision.
Parameters
----------
seed0: int or list of floats
The subdivisions along the first parametric direction of the element.
If an int, the subdivisions will be equally spaced between 0 and 1
Examples
--------
>>> line2_wts(4)
array([[ 0. , 1. ],
[ 0.25, 0.75],
[ 0.5 , 0.5 ],
[ 0.75, 0.25],
[ 1. , 0. ]])
"""
wts = at.gridpoints(seed0)
return column_stack([wts, 1-wts])
def line2_els(nx):
#n = nx+1
els = [array([0, 1]) + i for i in range(nx)]
return row_stack(els)
def tri3_wts(ndiv):
n = ndiv+1
seeds = arange(n)
pts = concatenate([
column_stack([seeds[:n-i], [i]*(n-i)])
for i in range(n)])
pts = column_stack([ndiv-pts.sum(axis=-1), pts])
return pts / float(ndiv)
def tri3_els(ndiv):
n = ndiv+1
els1 = [row_stack([array([0, 1, n-j]) + i for i in range(ndiv-j)]) + j * n - j*(j-1)//2 for j in range(ndiv)]
els2 = [row_stack([array([1, 1+n-j, n-j]) + i for i in range(ndiv-j-1)]) + j * n - j*(j-1)//2 for j in range(ndiv-1)]
elems = row_stack(els1+els2)
return elems
[docs]def quad4_wts(seed0, seed1):
""" Create weights for quad4 subdivision.
Parameters:
- 'seed0' : int or list of floats . It specifies divisions along the
first parametric direction of the element
- 'seed1' : int or list of floats . It specifies divisions along
the second parametric direction of the element
If these parameters are integer values the divisions will be equally
spaced between 0 and 1
This is equivalent with `~arraytools.gridpoints(seed0, seed1)`.
"""
return at.gridpoints(seed0, seed1)
[docs]def quad4_els(nx, ny):
"""Quad4 element connectivity for a regular stack of nx,ny elements.
The node numbers vary first in the x, then in the y direction.
"""
n = nx+1
els = [row_stack([array([0, 1, n+1, n]) + i for i in range(nx)]) + j * n for j in range(ny)]
return row_stack(els)
# TODO: remove or document in subdivide
quad9_wts=quad4_wts
quad9_els=quad4_els
[docs]def quadgrid(seed0, seed1, roll=0):
"""Create a quadrilateral mesh of unit size with the specified seeds.
Parameters:
- `seed0`,`seed1`: seeds for the elements along the parametric directions
0 and 1. Each can be one of the following:
- an integer number, specifying the number of equally sized elements
along that direction,
- a tuple (n,) or (n,e0) or (n,e0,e1), to be used as parameters in the
:func:`mesh.seed` function,
- a list of monotonously increasing float values in the range 0.0 to 1.0,
specifying the relative positions of the nodes. Normally, the first and
last values of the seeds are 0. and 1., leading to a unit square grid.
The node and element numbers vary first in the x, then in the y direction.
"""
from pyformex.elements import Quad4
seed0 = at.smartSeed(seed0)
seed1 = at.smartSeed(seed1)
wts = at.gridpoints(seed0, seed1)
n0 = len(seed0)-1
n1 = len(seed1)-1
E = Quad4.toMesh()
if roll:
E = E.rollAxes(roll)
X = E.coords.reshape(-1, 4, 3)
U = dot(wts, X).transpose([1, 0, 2]).reshape(-1, 3)
els = quad4_els(n0, n1)
e = concatenate([els+i*wts.shape[0] for i in range(E.nelems())])
M = Mesh(U, e, eltype=E.elType())
return M.fuse()
[docs]def hex8_wts(seed0, seed1, seed2):
""" Create weights for hex8 subdivision.
Parameters:
- 'seed0' : int or list of floats . It specifies divisions along the
first parametric direction of the element
- 'seed1' : int or list of floats . It specifies divisions along
the second parametric direction of the element
- 'seed2' : int or list of floats . It specifies divisions along
the t parametric direction of the element
If these parametes are integer values the divisions will be equally
spaced between 0 and 1
"""
return at.gridpoints(seed0, seed1, seed2)
[docs]def hex8_els(nx, ny, nz):
""" Create connectivity table for hex8 subdivision.
"""
n = nz+1
els = [row_stack([row_stack([asarray([array([0, 1, n+1, n]) + k for k in range(nz)])+i * n for i in range(nx)])]) +j * (n*(nx+1)) for j in range(ny+1)]
els = concatenate([row_stack(els[:-1]), row_stack(els[1:])], axis=1)
return els
[docs]def rectangle(L=1., W=1., nl=1, nw=1):
"""Create a plane rectangular mesh of quad4 elements.
Parameters:
- `L`,`W`: length,width of the rectangle.
"""
return quadgrid(nl, nw).resized([L, W, 1.0])
[docs]def rectangleWithHole(L, W, r, nr, nl, nw=None, e0=0.0, eltype='quad4'):
"""Create a quarter of rectangle with a central circular hole.
Parameters:
- `L`: float. Length of the (quarter) rectangle
- `W`: float. Width of the (quarter) rectangle
- `r`: float. Radius of the hole
- `nr`: integer. Number of elements over radial direction
- `nl`: integer. Number of elements over tangential direction along L
- `nw`: integer. Number of elements over tangential direction along W.
If None (default), it will be set equal to nl.
- `e0`: float. Concentration factor for elements in the radial direction
Returns a Mesh
"""
# L = W
from pyformex import elements
if nw is None:
nw = nl
base = elements.Quad9.vertices.scale([L, W, 1.])
F0 = Formex([[[r, 0., 0.]]]).rosette(5, 90./4)
F2 = Formex([[[L, 0.]], [[L, W/2.]], [[L, W]], [[L/2., W]], [[0., W]]])
F1 = F0.interpolate(F2, div=[0.5])
FL = [F0, F1, F2]
X0, X1, X2 = [F.coords.reshape(-1, 3) for F in FL]
trf0 = Coords([X0[0], X2[0], X2[2], X0[2], X1[0], X2[1], X1[2], X0[1], X1[1]])
trf1 = Coords([X0[2], X2[2], X2[4], X0[4], X1[2], X2[3], X1[4], X0[3], X1[3]])
seedr = at.smartSeed((nr, e0))
seedl = at.smartSeed(nl)
seedw = at.smartSeed(nw)
gridl = quadgrid(seedr, seedl).resized([L, W, 1.0])
gridw = quadgrid(seedr, seedw).resized([L, W, 1.0])
gridl = gridl.isopar('quad9', trf0, base)
gridw = gridw.isopar('quad9', trf1, base)
return (gridl+gridw).fuse()
[docs]def quadrilateral(x, n1, n2):
"""Create a quadrilateral mesh
Parameters:
- `x`: Coords(4,3): Four corners of the mesh, in anti-clockwise order.
- `n1`: number of elements along sides x0-x1 and x2-x3
- `n2`: number of elements along sides x1-x2 and x3-x4
Returns a Mesh of quads filling the quadrilateral defined by the four
points `x`.
"""
from pyformex.elements import Quad4
x = checkArray(x, (4, 3), 'f')
M = rectangle(1., 1., nl, nw).isopar('quad4', x, Quad4.vertices)
return M
[docs]def continuousCurves(c0, c1):
"""Make sure the two curves are continuous.
Ensures that the end point of curve c0 and the start point of curve c1
are coincident.
This is done by replacing these two points with their mean value.
"""
c0.coords[-1] = c1.coords[0] = 0.5 * (c0.coords[-1] + c1.coords[0])
[docs]def triangleQuadMesh(P0, C0, n, P0wgt=1.0):
"""Create a quad Mesh over a triangular region
The triangle can have a single non-straight edge. The domain is
described by a curve and a point. The straight lines between the
curve ends and the point are the other two sides.
Parameters:
- `P0`: a point
- `C`: a curve
- `ndiv`: a tuple of 3 int's. The quad kernel near the point will
have n0*n1 elements (n0 to the start of the curve, n1 to the end.
The zone near the curve has n0+n1 elements along the curve, and
n2 elements perpendicular to the curve.
"""
from pyformex.plugins.curve import PolyLine
# Make sure we have PolyLines
C = [
PolyLine([P0, C0.coords[0]]),
C0.approx(),
PolyLine([C0.coords[-1], P0]),
]
# Make sure the end points are connected
(continuousCurves(C[i], C[(i+1)%3]) for i in range(3))
# Number of divisions along each side
n = array(n)
nt = array([n[0]+n[2], n[1]+n[0], n[2]+n[1]])
# Divide the three sides
C = [C[i].approx(nseg=nt[i], equidistant=True) for i in range(3)]
# Split the curves in two parts
C = [C[i].split(n[i]) for i in range(3)]
# Create the center point
P1 = Coords.concatenate([Ci[1].coords[0] for Ci in C]).mean(axis=0)
if P0wgt > 0.0:
P1 = (3.*P1 + P0wgt*P0) / (3.+P0wgt)
# Create the central PolyLines
D = [PolyLine([C[i][1].coords[0], P1]).approx(nseg=n[(i+1)%3], equidistant=True) for i in range(3)]
# Create the submeshes
M = [Ci.toMesh().connect(Di.toMesh(), div=ni) for Ci, Di, ni in [
(C[0][0], D[2], n[1]),
(C[1][0], D[0], n[2]),
(C[1][1], D[2].reverse(), n[2]),
]]
# Concatenate Meshes
return Mesh.concatenate(M)
[docs]def quarterCircle(n1, n2):
"""
Create a mesh of quadrilaterals filling a quarter circle.
Parameters
----------
n1: int
Number of elements along the edges 01 and 23
n2: int
Number of elements along the edges 12 and 30
Returns
-------
Mesh
A 'quad4' Mesh filling a quarter circle with radius 1 and
center at the origin, in the first quadrant of the axes.
Notes
-----
The quarter circle mesh has a kernel of n1*n1 cells, and two
border meshes of n1*n2 cells. The resulting mesh has n1+n2 cells
in radial direction and 2*n1 cells in tangential direction (in the
border mesh).
"""
from pyformex.plugins.curve import Arc, PolyLine
r = float(n1)/(n1+n2) # radius of the kernel
P0, P1 = Coords([[0., 0., 0.], [r, 0., 0.]])
P2 = P1.rot(45.)
P3 = P1.rot(90.)
# Kernel is a quadrilateral
C0 = PolyLine([P0, P1]).approx(ndiv=n1).toMesh()
C1 = PolyLine([P3, P2]).approx(ndiv=n1).toMesh()
M0 = C0.connect(C1, div=n1)
# Border meshes
C0 = Arc(center=P0, radius=1., angles=(0., 45.)).approx(ndiv=n1).toMesh()
C1 = PolyLine([P1, P2]).approx(ndiv=n1).toMesh()
M1 = C0.connect(C1, div=n2)
C0 = Arc(center=P0, radius=1., angles=(45., 90.)).approx(ndiv=n1).toMesh()
C1 = PolyLine([P2, P3]).approx(ndiv=n1).toMesh()
M2 = C0.connect(C1, div=n2)
return M0+M1+M2
[docs]def wedge6_roll(elems):
"""Roll wedge6 elems to make the lowest node of bottom plane the first
This is a helper function for the :meth:`wedge6_tet4` conversion.
"""
elems = elems.reshape(-1, 2, 3)
r = elems[:, 0, :].argmin(axis=-1)
elemsout = []
for i in range(3):
w = where(r==i)[0]
if len(w) > 0:
els = roll(elems[w], -i, axis=-1)
elemsout.append(els)
elems = np.concatenate(elemsout)
return Connectivity(elems.reshape(-1, 6), eltype='wedge6')
[docs]def wedge6_tet4(M):
"""Convert a Mesh from wedge6 to tet4
This converts a 'wedge6' Mesh to 'tet4', by replacing each wedge
element with three tets. The conversion ensures that the subdivision
of the wedge elements are compatible in the common quad faces of
any two wedge elements.
Parameters
----------
M: Mesh
A Mesh of eltype 'wedge6'.
Returns
-------
Mesh
A Mesh of eltype 'tet4' representing the same domain as the
input Mesh. The nodes are the same as those of the input Mesh.
The number of elements is three times that of the input Mesh.
The order of numbering of the elements is dependent on the
conversion algorithm.
"""
from pyformex.elements import Wedge6
# First roll to put lowest node first
elems = wedge6_roll(M.elems)
M = Mesh(M.coords, elems, eltype='wedge6', prop=M.prop)
# Now convert to tet4
sl, sr = [Wedge6.conversions[c][0][1] for c in ['tet4-3l', 'tet4-3r']]
elems = M.elems.reshape(-1, 2, 3)
wl = where(elems[:, 0, 1] < elems[:, 0, 2])[0]
wr = at.complement(wl, elems.shape[0])
Ml = M.select(wl).selectNodes(sl, 'tet4')
Mr = M.select(wr).selectNodes(sr, 'tet4')
return Ml+Mr
# End
```