fc-hypermesh 0.0.9

Generate conforming meshes of any d-orthotopes by simplices or orthotopes with their m-faces

fc\_hypermesh package
=====================

The **fc\_hypermesh** Python package allows to mesh any d-orthotopes
(hyperrectangle in dimension d) and their m-faces by simplices or
orthotopes

This implements `Vectorized algorithms for regular tessellations of
d-orthotopes and their
faces <https://www.math.univ-paris13.fr/~cuvelier/docs/reports/HyperMesh/HyperMesh_0.0.4.pdf>`__
(Cuvelier F. and Scarella G., 2016)

Documentation is available
`here <http://www.math.univ-paris13.fr/~cuvelier/software/fc-hypermesh-Python.html>`__

Installation:
-------------

The **fc\_hypermesh** Python package is available from the Python Package Index, so to install/upgrade simply type

.. code::

pip3 install fc_hypermesh -U

Examples usage:
---------------

- Meshing the rectangle [-1,1]x[0,1] by simplices with 12+1 points in
x-axis and 5+1 points in y-axis:

.. code:: python

from fc_hypermesh import OrthMesh
oTh=OrthMesh(2,[12,5],type='simplicial',box=[[-1,1],[0,1]])
print(oTh)

The output of the ``print(oTh)`` command is::

OrthMesh object
d : 2
Mesh : EltMesh object
type (str): simplicial
type : 0
d : 2
m : 2
q : (2,78)
me : (3,120)

Number of 1-faces : 4
[ 0] (type,nq,nme) : (simplicial,6,5)
[ 1] (type,nq,nme) : (simplicial,6,5)
[ 2] (type,nq,nme) : (simplicial,13,12)
[ 3] (type,nq,nme) : (simplicial,13,12)
Number of 0-faces : 4
[ 0] (type,nq,nme) : (simplicial,1,1)
[ 1] (type,nq,nme) : (simplicial,1,1)
[ 2] (type,nq,nme) : (simplicial,1,1)
[ 3] (type,nq,nme) : (simplicial,1,1)

If ``matplotlib`` package is installed one can represent the mesh

.. code:: python

import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True)
plt.figure(2)
oTh.plotmesh(m=1,legend=True,linewidth=3)
plt.axis('off')

.. figure:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_2D_simplicial_fig1_Python360.png
:scale: 50 %
:alt:

.. figure:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_2D_simplicial_fig2_Python360.png
:alt:

- Meshing the rectangular cuboid [-1,1]x[0,1]x[0,2] by simplices with 11+1 points in
x-axis, 5+1 points in y-axis and 10+1 points in z-axis:

.. code:: python

from fc_hypermesh import OrthMesh
oTh=OrthMesh(3,[10,5,10],box=[[-1,1],[0,1],[0,2]])

If ``matplotlib`` package is installed one can represent the mesh

.. code:: python

from fc_tools.graphics import set_axes_equal
import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True,linewidth=0.5)
set_axes_equal()
plt.figure(2)
oTh.plotmesh(m=2,legend=True,edgecolor=[0,0,0])
plt.axis('off')
set_axes_equal()

.. figure:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_3D_simplicial_fig1_Python360.png
:alt:

.. figure:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_3D_simplicial_fig2_Python360.png
:alt:

- Meshing the rectangle [-1,1]x[0,1] by orthotopes with 12+1 points in
x-axis, 5+1 points in y-axis and 10+1 points in z-axis:

.. code:: python

from fc_hypermesh import OrthMesh
oTh=OrthMesh(2,[12,5],type='orthotope',box=[[-1,1],[0,1]])

If ``matplotlib`` package is installed one can represent the mesh

.. code:: python

from fc_tools.graphics import set_axes_equal
import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True)
set_axes_equal()
plt.figure(2)
oTh.plotmesh(m=1,legend=True,linewidth=3)
plt.axis('off')
set_axes_equal()

.. figure:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_2D_orthotope_fig1_Python360.png
:alt:

.. figure:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_2D_orthotope_fig2_Python360.png
:alt:

- Meshing the rectangular cuboid [-1,1]x[0,1]x[0,2] by orthotopes with 11+1 points in
x-axis, 5+1 points in y-axis and 10+1 points in z-axis:

.. code:: python

from fc_hypermesh import OrthMesh
oTh=OrthMesh(3,[10,5,10],type='orthotope', box=[[-1,1],[0,1],[0,2]])

If ``matplotlib`` package is installed one can represent the mesh

.. code:: python

from fc_tools.graphics import set_axes_equal
import matplotlib.pyplot as plt
plt.ion()
plt.figure(1)
oTh.plotmesh(legend=True,linewidth=0.5)
set_axes_equal()
plt.figure(2)
oTh.plotmesh(m=2,legend=True,edgecolor=[0,0,0])
plt.axis('off')
set_axes_equal()

.. image:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_3D_orthotope_fig1_Python360.png
:alt:

.. figure:: http://www.math.univ-paris13.fr/~cuvelier/software/codes/fc-hypermesh/snapshots/OrthMesh_3D_orthotope_fig2_Python360.png
:alt:

Testing :
---------
There are seven demos functions in the ``fc_hypermesh`` package named ``demo01`` to ``demo07``.
The source code is in module ``demos.py``.
For example, run the following code under Python:

.. code:: python

import fc_hypermesh
fc_hypermesh.demo01()