PyDistMesh_: A Simple Mesh Generator in Python
==============================================
PyDistMesh_ is a simple Python code for generating unstructured
triangular and tetrahedral meshes using *signed distance functions*. It
intends to have the same functionality as and similar interface to the
MATLAB-based DistMesh_. Like DistMesh, upon which it is based,
PyDistMesh is distributed under the `GNU GPL`_.
.. _PyDistMesh: https://github.com/bfroehle/pydistmesh
.. _DistMesh: http://persson.berkeley.edu/distmesh/
.. _`GNU GPL`: http://www.gnu.org/copyleft/gpl.html
2-D Examples
------------
* Uniform Mesh on Unit Circle::
>>> import distmesh as dm
>>> import numpy as np
>>> fd = lambda p: np.sqrt((p**2).sum(1))-1.0
>>> p, t = dm.distmesh2d(fd, dm.huniform, 0.2, (-1,-1,1,1))
* Rectangle with circular hole, refined at circle boundary::
>>> import distmesh as dm
>>> fd = lambda p: dm.ddiff(dm.drectangle(p,-1,1,-1,1),
... dm.dcircle(p,0,0,0.5))
>>> fh = lambda p: 0.05+0.3*dm.dcircle(p,0,0,0.5)
>>> p, t = dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1),
... [(-1,-1),(-1,1),(1,-1),(1,1)])
3-D Examples
------------
* 3-D Unit ball::
>>> import distmesh as dm
>>> import numpy as np
>>> fd = lambda p: np.sqrt((p**2).sum(1))-1.0
>>> p, t = dm.distmeshnd(fd, dm.huniform, 0.2, (-1,-1,-1, 1,1,1))
* Cylinder with hole::
>>> import distmesh as dm
>>> import numpy as np
>>> def fd10(p):
... r, z = np.sqrt(p[:,0]**2 + p[:,1]**2), p[:,2]
... d1, d2, d3 = r-1.0, z-1.0, -z-1.0
... d4, d5 = np.sqrt(d1**2+d2**2), np.sqrt(d1**2+d3**2)
... d = dm.dintersect(dm.dintersect(d1, d2), d3)
... ix = (d1>0)*(d2>0); d[ix] = d4[ix]
... ix = (d1>0)*(d3>0); d[ix] = d5[ix]
... return dm.ddiff(d, dm.dsphere(p, 0,0,0, 0.5))
>>> def fh10(p):
... h1 = 4*np.sqrt((p**2).sum(1))-1.0
... return np.minimum(h1, 2.0)
>>> p, t = dm.distmeshnd(fd10, fh10, 0.1, (-1,-1,-1, 1,1,1))
Demos
-----
For a quick demonstration, run::
$ python -m distmesh.demo2d
or::
$ python -m distmesh.demond
Dependencies
------------
PyDistMesh is compatible with both Python 2 and Python 3. (The author
has only tested it in Python 2.7 and Python 3.2). It requires several
common Python packages:
* NumPy_
* SciPy_
* matplotlib_ (optional)
Building the package requires a C compiler and LAPACK_. Cython_, if
available, can be used to rebuild the extension module bindings.
.. _NumPy: http://numpy.scipy.org/
.. _SciPy: http://scipy.org/
.. _matplotlib: http://matplotlib.sourceforge.net/
.. _Cython: http://cython.org/
.. _LAPACK: http://www.netlib.org/lapack/
References
----------
The DistMesh_ algorithm is described in the following two references.
If you use the algorithm in a program or publication, please
acknowledge its authors by adding a reference to the first paper
below.
* P.-O. Persson, G. Strang, **A Simple Mesh Generator in MATLAB**.
*SIAM Review*, Volume 46 (2), pp. 329-345, June 2004 (`PDF
<http://persson.berkeley.edu/distmesh/persson04mesh.pdf>`__)
* P.-O. Persson, **Mesh Generation for Implicit Geometries**.
Ph.D. thesis, *Department of Mathematics, MIT*, Dec 2004 (`PDF
<http://persson.berkeley.edu/thesis/persson-thesis-color.pdf>`__)
