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.

• 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, fig = dm.distmesh2d(fd, dm.huniform, 0.2, (-1,-1,1,1))
  >>> fig.savefig("output.png")
  

• 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, fig = dm.distmesh2d(fd, fh, 0.05, (-1,-1,1,1),
  ...                          [(-1,-1),(-1,1),(1,-1),(1,1)])
  >>> fig.savefig("output.png")
  

• 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, fig = 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, fig = dm.distmeshnd(fd10, fh10, 0.1, (-1,-1,-1, 1,1,1))
  

For a quick demonstration, run:

$ python -m distmesh.demo2d

or:

$ python -m distmesh.demond

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.

Install pydistmesh:

$ python setup.py install

You may want to do this if you are developing for pydistmesh or have made modifications.

Install pydistmesh in develop mode:

$ python setup.py develop

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)
• P.-O. Persson, Mesh Generation for Implicit Geometries. Ph.D. thesis, Department of Mathematics, MIT, Dec 2004 (PDF)