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.

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.

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