A Simple Mesh Generator in Python

## Project description

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.

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