Gmsh for Python.

pygmsh combines the power of Gmsh with the versatility of Python. It provides useful abstractions from Gmsh's own Python interface so you can create complex geometries more easily.

To use, install Gmsh itself and pygmsh from pypi:

[sudo] apt install python3-gmsh pip install pygmsh

This document and the tests/ directory contain many small examples. See here for the full documentation.

Flat shapes

| | | | | :-------------------------------------------------------------------: | :------------------------------------------------------------------: | :-------------------------------------------------------------------: | | Polygon | Circle | (B-)Splines |

Codes:

```python import pygmsh

with pygmsh.geo.Geometry() as geom: geom.addpolygon( [ [0.0, 0.0], [1.0, -0.2], [1.1, 1.2], [0.1, 0.7], ], meshsize=0.1, ) mesh = geom.generate_mesh()

mesh.points, mesh.cells, ...

mesh.write("out.vtk")

```

```python import pygmsh

with pygmsh.geo.Geometry() as geom: geom.addcircle([0.0, 0.0], 1.0, meshsize=0.2) mesh = geom.generate_mesh() ```

```python import pygmsh

with pygmsh.geo.Geometry() as geom: lcar = 0.1 p1 = geom.addpoint([0.0, 0.0], lcar) p2 = geom.addpoint([1.0, 0.0], lcar) p3 = geom.addpoint([1.0, 0.5], lcar) p4 = geom.addpoint([1.0, 1.0], lcar) s1 = geom.add_bspline([p1, p2, p3, p4])

p2 = geom.add_point([0.0, 1.0], lcar)
p3 = geom.add_point([0.5, 1.0], lcar)
s2 = geom.add_spline([p4, p3, p2, p1])

ll = geom.add_curve_loop([s1, s2])
pl = geom.add_plane_surface(ll)

mesh = geom.generate_mesh()

```

The return value is always a meshio mesh, so to store it to a file you can

python mesh.write("test.vtk")

The output file can be visualized with various tools, e.g., ParaView.

With

python pygmsh.write("test.msh")

you can access Gmsh's native file writer.

Extrusions

| | | | | :-------------------------------------------------------------------: | :-------------------------------------------------------------------: | :-----------------------------------------------------------------: | | extrude | revolve | twist |

```python import pygmsh

with pygmsh.geo.Geometry() as geom: poly = geom.addpolygon( [ [0.0, 0.0], [1.0, -0.2], [1.1, 1.2], [0.1, 0.7], ], meshsize=0.1, ) geom.extrude(poly, [0.0, 0.3, 1.0], numlayers=5) mesh = geom.generatemesh() ```

```python from math import pi import pygmsh

with pygmsh.geo.Geometry() as geom: poly = geom.addpolygon( [ [0.0, 0.2, 0.0], [0.0, 1.2, 0.0], [0.0, 1.2, 1.0], ], meshsize=0.1, ) geom.revolve(poly, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0], 0.8 * pi) mesh = geom.generate_mesh() ```

```python from math import pi import pygmsh

with pygmsh.geo.Geometry() as geom: poly = geom.addpolygon( [ [+0.0, +0.5], [-0.1, +0.1], [-0.5, +0.0], [-0.1, -0.1], [+0.0, -0.5], [+0.1, -0.1], [+0.5, +0.0], [+0.1, +0.1], ], meshsize=0.05, )

geom.twist(
    poly,
    translation_axis=[0, 0, 1],
    rotation_axis=[0, 0, 1],
    point_on_axis=[0, 0, 0],
    angle=pi / 3,
)

mesh = geom.generate_mesh()

```

OpenCASCADE

| | | | | :------------------------------------------------------------------------: | :---------------------------------------------------------------------------: | :------------------------------------------------------------------: | | | |

Gmsh also supports OpenCASCADE (occ), allowing for a CAD-style geometry specification.

```python from math import pi, cos import pygmsh

with pygmsh.occ.Geometry() as geom: geom.characteristiclengthmax = 0.1 r = 0.5 disks = [ geom.adddisk([-0.5 * cos(7 / 6 * pi), -0.25], 1.0), geom.adddisk([+0.5 * cos(7 / 6 * pi), -0.25], 1.0), geom.adddisk([0.0, 0.5], 1.0), ] geom.booleanintersection(disks)

mesh = geom.generate_mesh()

```

```python

ellpsoid with holes

import pygmsh

with pygmsh.occ.Geometry() as geom: geom.characteristiclengthmax = 0.1 ellipsoid = geom.add_ellipsoid([0.0, 0.0, 0.0], [1.0, 0.7, 0.5])

cylinders = [
    geom.add_cylinder([-1.0, 0.0, 0.0], [2.0, 0.0, 0.0], 0.3),
    geom.add_cylinder([0.0, -1.0, 0.0], [0.0, 2.0, 0.0], 0.3),
    geom.add_cylinder([0.0, 0.0, -1.0], [0.0, 0.0, 2.0], 0.3),
]
geom.boolean_difference(ellipsoid, geom.boolean_union(cylinders))

mesh = geom.generate_mesh()

```

```python

puzzle piece

import pygmsh

with pygmsh.occ.Geometry() as geom: geom.characteristiclengthmin = 0.1 geom.characteristiclengthmax = 0.1

rectangle = geom.add_rectangle([-1.0, -1.0, 0.0], 2.0, 2.0)
disk1 = geom.add_disk([-1.2, 0.0, 0.0], 0.5)
disk2 = geom.add_disk([+1.2, 0.0, 0.0], 0.5)

disk3 = geom.add_disk([0.0, -0.9, 0.0], 0.5)
disk4 = geom.add_disk([0.0, +0.9, 0.0], 0.5)
flat = geom.boolean_difference(
    geom.boolean_union([rectangle, disk1, disk2]),
    geom.boolean_union([disk3, disk4]),
)

geom.extrude(flat, [0, 0, 0.3])

mesh = geom.generate_mesh()

```

Mesh refinement/boundary layers

| | | | | :---------------------------------------------------------------------: | :------------------------------------------------------------------------------: | :-------------------------------------------------------------------------------: | | | |

```python

boundary refinement

import pygmsh

with pygmsh.geo.Geometry() as geom: poly = geom.addpolygon( [ [0.0, 0.0], [2.0, 0.0], [3.0, 1.0], [1.0, 2.0], [0.0, 1.0], ], meshsize=0.3, )

field0 = geom.add_boundary_layer(
    edges_list=[poly.curves[0]],
    lcmin=0.05,
    lcmax=0.2,
    distmin=0.0,
    distmax=0.2,
)
field1 = geom.add_boundary_layer(
    nodes_list=[poly.points[2]],
    lcmin=0.05,
    lcmax=0.2,
    distmin=0.1,
    distmax=0.4,
)
geom.set_background_mesh([field0, field1], operator="Min")

mesh = geom.generate_mesh()

```

```python

mesh refinement with callback

import pygmsh

with pygmsh.geo.Geometry() as geom: geom.addpolygon( [ [-1.0, -1.0], [+1.0, -1.0], [+1.0, +1.0], [-1.0, +1.0], ] ) geom.setmeshsizecallback( lambda dim, tag, x, y, z: 6.0e-2 + 2.0e-1 * (x2 + y2) )

mesh = geom.generate_mesh()

```

```python

ball with mesh refinement

from math import sqrt import pygmsh

with pygmsh.occ.Geometry() as geom: geom.add_ball([0.0, 0.0, 0.0], 1.0)

geom.set_mesh_size_callback(
    lambda dim, tag, x, y, z: abs(sqrt(x**2 + y**2 + z**2) - 0.5) + 0.1
)
mesh = geom.generate_mesh()

```

Optimization

pygmsh can optimize existing meshes, too.

```python import meshio

mesh = meshio.read("mymesh.vtk") optimized_mesh = pygmsh.optimize(mesh, method="") ```

You can also use the command-line utility

pygmsh-optimize input.vtk output.xdmf

where input and output can be any format supported by meshio.

Testing

To run the pygmsh unit tests, check out this repository and type

pytest

Building Documentation

Docs are built using Sphinx.

To build, run

sphinx-build -b html doc doc/_build

License

This software is published under the GPLv3 license.