pygmsh 7.1.17
Python frontend for Gmsh
Requires Python: >=3.7
Keywords: mesh,gmsh,mesh generation,mathematics,engineering

<p align="center">
  <a href="https://github.com/nschloe/pygmsh"><img alt="pygmsh" src="https://nschloe.github.io/pygmsh/logo-with-text.svg" width="60%"></a>
  <p align="center">Gmsh for Python.</p>
</p>

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pygmsh combines the power of [Gmsh](https://gmsh.info/) 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](https://pypi.org/project/pygmsh/):

```
[sudo] apt install python3-gmsh
pip install pygmsh
```

This document and the [`tests/`](https://github.com/nschloe/pygmsh/tree/main/tests/)
directory contain many small examples. See
[here](https://pygmsh.readthedocs.io/en/latest/index.html) for the full documentation.

#### Flat shapes

| <img src="https://nschloe.github.io/pygmsh/polygon.svg" width="100%"> | <img src="https://nschloe.github.io/pygmsh/circle.svg" width="100%"> | <img src="https://nschloe.github.io/pygmsh/splines.svg" width="100%"> |
| :-------------------------------------------------------------------: | :------------------------------------------------------------------: | :-------------------------------------------------------------------: |
|                                Polygon                                |                                Circle                                |                              (B-)Splines                              |

Codes:

```python
import pygmsh

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

# mesh.points, mesh.cells, ...
# mesh.write("out.vtk")
```

```python
import pygmsh

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

```python
import pygmsh

with pygmsh.geo.Geometry() as geom:
    lcar = 0.1
    p1 = geom.add_point([0.0, 0.0], lcar)
    p2 = geom.add_point([1.0, 0.0], lcar)
    p3 = geom.add_point([1.0, 0.5], lcar)
    p4 = geom.add_point([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](https://pypi.org/project/meshio/) mesh, so to
store it to a file you can

<!--pytest-codeblocks:skip-->

```python
mesh.write("test.vtk")
```

The output file can be visualized with various tools, e.g.,
[ParaView](https://www.paraview.org/).

With

<!--pytest-codeblocks:skip-->

```python
pygmsh.write("test.msh")
```

you can access Gmsh's native file writer.

#### Extrusions

| <img src="https://nschloe.github.io/pygmsh/extrude.png" width="100%"> | <img src="https://nschloe.github.io/pygmsh/revolve.png" width="100%"> | <img src="https://nschloe.github.io/pygmsh/twist.png" width="100%"> |
| :-------------------------------------------------------------------: | :-------------------------------------------------------------------: | :-----------------------------------------------------------------: |
|                               `extrude`                               |                               `revolve`                               |                               `twist`                               |

```python
import pygmsh

with pygmsh.geo.Geometry() as geom:
    poly = geom.add_polygon(
        [
            [0.0, 0.0],
            [1.0, -0.2],
            [1.1, 1.2],
            [0.1, 0.7],
        ],
        mesh_size=0.1,
    )
    geom.extrude(poly, [0.0, 0.3, 1.0], num_layers=5)
    mesh = geom.generate_mesh()
```

```python
from math import pi
import pygmsh

with pygmsh.geo.Geometry() as geom:
    poly = geom.add_polygon(
        [
            [0.0, 0.2, 0.0],
            [0.0, 1.2, 0.0],
            [0.0, 1.2, 1.0],
        ],
        mesh_size=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.add_polygon(
        [
            [+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],
        ],
        mesh_size=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

| <img src="https://nschloe.github.io/pygmsh/intersection.png" width="100%"> | <img src="https://nschloe.github.io/pygmsh/ellipsoid-holes.png" width="100%"> | <img src="https://nschloe.github.io/pygmsh/puzzle.png" width="100%"> |
| :------------------------------------------------------------------------: | :---------------------------------------------------------------------------: | :------------------------------------------------------------------: |
|                                                                            |                                                                               |

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.characteristic_length_max = 0.1
    r = 0.5
    disks = [
        geom.add_disk([-0.5 * cos(7 / 6 * pi), -0.25], 1.0),
        geom.add_disk([+0.5 * cos(7 / 6 * pi), -0.25], 1.0),
        geom.add_disk([0.0, 0.5], 1.0),
    ]
    geom.boolean_intersection(disks)

    mesh = geom.generate_mesh()
```

```python
# ellpsoid with holes
import pygmsh

with pygmsh.occ.Geometry() as geom:
    geom.characteristic_length_max = 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.characteristic_length_min = 0.1
    geom.characteristic_length_max = 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

| <img src="https://nschloe.github.io/pygmsh/boundary0.svg" width="100%"> | <img src="https://nschloe.github.io/pygmsh/mesh-refinement-2d.svg" width="100%"> | <img src="https://nschloe.github.io/pygmsh/ball-mesh-refinement.png" width="70%"> |
| :---------------------------------------------------------------------: | :------------------------------------------------------------------------------: | :-------------------------------------------------------------------------------: |
|                                                                         |                                                                                  |

```python
# boundary refinement
import pygmsh

with pygmsh.geo.Geometry() as geom:
    poly = geom.add_polygon(
        [
            [0.0, 0.0],
            [2.0, 0.0],
            [3.0, 1.0],
            [1.0, 2.0],
            [0.0, 1.0],
        ],
        mesh_size=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()
```

<!--pytest-codeblocks:skip-->

```python
# mesh refinement with callback
import pygmsh

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

    mesh = geom.generate_mesh()
```

<!--pytest-codeblocks:skip-->

```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.

<!--pytest-codeblocks:skip-->

```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](https://pypi.org/project/meshio/).

### Testing

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

```
pytest
```

### Building Documentation

Docs are built using [Sphinx](http://www.sphinx-doc.org/en/stable/).

To build, run

```
sphinx-build -b html doc doc/_build
```

### License

This software is published under the [GPLv3 license](https://www.gnu.org/licenses/gpl-3.0.en.html).