<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>
[](https://pypi.org/project/pygmsh/)
[](https://pypi.org/project/pygmsh/)
[](https://doi.org/10.5281/zenodo.1173105)
[](https://github.com/nschloe/pygmsh)
[](https://pypistats.org/packages/pygmsh)
[](https://discord.gg/hnTJ5MRX2Y)
[](https://pygmsh.readthedocs.io/en/latest/?badge=latest)
[](https://github.com/nschloe/pygmsh/actions?query=workflow%3Aci)
[](https://codecov.io/gh/nschloe/pygmsh)
[](https://lgtm.com/projects/g/nschloe/pygmsh)
[](https://github.com/psf/black)
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).
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"description": "<p align=\"center\">\n <a href=\"https://github.com/nschloe/pygmsh\"><img alt=\"pygmsh\" src=\"https://nschloe.github.io/pygmsh/logo-with-text.svg\" width=\"60%\"></a>\n <p align=\"center\">Gmsh for Python.</p>\n</p>\n\n[](https://pypi.org/project/pygmsh/)\n[](https://pypi.org/project/pygmsh/)\n[](https://doi.org/10.5281/zenodo.1173105)\n[](https://github.com/nschloe/pygmsh)\n[](https://pypistats.org/packages/pygmsh)\n\n[](https://discord.gg/hnTJ5MRX2Y)\n[](https://pygmsh.readthedocs.io/en/latest/?badge=latest)\n\n[](https://github.com/nschloe/pygmsh/actions?query=workflow%3Aci)\n[](https://codecov.io/gh/nschloe/pygmsh)\n[](https://lgtm.com/projects/g/nschloe/pygmsh)\n[](https://github.com/psf/black)\n\npygmsh combines the power of [Gmsh](https://gmsh.info/) with the versatility of Python.\nIt provides useful abstractions from Gmsh's own Python interface so you can create\ncomplex geometries more easily.\n\nTo use, install Gmsh itself and pygmsh from [pypi](https://pypi.org/project/pygmsh/):\n\n```\n[sudo] apt install python3-gmsh\npip install pygmsh\n```\n\nThis document and the [`tests/`](https://github.com/nschloe/pygmsh/tree/main/tests/)\ndirectory contain many small examples. See\n[here](https://pygmsh.readthedocs.io/en/latest/index.html) for the full documentation.\n\n#### Flat shapes\n\n| <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%\"> |\n| :-------------------------------------------------------------------: | :------------------------------------------------------------------: | :-------------------------------------------------------------------: |\n| Polygon | Circle | (B-)Splines |\n\nCodes:\n\n```python\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n geom.add_polygon(\n [\n [0.0, 0.0],\n [1.0, -0.2],\n [1.1, 1.2],\n [0.1, 0.7],\n ],\n mesh_size=0.1,\n )\n mesh = geom.generate_mesh()\n\n# mesh.points, mesh.cells, ...\n# mesh.write(\"out.vtk\")\n```\n\n```python\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n geom.add_circle([0.0, 0.0], 1.0, mesh_size=0.2)\n mesh = geom.generate_mesh()\n```\n\n```python\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n lcar = 0.1\n p1 = geom.add_point([0.0, 0.0], lcar)\n p2 = geom.add_point([1.0, 0.0], lcar)\n p3 = geom.add_point([1.0, 0.5], lcar)\n p4 = geom.add_point([1.0, 1.0], lcar)\n s1 = geom.add_bspline([p1, p2, p3, p4])\n\n p2 = geom.add_point([0.0, 1.0], lcar)\n p3 = geom.add_point([0.5, 1.0], lcar)\n s2 = geom.add_spline([p4, p3, p2, p1])\n\n ll = geom.add_curve_loop([s1, s2])\n pl = geom.add_plane_surface(ll)\n\n mesh = geom.generate_mesh()\n```\n\nThe return value is always a [meshio](https://pypi.org/project/meshio/) mesh, so to\nstore it to a file you can\n\n<!--pytest-codeblocks:skip-->\n\n```python\nmesh.write(\"test.vtk\")\n```\n\nThe output file can be visualized with various tools, e.g.,\n[ParaView](https://www.paraview.org/).\n\nWith\n\n<!--pytest-codeblocks:skip-->\n\n```python\npygmsh.write(\"test.msh\")\n```\n\nyou can access Gmsh's native file writer.\n\n#### Extrusions\n\n| <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%\"> |\n| :-------------------------------------------------------------------: | :-------------------------------------------------------------------: | :-----------------------------------------------------------------: |\n| `extrude` | `revolve` | `twist` |\n\n```python\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n poly = geom.add_polygon(\n [\n [0.0, 0.0],\n [1.0, -0.2],\n [1.1, 1.2],\n [0.1, 0.7],\n ],\n mesh_size=0.1,\n )\n geom.extrude(poly, [0.0, 0.3, 1.0], num_layers=5)\n mesh = geom.generate_mesh()\n```\n\n```python\nfrom math import pi\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n poly = geom.add_polygon(\n [\n [0.0, 0.2, 0.0],\n [0.0, 1.2, 0.0],\n [0.0, 1.2, 1.0],\n ],\n mesh_size=0.1,\n )\n geom.revolve(poly, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0], 0.8 * pi)\n mesh = geom.generate_mesh()\n```\n\n```python\nfrom math import pi\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n poly = geom.add_polygon(\n [\n [+0.0, +0.5],\n [-0.1, +0.1],\n [-0.5, +0.0],\n [-0.1, -0.1],\n [+0.0, -0.5],\n [+0.1, -0.1],\n [+0.5, +0.0],\n [+0.1, +0.1],\n ],\n mesh_size=0.05,\n )\n\n geom.twist(\n poly,\n translation_axis=[0, 0, 1],\n rotation_axis=[0, 0, 1],\n point_on_axis=[0, 0, 0],\n angle=pi / 3,\n )\n\n mesh = geom.generate_mesh()\n```\n\n#### OpenCASCADE\n\n| <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%\"> |\n| :------------------------------------------------------------------------: | :---------------------------------------------------------------------------: | :------------------------------------------------------------------: |\n| | |\n\nGmsh also supports OpenCASCADE (`occ`), allowing for a CAD-style geometry specification.\n\n```python\nfrom math import pi, cos\nimport pygmsh\n\nwith pygmsh.occ.Geometry() as geom:\n geom.characteristic_length_max = 0.1\n r = 0.5\n disks = [\n geom.add_disk([-0.5 * cos(7 / 6 * pi), -0.25], 1.0),\n geom.add_disk([+0.5 * cos(7 / 6 * pi), -0.25], 1.0),\n geom.add_disk([0.0, 0.5], 1.0),\n ]\n geom.boolean_intersection(disks)\n\n mesh = geom.generate_mesh()\n```\n\n```python\n# ellpsoid with holes\nimport pygmsh\n\nwith pygmsh.occ.Geometry() as geom:\n geom.characteristic_length_max = 0.1\n ellipsoid = geom.add_ellipsoid([0.0, 0.0, 0.0], [1.0, 0.7, 0.5])\n\n cylinders = [\n geom.add_cylinder([-1.0, 0.0, 0.0], [2.0, 0.0, 0.0], 0.3),\n geom.add_cylinder([0.0, -1.0, 0.0], [0.0, 2.0, 0.0], 0.3),\n geom.add_cylinder([0.0, 0.0, -1.0], [0.0, 0.0, 2.0], 0.3),\n ]\n geom.boolean_difference(ellipsoid, geom.boolean_union(cylinders))\n\n mesh = geom.generate_mesh()\n```\n\n```python\n# puzzle piece\nimport pygmsh\n\nwith pygmsh.occ.Geometry() as geom:\n geom.characteristic_length_min = 0.1\n geom.characteristic_length_max = 0.1\n\n rectangle = geom.add_rectangle([-1.0, -1.0, 0.0], 2.0, 2.0)\n disk1 = geom.add_disk([-1.2, 0.0, 0.0], 0.5)\n disk2 = geom.add_disk([+1.2, 0.0, 0.0], 0.5)\n\n disk3 = geom.add_disk([0.0, -0.9, 0.0], 0.5)\n disk4 = geom.add_disk([0.0, +0.9, 0.0], 0.5)\n flat = geom.boolean_difference(\n geom.boolean_union([rectangle, disk1, disk2]),\n geom.boolean_union([disk3, disk4]),\n )\n\n geom.extrude(flat, [0, 0, 0.3])\n\n mesh = geom.generate_mesh()\n```\n\n#### Mesh refinement/boundary layers\n\n| <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%\"> |\n| :---------------------------------------------------------------------: | :------------------------------------------------------------------------------: | :-------------------------------------------------------------------------------: |\n| | |\n\n```python\n# boundary refinement\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n poly = geom.add_polygon(\n [\n [0.0, 0.0],\n [2.0, 0.0],\n [3.0, 1.0],\n [1.0, 2.0],\n [0.0, 1.0],\n ],\n mesh_size=0.3,\n )\n\n field0 = geom.add_boundary_layer(\n edges_list=[poly.curves[0]],\n lcmin=0.05,\n lcmax=0.2,\n distmin=0.0,\n distmax=0.2,\n )\n field1 = geom.add_boundary_layer(\n nodes_list=[poly.points[2]],\n lcmin=0.05,\n lcmax=0.2,\n distmin=0.1,\n distmax=0.4,\n )\n geom.set_background_mesh([field0, field1], operator=\"Min\")\n\n mesh = geom.generate_mesh()\n```\n\n<!--pytest-codeblocks:skip-->\n\n```python\n# mesh refinement with callback\nimport pygmsh\n\nwith pygmsh.geo.Geometry() as geom:\n geom.add_polygon(\n [\n [-1.0, -1.0],\n [+1.0, -1.0],\n [+1.0, +1.0],\n [-1.0, +1.0],\n ]\n )\n geom.set_mesh_size_callback(\n lambda dim, tag, x, y, z: 6.0e-2 + 2.0e-1 * (x ** 2 + y ** 2)\n )\n\n mesh = geom.generate_mesh()\n```\n\n<!--pytest-codeblocks:skip-->\n\n```python\n# ball with mesh refinement\nfrom math import sqrt\nimport pygmsh\n\n\nwith pygmsh.occ.Geometry() as geom:\n geom.add_ball([0.0, 0.0, 0.0], 1.0)\n\n geom.set_mesh_size_callback(\n lambda dim, tag, x, y, z: abs(sqrt(x ** 2 + y ** 2 + z ** 2) - 0.5) + 0.1\n )\n mesh = geom.generate_mesh()\n```\n\n#### Optimization\n\npygmsh can optimize existing meshes, too.\n\n<!--pytest-codeblocks:skip-->\n\n```python\nimport meshio\n\nmesh = meshio.read(\"mymesh.vtk\")\noptimized_mesh = pygmsh.optimize(mesh, method=\"\")\n```\n\nYou can also use the command-line utility\n\n```\npygmsh-optimize input.vtk output.xdmf\n```\n\nwhere input and output can be any format supported by\n[meshio](https://pypi.org/project/meshio/).\n\n### Testing\n\nTo run the pygmsh unit tests, check out this repository and type\n\n```\npytest\n```\n\n### Building Documentation\n\nDocs are built using [Sphinx](http://www.sphinx-doc.org/en/stable/).\n\nTo build, run\n\n```\nsphinx-build -b html doc doc/_build\n```\n\n### License\n\nThis software is published under the [GPLv3 license](https://www.gnu.org/licenses/gpl-3.0.en.html).\n",
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