pygmsh

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:

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")

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()

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 mesh, so to store it to a file you can

mesh.write("test.vtk")

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

With

pygmsh.write("test.msh")

you can access Gmsh's native file writer.

Extrusions

extrude	revolve	twist

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()

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()

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

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

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()

# 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()

# 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

# 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()

# 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()

# 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.

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.