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.. "examples/02_gmsh-basic.py"
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.. only:: html
.. note::
:class: sphx-glr-download-link-note
:ref:`Go to the end <sphx_glr_download_examples_02_gmsh-basic.py>`
to download the full example code.
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_examples_02_gmsh-basic.py:
Basic Gmsh Example
==================
In this example we'll create some basic geometries and turn them into meshes.
to illustrate some of the mesh generation features that Gmsh provides in
combination with polygon, point, and linestring geometries represented by
geopandas.
The :py:class:`GmshMesher` supports the geometry show in the basic Triangle
example and has a number of additional features.
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.. code-block:: Python
import geopandas as gpd
import matplotlib.pyplot as plt
import numpy as np
import shapely.geometry as sg
import pandamesh as pm
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A simple rectangular mesh
-------------------------
The most simple example is perhaps a rectangle. We'll create a vector
geometry, store this in a geodataframe, and associate a cell size.
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.. code-block:: Python
polygon = sg.Polygon(
[
[0.0, 0.0],
[10.0, 0.0],
[10.0, 10.0],
[0.0, 10.0],
]
)
gdf = gpd.GeoDataFrame(geometry=[polygon])
gdf["cellsize"] = 2.0
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We'll use this polygon to generate a mesh. We start by initializing a
TriangleMesher, which is a simple wrapper around the Python bindings to the
Gmsh C++-library. This wrapper extracts the coordinates and presents them
in the appropriate manner for Gmsh.
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.. code-block:: Python
mesher = pm.GmshMesher(gdf)
vertices, triangles = mesher.generate()
pm.plot(vertices, triangles)
.. image-sg:: /examples/images/sphx_glr_02_gmsh-basic_001.png
:alt: 02 gmsh basic
:srcset: /examples/images/sphx_glr_02_gmsh-basic_001.png
:class: sphx-glr-single-img
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Before we can instantiate another GmshMesher, we need to ``finalize`` the old
one.
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.. code-block:: Python
mesher.finalize()
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As the name suggests, Triangle only generates triangular meshes. Gmsh is
capable of generating quadrilateral-dominant meshes, and has a lot more bells
and whistles for defining cellsizes.
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.. code-block:: Python
line = sg.LineString([(2.0, 8.0), (8.0, 2.0)])
gdf = gpd.GeoDataFrame(geometry=[polygon, line])
gdf["cellsize"] = [2.0, 0.5]
fig, (ax0, ax1) = plt.subplots(ncols=2)
mesher = pm.TriangleMesher(gdf)
vertices, triangles = mesher.generate()
pm.plot(vertices, triangles, ax=ax0)
mesher = pm.GmshMesher(gdf)
vertices, triangles = mesher.generate()
pm.plot(vertices, triangles, ax=ax1)
.. image-sg:: /examples/images/sphx_glr_02_gmsh-basic_002.png
:alt: 02 gmsh basic
:srcset: /examples/images/sphx_glr_02_gmsh-basic_002.png
:class: sphx-glr-single-img
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Gmsh allows for specifying cell sizes in a more flexible way. Triangle (left)
only supports polygons (regions) with fixed cell sizes and explicitly placed
vertices. Gmsh is capable of forcing refinement in a larger zone around
features as is visible around the diagonal (right).
Defaults
--------
The GmshMesher class is initialized with a number of default parameters:
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.. code-block:: Python
print(mesher)
mesher.finalize()
.. rst-class:: sphx-glr-script-out
.. code-block:: none
GmshMesher
initialized = True
xoff = 5.0
yoff = 5.0
fields = []
combination_field = CombinationField(fields=[], combination=<FieldCombination.MIN: 'Min'>, id=1, fields_list=[])
tmpdir = <TemporaryDirectory '/tmp/tmpt4p7eiyc'>
recombine_all = False
mesh_size_extend_from_boundary = True
mesh_size_from_points = True
mesh_size_from_curvature = False
field_combination = FieldCombination.MIN
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The parameters of Gmsh differ from Triangle, but they work the same: they can
be altered after initialization to control the triangulation.
Forcing points, lines, local refinement
---------------------------------------
We can force points and lines into the triangulation:
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.. code-block:: Python
outer = [(0.0, 0.0), (10.0, 0.0), (10.0, 10.0), (0.0, 10.0)]
inner = [(3.0, 3.0), (7.0, 3.0), (7.0, 7.0), (3.0, 7.0)]
donut = sg.Polygon(shell=outer, holes=[inner])
refined = sg.Polygon(inner)
y = np.arange(0.5, 10.0, 0.5)
x = np.full(y.size, 1.0)
points = gpd.points_from_xy(x, y)
line = sg.LineString(
[
[9.0, 2.0],
[9.0, 8.0],
]
)
gdf = gpd.GeoDataFrame(geometry=[donut, refined, line, *points])
gdf["cellsize"] = [2.0, 0.5, 2.0] + (len(points) * [2.0])
mesher = pm.GmshMesher(gdf)
vertices, triangles = mesher.generate()
mesher.finalize()
fig, ax = plt.subplots()
pm.plot(vertices, triangles, ax=ax)
gdf.plot(facecolor="none", edgecolor="red", ax=ax)
# Quadrilateral meshes
# --------------------
#
# One of the features of Gmsh is that it is also capable of generating
# quadrilateral (dominant) meshes, by recombining triangles. We can achieve
# this by changing a parameter on the mesher:
gdf = gpd.GeoDataFrame(geometry=[polygon])
gdf["cellsize"] = 2.0
mesher = pm.GmshMesher(gdf)
mesher.recombine_all = True
vertices, faces = mesher.generate()
pm.plot(vertices, faces)
.. rst-class:: sphx-glr-horizontal
*
.. image-sg:: /examples/images/sphx_glr_02_gmsh-basic_003.png
:alt: 02 gmsh basic
:srcset: /examples/images/sphx_glr_02_gmsh-basic_003.png
:class: sphx-glr-multi-img
*
.. image-sg:: /examples/images/sphx_glr_02_gmsh-basic_004.png
:alt: 02 gmsh basic
:srcset: /examples/images/sphx_glr_02_gmsh-basic_004.png
:class: sphx-glr-multi-img
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Writing to file
---------------
It's also possible to use the Python bindings to write a Gmsh ``.msh`` file.
This file can be opened using the Gmsh GUI to e.g. inspect the generated
mesh.
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.. code-block:: Python
mesher.write("my-mesh.msh")
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Conclusion
----------
In real use, the vector geometries will be more complex, and not based on
just a few coordinate pairs. Such cases are presented in the other examples,
but the same principles apply: we may use polygons, linestrings and points
with associated cell sizes to steer the triangulation; unlike Triangle,
for Gmsh cell sizes can associated to linestrings and points, not just
polygons.
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (0 minutes 0.362 seconds)
.. _sphx_glr_download_examples_02_gmsh-basic.py:
.. only:: html
.. container:: sphx-glr-footer sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: 02_gmsh-basic.ipynb <02_gmsh-basic.ipynb>`
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: 02_gmsh-basic.py <02_gmsh-basic.py>`
.. container:: sphx-glr-download sphx-glr-download-zip
:download:`Download zipped: 02_gmsh-basic.zip <02_gmsh-basic.zip>`
.. only:: html
.. rst-class:: sphx-glr-signature
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