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Plotting the shape functions of the Q9 quadrilateral

We use Richard Shewchuk’s two-dimensional quality mesh generator to triangulate the master cell of the Q9 quadrilateral, then we plot the shape functions with Matplotlib.

import matplotlib.pyplot as plt
import triangle as tr

from sigmaepsilon.mesh.cells import Q9

# get the coordinates of the master cell
mc = Q9.Geometry.master_coordinates()

# triangulate the master cell and plot with the `triangle` library
data = dict(vertices=mc)
triangulation = tr.triangulate(data, 'qa0.02')
tr.compare(plt, data, triangulation)
plt.show()

from sigmaepsilon.mesh.plotting import triplot_mpl_data
from sigmaepsilon.mesh import triangulate

# get the triangulation as a `matplotlib` triangulation object
*_, triobj = triangulate(points=triangulation["vertices"], triangles=triangulation["triangles"])

# evaluate shape functions at the vertices of the triangulation
values = Q9.Geometry.shape_function_values(triangulation["vertices"])

# plot the values
fig, ((ax1, ax2, ax3), (ax4, ax5, ax6), (ax7, ax8, ax9)) = plt.subplots(3, 3, figsize=(9, 6))
for i, ax in enumerate([ax1, ax2, ax3, ax4, ax5, ax6, ax7, ax8, ax9]):
    _ = triplot_mpl_data(triobj, fig=fig, ax=ax, data=values[:, i], nlevels=10)