Computing Mesh Quality

Leverage powerful VTK algorithms for computing mesh quality.

Here we will use the cell_quality() filter to compute the cell qualities. The following quality measures are available for various cell types:

Cell Quality Measures

Measure	TRIANGLE	QUAD	TETRA	HEXAHEDRON	PYRAMID	WEDGE
area
aspect_frobenius
aspect_gamma
aspect_ratio
collapse_ratio
condition
diagonal
dimension
distortion
jacobian
max_angle
max_aspect_frobenius
max_edge_ratio
med_aspect_frobenius
min_angle
oddy
radius_ratio
relative_size_squared
scaled_jacobian
shape
shape_and_size
shear
shear_and_size
skew
stretch
taper
volume
warpage

from __future__ import annotations

import pyvista as pv
from pyvista import examples

Triangle Cell Quality

Load a PolyData mesh and decimate() it to show coarse TRIANGLE cells for the example. Here we use download_cow().

mesh = examples.download_cow().triangulate().decimate(0.7)

Compute some valid measures for triangle cells.

measures = ['area', 'shape', 'min_angle', 'max_angle']
qual = mesh.cell_quality(measures)

Plot the meshes in subplots for comparison. We define a custom method for adding each mesh to each subplot.

def add_mesh(plotter, mesh, scalars=None, cmap='bwr', show_edges=True):
    # Create a copy to avoid reusing the same mesh in different plots
    copied = mesh.copy(deep=False)
    plotter.add_mesh(copied, scalars=scalars, cmap=cmap, show_edges=show_edges)
    plotter.view_xy()


pl = pv.Plotter(shape=(2, 2))
pl.link_views()
pl.subplot(0, 0)
add_mesh(pl, qual, scalars=measures[0])
pl.subplot(0, 1)
add_mesh(pl, qual, scalars=measures[1])
pl.subplot(1, 0)
add_mesh(pl, qual, scalars=measures[2])
pl.subplot(1, 1)
add_mesh(pl, qual, scalars=measures[3])
pl.show()

Static Scene

Interactive Scene

Visualize Acceptable Range

The previous plots show the full range of cell quality values present in the mesh. However, it may be more useful to show the acceptable range of values instead. Get the acceptable range for the shape quality measure using cell_quality_info().

info = pv.cell_quality_info('TRIANGLE', 'shape')
print(info)

CellQualityInfo(cell_type=<CellType.TRIANGLE: 5>, quality_measure='shape', acceptable_range=(0.25, 1.0), normal_range=(0.0, 1.0), full_range=(0.0, 1.0), unit_cell_value=1.0)

Plot the shape quality measure again but this time we color the cells based on the acceptable range for the measure. Cells outside of this range are saturated as blue or red and may be considered to be “poor” quality cells.

qual.plot(
    scalars='shape',
    clim=info.acceptable_range,
    cmap='bwr',
    below_color='blue',
    above_color='red',
    cpos='xy',
    zoom=1.5,
    show_axes=False,
)

Static Scene

Interactive Scene

Use extract_values() to extract the “poor” quality cells outside the acceptable range.

unacceptable = qual.extract_values(scalars='shape', ranges=info.acceptable_range, invert=True)

Plot the unacceptable cells along with the original mesh as wireframe for context.

pl = pv.Plotter()
pl.add_mesh(mesh, style='wireframe', color='light gray')
pl.add_mesh(unacceptable, color='lime')
pl.view_xy()
pl.camera.zoom(1.5)
pl.show()

Static Scene

Interactive Scene

Tetrahedron Cell Quality

Load a mesh with TETRA cells. Here we use download_letter_a().

mesh = examples.download_letter_a()

Plot some valid quality measures for tetrahedral cells.

measures = ['volume', 'collapse_ratio', 'jacobian', 'scaled_jacobian']
qual = mesh.cell_quality(measures)

pl = pv.Plotter(shape=(2, 2))
pl.link_views()
pl.subplot(0, 0)
add_mesh(pl, qual, scalars=measures[0])
pl.subplot(0, 1)
add_mesh(pl, qual, scalars=measures[1])
pl.subplot(1, 0)
add_mesh(pl, qual, scalars=measures[2])
pl.subplot(1, 1)
add_mesh(pl, qual, scalars=measures[3])
pl.show()

Static Scene

Interactive Scene

Tags: filter