Computing Mesh Quality

Computing Mesh Quality#

Download Python source code | Download Jupyter notebook

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`

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 with plot_compare(). Every subplot is drawn with the same arguments, so we compute each measure separately: cell_quality() makes the measure it computes the active scalars.

plot_kwargs = dict(cmap='bwr', show_edges=True)

datasets = {measure: mesh.cell_quality(measure) for measure in measures}

pv.plot_compare(datasets, cpos='xy', **plot_kwargs)

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']

datasets = {measure: mesh.cell_quality(measure) for measure in measures}

pv.plot_compare(datasets, cpos='xy', **plot_kwargs)