Mesh quality metrics

meshioplusplus.compute_quality(mesh) scores every cell of every block on a fixed set of geometric quality metrics and returns an aggregate report; meshioplusplus.attach_quality(mesh) returns a copy of the mesh with those metrics attached as cell_data (ready to write out and visualise). Metrics are evaluated on each cell's corner nodes (quadratic variants reduce to their linear parent), using only standard C++/numpy math, so they run under every mesh backend.

import meshioplusplus

mesh = meshioplusplus.read("part.vtu")
report = meshioplusplus.compute_quality(mesh)
print(report["num_inverted"], "inverted cells")
print(report["metrics"]["quality:scaled_jacobian"]["min"])

annotated = meshioplusplus.attach_quality(mesh)   # metrics as cell_data
meshioplusplus.write("part_quality.vtu", annotated)

Metrics

metric	triangle	quad	tetra	hexahedron	wedge	pyramid
quality:volume (area in 2D)	✓	✓	✓	✓	✓	✓
quality:scaled_jacobian	–	–	✓	✓	✓	✓
quality:aspect_ratio	✓	✓	✓	–	–	–
quality:skewness	–	✓	–	✓	–	–
quality:min_angle / quality:max_angle	✓	–	–	–	–	–
quality:warpage	–	✓	–	–	–	–
quality:min_dihedral / quality:max_dihedral	–	–	✓	–	–	–
quality:inverted / quality:degenerate	✓	✓	✓	✓	✓	✓

A metric that does not apply to a cell type is NaN for that cell. Ideal (perfectly regular) elements give the ideal value: scaled_jacobian = 1, aspect_ratio = 1, skewness = 0, warpage = 0, triangle angles = 60°, tetra dihedral ≈ 70.53°.

• quality:inverted is 1.0 when the signed volume/area is negative (a 2D triangle/quad embedded in 3D is unsigned, so never flagged).
• quality:degenerate is 1.0 when the cell is near-zero (collapsed volume/area, a zero-length edge, or a vanishing Jacobian); its divide-prone metrics are then NaN.

Quadratic and higher-order variants (tetra10, hexahedron20/27, quad8/9, triangle6, wedge15, pyramid13/14) are scored on their corners. Ragged/polyhedron and other unsupported blocks contribute all-NaN arrays and are excluded from the summaries and counts.

The report

compute_quality returns a dict:

• num_cells, num_inverted, num_degenerate — integer counts.
• metrics — metric name → {min, max, mean, count, histogram} (a 10-bin histogram over [min, max]; count is the number of cells with a finite value).
• cell_arrays — metric name → list of arrays (one (n, 1) array per cell block, NaN where the metric does not apply) — the arrays attach_quality writes into cell_data.

Cross-language

Available in every binding surface: Python (compute_quality/attach_quality), the C API (mio_attach_quality + mio_quality_counts), Fortran (mesh%attach_quality() / mesh%quality_counts(...)), and WASM (attachQuality), plus the CLI verb meshioplusplus quality.

Implementation

The metrics are in src/cpp/src/operations/quality.cpp (over the uniform mesh API, with the per-cell loop parallelised) with reusable vector math in src/cpp/include/meshioplusplus/detail/geometry.hpp. A pure-numpy twin (meshioplusplus._quality._compute_quality_py) mirrors the formulas and is checked against the C++ core in tests/python/test_quality.py.