Tetrahedron check

check_tetrahedra(mesh) reports whether the tetrahedra of a mesh are usable: how many are inverted, how many are degenerate, and how many pairs overlap across a shared face. It is the check behind the volume fix of octree_mesh, as a standalone operation on any mesh, and it leaves the mesh unchanged.

import meshioplusplus as mp

mesh = mp.read("model.vtu")

report = mp.check_tetrahedra(mesh)
report["valid"]           # False
report["num_inverted"]    # 3
report["num_overlaps"]    # 0

What it reports

The tetra and tetra10 cells are examined, a quadratic tetrahedron by its four corners; other cells are ignored, and a mesh without tetrahedra reports zeros with a warning.

Defect	Rule	Counted as
inverted	the signed volume is below minus the tolerance	num_inverted
degenerate	the volume is within the tolerance, either sign	num_degenerate
overlap	two tetrahedra share a face, no other tetrahedron uses it, and their opposite nodes lie on the same side of it	num_overlaps, per pair

The tolerance of a tetrahedron is zero_volume_factor (default 1e-6) times the cube of its longest edge, plus the effect of six significant digits of written coordinates (1e-6 times its largest coordinate times its longest edge squared), so a sliver of a fine mesh is not flagged because of a large coordinate offset. A face used by three or more tetrahedra is not examined. A conforming mesh of a valid solid has no overlap whatever its materials, since the tetrahedra on the two sides of an interface have their opposite nodes on opposite sides.

The report also has num_tetrahedra, min_volume and max_volume (signed, 0 without tetrahedra), valid (no inverted or degenerate tetrahedron and no overlap) and warnings.

Where it is

Where	Name
Python	meshioplusplus.check_tetrahedra(mesh, zero_volume_factor=1e-6), with a numpy twin when the compiled core is missing
CLI	check-tetrahedra INFILE [--zero-volume-factor X] [--json]: exit 0 valid, 1 not valid, 2 could not check
Pipeline	the CheckTetrahedra step: ZeroVolumeFactor (1e-6), Require (true); a gate by default, counters NumTetrahedra, NumInverted, NumDegenerate, NumOverlaps
MCP	the check_tetrahedra tool
C++	check_tetrahedra(mesh, TetrahedraCheckOptions) in meshioplusplus/operations/check_tetrahedra.hpp
C	mio_check_tetrahedra (C API)
Fortran, Julia, R, Octave / MATLAB, WASM	Fortran, Julia, R, Octave, WASM