Probe reference

All descriptions below follow geomcheck/probes.py, the single source of truth for every threshold. compute_all returns one flat dictionary with the keys listed here.

Pipeline

1. Load. load_mesh(path) reads any Trimesh-readable file as a single triangle mesh, with scene transforms applied and materials skipped (trimesh.load(..., force="mesh", process=False)).
2. Normalise and weld. normalise_and_weld centres the bounding box at the origin and scales its diagonal to 1. Vertices are welded by rounding the normalised coordinates to 10⁻⁶ (merge_decimals=6); each welded group is replaced by its mean position. Welding matters for GLB files, which often split vertices along UV seams — without it a closed sphere would look like a soup of open triangles.
3. Optional decimation. With decimate_to=N and more than N faces, the mesh is decimated by PyMeshLab quadric edge collapse with preservetopology=True, preserveboundary=True, preservenormal=True, planarquadric=True, then normalised and welded again. Topology preservation avoids creating holes or self-intersections that the probes would then measure.
4. Probes. Topology/boundary, triangle quality and roughness always run; self-intersection (do_self_intersection) and the ray probes (do_rays) can be switched off.

Lengths are in units of the bounding-box diagonal; "faces", "edges" and "samples" below refer to the normalised (and, if requested, decimated) mesh.

Size and bookkeeping

Key	Meaning
orig_bbox_diag	Bounding-box diagonal of the input, in the file's own units (the only unnormalised value).
orig_n_faces	Face count after welding, before any decimation.
n_vertices, n_faces, n_edges	Counts on the probed mesh (edges are undirected and unique).
degenerate_face_frac	Fraction of faces with area below 10⁻¹².
duplicate_face_frac	Fraction of faces that repeat another face's vertex set (extra copies only).

Boundary and manifoldness

Each undirected edge is counted by how many faces use it: 1 = boundary, 2 = manifold, more than 2 = non-manifold.

Key	Meaning
boundary_edge_frac	Fraction of edges used by exactly one face (open boundary / hole rims).
boundary_length	Total length of boundary edges, in bbox-diagonal units.
n_boundary_loops	Connected components of the boundary-edge graph (≈ number of holes or open rims).
nonmanifold_edge_frac	Fraction of edges used by more than two faces.
winding_inconsistent_edge_frac	Among manifold edges, the fraction whose two half-edges run in the same direction, i.e. adjacent faces with inconsistent orientation.
watertight	True when there is no boundary edge and no non-manifold edge.

Topology: components and floaters

Faces are grouped into connected components through shared edges (manifold or not).

Key	Meaning
n_components	Number of face-connected components.
largest_component_area_frac	Area of the largest component / total area.
n_small_components	Components smaller than 1 % of the total surface area (small_comp_area_frac=0.01) — floaters and debris.
small_component_area_frac	Their total area / total area.
n_large_components	Remaining components.
euler_characteristic	χ = V − E + F, with V the number of vertices referenced by a face. A closed sphere has χ = 2.

The paper's classifier derives a genus proxy g = max(0, 2C − χ)/2 from n_components (C) and χ; it is not returned by compute_all.

Triangle quality

For a triangle with area A and edge lengths a, b, c the quality is q = 4√3·A / (a² + b² + c²), which is 1 for an equilateral triangle and 0 for a degenerate one.

Key	Meaning
tri_quality_median, tri_quality_p05	Median and 5th percentile of q.
sliver_face_frac, sliver_area_frac	Fraction of faces, and of area, with q < 0.1 (sliver_q).
edge_length_cv	Coefficient of variation (std / mean) of all triangle edge lengths.

Roughness

On every interior manifold edge the dihedral angle is the angle between the two incident face normals (0° on a flat surface).

Key	Meaning
dihedral_mean_deg	Edge-length-weighted mean of that angle, in degrees.
dihedral_gt30_lenfrac, dihedral_gt60_lenfrac, dihedral_gt90_lenfrac	Fraction of interior edge length whose angle exceeds 30°, 60°, 90°.
angle_defect_mean, angle_defect_p95	Mean and 95th percentile of the absolute angle defect (discrete Gaussian curvature) on vertices whose star is closed and manifold. NaN if it cannot be computed.

Self-intersection

PyMeshLab's compute_selection_by_self_intersections_per_face marks every face that intersects another face of the same mesh — interpenetrating parts, crossing sheets.

Key	Meaning
self_intersect_face_frac	Fraction of faces marked.
self_intersect_area_frac	Fraction of area marked (NaN if PyMeshLab returned a different face count).

Hidden surface and thin walls (ray probes)

20,000 points are sampled on the surface, area-weighted, with seed 0 (n_surface_samples, seed). Rays are cast with Embree, starting 10⁻⁴ off the surface (ray_eps).

Key	Meaning
hidden_surface_frac	Fraction of samples from which a ray fails to escape in every one of 64 Fibonacci-sphere directions (n_visibility_dirs): surface that can never be seen from outside, such as internal shells or enclosed parts.
thickness_defined_frac	Fraction of samples at which a thickness could be measured.
thin_frac_0.005, thin_frac_0.01	Fraction of samples thinner than 0.005 and 0.01 diagonals (thin_tau).
thickness_median	Median thickness over samples where it is defined (NaN if none).

Thickness at a sample is the shorter of two rays, along the inward and the outward normal, that hit a face whose normal points the same way as the ray — that is, the ray travelled through material and exited the surface. Rays that escape or hit a front-facing surface do not define a thickness.

Configuration

CONFIG = dict(
    merge_decimals=6,          # vertex welding: round normalised coordinates to 1e-6
    small_comp_area_frac=0.01, # component counted as 'small/floater' if < 1% of total area
    n_surface_samples=20000,   # area-weighted surface samples for ray probes
    n_visibility_dirs=64,      # Fibonacci-sphere directions for hidden-surface probe
    ray_eps=1e-4,              # ray origin offset (units of bbox diagonal)
    thin_tau=(0.005, 0.01),    # thin-wall thresholds (units of bbox diagonal)
    sliver_q=0.1,              # triangle quality below this => sliver
    dihedral_thresholds_deg=(30.0, 60.0, 90.0),
    seed=0,
)

These values were frozen before the paper's expert-set scoring. Changing them changes the meaning of the features; the frozen classifiers in the repository assume the defaults.

Per-face flags and rendering

geomcheck.visualize (needs pip install "geomcheck[viz]" for matplotlib) exposes face_flags(V, F), which returns boolean per-face masks — self_intersect, small_component, thin (< 0.005), hidden, boundary — using the same rules as the probes but evaluated at face centroids, and render(ax, V, F, flags), the dependency-light shaded renderer used for the gallery figures. prepare(path, decimate_to=10000) loads, normalises and optionally decimates a file into (V, F) for both.

Determinism

Probe outputs are deterministic for a given input file and library versions (fixed seed, no learned parameters); the test suite checks that two runs are identical. The paper does not claim bit-identity across library versions it did not run.