face_areas — 3D `mesh_process` op

• Data kinds: mesh → signal

• Call: import fullseye as fs; fs.ledger.face_areas(mesh) -> 'np.ndarray' (to call the implementation directly, import mesh_props; mesh_props.face_areas(mesh) -> 'np.ndarray'; from the registry, ops3d.get("face_areas"))

Usage

Area of each face of a triangle mesh → (M,).

Returns area = 0.5·|cross(v1−v0, v2−v0)| per face (mesh_area is their sum). The areas exist to be used as weights -- "the area of faces pointing downward", "the out-of-tolerance area" and "the area-weighted mean of curvature" are all quantities that need per-face areas and cannot be built from the sum.

Args:

mesh: tuple of (vertices (N,3), faces (M,3)).

Returns:

(M,) float64 (non-negative). The order is that of faces, the same

ordering as face_normals, so they combine directly, as in areas[normals[:, 2] < 0].sum().

Raises:

ValueError: when mesh is not the 2 elements (vertices, faces), the shape is invalid,

coordinates are non-finite, an index is non-integer or out of range, or it is empty.

Note: as with mesh_area, degenerate triangles (area 0) are not rejected; 0 is returned (face_normals rejects them because the normal is undefined -- the same mesh passes here). Duplicate faces and double-sided faces (2 sheets, front and back) are each counted as 1 face. The unit is the square (power 2) of the coordinate unit.

Background guides (the physics and conventions behind this op)

• blender_interop — Using Blender alongside — build the shape, measure it with fullseye (pitfalls: axes, units, ground truth)

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

• mesh_props — py -3.11 examples_3d/mesh_props.py

Ops the type connects to (they accept `signal` as input)

fuse_to_voxel

Same category (`mesh_process`)

laplacian_smooth · taubin_smooth · decimate_qem · face_normals · vertex_normals · mesh_area · vertex_curvature · mesh_volume

*Provenance: mesh_props.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

face_areas — 3D mesh_process op