taubin_smooth — 3D `mesh_process` op

• Data kinds: mesh → mesh

• Call: import fullseye as fs; fs.ledger.taubin_smooth(mesh: 'Sequence', iters: 'int' = 10, lam: 'float' = 0.33, mu: 'float' = -0.34) -> 'Mesh' (to call the implementation directly, import mesh_smooth; mesh_smooth.taubin_smooth(mesh: 'Sequence', iters: 'int' = 10, lam: 'float' = 0.33, mu: 'float' = -0.34) -> 'Mesh'; from the registry, ops3d.get("taubin_smooth"))

Usage

Non-shrinking smoothing by the Taubin λ|μ filter. → (verts, faces).

Each iteration applies, in succession, "a step pulling with positive lam" → "a step pushing back with negative mu". With |mu| > lam it becomes a band-pass filter that passes low frequencies (overall shape) and attenuates only high frequencies (noise), cancelling the shrinkage artifact of Laplacian smoothing (the mean radius of a sphere is almost preserved). The default lam=0.33, mu=-0.34 is close to the recommendation of Taubin (1995).

Args:

mesh: sequence of (verts (N,3), faces (M,3)[, ...]). faces are unchanged.

iters: number of iterations of λ|μ pairs (positive integer).

lam: coefficient of the pull step, 0 < lam < 1.

mu: coefficient of the push-back step, mu < 0 and |mu| > lam (the condition that cancels shrinkage).

Returns:

(verts (N,3) float64, faces (M,3) int64). faces are kept from the input.

Raises:

ValueError: invalid mesh shape, face index out of range, or invalid iters/lam/mu (fail-closed).

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_smooth — py -3.11 examples_3d/mesh_smooth.py

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

mesh_to_voxel · mesh_to_points · to_points · fuse_to_voxel · ambient_occlusion · cast_shadow · supersample_mesh · render_beauty

Same category (`mesh_process`)

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

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

taubin_smooth — 3D mesh_process op