laplacian_smooth — 3D mesh_process op

• Data kinds: mesh → mesh

• Call: import fullseye as fs; fs.ledger.laplacian_smooth(mesh: 'Sequence', iters: 'int' = 10, lam: 'float' = 0.5) -> 'Mesh' (to call the implementation directly, import mesh_smooth; mesh_smooth.laplacian_smooth(mesh: 'Sequence', iters: 'int' = 10, lam: 'float' = 0.5) -> 'Mesh'; from the registry, ops3d.get("laplacian_smooth"))

Usage

Triangle-mesh smoothing by the umbrella Laplacian. → (verts, faces).

Each iteration updates every vertex as v_i += lam * (mean(隣接 v_j) - v_i). It reliably reduces high-frequency noise, but on a closed surface it shrinks inward (shrinkage), like mean curvature flow (a sphere shrinks with the iterations). To avoid shrinkage use taubin_smooth.

Args:

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

iters: number of iterations (positive integer).

lam: pull rate of each step, 0 < lam <= 1 (1 pulls fully to the neighbour mean).

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 (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)

taubin_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).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.