surface op• Data kinds: none → mesh (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.gyroid_isosurface(shape=(64, 64, 64), level=0.0, periods=1.0) (to call the implementation directly, import render3d; render3d.gyroid_isosurface(shape=(64, 64, 64), level=0.0, periods=1.0); from the registry, ops3d.get("gyroid_isosurface"))
The gyroid — a triply periodic surface from its nodal approximation.
Samples `sin x cos y + sin y cos z + sin z cos x over periods` unit
cells and extracts the level set. At `level = 0` the field is **odd under
the body-centred inversion**, so the two sides have exactly equal volume —
a symmetry fact, independent of the meshing, that the existing
`mesh_volume` can be pointed at.
★Honest limit, stated in the contract: this is the *nodal approximation*
to the gyroid, not the exact triply periodic minimal surface. Schoen's gyroid
has `H = 0` everywhere; the nodal surface has a residual mean curvature
(measured, not hidden) of about 12 % of the principal-curvature scale at a
64³ grid —— compare the exact families in :func:minimal_surface, whose
`|H|` median is 1e-4 against a curvature scale of order 1. Use the gyroid as
a scaffold and a picture, not as a claim of minimality.
Parameters
----------
shape : (nz, ny, nx)
level : float
Iso value. 0 gives the balanced surface; non-zero splits the volume.
periods : float
Unit cells along each axis.
Returns a `mesh` (vertices, faces).
★The thickened solid form lives in :func:gyroid_solid_mask, not behind
a keyword here —— one function that returns a mesh or a volume depending on an
argument cannot be given a single declared output type, and a ledger row that
lies about its output is the defect class this library keeps catching
(`indices_to_labels`: one word covering a 1-D mask and a 3-D volume).
Raises `ValueError`: a grid below 8 per axis or over the cap;
non-positive periods; a level outside the field's range (no surface exists
there — reported rather than returning an empty mesh); negative thickness.
• 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.
• minimal_surfaces — py -3.11 examples_3d/minimal_surfaces.py
mesh as input)mesh_to_voxel · mesh_to_points · to_points · fuse_to_voxel · ambient_occlusion · cast_shadow · supersample_mesh · render_beauty
surface)minimal_surface · minimal_surface_bend · gyroid_solid_mask · curve3d_tube_mesh
*Provenance: render3d.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.