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.minimal_surface_bend(t=0.0, nu=80, nv=120, extent=1.5, scale=1.0) (to call the implementation directly, import render3d; render3d.minimal_surface_bend(t=0.0, nu=80, nv=120, extent=1.5, scale=1.0); from the registry, ops3d.get("minimal_surface_bend"))
The catenoid-helicoid bend — every member of the family is still minimal.
The *associate family* `cos(t) * helicoid + sin(t) * catenoid` (in the
Weierstrass sense) deforms one into the other without stretching: the
surfaces are isometric at every `t`, and every one of them is minimal.
`t = 0 is the helicoid, t = pi/2` the catenoid.
★Why this earns its place: it turns "minimal" from a property of two
named surfaces into a one-parameter claim that must hold throughout. If
an implementation is only accidentally right at the endpoints, the middle of
the family exposes it — and the intrinsic geometry (first fundamental form)
must not change along the way, which is a second, independent check.
Returns a `mesh`.
Raises `ValueError`: the same shape/scale contracts as
:func:minimal_surface; a non-finite `t`.
• 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 · gyroid_isosurface · 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.