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(kind='catenoid', nu=80, nv=120, extent=1.5, scale=1.0) (to call the implementation directly, import render3d; render3d.minimal_surface(kind='catenoid', nu=80, nv=120, extent=1.5, scale=1.0); from the registry, ops3d.get("minimal_surface"))
A classical minimal surface, from its exact parametrisation.
catenoid (c cosh(u/c) cos v, c cosh(u/c) sin v, u), helicoid (u cos v, u sin v, c v), enneper (u - u^3/3 + u v^2, v - v^3/3 + v u^2, u^2 - v^2) and scherk z = log(cos y / cos x) (the doubly periodic surface, over one cell).
★★Why this earns its place — the definition is the gate. A minimal surface is one whose mean curvature vanishes everywhere, and the existing vertex_curvature op measures exactly that. So the claim "this is a minimal surface" is checked by an op that knows nothing about how the surface was built. ★A trap worth naming: the catenoid and the helicoid are *isometric*, so their Gaussian curvatures agree pointwise — but that is a necessary, not sufficient condition for minimality (a sphere and a plane differ in K, yet matching K would not make either minimal). Grade on H.
kind : str
One of MINIMAL_SURFACES.
nu, nv : int
Grid resolution along the two parameters.
extent : float
Half-range of the first parameter (how much of the surface to take).
scale : float
The surface's own scale parameter (c for catenoid and helicoid).
Returns a mesh: (vertices, faces).
Raises ValueError: unknown kind; a grid below 4x4 or over the cap; non-positive scale; an extent that reaches the singularity (Scherk's surface is only defined where cos x and cos y share a sign, so an extent at or beyond pi/2 is refused rather than silently clipped to infinity).
HALCON: no operator.
• 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_bend · 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.