surface op• 데이터 종류: 없음 → mesh(인자만으로 정해지는 연산자 —— 이미지나 데이터 입력을 받지 않습니다)
• 호출: import fullseye as fs; fs.ledger.minimal_surface(kind='catenoid', nu=80, nv=120, extent=1.5, scale=1.0)(구현을 직접 호출하려면 import render3d; render3d.minimal_surface(kind='catenoid', nu=80, nv=120, extent=1.5, scale=1.0), 원장에서 가져오려면 ops3d.get("minimal_surface"))
고전적인 극소 곡면을, 엄밀한 매개변수 표시에서 만든다。
> 아래 상세 설명은 원문입니다 —— 요약과 제목은 번역되어 있습니다.
`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.
Parameters
----------
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.
• 샘플 데이터 카탈로그(DL URL / 라이선스) —— 2-D 는 skimage.data(BSD/public)+ 합성, 3-D 는 실데이터 소스(Stanford/PDS 등)의 DL URL.
• 연산자의 내력·참고문헌 —— 이 연산자 족의 바탕이 된 연구/기법의 출처.
• minimal_surfaces — py -3.11 examples_3d/minimal_surfaces.py
mesh 를 입력으로 받는 것)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 연산자 레지스트리. 이 op 노트는 tools/opdocs.py md 가 자동 생성합니다(직접 편집하지 마세요).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.