surface op• 資料種類:無 → mesh(僅由參數決定的運算子 —— 不接受影像或資料輸入)
• 呼叫: import fullseye as fs; fs.ledger.minimal_surface(kind='catenoid', nu=80, nv=120, extent=1.5, scale=1.0)(要直接呼叫實作,import render3d; render3d.minimal_surface(kind='catenoid', nu=80, nv=120, extent=1.5, scale=1.0);從台帳取用則 ops3d.get("minimal_surface"))
由精確參數化生成的經典極小曲面。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
`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.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• minimal_surfaces — py -3.11 examples_3d/minimal_surfaces.py
mesh 作為輸入)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 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.