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_bend(t=0.0, nu=80, nv=120, extent=1.5, scale=1.0)(要直接呼叫實作,import render3d; render3d.minimal_surface_bend(t=0.0, nu=80, nv=120, extent=1.5, scale=1.0);從台帳取用則 ops3d.get("minimal_surface_bend"))
懸鏈面 ⇄ 螺旋面的彎折 —— 族中每一個仍然是極小曲面。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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`.
• 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 · 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.