polyhedron op• 数据种类:无 → mesh(仅由参数决定的算子 —— 不接受图像或数据输入)
• 调用: import fullseye as fs; fs.ledger.geodesic_dome(frequency=3, radius=1.0, hemisphere=False)(要直接调用实现,import render3d; render3d.geodesic_dome(frequency=3, radius=1.0, hemisphere=False);从台账取用则 ops3d.get("geodesic_dome"))
对正二十面体细分得到的测地球 —— 决定形状的是欧拉公式。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
Each icosahedron face is cut into frequency**2 triangles and every vertex is pushed out to the sphere. The counts are then forced, not chosen:
F = 20*f**2, E = 30*f**2, V = 10*f**2 + 2, and Euler's formula V - E + F == 2 holds exactly.
★Why this earns its place: Euler also forces the *irregularity*. If every vertex had degree 6 then 2E = 6V, which contradicts V - E + F = 2; counting degrees gives sum(6 - deg(v)) == 12 over all vertices, so a triangulated sphere built from hexagons must contain exactly twelve pentagons — no more, no fewer, at any frequency. That is why a football has twelve black patches, and it is an integer this operator must reproduce exactly. Nothing about the drawing can be "close enough".
Returns a mesh (V, F): V is (n, 3) float, F is (m, 3) int. With hemisphere=True the vertices below z = 0 and the faces touching them are dropped (then Euler no longer gives 2, and the twelve-pentagon count applies to the full sphere only — said here rather than letting the gate quietly change meaning).
Raises ValueError: frequency < 1; radius <= 0; the mesh would exceed the cap.
HALCON: no operator (gen_sphere_object_model_3d makes a UV sphere, whose poles are degenerate — a different object).
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• geodesic_dome — py -3.11 examples_3d/geodesic_dome.py
mesh 作为输入)mesh_to_voxel · mesh_to_points · to_points · fuse_to_voxel · ambient_occlusion · cast_shadow · supersample_mesh · render_beauty
polyhedron)—
*Provenance: render3d.py — 3D 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.