polyhedron op• データ種: なし → mesh(引数だけで決まる op —— 画像やデータの入力を取らない)
• 呼び出し: import fullseye as fs; fs.ledger.geodesic_dome(frequency=3, radius=1.0, hemisphere=False) (実装を直接呼ぶなら import render3d; render3d.geodesic_dome(frequency=3, radius=1.0, hemisphere=False)、台帳から引くなら ops3d.get("geodesic_dome"))
Geodesic sphere from a subdivided icosahedron — Euler decides the shape.
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).
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• geodesic_dome — py -3.11 examples_3d/geodesic_dome.py
mesh を入力に取れる)mesh_to_voxel · mesh_to_points · to_points · fuse_to_voxel · ambient_occlusion · cast_shadow · supersample_mesh · render_beauty
polyhedron)—
*Provenance: render3d.py — 3D operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.