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"))
正二十面体を細分した測地球 —— 形を決めているのはオイラーの公式。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
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.