polyhedron op• Data kinds: कोई नहीं → mesh (केवल arguments से तय होने वाला op — यह कोई image या data input नहीं लेता)
• Call: import fullseye as fs; fs.ledger.geodesic_dome(frequency=3, radius=1.0, hemisphere=False) (implementation को सीधे call करना हो तो import render3d; render3d.geodesic_dome(frequency=3, radius=1.0, hemisphere=False), registry से लेना हो तो ops3d.get("geodesic_dome"))
subdivided icosahedron से geodesic sphere — shape Euler तय करता है।
> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।
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).
• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।
• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।
• geodesic_dome — py -3.11 examples_3d/geodesic_dome.py
mesh को input के रूप में लेते हैं)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. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.