geometry op• Data kinds: none → mesh (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.mesh_torus(R: 'float' = 2.0, r: 'float' = 0.7, n_u: 'int' = 32, n_v: 'int' = 16) -> 'tuple' (to call the implementation directly, import mathgeometry; mathgeometry.mesh_torus(R: 'float' = 2.0, r: 'float' = 0.7, n_u: 'int' = 32, n_v: 'int' = 16) -> 'tuple'; from the registry, opsmath.get("mesh_torus"))
> This operator's description has not been translated yet. The original text follows as it is.
トーラス(ドーナツ)の閉じた三角形メッシュ (vertices, faces)。大きい半径 R・管の半径 r(R > r > 0)。
種数 1 の曲面の見本: χ = 0、角欠損の総和 = 0(外側の凸の部分が正、内側の鞍の部分が負で打ち消し合う)。
頂点は (u, v) の格子(u が大円、v が管のまわり)の順で、`u = i·2π/n_u、v = j·2π/n_v` の頂点が i·n_v + j 番。
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• geometry_tour — py -3.11 examples/geometry_tour.py
mesh as input)mesh_euler_characteristic · angle_defect · geodesic_heat
geometry)mesh_euler_characteristic · angle_defect · delaunay_triangulate · geodesic_heat · geodesic_heat_grid · nurbs_curve · nurbs_circle · nurbs_surface
*Provenance: mathgeometry.py — MATH operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.