geometry op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.nurbs_curve(control_points, weights=None, *, degree: 'int' = 3, knots=None, n: 'int' = 200) -> 'dict' (to call the implementation directly, import mathgeometry; mathgeometry.nurbs_curve(control_points, weights=None, *, degree: 'int' = 3, knots=None, n: 'int' = 200) -> 'dict'; from the registry, opsmath.get("nurbs_curve"))
> This operator's description has not been translated yet. The original text follows as it is.
NURBS 曲線を評価する(重みつき・制御点は一般に通らない)。
Args:
control_points: (m, d) の制御点(d = 2 なら平面、3 なら空間)。
weights: 長さ m の正の重み。省略すると全部 1(= 普通の B スプライン)。重みを大きくすると曲線がその点に寄る。
degree: 次数 p(m − 1 以下)。
knots: 長さ m + p + 1 の節点列。省略すると両端 p+1 重の一様節点(端点だけは制御点を通る)。
n: 評価する点の数(定義域を等分)。
Returns:
`points (n, d) 曲線上の点、u パラメータ、basis` (n, m) 有理基底 R_i(u)(各行の和は 1)、
`knots・weights・degree`。
例: 9 点の 2 次 NURBS で円を 厳密に 描く(`nurbs_circle` が制御点・重み・節点を返す)。多項式の
B スプラインでは円は近似しかできない —— 重みが要る理由がここにある。
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
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
geometry)mesh_euler_characteristic · angle_defect · delaunay_triangulate · geodesic_heat · geodesic_heat_grid · mesh_torus · 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.