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"))
Evaluates a NURBS curve (weighted; in general it does not pass through the control points).
Args:
control_points: (m, d) control points (d = 2 for planar, 3 for spatial).
weights: positive weights of length m. If omitted, all 1 (= an ordinary B-spline). Increasing a weight pulls the curve toward that point.
degree: degree p (at most m − 1).
knots: knot vector of length m + p + 1. If omitted, uniform knots with multiplicity p+1 at both ends (the curve passes through the control points only at the endpoints).
n: number of points to evaluate (the domain is divided equally).
Returns:
points (n, d) points on the curve, u parameters, basis (n, m) rational basis R_i(u) (each row sums to 1),
knots, weights, degree.
Example: a degree-2 NURBS with 9 points draws a circle exactly (nurbs_circle returns the control points, weights and knots). A polynomial B-spline can only approximate a circle —— this is why weights are needed.
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.