geometry op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.nurbs_surface(control_net, weights=None, *, degree=(3, 3), knots_u=None, knots_v=None, n=(48, 48)) -> 'dict' (to call the implementation directly, import mathgeometry; mathgeometry.nurbs_surface(control_net, weights=None, *, degree=(3, 3), knots_u=None, knots_v=None, n=(48, 48)) -> 'dict'; from the registry, opsmath.get("nurbs_surface"))
Evaluates a NURBS surface (tensor product).
Args:
control_net: (mu, mv, 3) control net.
weights: (mu, mv) positive weights (all 1 if omitted).
degree: (p, q). knots_u, knots_v: knot vectors in each direction (clamped uniform if omitted).
n: (nu, nv) grid of evaluation points.
Returns:
points (nu, nv, 3), mesh = (V, F) triangle mesh (can be passed as is to geodesic_heat etc.), u, v, knots_u, knots_v, weights.
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.
• (none yet)
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_curve · nurbs_circle
*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.