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NURBS Surface Second-Jet & Principal Curvatures
x402
NURBS Surface Second-Jet & Principal Curvatures is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).
Computes local differential geometry (second fundamental form, principal curvatures, and related quantities) of an explicit regular NURBS patch at given parameter points.
Price / call$0.003
Success—
StatusUnknown
How this service works
Compute local differential geometry of an explicit regular NURBS patch.
Output
Returns the computed local differential geometry of the NURBS patch at each queried parameter point, including components of the second fundamental form (L, M, N coefficients), principal curvatures (κ₁, κ₂), principal curvature directions, Gaussian curvature (K = κ₁·κ₂), and mean curvature (H = (κ₁+κ₂)/2).
Example use cases
CAD surface quality inspection
“I have a bicubic NURBS surface from my CAD model — degree 3 in both u and v — and I need to check its curvature at the point (0.3, 0.7) to verify it's smooth enough for a Class-A automotive surface. Can you compute the principal curvatures and Gaussian curvature for me?”
CNC toolpath curvature analysis
“For our CNC machining pipeline, I need the principal curvatures of a NURBS patch at 8 sample parameter points so we can adapt the tool contact radius. The patch is degree 2×3, here are my knot vectors, control net, and weights — please evaluate the second fundamental form at all those points.”
Mesh refinement curvature-driven sampling
“I'm building an adaptive mesh of a NURBS hull surface and I need to know the Gaussian and mean curvature at several candidate parameter locations to decide where to add more triangles. Can you give me the full second-jet differential geometry data at those points for a degree-2×2 rational NURBS patch?”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B005/nurbs-surface-second-jet-fundamental-principal-curvatures?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need analytically exact local differential geometry (second-order quantities) of a NURBS surface rather than finite-difference approximations from a mesh. It is ideal for CAD/CAM pipelines, surface quality inspection, curvature-driven adaptive sampling, and any workflow where the surface is already represented as a NURBS patch with explicit knot vectors and control nets. Prefer it over mesh-based curvature estimators when precision and mathematical exactness matter.
Side effects
- Invalid or non-clamped knot vectors (knots not in [0,1] or wrong count for given degree and control net) → validation error
- Control net dimensions inconsistent with degree or weight array dimensions → schema validation failure
- Evaluation at a singular or degenerate point where the surface normal vanishes → undefined geometry error
- Degree outside allowed range 1–3 → validation rejection
- Parameter values outside domain implied by knot vectors → out-of-domain error
- Payment not included or insufficient USDC → HTTP 402 Payment Required
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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