Module surface 

Surface/point containment by per-axis fat line clipping — the design is surface.md next to this file, the curve version it extends is curve.md / super::curve.

Each Cartesian axis k gives a polynomial tensor-product spline g_k(u, v) = H_k(u, v) - p_k W(u, v) whose zeros are exactly where that coordinate matches. Its control net is collapsed onto each parameter axis by interval union over the other index, and the resulting 1-D envelopes are clipped with the same fat line as curves ([clip_tensor]). Intersecting over the axes shrinks the patch towards the solution in both directions at once.

Functions

boundary_curve

The boundary of patch at the start (first) or end of its u domain (u_fixed) or v domain, as a curve along the other parameter — the first/last control row, which is the surface there when the knot vector is clamped at that end. None if it isn’t.

surface_could_contain

Every (u, v) at which surface could pass through point (surface.md §§4–5): the componentwise union of every converged patch’s clipped (u, v) box, exploring breadth-first.