nurbs

This node represents a NURBS surface patch — a tensor-product spline defined by a grid of control points, two knot vectors, and an order in each parametric direction. It has the following required attributes:

Control-point count along u. Total control-point count is nu * nv. Should be at least uorder; if smaller, the surface is rendered with order equal to nu.

Control-point count along v. Same constraint as nu relative to vorder.

Order along u: degree + 1, so 2 is linear, 3 quadratic, 4 cubic. Must be at least 2. May differ from vorder.

Order along v. See uorder.

Knot vector along u. Length must equal nu + uorder. Values must be non-decreasing.

Knot vector along v. Length must equal nv + vorder. Values must be non-decreasing.

The surface’s active parameter range can be restricted with the optional umin/umax/vmin/vmax attributes. Unlike other geometric primitives, NURBS surfaces do not assume [0, 1] parameter ranges — by default, the active range is the full extent of the corresponding knot vector.

Lower bound of the active range along u. Must be less than umax and at least the (uorder − 1)-th value of uknot.

Upper bound of the active range along u. Must be greater than umin and at most the nu-th value of uknot.

Lower bound of the active range along v. Must be less than vmax and at least the (vorder − 1)-th value of vknot.

Upper bound of the active range along v. Must be greater than vmin and at most the nv-th value of vknot.

One of P or Pw must be supplied to provide the control points. P defines a polynomial surface; Pw defines a rational one.

The nu * nv control points (xyz), stored row-major: P[i*nu + j] is the point at row i, column j.

Rational alternative to P: each control point is four floats (x, y, z, w), enabling rational NURBS. Pass as a single flat array of 4 * nu * nv floats — do not declare it with array_len(4).

Trim Curves

Trim curves carve a region out of the surface’s parameter domain. They are NURBS curves in homogeneous (u, v, w) parameter space — the actual (u, v) of a control point is (u/w, v/w). Curves are organised into loops: within a loop they connect head-to-tail. Each loop must be explicitly closed — the last point of the last curve must coincide with the first point of the first curve.

The trimcurves.* attributes are all-or-nothing: supply the full set or omit it entirely.

The number of trim loops.

The number of curves in each loop. One value per loop.

The control-point count of each curve. One value per curve.

The order of each curve. One value per curve.

The concatenated knot vectors for all curves. The total length is the sum over curves of n[i] + order[i].

The parametric start of each curve. One value per curve.

The parametric end of each curve. One value per curve.

Concatenated u coordinates of all trim-curve control points. The total length is the sum over curves of n[i].

Concatenated v coordinates of all trim-curve control points. The total length is the sum over curves of n[i].

Concatenated weights of all trim-curve control points. The total length is the sum over curves of n[i]. Use 1.0 for non-rational curves.

The sense of each loop. One value per loop. A value of 0 keeps the surface inside the loop; a value of 1 keeps the surface outside the loop (i.e. the loop describes a hole).