NURBS¶

NURBS (Non-Uniform Rational B-Spline) curves give you a smooth, analytic curve with predictable behavior under deformation, extrusion, and lofting. The Designer's NURBS implementation is small but complete enough to author CAD-style profiles.

Create¶

Surfaces > NURBS > Create NURBS Curve. The Designer drops an empty NURBS curve at the cursor; click on the canvas to add control points; press Enter or Esc to close authoring.

For closed NURBS: toggle closed in the Properties pane.

Parameters¶

Property	Default	Range	Effect
degree	3	1 - 7	Polynomial order; 3 = cubic (most common)
knot_kind	clamped	clamped / open / periodic	Knot vector spacing
weights	1.0 each	0.1 - 10.0 per CV	Rational weights for the CVs
control_points	(authored)	n ≥ degree + 1	The control polygon

The degree and knot kind together determine the curve's continuity. Cubic clamped curves pass through their first and last CVs, which is usually what you want.

Editing CVs¶

Click any CV to select it; drag to move.
Shift-click to extend selection.
Right-click a CV for: Add CV After / Before, Delete CV, Reset Weight to 1.0.
Type a new weight in the Properties pane's weight field.

Increasing a CV's weight pulls the curve toward that CV; useful for steering analytic curves to pass closer to a reference point.

Insert vs raise degree¶

To get more shape control without distorting existing geometry:

Insert Knot (Surfaces > NURBS > Insert Knot): adds a new CV by knot insertion. Curve shape stays identical; you gain a new editable point.
Raise Degree (Surfaces > NURBS > Raise Degree): raises the polynomial order by 1 (adds one CV). Curve shape stays identical.

Both are non-destructive.

Convert between NURBS and Bezier¶

Surfaces > Convert > NURBS to Bezier and the inverse. Convert to Bezier when you want to edit with tangent handles instead of CVs; convert to NURBS when you want to loft or use a deformer that prefers analytic input.

The conversion preserves shape exactly for cubic curves; lower / higher degrees may introduce sub-pixel error.

Closing a NURBS¶

For closed analytic curves choose knot_kind = periodic and set closed = true. The curve wraps so its end CV connects smoothly back to its start CV with full C^(degree-1) continuity.

For a sharp-cornered closed NURBS, use clamped + closed = true; the corner appears at the duplicated start/end CV.

Lofting¶

Two or more NURBS curves can be lofted into a Mesh3D surface; see Loft to Mesh. NURBS lofts produce predictable quad meshes; Bezier lofts approximate.

Limitations¶

NURBS surfaces (not just curves) are on the roadmap but not in v1. You can fake them with a series of lofted NURBS curves.
The Designer's NURBS solver is fixed-precision (double). Very long curves (> 10^6 px) may accumulate visible deviation in the CV-to-curve evaluator.