NURBS

Also called nurb, b-spline, spline, knot vector, trimmed surface

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A curve or surface defined by control points, a degree, a knot vector, and a weight per point. Non-uniform knots allow unequal spans and local sharpening; rational weights let it represent conics exactly — a true circle, which no polynomial Bézier can produce. That exactness is why it became the CAD standard.

A degree-three B-spline with its control polygon dashed, knot positions ticked along the curve, and one control point shown at two weights with the resulting curve drawn in both positions.

In practice

A 'NURBS surface' in practice means a trimmed patch: the underlying sheet is always a rectangular grid, and the visible hole or boundary is a 2D curve masking it. Trims are why NURBS models tessellate badly and boolean worse.

Not to be confused with

BézierA polynomial curve defined by control points and evaluated by repeated linear interpolation between them — de Casteljau's algorithm. It passes through its first and last points, is merely pulled toward the rest, and never leaves their convex hull. Cubic, four points, is the standard: the lowest degree admitting an inflection.

Origin

The acronym unpacks its three generalizations: Non-Uniform knot spacing, Rational (weighted, projective) control points, B-Spline basis. 'Spline' is itself the shipwright's flexible batten, bent through lead weights called ducks to fair a hull.

How this term connects

Related Confused with

In practice

Not to be confused with

Origin

Related

How this term connects

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