Definition:Spline Function/Knot

Definition

Let $\closedint a b$ be a closed real interval.

Let $T := \set {a = t_0, t_1, t_2, \ldots, t_{n - 1}, t_n = b}$ form a subdivision of $\closedint a b$.

Let $S: \closedint a b \to \R$ be a spline function on $\closedint a b$ on $T$.

The points $T := \set {t_0, t_1, t_2, \ldots, t_{n - 1}, t_n}$ of $S$ are known as the knots.

The ordered $n + 1$-tuple $\mathbf t := \tuple {t_0, t_1, t_2, \ldots, t_{n - 1}, t_n}$ of $S$ is known as the knot vector.

The knots of a spline function are also known as nodes.

Some sources refer to them as control points.