Definition:Spline Function/Uniform
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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 $T$.
$S$ is a uniform spline if and only if $T$ is a normal subdivision.
That is, if and only if the knots of $S$ are equally spaced.