# Dimension of a Spline Space

What is the dimension of a given spline space S(k,t)? What does the dimension of spline space refer to? It seems like it might refer to the dimensionality of the control points, but maybe I'm missing something.

I'm reading about geometric modeling with splines and this question came up.

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If the splines are of order $k$ (degree $k-1$), and you have $n$ knots, then the dimension of the spline space is $n-k$, I think. It's messy because the spline representations that are typically used in geometric modeling have a knot value at each end that's really not used, and could be omitted. For example, to represent a cubic Bezier curve, many people would use a knot sequence of $\{0,0,0,0,1,1,1,1\}$. But $\{a,0,0,0,1,1,1,b\}$ will give you exactly the same curve provided $a\le0$ and $b\ge1$. –  bubba Jan 6 '13 at 5:35