What is the difference between cubic splines and cubic b-splines?

Question

I am dealing with a numerical problem with cubic spline, but I am a little bit confused while using them because of terms spline and b-spline.

In simple words, what is the difference between the cubic spline and cubic b-spline? Are these both terms the same, or is the b-spline another name for cubic spline?

I don't understand the difference between "are these two terms the same" and "is B-spline another name for cubic spline". Are those two options the same, or is "term" another name for "name"? — joriki, Feb 03 '13 at 13:27
later duplicate question: http://math.stackexchange.com/q/699113/115115 — Lutz Lehmann, Mar 07 '14 at 07:56
A cubic B-spline is a special instance of the set of all cubic splines. So no, they are not the same, and they are names for different, albeit related, things. — Lutz Lehmann, Mar 07 '14 at 07:59

score 5 · Answer 1 · answered Feb 04 '13 at 05:10

A spline is a curve that is formed by stringing together polynomial pieces in a clever way (so that continuity between the pieces can be controlled). The polynomial pieces can have any degree. A common choice is degree = 3, in which case the spline is called a "cubic" spline.

Any spline (of any degree) can be represented in b-spline form. From a mathematical point of view, this is because b-splines can be used to construct a basis for any spline space.

So, to answer your question: a cubic b-spline is one possible way to represent a cubic spline, just as "XVI" is one way to represent the number sixteen.

What is the difference between cubic splines and cubic b-splines?

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