# In B-spline, why is the number of knot spans equal to the number curve segments?

I will show one example to explain my questions.

Let's say we have 11 control points, degree 3 and 15 knots with first four and last four knots clamped. The number of knot spans is equal to 8. The number curve segments are also equal to 8 (see figure). Why?

• A curve segment is defined over each knot span. Therefore, their numbers will always be the same. – fang Jul 1 at 1:29
• @fang I see. So based on your answer, when the parameter value goes through one knot span. Let's say it is $$u \in [u_0,u_1]$$. When u at u_0, its corresponding point is at the one side of the curve segment. When u at u_1, its corresponding point is at another side of the curve segment. Am I right? – ytyyutianyun Jul 1 at 20:07
• @OP: yes. you are correct. – fang Jul 2 at 1:00