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? enter image description here

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    $\begingroup$ A curve segment is defined over each knot span. Therefore, their numbers will always be the same. $\endgroup$ – fang Jul 1 at 1:29
  • $\begingroup$ @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? $\endgroup$ – ytyyutianyun Jul 1 at 20:07
  • $\begingroup$ @OP: yes. you are correct. $\endgroup$ – fang Jul 2 at 1:00

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