Finding a point on B-spline

Question

I would like to find a point on B-spline.
For Bezier curves, only control points and degree of curve are needed find coordinates of point $u$, $$ C(u) = \sum_{i=0}^n B_{n,i}(u) P_i $$ $$ B_{n,i}(u) = \frac {n!}{i! (n-i)!} u^i (1-u)^{n-i}$$ $$ 0 \le u \le 1 $$ For B-spline, how do I find (x,y) coordinates of a point on it? Do I need to consider knot values and fit points in calculation beside control points?

Answer 1

You need to consider knot values when evaluating a point on a b-spline curve from a given parameter as that it is part of the b-spline curve definition. You don't need to consider fit points which are merely used to construct the b-spline curve.