In B-spline curve, Local control is imposed on a curve, means a B-spline curve usually divide into segments and changing control points respective to a particular segment would only change that shape of that region only. In Bezier curve, controls are global, changing a control will lead to change the entire shape of a curve.
Each and every segment uses a unique basis function
S(t) = ∑ni=0 SiNi, p(u) 0<=t<=n-p+2
p are the points that control a segment
S is number of control points
Ni, p(t) = (u-ki)Ni,p-1(u)/ki+p-1-ki (u-ki+p)Ni+1,p-1(u)/ki+p-ki +1
k are the number of knot points
ki where i lies ( 0<= i <= n+p )
ki = 0, if i< p
ki = i-p +1 , if p<= i<= n
ki = n-p+2, if i>n
Ni, p(u) = 1 if ki <= u <= ki+1
Properties of B-spline curve
1) B-spline curve consists of n+1 control points and p order of the curve.
2) It has local control over curve that controls segments separately.
3) A degree of polynomial depends on the order of the curve which is p-1.
4) B-spline consists of n-p+2 segments.
5) Number of control points can be changed without affecting the degree of a polynomial
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