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) = ∑ ^{n}_{i=0 } S_{i}N_{i, p}(u) 0<=t<=n-p+2**

p are the points that control a segment

S is number of control points

**N _{i, p}(t) = (u-k_{i})N_{i,p-1}(u)/k_{i+p-1}-k_{i } (u-k_{i+p})N_{i+1,p-1}(u)/k_{i+p}-k_{i +1}**

k are the number of knot points

k_{i} where i lies ( 0<= i <= n+p )

k_{i} = 0, if i< p

k_{i} = i-p +1 , if p<= i<= n

k_{i} = n-p+2, if i>n

N_{i, p}(u) = 1 if k_{i }<= u <= k_{i+1}

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**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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