B-樣條基函數 matlab實現

B-樣條基函數的遞歸形式如下：

matlab實現：

function result = Bbase(i,k,u,NodeVector)
% 計算基函數result
% i爲控制頂點的序號    k爲次數  u爲帶入的值  NodeVector爲節點向量
if k==0 
    if NodeVector(i)<=u && u<=NodeVector(i)
        result=1;
        return;
    else
        result=0;
        return;
    end
end
    if NodeVector(i+k)-NodeVector(i)==0 
        alpha=0;
    else
        alpha=(u-NodeVector(i))/(NodeVector(i+k)-NodeVector(i));
    end
    if NodeVector(i+k+1)-NodeVector(i+1)==0
         beta=0;
    else
        beta=(NodeVector(i+k+1)-u)/(NodeVector(i+k+1)-NodeVector(i+1));
    end
result=alpha*Bbase(i,k-1,u,NodeVector)+beta*Bbase(i+1,k-1,u,NodeVector);
end