Using the conditions si(xi)=yi and si(xi+1)=yi+1 we can in turn determine the constants c and d resulting in si(x)=fi6(xi+1−xi)(xi+1−x)3+fi+16(xi+1−xi)(x−xi)3+(yi+1xi+1−xi−fi+1(xi+1−xi)6)(x−xi)+(yixi+1−xi−fi(xi+1−xi)6)(xi+1−x).