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Splines

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+1xi)(xi+1x)3+fi+16(xi+1xi)(xxi)3+(yi+1xi+1xifi+1(xi+1xi)6)(xxi)+(yixi+1xifi(xi+1xi)6)(xi+1x).