Aitken’s Four Point Construction is Equivalent to the Four Point Lagrange Polynomial

Using the FLINE equations for a straight line, I will show that the Four Point Aitken Cubic Construction is equivalent to the Four Point Lagrange Polynomial for a Cubic.

The FLINE form provides a compact expression for the parametric equation for the straight line from the left-most point (XL,YL) to the right-most point (XR,YR).


Using this form the Aitken Construction for points on the cubic curve that passes through the points (X1,Y1), (X2,Y2), (X3,Y3) and (X4,Y4) is then:







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