Aitken Lagrange Parabola Construction

A few weeks ago Peter Bartholomew (uk.linkedin.com/in/peterbartholomew )visited my blog. He made a very valuable suggestion â€“ put up a demonstration for the construction of points on a parabola using the Aitken- Lagrange construction.

He sent me a sample workbook that demonstrated the point wise construction of a Bezier Cubic.

I have now re-engineered his workbook and have generated a user controlled demonstration for the Aitken-Lagrange construction of points on a parabola.

This workbook also demonstrates the technique of incorporating User Define Functions in Named Ranges. I believe that Bob Umlas (www.linkedin.com/pub/bob-umlas/46/278/479 )was the first to discover this technique.

The User Defined Functions employed by this demonstration are:

Name Definition

X_Values =OFFSET(Aitken_Lagrange!$D1,0,0)

y_12_FLINE =(Y_P1*(X_P2-X_Values)+Y_P2*(X_Values-X_P1))/(X_P2-X_P1)

Y_23_FLINE =(Y_P2*(X_P3-X_Values)+Y_P3*(X_Values-X_P2))/(X_P3-X_P2)

Y_123_FLINE =(y_12_FLINE*(X_P3-X_Values)+Y_23_FLINE*(X_Values-X_P1))/(X_P3-X_P1)

Note well: The definition for the X_Values coming from Column D on Aitken_Lagrange Sheet enables the calculation of both the XStar lookup at the top of the sheet as well as the table of values at the bottom of the sheet.

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