Aitken Lagrange Parabola Construction
A few weeks ago Peter Bartholomew (uk.linkedin.com/in/peterbartholomew )visited my blog. He made a very valuable suggestion – 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.
alfred-excel-vachris 