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Dot to Dot Calculus

A User Controlled Demonstration of the Aitken-Lagrange Construction for Points on a Parabola.

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.

By excel1star

Senior Excel VBA Automation Developer.
Ex Aerospace Engineer with Grumman Aerospace

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