Lagrange Interpolation

Lagrange interpolation gives a way of fitting a polynomial through at set of points. The basic polynomial is

where

In order to generate a curve in space it is convenient to consider this as a four dimensional problem with parameter as the independent variable. This ensures that is monotonic avoid singularities. The resulting modified equations are

where

For convenience the values are assumed to be in the range .

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Archer, Branden and Weisstein, Eric W. "Lagrange Interpolating Polynomial." From MathWorld--A Wolfram Web Resource. (opens new window)