Cartesian parametrization:  where  is the unique polynomial (called "Lagrange polynomial") of degree £ n satisfying  where  is an increasing sequence of real numbers. The interpolation is said to be "uniform" if the  are equal, and "proportional to the chords" if the  are proportional to the lengths .

 

Given a broken line (called control polygon, the Ak being the control points, the associated interpolating Lagrange curves are the polynomial curves of degree less than or equal to n passing through the points  in that order. Opposite, in green the uniform interpolation, and in red the interpolation proportional to the chords (closer to the control polygon).

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© Robert FERRÉOL 2017