It would be more interesting to construct a cubic passing through four points. But which is the distinguished way to do something like that? If in the previous parametric representation p(t), we require that p(t1) = p1, p(t2) = p2, etc., then a linear system results, expressing p1, p2, ... through A, B, C and D. The coefficients of this system are powers of t1, t2, ... and the corresponding matrix is of Vandermonde type. Such a cubic, drawn again through a [user-tool], is contained in the file CubicFitting4.html . There the cubic passes through the 4 points, for corresponding parameter-values: 0, 1, 2, 3 and the script uses the inverse of the corresponding Vandermonde matrix.

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