Ferguson's cubic

    This curve was established in year 1964 J.C. Ferguson. It is determined by two operative dots V1 and V2 and values of vectors in these dots v1 and v2. Curve starts in dot V1 and ends in dot V2. The form of curve is determined by direction and size of  vectors v1 and v2. If both vectors are zero, then resultant curve will be line. Ferguson's cubic can be written as

          |  2 -2  1  1 | | V1 |
B(t)= T . | -3  3 -2 -1 |.| V2 |,
          |  0  0  1  0 | | v1 |
          |  1  0  0  0 | | v2 |
where T = | t3, t2, t, 1 |, t ∈ <0,1>.

By this modification we receive     B(t) = V1*F1(t) + V2*F2(t) + v 1*F3(t) + v2*F4(t), where
    F1(t) = 2t3 - 3t2 +1
    F2(t) = 2t3 + 3t2
    F3(t) = t3  - 2t2 +t
    F4(t) = t3  - t2.

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Ferguson's cubic

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