Point-wise Polynomial Builder

Build a polynomial by specifying a set of R point-wise conditions under the form: y,D_r(t_r) = zeta_r , where D_r represents the derivative order, t_r represents the time-location, and zeta_r represents the value for condition r.

For function call

[c] = polycondition(t_r,D_r,zeta_r)

Define all input via row vectors length R.Output c is the standard form polynomial coefficient vector (i.e. y(t) = c_0 + c_1t + c_2t^2 ... c_Kt^K)

Example: determine the unique polynomial that has a value of 2, a slope of 3, and a 2nd derivative of 1 all at the point t=1, and a value of 9 at the point t=4.
[c] = polycondition([1 1 1 4],[0 1 2 0],[2 3 1 9])

Answer:
c = [ -7/27 23/18 11/9 -13/54 ]
See Image for plot.

[1] https://qr.ae/pNr4hB