basis(t)

Compute the basis functions of cubic Hermite spline interpolation. They are: H{00} = 2t^3 - 3t^2 + 1 = (1+2t)(t-1)^2 H{10} = t^3 - 2t^2 + t = t(t-1)^2 H{01} = -2t^3 + 3t^2 = t^2(3-2t) H{11} = t^3 - t^2 = t^2(t - 1)

basis_derivative(t)

Compute the basis functions of cubic Hermite spline interpolation. They are: H{00} = 6t^2 - 6t = 6t(t-1) H{10} = 3t^2 - 4t + 1 = (3t-1)(t-1) H{01} = -6t^2 + 6t = -6t(t-1) H{11} = 3t^2 - 2t = t(3t - 2)