I am drawing a spline based parametric curve which is described with the following functions (U for horizontal axis and Y for vertical).
$$U = A_u+B_u*p +C_u*p^2+D_u*p^3\\V = A_v+B_v*p +C_v*p^2+D_v*p^3$$ $$$$ How to rotate such a function $v(u)$ by $\theta$ degrees?
$$$$ My output equation should be composed of powers of three at max. Many thanks in advance
PS. I have seen a video How to Rotate any Curve by any Angle, but couldn't come up with a proper solution to my more complicated equation.
A plane rotation is represented as
$$ R(\theta) = \left( \begin{array}{cc} \cos (\theta ) & -\sin (\theta ) \\ \sin (\theta ) & \cos (\theta ) \\ \end{array} \right) $$
and the rotated curve
$$ \left( \begin{array}{c} U\\ V \end{array} \right)_{\theta} = R(\theta)\left( \begin{array}{c} U\\ V \end{array} \right) $$