I have a plane defined through a point P and two 3D-vectors $\overrightarrow{X}$ and $\overrightarrow {Y}$.
I wish to convert coordinates of points on this plane between local 2D-parametric and world 3D coordinate systems.
I know the conversion from 2D Parametric to 3D is
$C(u, v) = P + u\cdot \overrightarrow {X} + v\cdot \overrightarrow {Y}$
however i have been unable to find a way for the inverse case
$C'(x, y, z)$ which should give me the parameters $u$ and $v$ for any point $(x, y, z)$ in the plane.
How does this conversion work?