There is a plane defined by a normal and an origin. For simplicity's sake, the origin is $(0,0,0)$.
And then, there are two coordinates ($x$ and $z$) of a point on this plane.
How can I find the third coordinate ($y$) of the point ?
- The plane is never vertical, so the point always exists.
- This is exactly like finding the interection between the plane and an infinite vectical vector passing trough $(x,0,z)$
- In this space, the vertical (up) vector is $(0,1,0)$
- The computation needs to be cheap/fast.