I have a bohemian dome given by the parametric equation
$$x= a \cos u$$ $$y = b \cos v + a\sin u -1$$ $$z=c\sin v$$
, where
$$a= 0.5$$ $$b = 1.5 $$ $$c= 1$$ , and $u,v \in [0,2\pi)$ . I know that I can somehow find a curve lying on the surface by expressing $v$ in terms of $u$, meaning by using the same parametric equation but such that $v = u x$. I just don't know how to find this correlation between $u$ and $v$.
Any help is appreciated!