Consider the torus obtained by rotating the circle $(x-R)^2+z^2=r^2$ about the $z$-axis, where $R>r>0$. Parametrize the part of this torus where $z>x+y$.
My approach to this so far is to use the standard parametrization for the torus, $\gamma{(\theta,\phi)}=((R+r\cos{\theta})\cos{\phi}, (R+r\cos{\theta})\sin{\phi}, r\sin{\theta})$, where the domain of $\gamma$ is $[0,2\pi)$x$[0,2\pi)$, and then restrict the domain to be a subset of this. I'm having trouble doing this--figuring out how to express the intersection of the plane and the torus using these parameters seems to be difficult. Is this a sensible approach, or is there a better way?