I want to plot and find out the section of a sphere remaining after putting constraints in terms of cartesian planes. How it can be done?
For example, if I have a sphere of $r = 1$, and I put the constraint $z > 0$ on it, simple imagination would suggest that it leaves half the sphere as defined by limits $\theta\in [0, \pi/2]$ and $\phi\in [0, 2\pi]$. Adding the constraint $x > 0$ leaves a quarter of the sphere with $\theta\in [0, \pi/2]$ and $\phi,\in [0, \pi]$, and so on.
I want to achieve the same using Mathematica. I want find the $(\phi, \theta)$ limits for more complex Cartesian constraints applied simultaneously, such as $x > y \land z > y$.
Will appreciate any suggestions.