I have a rectangular field of view (FOV) through which I am viewing a sphere at a distance such that I can only see small parts of the sphere through the FOV at a time. Usually my FOV contains part of the sphere and free space. My question is: how can I calculate the surface area of the sphere I am viewing in my FOV? I think this will be solved with a double integral of the form A = INTGRL INTGRL r^2 * sin(latitude) d(latitude) d(longitude) but I'm not sure what my limits of integration should be, especially because 1) the edges of my FOV aren't necessarily parallel to the longitude or latitude lines (though maybe it doesn't matter, as the sphere is symmetric) and 2) the FOV goes off the edge of the sphere and I don't know how to handle this. Or I could be going about this the completely wrong way, lol. Can anyone help? Or think of some references or key words I can search on? Thanks!