What is the effect on the plane equation of projecting a plane onto the surface of a sphere.
Assume we are starting with the standard point-normal plane equation:
$$ax + by + cz + d = 0$$
or alternatively:
$$\hat{n}x + d = 0$$
where $\hat{n}$ is the plane normal, $x$ is a point on the plane, and $d$ is the distance from the origin.
Mathematically, how does one project this plane onto a sphere?