SmashMaster

/**
 * Projects a sphere with the given radius and distance onto a unit sphere at
 * the origin, creating a spherical cap. Returns the angular radius of the cap,
 * as well as its surface area as a fraction of the total solid angle.
 */
void sphereCap(float radius, float distance, out float angularRadius, out float solidAngleFrac) {
    float apparentRadius = radius/distance;
    angularRadius = asin(apparentRadius);
    solidAngleFrac = 0.5 - sqrt(1.0 - apparentRadius)*0.5;
}