This is the same algorithm (and code) as for the torus. The continuation is limited to the inside of a box, so you only see the yellow spheres until they cross that. The polyhedra around the spheres are more visible. They're used to find the boundary of the union of spherical balls.

This is an animation of an algorithm for covering a torus with the projection of disks tangent to the surface. Red is the boundary, and the yellow contribute to the boundary. Blue ones are interior.

Each step picks a point on the boundary for a new disk. The boundary is a simple list.