An idea for a manually ray-traced, reflective sphere:
Step 1: A large sphere made of small facets – the pole to the right would have a laser-pointer attached at the top as the “light source”
Step 2: The laser traces four lines, one from the source to each of the corners – the points that they meet the floor are noted
Step 3: The resulting square is the shadow cast by that facet; the process is repeated for each facet
Step 4: A mirror is affixed to the facet and the laser is pointed at the center, reflecting out into the room
Step 5: The spot that the reflected laser beam hits is photographed, printed, and affixed to the facet on the sphere; this process is repeated for each facet