Comment by periodontal

While theoretically possible, it'll be very difficult to realize physically. If you allow fractal constructions, purely unrectifiable sets can fit the bill. For example, here's an example in 2-dimensional space that casts a solid shadow when the light source is along one axis but not from any other: https://books.google.com/books?id=usjNBQAAQBAJ&lpg=PP1&dq=&p...