A furnace render: an albedo-1 sphere inside a uniform environment of radiance 0.5.

There’s a sphere in that picture. Can you see it? No, you can’t. If you could, my renderer would be wrong, and I wouldn’t like that.

What is the furnace test?

Put a sphere of albedo 1 (a surface that absorbs nothing) inside an environment of radiance

L L in every direction. Every camera ray either misses the sphere or hits it.

P P : a miss reads L L . It escapes straight to the environment.

Q Q : a hit bounces until it misses, so it reads L L too. It keeps everything on the way, 1 × L = L 1 \times L = L .

R R : the square is flat grey. Every pixel reads L L , so the sphere has no edge.

P ∧ Q ⇒ R P \wedge Q \Rightarrow R

Two camera rays in the furnace. One misses the sphere and reads the environment, L. The other hits the sphere, keeps all of its energy, bounces, and escapes to the same environment: 1 × L = L. Both pixels read L, so the sphere has no edge.

The test runs it backwards.…