Posted 05 April 2013 - 08:57 PM

Fresnel doesn't add or remove energy, it simply controls the ratio of refraction to reflection.

Though when considering opaque materials, the refracted part is typically considered absorbed (and is, to a first order approximation). The BRDF doesn't have to sum up to exactly 1 over the hemisphere, it just can't sum up to more than 1 (or less than zero, obviously). The Fresnel equations are already normalized as Chris_F notes, being physically based and all, so you don't need to worry about it.

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

- *Pessimal Algorithms and Simplexity Analysis*