Constant-time energy-normalization for the Phong specular BRDFs

摘要

The Phong and Modified Phong specular BRDFs, although of limited physical basis, are nevertheless some of the simplest BRDFs exhibiting glossy and specular qualities to understand and to implement, making them useful for validation and teaching. Unfortunately, although it is well-known how to make these BRDFsconserveenergy (that is, never gain energy), making them energy-normalized(that is, never lose nor gain energy) is far more difficult. Lesser-known algorithms exist, but require the specular exponentnto be integer-valued, and haveO(n) runtime cost. We express these algorithms as mathematical formulae and generalize to the real-valued specular exponent case. We then simplify and optimize to finally attain an algorithm that isO(1). Energy normalization makes the Phong BRDFs more physically plausible and therefore both more practically and theoretically useful-and our improvements allow for this energy normalization to be done efficiently and without arbitrary limitations.