Continued fractions, diophantine approximations, and design of color transforms
Yuriy A. Reznik · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2008
We study a problem of approximate computation of color transforms (with real and possibly irrational factors) using integer arithmetics. We show that precision of such computations can be significantly improved if we allow input or output variables to be scaled by some constant. The problem of finding such a constant turns out to be related to the classic Diophantine approximation problem. We use this relation to explain how best scaled approximations can be derived, and provide several examples of using this technique for design of color transforms.