Notation used in this site.

R - set of real number

RxR - Descates's product of R and R

RxRxR - Descartes's product of R and R and R

N- normal at object's surface

index - index of refraction at P

index1 - also index of refraction at P

index2 - another index of refraction at P

index3 -and another index of refraction at P

Perlin's functions:

noise1: RxRxR -> R

noise3: RxRxR -> RxRxR

turbylency1: RxRxR -> R

turbylency3: RxRxR -> RxRxR

bias(g,t): RxR->R; pow( t, log( g ) / log( 0.5 ) )