Convert RGB Color Value to Spherical Coordinates

rgb2sph <- function(rgb, nbits)
{ 
    ## Purpose: Convert RGB Color Value to Spherical Coordinates
    ## Arguments:
    ##   rgb: a (N X 3) matrix of RGB values (each row is a triplet of R, G, B).
    ##          Assume each integer value range from 0 to (2^nbits - 1).
    ##   nbits: number of bits used to code each of R, G, B channel. 
    ## Return: a (N X 3) matrix of Shperical Coordinates (each row is a triplet of M, Theta, Phi), which are scaled to be within (0, 1).
    ## Author: Feiming Chen, Date:  5 Apr 2017, 10:21
    ## ________________________________________________
    
    max.scale <- 2^nbits
    M.scale <- sqrt(3 * max.scale^2)  
    angle.scale <- pi / 2

    t(apply(rgb + 1, 1, function(x) {
        M <- sqrt(sum(x^2))             # Color Intensity/Luminosity (0-1) 
        Theta <- atan(x[2] / x[1])      # Azimuthal Angle
        Phi <- acos(x[3] / M)           # Zenith Angle 
        c(M / M.scale, Theta / angle.scale, Phi / angle.scale)
    }))
}
if (F) {                                # Unit Test
    rgb <- matrix(c(0, 0, 0,  4095,4095,4095, 3527, 3513, 3504, 2470, 3034,3218), ncol=3, byrow = T)
    rgb2sph(rgb, nbits = 12)
##            [,1]    [,2]    [,3]
## [1,] 0.00024414 0.50000 0.60817
## [2,] 1.00000000 0.50000 0.60817
## [3,] 0.85832017 0.49873 0.60954
## [4,] 0.71428036 0.56498 0.56181
}