RGB colour system derivation routines

Functions for deriving RGB→XYZ and XYZ→RGB conversion matrices for given RGB colour system (such as sRGB colour space). The calculations are performed from the definition of such system provided in the form of chromacities of the reference white point and the red, green and blue primaries. Alternatively, constructions from XYZ coordinates of primaries is also available.

The crate supports arithmetic with rational and big integer types such that the calculations can be performed without any loss of precision if desired. So long as a type implements the four basic arithmetic operations, it can be used with this library. For example, f32, num::Rational64 and num::BigRational can all be used.

Usage

Using this package with Cargo projects is as simple as adding a single dependency:

[dependencies]
rgb_derivation = "0.1"

With that dependency in place, it’s now simple to write an application which converts an sRGB colour into other colour spaces:

type Scalar = num::rational::Ratio<i128>;
type Chromaticity = rgb_derivation::Chromaticity<Scalar>;

fn chromaticity(x: (i128, i128), y: (i128, i128)) -> Chromaticity {
    Chromaticity::new(Scalar::new(x.0, x.1), Scalar::new(y.0, y.1)).unwrap()
}

fn print_vector(header: &str, vector: &[Scalar; 3]) {
    print!("{}: [", header);
    for (idx, value) in vector.iter().enumerate() {
        print!("{} {} / {}",
               if idx == 0 { "" } else { "," },
               value.numer(), value.denom());
    }
    println!(" ]");
}

fn print_matrix(header: &str, matrix: &[[Scalar; 3]; 3]) {
    static OPEN: [char; 3] = ['⎡', '⎢', '⎣'];
    static CLOSE: [char; 3] = ['⎤', '⎥', '⎦'];

    fn make_array<T>(f: impl Fn(usize) -> T) -> [T; 3] { [f(0), f(1), f(2)] }

    let formatted = make_array(|row| make_array(|col| {
        let value = &matrix[row][col];
        (format!("{}", value.numer()), format!("{}", value.denom()))
    }));
    let lengths = make_array(|col| (
        formatted.iter().map(|row| row[col].0.len()).max().unwrap(),
        formatted.iter().map(|row| row[col].1.len()).max().unwrap(),
    ));

    let indent = header.chars().count();
    for (idx, row) in formatted.iter().enumerate() {
        if idx == 1 {
            print!("{}: {}", header, OPEN[idx]);
        } else {
            print!("{:indent$}  {}", "", OPEN[idx], indent = indent);
        }
        for (idx, value) in row.iter().enumerate() {
            print!("{comma} {numer:>numer_len$} / {denom:>denom_len$}",
                   comma = if idx == 0 { "" } else { "," },
                   numer = value.0, numer_len = lengths[idx].0,
                   denom = value.1, denom_len = lengths[idx].1);
        }
        println!(" {}", CLOSE[idx]);
    }
}

fn main() {
    let white_xy = chromaticity((312713, 1000000), (329016, 1000000));
    let primaries_xy = [
        chromaticity((64, 100), (33, 100)),
        chromaticity((30, 100), (60, 100)),
        chromaticity((15, 100), (6, 100)),
    ];

    let white_xyz = white_xy.to_xyz();
    let matrix = rgb_derivation::matrix::calculate(
        &white_xyz, &primaries_xy).unwrap();
    let inverse = rgb_derivation::matrix::inversed_copy(&matrix).unwrap();
    let primaries_xyz = rgb_derivation::matrix::transposed_copy(&matrix);

    print_vector("sRGB white point (D65)", &white_xyz);
    print_matrix("sRGB primaries", &primaries_xyz);
    print_matrix("sRGB→XYZ", &matrix);
    print_matrix("XYZ→sRGB", &inverse);
}