# Crate rgb_derivation[−][src]

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.

# Example

```type Scalar = num::BigRational;
type Chromaticity = rgb_derivation::Chromaticity<Scalar>;

fn scalar(numer: i64, denom: i64) -> num::BigRational {
num::BigRational::new(numer.into(), denom.into())
}

fn chromaticity(x: (i64, i64), y: (i64, i64)) -> Chromaticity {
Chromaticity::new(scalar(x.0, x.1), scalar(y.0, y.1)).unwrap()
}

let white_xy = chromaticity((31, 100), (33, 100));
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);

assert_eq!([scalar(31, 33), scalar(1, 1), scalar(12, 11)], white_xyz);
assert_eq!([
[scalar(1088, 2739), scalar(17, 83), scalar(17, 913)],
[scalar(  30,   83), scalar(60, 83), scalar(10,  83)],
[scalar(  15,   83), scalar( 6, 83), scalar(79,  83)]
], primaries_xyz);
assert_eq!([
[scalar(1088, 2739), scalar(30, 83), scalar(15, 83)],
[scalar(  17,   83), scalar(60, 83), scalar( 6, 83)],
[scalar(  17,  913), scalar(10, 83), scalar(79, 83)]
], matrix);
assert_eq!([
[scalar( 286,  85), scalar(-407,  255), scalar(-44,  85)],
[scalar(-863, 900), scalar(5011, 2700), scalar( 37, 900)],
[scalar(   1,  18), scalar( -11,   54), scalar( 19,  18)]
], inverse);```

(Note: if you need matrices for the sRGB colour space, the `srgb` crate provides them along with gamma functions needed to properly handle sRGB)

## Modules

 matrix Functions for calculating RGB↔XYZ conversion matrices and performing basic matrix manipulation.

## Structs

 Chromaticity A colour chromaticity represented as `(x, y)` coordinates.

## Enums

 Error Possible errors which can occur when performing calculations.