1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210

//!This module provides simple matrix operations on 3x3 matrix to aid in chromatic adaptation and
//!conversion calculations.

use float::Float;

use core::marker::PhantomData;

use {Component, Xyz};
use white_point::WhitePoint;
use rgb::{Primaries, Rgb, RgbSpace};
use encoding::Linear;
use convert::IntoColor;

///A 9 element array representing a 3x3 matrix
pub type Mat3<T> = [T; 9];

///Multiply the 3x3 matrix with the XYZ color
pub fn multiply_xyz<Swp: WhitePoint, Dwp: WhitePoint, T: Component + Float>(
    c: &Mat3<T>,
    f: &Xyz<Swp, T>,
) -> Xyz<Dwp, T> {
    Xyz {
        x: (c[0] * f.x) + (c[1] * f.y) + (c[2] * f.z),
        y: (c[3] * f.x) + (c[4] * f.y) + (c[5] * f.z),
        z: (c[6] * f.x) + (c[7] * f.y) + (c[8] * f.z),
        white_point: PhantomData,
    }
}
///Multiply the 3x3 matrix with the XYZ color into RGB color
pub fn multiply_xyz_to_rgb<S: RgbSpace, T: Component + Float>(
    c: &Mat3<T>,
    f: &Xyz<S::WhitePoint, T>,
) -> Rgb<Linear<S>, T> {
    Rgb {
        red: (c[0] * f.x) + (c[1] * f.y) + (c[2] * f.z),
        green: (c[3] * f.x) + (c[4] * f.y) + (c[5] * f.z),
        blue: (c[6] * f.x) + (c[7] * f.y) + (c[8] * f.z),
        standard: PhantomData,
    }
}
///Multiply the 3x3 matrix with the  RGB into XYZ color
pub fn multiply_rgb_to_xyz<S: RgbSpace, T: Component + Float>(
    c: &Mat3<T>,
    f: &Rgb<Linear<S>, T>,
) -> Xyz<S::WhitePoint, T> {
    Xyz {
        x: (c[0] * f.red) + (c[1] * f.green) + (c[2] * f.blue),
        y: (c[3] * f.red) + (c[4] * f.green) + (c[5] * f.blue),
        z: (c[6] * f.red) + (c[7] * f.green) + (c[8] * f.blue),
        white_point: PhantomData,
    }
}

///Multiply a 3x3 matrix with another 3x3 matrix
pub fn multiply_3x3<T: Float>(c: &Mat3<T>, f: &Mat3<T>) -> Mat3<T> {
    let mut out = [T::zero(); 9];
    out[0] = c[0] * f[0] + c[1] * f[3] + c[2] * f[6];
    out[1] = c[0] * f[1] + c[1] * f[4] + c[2] * f[7];
    out[2] = c[0] * f[2] + c[1] * f[5] + c[2] * f[8];

    out[3] = c[3] * f[0] + c[4] * f[3] + c[5] * f[6];
    out[4] = c[3] * f[1] + c[4] * f[4] + c[5] * f[7];
    out[5] = c[3] * f[2] + c[4] * f[5] + c[5] * f[8];

    out[6] = c[6] * f[0] + c[7] * f[3] + c[8] * f[6];
    out[7] = c[6] * f[1] + c[7] * f[4] + c[8] * f[7];
    out[8] = c[6] * f[2] + c[7] * f[5] + c[8] * f[8];

    out
}

///Invert a 3x3 matrix and panic if matrix is not invertable.
pub fn matrix_inverse<T: Float>(a: &Mat3<T>) -> Mat3<T> {
    let d0 = a[4] * a[8] - a[5] * a[7];
    let d1 = a[3] * a[8] - a[5] * a[6];
    let d2 = a[3] * a[7] - a[4] * a[6];
    let det = a[0] * d0 - a[1] * d1 + a[2] * d2;
    if !det.is_normal() {
        panic!("The given matrix is not invertible")
    }
    let d3 = a[1] * a[8] - a[2] * a[7];
    let d4 = a[0] * a[8] - a[2] * a[6];
    let d5 = a[0] * a[7] - a[1] * a[6];
    let d6 = a[1] * a[5] - a[2] * a[4];
    let d7 = a[0] * a[5] - a[2] * a[3];
    let d8 = a[0] * a[4] - a[1] * a[3];

    [
        d0 / det,
        -d3 / det,
        d6 / det,
        -d1 / det,
        d4 / det,
        -d7 / det,
        d2 / det,
        -d5 / det,
        d8 / det,
    ]
}

///Geneartes to Srgb to Xyz transformation matrix for the given white point
pub fn rgb_to_xyz_matrix<S: RgbSpace, T: Component + Float>() -> Mat3<T> {
    let r: Xyz<S::WhitePoint, T> = S::Primaries::red().into_xyz();
    let g: Xyz<S::WhitePoint, T> = S::Primaries::green().into_xyz();
    let b: Xyz<S::WhitePoint, T> = S::Primaries::blue().into_xyz();

    let mut transform_matrix = mat3_from_primaries(r, g, b);

    let s_matrix: Rgb<Linear<S>, T> = multiply_xyz_to_rgb(
        &matrix_inverse(&transform_matrix),
        &S::WhitePoint::get_xyz(),
    );
    transform_matrix[0] = transform_matrix[0] * s_matrix.red;
    transform_matrix[1] = transform_matrix[1] * s_matrix.green;
    transform_matrix[2] = transform_matrix[2] * s_matrix.blue;
    transform_matrix[3] = transform_matrix[3] * s_matrix.red;
    transform_matrix[4] = transform_matrix[4] * s_matrix.green;
    transform_matrix[5] = transform_matrix[5] * s_matrix.blue;
    transform_matrix[6] = transform_matrix[6] * s_matrix.red;
    transform_matrix[7] = transform_matrix[7] * s_matrix.green;
    transform_matrix[8] = transform_matrix[8] * s_matrix.blue;

    transform_matrix
}

#[cfg_attr(rustfmt, rustfmt_skip)]
fn mat3_from_primaries<T: Component + Float, Wp: WhitePoint>(r: Xyz<Wp, T>, g: Xyz<Wp, T>, b: Xyz<Wp, T>) -> Mat3<T> {
    [
        r.x, g.x, b.x,
        r.y, g.y, b.y,
        r.z, g.z, b.z,
    ]
}

#[cfg(test)]
mod test {
    use Xyz;
    use rgb::Rgb;
    use encoding::{Linear, Srgb};
    use chromatic_adaptation::AdaptInto;
    use white_point::D50;
    use super::{matrix_inverse, multiply_xyz, rgb_to_xyz_matrix, multiply_3x3};

    #[test]
    fn matrix_multiply_3x3() {
        let inp1 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0, 2.0, 1.0, 3.0];
        let inp2 = [4.0, 5.0, 6.0, 6.0, 5.0, 4.0, 4.0, 6.0, 5.0];
        let expected = [28.0, 33.0, 29.0, 28.0, 31.0, 31.0, 26.0, 33.0, 31.0];

        let computed = multiply_3x3(&inp1, &inp2);
        assert_eq!(expected, computed)
    }

    #[test]
    fn matrix_multiply_xyz() {
        let inp1 = [0.1, 0.2, 0.3, 0.3, 0.2, 0.1, 0.2, 0.1, 0.3];
        let inp2 = Xyz::new(0.4, 0.6, 0.8);

        let expected = Xyz::new(0.4, 0.32, 0.38);

        let computed = multiply_xyz(&inp1, &inp2);
        assert_relative_eq!(expected, computed)
    }

    #[test]
    fn matrix_inverse_check_1() {
        let input: [f64; 9] = [3.0, 0.0, 2.0, 2.0, 0.0, -2.0, 0.0, 1.0, 1.0];

        let expected: [f64; 9] = [0.2, 0.2, 0.0, -0.2, 0.3, 1.0, 0.2, -0.3, 0.0];
        let computed = matrix_inverse(&input);
        assert_eq!(expected, computed);
    }
    #[test]
    fn matrix_inverse_check_2() {
        let input: [f64; 9] = [1.0, 0.0, 1.0, 0.0, 2.0, 1.0, 1.0, 1.0, 1.0];

        let expected: [f64; 9] = [-1.0, -1.0, 2.0, -1.0, 0.0, 1.0, 2.0, 1.0, -2.0];
        let computed = matrix_inverse(&input);
        assert_eq!(expected, computed);
    }
    #[test]
    #[should_panic]
    fn matrix_inverse_panic() {
        let input: [f64; 9] = [1.0, 0.0, 0.0, 2.0, 0.0, 0.0, -4.0, 6.0, 1.0];
        matrix_inverse(&input);
    }

    #[cfg_attr(rustfmt, rustfmt_skip)]
    #[test]
    fn d65_rgb_conversion_matrix() {
        let expected = [
            0.4124564, 0.3575761, 0.1804375,
            0.2126729, 0.7151522, 0.0721750,
            0.0193339, 0.1191920, 0.9503041
        ];
        let computed = rgb_to_xyz_matrix::<Srgb, f64>();
        for (e, c) in expected.iter().zip(computed.iter()) {
            assert_relative_eq!(e, c, epsilon = 0.000001)
        }
    }

    #[test]
    fn d65_to_d50() {
        let input: Rgb<Linear<Srgb>> = Rgb::new(1.0, 1.0, 1.0);
        let expected: Rgb<Linear<(Srgb, D50)>> = Rgb::new(1.0, 1.0, 1.0);

        let computed: Rgb<Linear<(Srgb, D50)>> = input.adapt_into();
        assert_relative_eq!(expected, computed, epsilon = 0.000001);
    }
}