Optimised Hue shift function in GLSL

Webgl shader Hue Shift function

vec3 hueShift( vec3 color, float hueAdjust ){

    const vec3  kRGBToYPrime = vec3 (0.299, 0.587, 0.114);
    const vec3  kRGBToI      = vec3 (0.596, -0.275, -0.321);
    const vec3  kRGBToQ      = vec3 (0.212, -0.523, 0.311);

    const vec3  kYIQToR     = vec3 (1.0, 0.956, 0.621);
    const vec3  kYIQToG     = vec3 (1.0, -0.272, -0.647);
    const vec3  kYIQToB     = vec3 (1.0, -1.107, 1.704);

    float   YPrime  = dot (color, kRGBToYPrime);
    float   I       = dot (color, kRGBToI);
    float   Q       = dot (color, kRGBToQ);
    float   hue     = atan (Q, I);
    float   chroma  = sqrt (I * I + Q * Q);

    hue += hueAdjust;

    Q = chroma * sin (hue);
    I = chroma * cos (hue);

    vec3    yIQ   = vec3 (YPrime, I, Q);

    return vec3( dot (yIQ, kYIQToR), dot (yIQ, kYIQToG), dot (yIQ, kYIQToB) );

}

@viruseg Indeed, it is a more elegant solution, and simple to convert to GLSL, thanks.

vec3 hueShift(vec3 color, float hue) {
    const vec3 k = vec3(0.57735, 0.57735, 0.57735);
    float cosAngle = cos(hue);
    return vec3(color * cosAngle + cross(k, color) * sin(hue) + k * dot(k, color) * (1.0 - cosAngle));
}

There was a typo, this one works for me:

vec3 hueShift(vec3 color, float hue)
{
const vec3 k = vec3(0.57735, 0.57735, 0.57735);
float cosAngle = cos(hue);
return vec3(color * cosAngle + cross(k, color) * sin(hue) + k * dot(k, color) * (1.0 - cosAngle));
}

Does anyone know where the 0.57735 come from?

@RichardBray it's sqrt(3)/3 or 1/sqrt(3). It's one of those values that you see often in trigonometry, see e.g. http://mathforum.org/dr.math/faq/formulas/faq.trig.html (Not super often though; I had to do some digging to find this one too 😅). Not sure how to arrive at this formula from scratch though. 😕

Ah: https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

@janpaul123 Thanks that makes more sense. But yeah I still can't figure out how that formula was reached.

Thank you so much for this! Contrary to what you seem to think though, your original function produces much more natural looking/beautiful results than the cheaper hueshift function provided by @viruseg. Of course it depends on context whether or not that's needed, but I for one deeply appreciate it!
EDIT but, I believe this is a faster implementation ->

vec2 rotate2(vec2 v, float fi) {
return v*mat2(cos(fi), -sin(fi), sin(fi), cos(fi));
}

// YIQ color rotation/hue shift
vec3 hueShiftYIQ(vec3 rgb, float hs) {
float rotAngle = hs*-6.28318530718;
const mat3 rgb2yiq = mat3(0.299, 0.596, 0.211,
0.587, -0.274, -0.523,
0.114, -0.322, 0.312);
const mat3 yiq2rgb = mat3(1, 1, 1,
0.956, -0.272, -1.106,
0.621, -0.647, 1.703);
vec3 yiq = rgb2yiq * rgb;
yiq.yz *= rot(rotAngle);
return yiq2rgb * yiq;
}

Thank you so much for this! Contrary to what you seem to think though, your original function produces much more natural looking/beautiful results than the cheaper hueshift function provided by @viruseg.

I had the same conclusion. The idea to use Rodrigues rotation formula is clever, but the problem is that the RGB to YIQ translation isn't a pure rotation. It also has skew and scaling components. So the output won't be the same.

The most compact version I could come up with, with some symbolic manipulation (along the same lines as Rodrigues' but replacing the cross product), that should be equivalent, is:

vec3 hue_shift(vec3 color, float dhue) {
	float s = sin(dhue);
	float c = cos(dhue);
	return (color * c) + (color * s) * mat3(
		vec3(0.167444, 0.329213, -0.496657),
		vec3(-0.327948, 0.035669, 0.292279),
		vec3(1.250268, -1.047561, -0.202707)
	) + dot(vec3(0.299, 0.587, 0.114), color) * (1.0 - c);
}

(Godot shader, but should be compatible to GLSL)