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# Minimal AgX Implementation

By Benjamin Wrensch

Summary: Contains a minimal implementation of Troy Sobotka's AgX display transform, which is easy to drop into any existing codebase - especially for testing purposes.

While working on the following more extensive blog post on color grading and while building a shadertoy in this context, I thought it would be nice to have a minimal version of Troy Sobotka's AgX  display transform that is easy to drop into any existing codebase - especially for testing purposes.

AgX's picture formation process works by applying the following steps:

• A matrix transformation on the input data (inset)
• An encoding to log2 space followed by the application of a sigmoid curve
• An optional ASC-CDL-based look transform; I've included the default looks "Golden" and "Punchy"
• The inverse of the input matrix transform (outset) followed by the fitting EOTF

The OCIO reference implementation of AgX uses a lookup table for the sigmoid curve, which is backed by a relatively complex tunable function. I replaced the lookup table and function with a simple polynomial approximation to limit the code footprint to a minimum.

The following graphic shows a comparison between the approximation and the reference.

Close enough, in my opinion, with a mean squared error of roughly 3.6705141e-06. If you want to get even closer, I've added a 7th-order variant with an MSE of around 1.85907662e-06 to the appendix of this post.

You can grab the whole source of the implementation from the following shadertoy :

The code is also available in the appendix of this post - easy to understand and integrate.

Enjoy!

## Appendix

### AgX Minimal Source

``````// 0: Default, 1: Golden, 2: Punchy
#define AGX_LOOK 0

// Mean error^2: 3.6705141e-06
vec3 agxDefaultContrastApprox(vec3 x) {
vec3 x2 = x * x;
vec3 x4 = x2 * x2;

return + 15.5     * x4 * x2
- 40.14    * x4 * x
+ 31.96    * x4
- 6.868    * x2 * x
+ 0.4298   * x2
+ 0.1191   * x
- 0.00232;
}

vec3 agx(vec3 val) {
const mat3 agx_mat = mat3(
0.842479062253094, 0.0423282422610123, 0.0423756549057051,
0.0784335999999992,  0.878468636469772,  0.0784336,
0.0792237451477643, 0.0791661274605434, 0.879142973793104);

const float min_ev = -12.47393f;
const float max_ev = 4.026069f;

// Input transform (inset)
val = agx_mat * val;

// Log2 space encoding
val = clamp(log2(val), min_ev, max_ev);
val = (val - min_ev) / (max_ev - min_ev);

// Apply sigmoid function approximation
val = agxDefaultContrastApprox(val);

return val;
}

vec3 agxEotf(vec3 val) {
const mat3 agx_mat_inv = mat3(
1.19687900512017, -0.0528968517574562, -0.0529716355144438,
-0.0980208811401368, 1.15190312990417, -0.0980434501171241,
-0.0990297440797205, -0.0989611768448433, 1.15107367264116);

// Inverse input transform (outset)
val = agx_mat_inv * val;

// sRGB IEC 61966-2-1 2.2 Exponent Reference EOTF Display
val = pow(val, vec3(2.2));

return val;
}

vec3 agxLook(vec3 val) {
const vec3 lw = vec3(0.2126, 0.7152, 0.0722);
float luma = dot(val, lw);

// Default
vec3 offset = vec3(0.0);
vec3 slope = vec3(1.0);
vec3 power = vec3(1.0);
float sat = 1.0;

#if AGX_LOOK == 1
// Golden
slope = vec3(1.0, 0.9, 0.5);
power = vec3(0.8);
sat = 0.8;
#elif AGX_LOOK == 2
// Punchy
slope = vec3(1.0);
power = vec3(1.35, 1.35, 1.35);
sat = 1.4;
#endif

// ASC CDL
val = pow(val * slope + offset, power);
return luma + sat * (val - luma);
}

// Sample usage
void main(/*...*/) {
// ...
value = agx(value);
value = agxLook(value); // Optional
value = agxEotf(value);
// ...
}``````

### 7th Order Polynomial Approximation

``````// Mean error^2: 1.85907662e-06
vec3 agxDefaultContrastApprox(vec3 x) {
vec3 x2 = x * x;
vec3 x4 = x2 * x2;
vec3 x6 = x4 * x2;

return - 17.86     * x6 * x
+ 78.01     * x6
- 126.7     * x4 * x
+ 92.06     * x4
- 28.72     * x2 * x
+ 4.361     * x2
- 0.1718    * x
+ 0.002857;
}``````

## Changelog

• No changes (yet)

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