Fix AgX sigmoid contrast curve approximation

[allenwp]

• Fixes/improves Add AgX tonemapper option to Environment #87260.

Not cherry-pickable to 4.3, as AgX is only in 4.4.

This changes the polynomial function so that a lower input always results in a lower output and vice-versa. Additionally, the new function returns a value that is much closer to 1.0 when given an input of 1.0.

The polynomial regression for the AgX sigmoid contrast curve was my first attempt because I was rushed to get the change in before going on holiday. Upon review, I discovered a mistake that causes incorrect behavior in some cases.

Given:

x = agx_default_contrast_approx(a)
y = agx_default_contrast_approx(b)

For all values of a and b in the range [0.0, 1.0], x should always be less than y when a is less than b.

This is not the case with the current function in master for near-zero values. Additionally, when given an input of 1.0 the current function returns 1.00927498 when it should return 1.0.

After having more time to fiddle with polynomial regression calculators, I generated a new formula that fits the logical requirements of a tonemapper’s contrast function and gives an output of 1.0001 when given an input of 1.0.

This new function reduces banding in the transition from green to white in the Compatibility renderer:

master	this PR

[Calinou]

Tested locally, it works as expected.

This only results in a very slight visual difference, so nothing should require manual adjustments from users:

master	This PR

Remember to update tonemap_inc.glsl for Compatibility too.

[allenwp]

Thanks! I've pushed the updates to the Compatibility renderer and have finished reviewing my Forward+ test images to ensure there are no unexpected changes. I see that it's already been moved to "ready for review" and approved. Thanks! I'm happy my hastily put together first attempt at an approximation isn't going to stick around for any length of time 🙂

[akien-mga]

Thanks!