In a BRDF $f_r$, assume Cook-Torrance model, we have a microfacets distribution $D$. This microfecets distribution essentially models the rougheness of the material as far as I've understood. Given a direction $v$ it models the amount of microfacets having that orientation.

Now say we have a material, for each point $p$ in theory we have a 3D function that tell us the orientation in a given direction.

This explantion (not detailed) makes sense to me, however when I read about the roughness map what I see is that it's a kind of texture where each pixel has values between 0 and 1 (from black to white) I do struggle to understand the relationship between this map and the microfacets distribution.

Could anyone clarify?

In a BRDF $f_r$, assume Cook-Torrance model, we have a microfacets distribution $D$. This distribution essentially models the rougheness of the material as far as I've understood. Given a direction $v$ it models the amount of microfacets having that orientation.

Now say we have a material, for each point $p$ in theory we have a 3D function that tell us the orientation in a given direction.

This explantion (not detailed) makes sense to me, however when I read about the roughness map what I see is that it's a kind of texture where each pixel has values between 0 and 1 (from black to white) I do struggle to understand the relationship between this map and the microfacets distribution.

Could anyone clarify?