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I have an old collection of materials that are represented by diffuse, bump and specular maps. Like this. With Principled shader, where should I plug in the specular map? In the previous version, I used to use it as a mix factor between diffuse and glossy shaders, and it was fine.

In Principled shader, I tried to use it in roughness or specular. Inverted or not. Anyway, it does not look right.

What should I do with materials that provide separate maps for "reflectivity", "specularity" and "glossiness" and recommend to use them all?

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There isn't an exact answer to this. In older-style shaders it was typical to independently control specular intensity and specular size(also called hardness or glossiness and other names). This isn't how real-world surfaces actually work though. The reflectivity of a real surface is determined by the refractive index of the surface, and the roughness of microscopic imperfections in the surface.

The principled BSDF mimics this with a "specular" control that adjusts index of refraction (IOR) within a narrow range (specular=0 is IOR=1, specular=1 is IOR=1.8). Then there is a roughness control which controls the imperfections of the surface. The result of this is that "specular" controls intensity of reflections and how quickly they fade when viewed straight-on, and "roughness" controls the intensity of reflections and the blurryness of reflections. (worth mentioning here that "specular highlights" are nothing more than reflections of light sources).

So, what do we do with specular, gloss, and reflection maps?

Gloss/specular-size is easy. Plug it into roughness. You may need to invert it. But otherwise, it should pretty much work.

Reflection and Specular: You may not even need them. Both of these map types were just used to deal with reflections not being dependent on roughness, or handling lamp speculars being calculated separately from reflections.* Since this stuff is all handled in the "physically correct" way based on roughness, these maps are essentially unnecessary. They were to compensate for a missing feature which is no longer missing (fading reflections based on roughness).

With that said, you might find putting one of them (try each one!) on the "specular" input gives better results. It's all trial and error. There isn't really any convention for traditional specular materials the way PBR materials have, so those textures really only have a "correct" setup in the software+shader they were originally authored for. So just poke and prod with different inputs to see what looks good. Hopefully the info in this answer is enough to get you started.

*Fun fact: in realtime PBR shaders reflections and spec are still calculated as separate elements. They're just controlled together by roughness and merged under the hood!

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