Quote - Math node or no math node, putting the displaced part of the map is always going to create a step when butted up to a mesh that doens't have one.

No. If you had read the several threads I linked to you would see my exact demonstration that the it is possible for a displacement to have no actual movement from the original position, which would make it possible to match an undisplaced surface.

What I think you're laboring under is:

1. We say .5 but we don't mean it. We mean 128/255 or 127/255, neither of which is precisely .5, which is halfway between those two. If you want to match the neutral displacement field value exactly with zero movement, you have to look at what that value is, and use the exact number that represents that color. 127/255 is 0.49803921568. 128/255 is 0.50196078431. In one of the linked threads, a person had posted a displacement map with the neutral field color at 149, so his neutral offset should have been 0.58431372549.

or

2. You have render gamma turned on and you forgot to set the displacement map gamma to 1. If you leave the default it will be applying gamma to the map and shifting the neutral field value down to 0.21951971807, creating a very obvious step when you misinterpret that as .5. Set the image gamma on all maps to 1 except for actual color maps.

I really think you should read the threads I linked to. All of the questions or confusions brought up in this thread were explictly addressed in them. You either didn't read them, or you read them too fast to notice they were talking to you.

Note: The last point should be this - if the edge of the displacement-affected area is not set to your neutral field value, then you will have a step there. You can't match up multiple, different edge values - they can't all be 0. Only one value becomes 0. If that's what you meant (that a uniform, zero displacement can't exist at the edge unless all the edge values are the same), well that's true.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)