Summary
I'm trying to apply an offset map (elevation map) to a fairly simple object (hexagonal plane), and I get unexpected results. I use shades of gray and as such, I was impressed that my height map should only affect the Z values โโof my grid. However, the displacement map that I created stretches the grid through the X and Y planes. Also, it looks like I did not use the UV mapping that was created for all the other textures.
Model and UV Card
Here are the reference images of my hexagonal grid and its corresponding UV map in Blender.

Diffuse and offset textures
These are the textures of the diffuse and offset maps, which I apply to my grid through Three.JS.

Visualizes
When I draw a plane without a displacement map, you can see that the hexagonal plane remains inside the lines. However, when I add a displacement map, it clearly affects the positions of the X and Y vertices, and does not affect only Z, expanding the plane well along the lines.

code
Here is the corresponding .ru code:
Hypotheses
I am currently juggling in three ways why this might go wrong:
- The UV map does not apply to my displacement map.
- I did the wrong displacement map.
- I missed an important step in this process that would only block the offset Z.
And, of course, the secret option number 4, which is none of the above, and I just really don't know what I'm doing. Or any mixture of the above.
Living example
You can view a live example here .
If anyone with more knowledge on this subject can guide me, I would be very grateful!
Change 1 . As suggested, I commented on computeFaceNormals() and computeVertexNormals() . Although this made a slight improvement, the mesh is still deformed.