Model exporting

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No, I'm not talking about the stretching. I'm talking about the gap that randomly appears when I move my camera.

Gap? Oh you mean that upper element becoming see-through on one of the pictures? I didn't even notice that because I was so focussed on the textures ^^ That kinda looks to me like what happens if a model isn't properly triangulated. Maybe you shouldn't leave triangulating to the exporter but do it beforehand: select mesh in Maya, go to Mesh> Triangulate and see if that helps.

If that doesn't fix it, you can also make a mesh cleanup to see if you have non-manifold geometry (Edges with more than two adjacent Polygons and the like) or other nasty stuff in there: Go to Mesh> Cleanup and make sure you have "select matching polygons" checked, not "cleanup matching polygons" (Otherwise Maya will try to fix stuff on its own which might be desastrous!). Then check everything you want Maya to search for and apply. The tool will select everything that's odd, showing you errors in your mesh.

Another idea would be to check your normals. First, go to shading > Backface Culling, right above your viewport. See any holes in your mesh now? That's reversed normals. They can be flipped by selecting the affected polygons and clicking normals> reverse.