Ok, first off, Texturing preview is shown by hitting the 6 key! Kind of the difference between a grey box,and the actual texture.
Now, first off, I've set up a scene with 3 objects,with the same material,a checker board pattern (Part of Maya's default textures)
First off, here's the Sphere, pipe and cube with their default UV maps.
And here is the UV editor! Mainly this shows off how the Mesh you selected unwrapped, in order to show what part of the mesh looks like what (So projection). You can edit the points manually, by moving the mesh in the UV editor mode as a whole, moving face by face, edge by edge etc.
Firstly, there's three wrapping methods, Planar(Which is firing the texture onto the mesh from one angle)
Cylinder which attempts to fire the texture on a curve, But any adjacent faces will stretch out.
And Sphere is like Cylinder,but, it fires from all angles from the center point.
Here we have A sphere with Cylinder wrapping, as you see the tips don't properly scale,so you have triangle tips.
Here's the sphere projection, which as you can see, the texture is pointing tot he center of the mesh
Next is the flat projection, which fires the texture onto the mesh from the front of it, and essentially carries the texture all the way into the back, like a lazer of sorts.
Here's the flat projection on the cube... As you can see, squares on the front, lines on the sides.
(Note, Cylinder is like a vertical planar, but the top is textureless)
And finally, the sphere projection on the cube, and as you can see, it doesn't really translate well...It's trying to translate well, but it's just... Not hitting the right notes.,It's trying to project evenly,but the mesh...Isn't having it.
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