Introduction to UV Mapping - Part 2 Terminology

A point in space is defined by the set of coordinates x,y,z.  
x is left to right horizontal, y is up to down vertical, and z is foreground to background depth.
In Maya, x is red, y is green and z is blue.
Anytime we are talking about XYZ space, we are referring to 3D space.

A point in 3D or XYZ space

"UV" mapping refers to a separate, related set of coordinates where
 U is left to right horizontal and V is up to down vertical.
Whenever we talk about "UV's" and UV space we are always talking about flat, 2D space.

Look Ma, no blue! The humdrum 2D world of UV space as seen in the UV editor

NerdNote: You'll also hear UV space referred to as UVW space. Yes, there is a "W" coordinate equivalent to 3D "Z". For our introductory purposes, however, we should consider W as an unholy abomination against nature not to be spoken of in polite society.

Introduction to UV Mapping - Part 1

UV Mapping 101: Dang, Leatherface flattened out all that skin. Wrapping it around his head now requires unsightly seams!

How do you wrap a 2D image around a 3D object? It's a bit of a conundrum, and there's no perfect or easy way to do it (see Leatherface, above). It's more art than science, more ballet than ballistics, more Texas Chainsaw Massacre than . . . well, you get the picture. I've always been freaked out by the fact that there's no perfect way to translate the earth's surface to a 2D plane. Cartographers have been at it for ages. You either get distortion (Mercator's giant Greenland issue) or several discontinuous surfaces. In any event, you ALWAYS get a seam(s).

Aieee! Fair North America split in twain!!! The "orange slices" required to unwrap the globe using an "interrupted sinusoidal" projection. 

Fools! Greenland will destroy you all!!! - The polar aggrandizement of the Mercator projection.

So. . . covering 3D surfaces with 2D imagery is an imperfect business fraught with peril, but that's the fun of it. Take lots of deep breaths and romantic walks in the park, and you'll be fine.

UV Mapping Thursday

Not a catchy name, but here we are. Here is a .pdf file on UV mapping in Maya for you to cut your teeth on. It's Dio-intensive, so watch out.