In working with textures, does "UVW mapping" mean the same thing as "UV mapping"?
If so why are there two terms, and what is the "W"?
If not, what's the difference between them?
[Wikipedia currently isn't illuminating on this question: http://en.wikipedia.org/wiki/Talk:UVW_mapping]
U and V are the coordinates for a 2D map. Adding the W component adds a third dimension.
It's tedious to say the least to actually hand generate a 3D texture map, but they are useful if you have a procedural way to generate texture data. E.g. if you wanted your object to look like it's a solid chunk of marble, it may be easiest to "model" the marble "texture" as a 3D procedural texture and then use 3D coordinates to draw data out of the procedural texture.
UVW is to XYZ as XYZ is to world coordinates. Since XYZ was already being used to refer to world coordinates, UV is used to refer to the X and Y (2D) coordinates of a flat map. By extrapolation, the W is the Z in XYZ.
UVW infers a more complex 2d representation which is, in effect, the skin of the object that has been 'unwrapped' from a 3d object. Imagine a box 'unwrapped'. You now have a flat UVW map that you can paint on to your hearts content and then wrap back onto the six-sided box with no distortion. In short the UVW map knows where to rewrap the x, y and z points to reform the box.
Now imagine a sphere 'unwrapped'. You might end up with something like a Mercator projection. The hitch is that with this problem, when you wrap this 2d representation back onto the sphere, you will get some distortion.
The term UV mapping is very commonly used. I don't hear the term UVW as often except as described above.
The term procedural mapping can be misleading. Simply put, it means the computer is following some algorithms to paint a realistic representation of a material, like wood, onto the object, giving you the impression that the grain travels completely through the wood so it can be seen properly on both sides of the object. Procedural mapping can use images or not, or a combination of approaches...it all depends on the 'procedure'.
Lastly, there is no requirement to transform a '3d procedural texture' to 'UVW' first, since UVW and XYZ mean effectively the same thing - they are either referring to the world, or an unwrapped image of on object in the world, or for that matter of a 'chunk' of the world, as in the sky. The point is that UV or UVW refers to image/texture mapping.