PROJECTION MAPPING

 Planar/Flat

Planar/Flat [Multi]

Cubic [Box]

Cylindrical

Spherical

For projection mapping the texture is projected, like a photographic slide, onto the surface of the object. There are a number of options available to fit the basic shape of your object.

Planar or Flat Mapping
As the name might suggest this method applies the texture flat-on, to one of six sides. This means you can usefully apply a different texture to each of the sides. See Texturing Techniques 1.

Cubic or Box Mapping
This method projects the same image onto each face of a cube. The projected texture will stretch or shrink to fit each side of the box no matter what the proportions.

Cylindrical Mapping
With cylindrical mapping a flat image is wrapped around and projected onto virtual cylinder, like the label on tinned food. Each end of the cylinder will be highly stretched and pinched so if required the ends would have to be flat mapped using a circular mask.

Spherical Mapping
The spherical mapping option wraps the texture round the object like shrink wrap. However to get the image to fit results in the texture being pinched quite noticably at the poles. There are ways to reduce this though, see Texturing Techniques 3 and Texturing Techniques 4

UV MAPPING

UV or UVW

Parametric

UV or UVW Mapping
With UV mapping the texture image is actually pinned to points on the object. This means that if the object is warped the texture will be warped with it and there is no smearing of the texture. The UV are co-ordinates similar to  X and Y in 3D programs. The W co-ordinate, now available in some 3D applications, is the Z direction and means the texture fills the volume of an object [cut into it and the texture remains inside].
Parametric mapping applies a UV mapped texture to every side of an object. This is good for preventing smearing but you could have problems with the seams.