The cylindrical wrap treats the texture as if it were a piece of paper that is wrapped around a cylinder so that the left edge is joined to the right edge. The object is then placed in the middle of the cylinder and the texture is deformed inward onto the surface of the object.
For a cylindrical texture map, the effects of the various vectors are shown in the following illustration.
The direction vector specifies the axis of the cylinder, and the up vector specifies the point on the outside of the cylinder where u equals 0. To calculate the texture [u v] coordinates for a vector [x y z], the system uses the following equations:
Typically, u would be left unscaled and v would be scaled and translated so that the range of z maps to the range from 0 to 1 for v.