In creating the texture map, rounding error will become a
significant problems when using an eight-bit rather than a twelve-bit texture
map. If an eight-bit texture map is used, then rounding errors are up to one
half of 1/256. In this case, rounding error may become detrimental if only few
hundred slices are used. But this problem become negligible when a twelve-bit
texture map is used and rounding error is reduced to one half of 1/4096.
Essentially, Gelder et al. construct a bounding cube built up by a stack of slices centered on the origin. The bounding cube is large enough to manipulate any rotation of an image inside the cube. Besides, the mapping from world space to texture space is linear, and therefore any rotation of it is also linear. Trilinear interpolation of linear functions can either precede or follow rotation. These good properties ensure that the image inside the volume is not deformed.