# What is the term for the projection of a vector onto the unit cube?

Normalizing a vector sets its magnitude to $1$ and retains its direction. In three dimensions, it projects the vector onto the unit sphere.

Is there a term associated with projecting it onto the unit cube (where at least one coordinate is equal to 1), or clamping to the unit cube?

-
"where at least one coordinate is equal to 1" - it's still a normalization, but with respect to the max-norm instead of the Euclidean norm... –  Guess who it is. Oct 10 '11 at 12:41
Or put J.M.'s comment in geometric terms, the unit ball with respect to max norm is the unit cube geometrically. –  user13838 Oct 10 '11 at 14:28
@J.M.: You could post that as an answer. –  joriki Oct 10 '11 at 15:18

"Normalization" is actually quite a general term. The one you're accustomed to is the normalization $\dfrac{\mathbf v}{\|\mathbf v\|_2}$, where $\|\mathbf v\|_2=\sqrt{v_1^2+\cdots+v_n^2}$ is the Euclidean norm. What you want to do corresponds to the normalization $\dfrac{\mathbf v}{\|\mathbf v\|_\infty}$, where $\|\mathbf v\|_\infty=\max(|v_1|,\cdots,|v_n|)$ is the Chebyshev (max) norm.