TITLE: What is the term for the projection of a vector onto the unit cube?
QUESTION [5 upvotes]: 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?

REPLY [8 votes]: "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.