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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?

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"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... – J. M. 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
up vote 7 down vote accepted

"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.

share|cite|improve this answer ... cool stuff – Steven Lu Feb 22 '14 at 16:08

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