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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
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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
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@J.M.: You could post that as an answer. –  joriki Oct 10 '11 at 15:18
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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.

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en.wikipedia.org/wiki/Lp_space ... cool stuff –  Steven Lu Feb 22 at 16:08
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