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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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    @J.M.: You could post that as an answer.2011-10-10

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"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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    http://en.wikipedia.org/wiki/Lp_space ... cool stuff2014-02-22