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In one dimension a real number can be constrained by two real numbers x in [a,b] or (a,b). In n-dimensions an n-dimensional point can be constrained by an (open) or [closed] simplex with n+1 vertices. I imagine it would usually be more useful to use an n-dimensional ball or cuboid for higher-dimensional interval analysis rather than a simplex, but can you give examples of where a simplex-interval would be used.

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  • $\begingroup$ Not a research question. $\endgroup$
    – Igor Rivin
    Commented Sep 16, 2011 at 17:54

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A typical operation is an affine transformation. The set of simplices is preserved by this, the set of balls is not.

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