> From: Kip Murray
>
> Raul, Oleg, and Andrew
...
> I would like for you to subject your solutions to one more test: try them on
> the
> box with diagonal 4 3 0 ,: _4 _3 _2 . This moves the previous example
> 0 0 0 ,: 4 3 2 down two units, so the top face of the new example is in the xy
> plane, and the bottom face is two units below the xy plane. Do your verbs give
> correct results for this new example?
cr=:(<./ ,:>./)&.(+/\)
faces=:[: ,/ ((({:@[ * -...@]) ,:"1~ {...@[ ,: {...@[ + {:@[ * ])"2 1
=...@i.@{:@$)
cr 4 3 0 ,: _4 _3 _2
0 0 _2
4 3 2
<"2 faces cr 4 3 0 ,: _4 _3 _2
┌──────┬──────┬──────┬──────┬──────┬─────┐
│0 0 _2│4 0 _2│0 0 _2│0 3 _2│0 0 _2│0 0 0│
│0 3 2│0 3 2│4 0 2│4 0 2│4 3 0│4 3 0│
└──────┴──────┴──────┴──────┴──────┴─────┘
<"2 faces 4 3 0 ,: _4 _3 _2
┌───────┬───────┬───────┬───────┬───────┬────────┐
│4 3 0│0 3 0│ 4 3 0│ 4 0 0│ 4 3 0│ 4 3 _2│
│0 _3 _2│0 _3 _2│_4 0 _2│_4 0 _2│_4 _3 0│_4 _3 0│
└───────┴───────┴───────┴───────┴───────┴────────┘
faces gives normalized (canonic) faces on normlized input and non-normalized
(but still valid) faces on non-normalized input.
I briefly considered rewriting the verb so it returns all set of k-faces of
arbitrary n-dimensional cube. It adds complexity quite a bit.
What are your use cases? Are higher dimensions interesting, or is it just 3?
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