Excellent. And easy extendable to higher dimensions: (3 : '(([:+/"(1) 0=]) </.]) 3 #.^:_1 i.3^y')4 +-------+-------+-------+-------+-------+ |0 0 0 0|0 0 0 1|0 0 1 1|0 1 1 1|1 1 1 1| | |0 0 0 2|0 0 1 2|0 1 1 2|1 1 1 2| | |0 0 1 0|0 0 2 1|0 1 2 1|1 1 2 1| | |0 0 2 0|0 0 2 2|0 1 2 2|1 1 2 2| | |0 1 0 0|0 1 0 1|0 2 1 1|1 2 1 1| | |0 2 0 0|0 1 0 2|0 2 1 2|1 2 1 2| | |1 0 0 0|0 1 1 0|0 2 2 1|1 2 2 1| | |2 0 0 0|0 1 2 0|0 2 2 2|1 2 2 2| | | |0 2 0 1|1 0 1 1|2 1 1 1| | | |0 2 0 2|1 0 1 2|2 1 1 2| | | |0 2 1 0|1 0 2 1|2 1 2 1| | | |0 2 2 0|1 0 2 2|2 1 2 2| | | |1 0 0 1|1 1 0 1|2 2 1 1| | | |1 0 0 2|1 1 0 2|2 2 1 2| | | |1 0 1 0|1 1 1 0|2 2 2 1| | | |1 0 2 0|1 1 2 0|2 2 2 2| | | |1 1 0 0|1 2 0 1| | | | |1 2 0 0|1 2 0 2| | | | |2 0 0 1|1 2 1 0| | | | |2 0 0 2|1 2 2 0| | | | |2 0 1 0|2 0 1 1| | | | |2 0 2 0|2 0 1 2| | | | |2 1 0 0|2 0 2 1| | | | |2 2 0 0|2 0 2 2| | | | | |2 1 0 1| | | | | |2 1 0 2| | | | | |2 1 1 0| | | | | |2 1 2 0| | | | | |2 2 0 1| | | | | |2 2 0 2| | | | | |2 2 1 0| | | | | |2 2 2 0| | +-------+-------+-------+-------+-------+
where each box contains the hyper planes of fixed dimension. R.E. Boss > -----Oorspronkelijk bericht----- > Van: [email protected] [mailto:programming- > [email protected]] Namens Bo Jacoby > Verzonden: vrijdag 2 april 2010 20:40 > Aan: Programming forum > Onderwerp: Re: [Jprogramming] cubes > > John's solution below may be modified. > > Let the eight corners be >:#:i.8 > 1 1 1 > 1 1 2 > 1 2 1 > 1 2 2 > 2 1 1 > 2 1 2 > 2 2 1 > 2 2 2 > > Use the zero as a wildcard character. So the twelve edges are > 0 1 1 > 0 1 2 > 0 2 1 > 0 2 2 > 1 0 1 > 1 0 2 > 1 1 0 > 1 2 0 > 2 0 1 > 2 0 2 > 2 1 0 > 2 2 0 > > and the six faces are > 0 0 1 > 0 0 2 > 0 1 0 > 0 2 0 > 1 0 0 > 2 0 0 > > and the cube itself is > 0 0 0 > > The twentyseven elements of the cube are coded by > 3 3 3 #: i.27 > 0 0 0 > 0 0 1 > 0 0 2 > 0 1 0 > 0 1 1 > 0 1 2 > 0 2 0 > 0 2 1 > 0 2 2 > 1 0 0 > 1 0 1 > 1 0 2 > 1 1 0 > 1 1 1 > 1 1 2 > 1 2 0 > 1 2 1 > 1 2 2 > 2 0 0 > 2 0 1 > 2 0 2 > 2 1 0 > 2 1 1 > 2 1 2 > 2 2 0 > 2 2 1 > 2 2 2 > > > --- Den fre 2/4/10 skrev John Randall <[email protected]>: > > Fra: John Randall <[email protected]> > Emne: Re: [Jprogramming] cubes > Til: "Programming forum" <[email protected]> > Dato: fredag 2. april 2010 16.59 > > Raul Miller wrote: > > I am looking for elegant ways of describing cubes in J. > > Here is an alternative system for cube coordinates. > > Label the points > > #: i. 8 > 0 0 0 > 0 0 1 > 0 1 0 > 0 1 1 > 1 0 0 > 1 0 1 > 1 1 0 > 1 1 1 > > Now a face is given by a set of points with 1 coordinate fixed, e.g. > > 0 0 0 > 0 0 1 > 1 0 0 > 1 0 1 > > and an edge is given by a set of points with 2 coordinates fixed, e.g. > > 1 0 0 > 1 0 1 > > This generalizes to higher dimensional cubes. > > Best wishes, > > John > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > > __________________________________________________ > Bruger du Yahoo!? > Er du træt af spam? Yahoo!Mail har den bedste spambeskyttelse, der findes > http://dk.mail.yahoo.com > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
