I have assumed the orientation implicit in my drawing of a 0-1-2 coordinate
system:
2
|
|
|______1
/
/
0
So I am covered in the three-dimensional case but not in higher dimensions
where
I have not specified an orientation. (In fact I did not consider orientation
explicitly, I provided the drawing to make clear what I meant by the "lower
left
rear" corner of a box.)
I suppose an orientation in three dimensions is fundamentally a circular
ordering of the standard unit vectors 1 0 0 and 0 1 0 and 0 0 1. The circular
ordering I have chosen is their order as rows in the identity matrix
1 0 0
0 1 0
0 0 1
where it is understood that 0 0 1 is between 0 1 0 and 1 0 0.
For n dimensions the orientation I choose is the circular order of the standard
unit vectors as rows in the n by n identity matrix, it being understood that
the
last row is between the next to last row and the first row.
Thank you for pointing out this issue.
Raul Miller wrote:
> On Sun, Apr 4, 2010 at 6:30 PM, Kip Murray <[email protected]> wrote:
>> A "located vector" is represented by a table a ,: h in which vector a gives
>> the
>> location of the vector's tail, and vector h contains the components, thus
>> providing the direction and length of the located vector. The located vector
>> goes from location a (the tail) to location a+h (the head).
>
> Note that you have provided one axis and have not defined
> how to determine the orientation of the cube about that axis.
>
> How do you avoid issues from spinning cubes?
>
> (P.S. when I started this thread, I was treating the issue
> of locating the points as a solved problem -- I was concerned
> with the topology of tracing the edges of the faces. It is
> ok to go back to issues of where the points are located,
> but I would prefer if assumptions like orientation were
> not assumptions but were explicitly stated.)
>
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