[yt-dev] Orientation vectors

[Nathan Goldbaum]

Hi John,

If you mean a reference to a paper or something like that, no. Given a 
normal vector, it first generates an east vector by taking the cross 
product between the normal vector and the axis vector that makes the 
largest angle with the normal vector.  It then generates a north vector 
by taking the cross product between the east vector and north vector.  
Since there are an infinite number of possible bases given a single 
normal vector, I decided to choose the preferred basis based on the 
orientation of the simulation box.

This isn't necessarily the cleanest approach and it may very well be 
that there are better solutions.

Cheers,

-Nathan

On 8/23/12 12:50 AM, John ZuHone wrote:
> Hi Nathan,
>
> Do you have a reference for the calculation of the north and east vectors?
>
> John
>
> On Aug 22, 2012, at 11:21 AM, Nathan Goldbaum wrote:
>
>> Hey John,
>>
>> I think the issue is that yt uses a left-handed coordinate system internally.  This particular choice makes it so that if you create a volume rendering, off axis slice plot, or off axis projection it is oriented in the same way as a regular slice or projection.  Of course if you don't like that convention you can always specify a north_vector.
>>
>> If you want to transform to your sky coordinate frame you will need to come up with a more general transformation matrix rather than multiplying by x, y, and z scalars (i.e. a diagonal transformation matrix).  Fortunately the orientation class already does the hard work for you, I think all you need to do is multiply the (x,y,z) vector by the orientation.unit_vectors matrix (maybe orientation.inv_matrix, sorry, this 3D geometry stuff always confuses me ;)
>>
>> Hope that helps.
>>
>> Nathan
>>
>> On 8/22/12 10:23 PM, John ZuHone wrote:
>>> Hi all, and specifically to those of you with experience with the Orientation vectors...
>>>
>>> Doing some testing, I set up an orienter like this:
>>>
>>> orient = Orientation([0.0,0.0,1.0])
>>>
>>> and the output of orient.unit_vectors is:
>>>
>>> [array([ 0., -1.,  0.]), array([ 1.,  0., -0.]), array([ 0.,  0.,  1.])]
>>>
>>> which I would have expected
>>>
>>> [array([ 1., 0.,  0.]), array([ 0.,  1., 0.]), array([ 0.,  0.,  1.])]
>>>
>>> although I know I could fix this by specifying a north_vector, why would the latter not be the default?
>>>
>>> I'm asking because I was attempting to set up new coordinates like so:
>>>
>>> orient = Orientation(L)
>>>
>>> x_hat = orient.unit_vectors[0]
>>> y_hat = orient.unit_vectors[1]
>>> z_hat = orient.unit_vectors[2]
>>>          xsky = x*x_hat[0] + y*x_hat[1] + z*x_hat[2]
>>> ysky = x*y_hat[0] + y*y_hat[1] + z*y_hat[2]
>>> zsky = x*z_hat[0] + y*z_hat[1] + z*z_hat[2]
>>>
>>> but this will rotate the x,y plane by 90 degrees.
>>>
>>> Best,
>>>
>>> John
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