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Re: [Imgcif-l] Electron density map parameters

Herbert J. Bernstein wrote:
> How about
> 
>    _array_structure_list_axis.fract_grid_divisions
> 
> to specify the number of divisions into which the axis is
> intended to be divided?  Computationally this would simply
> imply the fract_displacement_increment as the reciprocal
> of fract_grid_divisions.
This sounds useful. One thing that can be confusing is the definition of 
the unit cell versus the definition of the map. This is a distinction 
that detectors don't have, but may be related to a multi-part detector 
(i.e. a quad CCD). Does this fit into the current scheme somehow?

I also considered the idea of using axis vectors, etc., to define a grid 
coordinate system, and then define axis.displacement in grid units. In 
this case, displacement_increment is always one. Would that work?

> 
> The "spec" does not say that "The map sampling is being done
> in the middle of each grid division".  That sentence is
> just an explanation of that particular example which has
> a value of 0.01 for _array_structure_list_axis.fract_displacement.
> You are free to pick any point in the cell to start placing
> your samples, but they have to be placed somewhere.  It is
> hard to contour a map when you are not sure where it is
> relative to the cell.
Oh, I see... the displacement indicates the offset to a sample point. In 
the above sentence, "grid division" is indicating the grid of source 
density, rather than the grid of sample points. So, it is a terminology 
issue. Does the imgCIF group use the term grid to refer to pixels, and 
not sample points?

> 
> Fractional coordinates are inherently dimensionless, but
> the system is, of course, based unit cell vectors.
> 
> The choice of symbolic symmetry ops versus matrices to give
> the symmetry of a map is up to the user, but it would seem more natural
> to use space group symbols or symbolic operations when working in 
> fractional coordinates, and to use matrices and vectors when working
> in orthogonal coordinates.
Fractional coordinates actually are a nice fit to matrices and vectors. 
Many crystallography programs store fractions symmetry operators a 
integer matrices and fractional vectors. The rotation is a simple matrix 
of -1,0,1, and the translation vector is in 1/24 fractional units. This 
makes it easy to represent any space group with no rounding errors. It 
also turns out to be fairly easy to parse standard symbolic operations 
into this integer form.

It is interesting to note that CCP4 maps include a spacegroup definition 
and also allow for an explicit symmetry operator list. The symm-op list 
used to be common, but is almost never used now. So, it is probably 
reasonable for electron density just to give a spacegroup name or number.

However, I am trying to think a bit more general. For example, there are 
some quasi-crystal materials that have a symmetric diffraction pattern. 
But, maybe something like this is to general for the current imgCIF plans.

> 
> At 11:09 PM -0500 2/26/07, Joe Krahn wrote:
>> A few comments on the work-in-progress for density (etc.) maps.
>>
>> The current spec says:
>> "The map sampling is being done in the middle of each grid division"
>>
>> This conflicts with Fourier maps, where values are on grid vertices,
>> rather than the pixel/voxel centers. The reason is that Fourier maps
>> represent point samples, rather than the integration of a pixel/voxel,
>> as it is in the case of most images. Rather than making density maps
>> special, maybe there should be a property that distinguishes between
>> point samples and integrated divisions. This sort of problem is common
>> in graphics rasterization, and imaging/graphics APIs often have
>> alternate origin choices.
>>
>> For grid divisions, maps have one of the following two representations,
>>from the examples:
>>          loop_
>>           _array_structure_list_axis.axis_id
>>           _array_structure_list_axis.fract_displacement
>>           _array_structure_list_axis.fract_displacement_increment
>>           CELL_A_AXIS 0.01 0.02
>>           CELL_B_AXIS 0.01 0.02
>>           CELL_C_AXIS 0.01 0.02
>>
>>
>>           loop_
>>           _array_structure_list_axis.axis_id
>>           _array_structure_list_axis.displacement
>>           _array_structure_list_axis.displacement_increment
>>           X 7.5e-8 1.5e-7
>>           Y 7.5e-8 1.5e-7
>>           Z 7.5e-8 1.5e-7
>>
>>
>> Both of these have the problem that the displacement increment can
>> produce cumulative rounding errors. It would be better to have a system
>> that better allows for an integer number of grid divisions per unit
>> cell. Detector images could benefit from this sometimes as well. One
>> possibility is to specify a displacement-maximum, instead of an
>> increment. Another possibility is to specify the inverse of the
>> fract_displacement parameters.
>>
>> In the case of fract_displacement, is it intended that _axis.vector[*]
>> be the unit-cell, rather than a dimensionless unit vector?
>>
>> Another thing important to electron density maps is symmetry operations,
>> which are already defined for structures in category _symmetry_equiv. It
>> might be useful to define symmetry with simply matrices/vectors instead.
>> Are there any ideas already being considered in this area?
>>
>> Joe Krahn
>> _______________________________________________
>> imgcif-l mailing list
>> imgcif-l@iucr.org
>> http://scripts.iucr.org/mailman/listinfo/imgcif-l
> 
> 

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