The topic of the day is ... How do you define the 'center' of a group of
atoms?
Maybe it isn't that interesting, and it probably isn't that critical, but
the subject has come up in passing several times and we need to get it
resolved.
This is the default center that is used when the molecule is first
displayed. It is also important because it has a direct impact on the
scaling that is used to map from Angstroms to screen coordinates. (Once
the center is chosen, the distance to the outermost point determines the
scale ... we want that point to fit on the screen.)
We are going to talk about different ways to define it. And I am
interested in knowing which of these should be used and under what
circumstances.
I can think of 4 ways to do it ... maybe there are others.
1. Minimal Enclosing Sphere
2. Center of the bounding box (aligned with euclidean axes)
3. Center of Mass/Gravity
4. Average location (Unweighted center of gravity)
1. Minimal Enclosing Sphere
---------------------------
Calculate the smallest sphere that could contain all of the atoms
option a - use the center point of each atom
option b - use the outer edge of each atom at 100% vdw radius
The center of that sphere is the center of the group of atoms.
Advantage:
* Maximizes the screen real estate. That is, we can then adjust the
scaling so that the molecule can be the largest possible size, yet
still fit within the screen boundaries, regardless of the orientation.
Disadvantage:
* difficult to calculate
Center of the bounding box
--------------------------
Find the minimum and maximum points along the x, y, and z axes:
option a - use the center point of each atom
option b - use the outer edge of each atom at 100% vdw radius
The center of that box is the center of the group of atoms.
Advantages:
* Easy to calculate.
* This is the way that Jmol works today.
* Probably RasMol/Chime do it this way too.
* Does a pretty good job of maximizing screen real estate.
* When the user turns on the bounding box, it is centered
Center of Mass/Gravity
----------------------
This is a physics/engineering problem. Multiply weights by distances.
Find the point that would balance the entire structure.
Advantages:
* Easy to calculate.
* Models Newtonian Physics that people are familiar with:
- If you built a physical model and could balance it
on or suspend it from a single point,
then this would be your center.
- If you wanted to find the axis that minimizes
angular momentum, it would pass through this point.
Average Location/Unweighted Center of Gravity
---------------------------------------------
Take all the points, add them together, divide by the number of points.
This would give you the same result as the 'Center of Mass' *if* you
gave all the atoms the same mass. Hence 'Unweighted Center of Gravity'
Advantage:
* Easy to calculate.
In my discussions with Richard Ball about crystals, he has mentioned
'unweighted center of gravity' several times. I was, frankly, a little
surprised by this. Because of the 4, that one makes the least sense to
me. But since he brought it up I assume that it must be popular in
crystallography.
[Currently, I am using the center of the bounding box (in fractional
coordinates) to decide whether or not the asymmetric unit needs to be
translated into the unitcell cage.]
Thoughts and comments appreciated.
Miguel
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