less random 3D point selection : use sphere of possibilities at attachment points

[jdkent]

@kellnett

The next solution could be using the current spine attachment points (which we have as 3D coordinates) as the origin of a sphere with a radius equal to the maximum spine length and generate a random 3D coordinate within that spherical volume for each attachment point along the dendrite.

This could possibly help control for any biological process that determines where the spines begin to form (since my data do show some degree of attachment point clustering)

[jdkent]

For this we are interested primarily in the spine attachments or where the spine heads are located?

[kellnett]

Well, both. We are still interested in clustering at the spine head (so in 3D), but when selecting random points it has to be a certain distance away from a known attachment point.

So, if observed spine 'A' has attachment point 'a', then using the maximum observed spine length, say of 2um, we 'make a circle' with a radius of 2um around point 'a'. Then constrain the selection of the random XYZ point to within circle 'a'. Then we would repeat for spine 'B' with attachment point 'b', etc. until we select a point for each observed spine.

Does that make more sense?

[kellnett]

We still sort of have the less clustering in 3D problem, but this does constrain it somewhat more than the cylinder.