Yes, unfortunately the interpretation of these methods of continuous heterogeneity analysis are a bit hard to interpret! You are certainly not alone in being confused by them!
Unfortunately, directly comparing differences in the results of a 3DVA job across datasets is not really possible. There’s no guarantee that the same type of motion will be assigned to the same component. Put another way, in dataset A a certain type of movement might be component 0, but in dataset B that type of movement might be component 1 instead. You’ll have to manually inspect the components to see if there are any that correlate with each other.
As to how the trajectories are calculated, that has a more definitive answer. There are three different modes of 3DVA Display: Simple, Intermediate, and Cluster. There’s a lot of information on these modes in the guide pages for the 3DVA tutorial, but I’ll summarize for you here. If you’re not familiar with the inner workings of 3DVA, you may want to check out the paper describing the technique. I’ve also written a bit about the difference between 3DVA and 3D Flex in another forum post.
Simple
The Simple mode takes the difference volume for the component and scales it by the coordinate, then adds that to the consensus volume. So (-1, 0, 0) corresponds to subtracting the component zero difference volume from the consensus, while (50, 0, 0) corresponds to scaling the component zero difference volume by 50, then adding that to the consensus.
You’ve already noticed the tricky bit of this method: you’re not actually taking into account how many particles might be near the coordinate you make a reconstruction for! For instance, there might be very few particles anywhere near (-100, 0, 0). The simple mode calculates the volume anyway. This usually results in the most extreme frames of a simple display job being quite noisy.
Intermediate
In the intermediate mode, we choose several points along each component, like for Simple mode. However, this time, we perform reconstructions of actual particles, weighted by how close they are to those positions. You thus still get maps that are sampled along a single coordinate, but they take into account real particle images that have a value similar to that coordinate.
Note that they are not necessarily nearby — for instance, a particle at (0.5, 0, 0) and a particle at (0.5, 100, 100) would be used to create the “coordinate 0 == 0.5” map in Intermediate mode.
Cluster
In clustering mode, the particles are clustered, taking into account all of the coordinates at once. These clusters are then used to reconstruct maps. If there are distinct clusters, this can create very distinct classes. In a situation like yours, with a relatively spherical distribution of coordinates, it can still be helpful since it takes into account all of the coordinates at once, but you lose the nice sense of sequence (i.e., cluster 1 might be right next to cluster 9).
I hope that’s helpful @vincent! I’m happy to answer any more questions you might have, sorry it took me a little bit to understand what you were looking for!