Given the latitude and longitude of a prior planetary rotation axis (or pole), and given a set of latitude and longitude points defining a number of features on the surface of the planet, determine the latitude and longitude points describing the location of the features in the prior rotational regime.
I know. Someone’s already solved this problem. His name was Euler, and he did it in a more general case. So much more general, that all of the descriptions I can find of his solutions are a little opaque.
I’m now able to successfully discriminate plausible NSR fits by:
calculating several “good” fits, that is, any local minimum in the fit curve that is within 10% of the overall curve’s amplitude, of the minimum fit.
screening these good fits based on whether or not endpoint doppelgangers generated at those amounts of backrotation are with in an MHD of less than 0.1*lin.length() of lin.
This screening process:
almost always results in a unique best fit
screens out many bad fits (because even at their minima, they can’t create synthetic lineaments)
very occasionally permits more than one fit to be included as good enough
I think it’s good enough to be able to avoid doing the monte carlo thing for now.
I looked at several bands of lineament length, especially the short ones, to see if there were perhaps a trend toward noise in the shorter lineaments, which is what I would expect, given how easy it is for them to fit somewhere in backrotational space. But it turned out that they still display approximately the same aggregate fit curve and activity histogram:
It would be good to create a map of the lineaments, color coded by where their good fits occur, and compare that to the map of resolution and illumination angle that I got from Trent, just to see if there’s any kind of correlation.
Now I need to transform the lineaments into the paleo-orientation suggested by Schenk and Nimmo, and re-run the analysis, to see if magically, that shell orientation gives a more convincing story.