UmbralRaptop changed the topic of #principia to: READ THE FAQ: http://goo.gl/gMZF9H; The current version is Διόφαντος. We currently target 1.3.1, and 1.4.x. <scott_manley> anyone that doubts the wisdom of retrograde bop needs to get the hell out | https://xkcd.com/323/ | <egg> calculating the influence of lamont on Pluto is a bit silly…
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<novasilisko>
tri-axial ellipsoids!
<novasilisko>
if that got your attention, you might be able to help me stop losing my mind
* UmbralRaptor
hands novasilisko a deVaucaleurs distribution
<novasilisko>
aaahhhhhh
<novasilisko>
i'm scared of all this now after the past two days
<novasilisko>
i have one problem
<novasilisko>
okay, i have a ton of problems
<novasilisko>
but the one right now is one that sounds simple but is making me catch on fire
<novasilisko>
i would like to find the nearest point on an ellipsoid to another arbitrary point outside it
<novasilisko>
these points can be assumed to be in the same coordinate space
<novasilisko>
(i'm not a complete maniac)
<UmbralRaptor>
But you don't have conversion formulae between the weird elliptic coordinates and rectangular, it something?
<novasilisko>
i'm pretty much just dealing with cartesian right now
<novasilisko>
the things i've found seem to fall into two main categories - iterative approaches, and "PDFs consisting entirely of walls of formulae"
<novasilisko>
i will have to ask you all to forgive me for my ignorance across the board here, i have a really hard time translating between human language, mathematical language, and programming languages
<novasilisko>
anyway yeah... i'm looking for cartesian to cartesian with whatever unholy conversions in between may be required
<novasilisko>
@egg are you perchance hatched at the moment?
<UmbralRaptor>
There's a real risk that he's asleep right now.
<novasilisko>
just when i decide to put faith in the sleep tags to inform me of status
* UmbralRaptor
meows at egg
<novasilisko>
a meowing raptor
<novasilisko>
i thought i'd seen it all
<UmbralRaptor>
<_<
<novasilisko>
[jeff goldblum angst]
<novasilisko>
my current solution to my problem is iterative, basically just taking an equivalently shaped mesh and working through it to find the triangle with the normal closest to the desired direction, then using that to define a plane, and sampling the nearest point on that plane
<novasilisko>
which feels insane for such a relatively straightforward seeming geometric shape as an ellipsoid
<novasilisko>
(and is obviously lumpy)
* UmbralRaptor
is vaguely worried that it might end up being like the Kepler equation.
<novasilisko>
that was a fun one to realize a few months ago
<novasilisko>
maybe i'll have to try in here at a slightly more active time of day/night
<novasilisko>
when all the geometric people are awake
<novasilisko>
going to be out of here for a bit, i designate @GregroxMun as my official poker when someone turns up with some help
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<GregroxMun>
but wait I didn't consent to this
<UmbralRaptor>
Well, there's always Twitter
<UmbralRaptor>
blarg, still not entirely clear on the problem
<novasilisko>
for a given ellipsoid of 3 axes, i am trying to find the position at the cross, based on the position at the circle
<novasilisko>
basically a point on the surface of the ellipsoid, perpendicular to its surface normal
<novasilisko>
@egg i'm the here
<novasilisko>
[montage of us missing each other being around for 4 days]
<UmbralRaptor>
egg:
<egg>
novasilisko: meow?
<egg>
novasilisko: you were in kspacademia but i missed you
<novasilisko>
i thought i was in here?
<novasilisko>
or is that the joke name for this place
<novasilisko>
this is the first time i've done IRC possibly since last year
<egg>
oh wait no I'm stupid
<egg>
I misread the channel name
<egg>
this one is usually quiet, so since there was a conversation I assumed it was #kspacademia
<egg>
novasilisko: yeah there's definitely a non-iterative solution
<novasilisko>
well, i appear to have managed to start one here at least
<egg>
novasilisko: but not at half past three in the morning
<egg>
geometry ceases to work properly that late at night
<egg>
novasilisko: but it's a classic, it's geoid height or something
<egg>
this stuff comes up all the time with geodesy
<egg>
(and the mix of the two kinds of latitudes is infinitely confusing)
<novasilisko>
what i have to work with is an ellipsoid defined by 3 dimensions (right now it's X/Y/Z dimensions, but that's easy to reconfigure to be whatever), and a point
<novasilisko>
if i have to make some infernal ellipsoidal lat-long conversion, so be it
<egg>
oh great, it's not a revolution ellipsoid, so you get funky longitudes as well as funky latitudes
<novasilisko>
ssssssorry?
<novasilisko>
(that was an apology sorry not a confusion sorry)
<egg>
haha
<egg>
novasilisko: I'll look into that when i have time and it's not that late
<novasilisko>
alright
<egg>
if I derive something at this hour every other sign will be wrong
<novasilisko>
i mean, i could always just flip them around randomly until it works
<egg>
it's probably too annoying for that to be viable
<egg>
stochastic geometry
<novasilisko>
at this rate i'll take anything, iterating through a few thousand triangles is not exactly the speediest way to do this
<novasilisko>
supposedly there isn't a non-iterative solution but i haven't really found much in the way of explanation
<egg>
I mean, it's obvious that there is a non-iterative solution from the kind of problem this is
<egg>
but I would need to get out of bed and wake up
<novasilisko>
i worry that some of the things i'm looking at are finding like... the intersection point of the ellipsoid's surface, on a line going from the center of it to the test position
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<novasilisko>
@egg @UmbralRaptor i return
<UmbralRaptor>
s/@//g
<Qboid>
UmbralRaptor meant to say: eg: 12:19:59 <egg> (obviously if you have very large masses but keep having small masses your problem is that, rather than inherent scale)
<UmbralRaptor>
no, Qboid
<novasilisko>
so, regarding ellipsoids again
<novasilisko>
i'd settle for a simpler iterative solution than what I have now
<novasilisko>
right now i'm treating the thing like a mesh and checking every vertex or triangle
<novasilisko>
if there's some sort of approach that, say, gets more accurate the more steps you run, like kepler's equation, that would still be so much better
<novasilisko>
(or whatever the kepler problem was formally called)
<egg>
novasilisko: tbh I don't think coming up with an iterative solution would be simpler than just solving it, I just need to get around to it
<novasilisko>
an answer i got elsewhere, btw: "All solutions will involve some kind of approximation, since the core of the problem results in a big nasty high degree polynomial, which must be solved iteratively."
<egg>
huh, is it high degree? Ꙩ_ꙩ
<egg>
cc bofh^28
<novasilisko>
i have two documents on this if you didn't see them