egg|nomz|egg changed the topic of #kspacademia to: https://gist.github.com/pdn4kd/164b9b85435d87afbec0c3a7e69d3e6d | Dogs are cats. Spiders are cat interferometers. | Космизм сегодня! | Document well, for tomorrow you may get mauled by a ネコバス. | <UmbralRaptor> egg|nomz|egg: generally if your eyes are dewing over, that's not the weather. | <ferram4> I shall beat my problems to death with an engineer.
<B787_300>
is our egg out in the field with his scope?
<oeuf>
nah
<oeuf>
i'm zzz
<B787_300>
ah
<UmbralRaptop>
œuf IRCs a lot in his sleep.
<oeuf>
yes
<oeuf>
that's how sleep works, right?
<B787_300>
i IRCed from bed last night becasue i thought i could fall asleep during the election
<awang>
There's an arc with a tangent line attached to one end
<awang>
At B
<awang>
And a line AD connecting a point on the arc with a point on the tangent line
<awang>
C is located at the midpoint of AD
<awang>
I'm wondering if there is an analytical solution for the length of little r given theta such that B is between AD, the radius of the arc, and the length of AD
<awang>
Please excuse any notational faux pas; it's been a while
<awang>
I should also probably note that theta is the angle between CO and the positive x-axis
<UmbralRaptop>
I suspect so, especially if you extend the arc to be a circle, so some subset of AD is a secant.
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<awang>
Would that produce useful information, though?
<awang>
You know the angle to CO, but not AO
<SnoopJeDi>
how is the position of A determined, then?
<SnoopJeDi>
there should be an analytical solution though, this is "just" trig, which of course means it's a nightmare to properly label the givens :)
<awang>
AD has to be a straight line, AD is some length $g$ and C is the midpoint of AD
<awang>
So the position of A is "whatever fits those constraints"
<awang>
It seems somewhat underspecified to me, but I'm hoping that you guys are more clever than I am
<SnoopJeDi>
yea I'm having trouble putting the quantities in the right order, but knowing that L(AD) is constrained is definitely a useful additional piece of information.
<SnoopJeDi>
awang, the way to proceed with these IME is usually to walk through the construction and handle each quantity in turn. It sounds like you start with (ρ, ℓ) and construct OB, then the tangent to the circle, but I'm a little murky about the order of operations here...
<awang>
OB is the radius of the circle
<awang>
B is just the point that you transition from arc to line
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<SnoopJeDi>
sure I get that, but it seems like A is constructed in terms of some other quantity (conventional naming seems to be "construction order")
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<awang>
Oh, do the point names actually give that information?
<awang>
Oops
<awang>
Ignore those then
<awang>
I just wanted labels to be able to refer to specific points
<awang>
I didn't realize that they were supposed to give some indication as to how to approach a problem
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<SnoopJeDi>
uhh I'm not sure if that's an actual convention so don't read too much into it
<SnoopJeDi>
I tend to do things that way just because when I move from [thing] to [thing+1], I advance the letter by one :P
<SnoopJeDi>
awang, okay so suppose I've never seen that image and want to construct exactly that figure. What's the order of operations?
<awang>
SnoopJeDi: Sorry, coworker came in to ask a question
<awang>
The way I drew it:
<awang>
1. Draw the x-axis
<awang>
2. Draw an arc starting at the negative x-axis and proceeding in the clockwise direction
<awang>
3. Mark the end point of the arc "B"
<awang>
4. Draw the tangent line to the arc at "B" starting at "B" and extending away from the arc
<awang>
5. Draw the arc radius BO
<awang>
6. Pick a point on the arc to the left of "B" and call that point "A"
<SnoopJeDi>
pick it how
<awang>
I just picked it arbitrarily
<SnoopJeDi>
Δθ, Δx, Δs from B, etc?
<awang>
I guess that's part of the issue then
<SnoopJeDi>
you'll likely need to express A in terms of *something*, yes
<awang>
I can describe how to draw the diagram showing what quantity I want to solve for, but that would just show relative positions
<SnoopJeDi>
Δθ seems geometrically natural since it's an arc, but Δs might be more useful for the context ("A is the point [some length] back along the arc from B")
<awang>
I can't describe exactly how to pick A, C, or D. I only know L(AD) and that L(AC) = L(CD)
<awang>
And that B is "between" A and D for some nebulous definition of "between"
<awang>
I don't know the distance L(AB) or L(BD) ahead of time
<SnoopJeDi>
can you say a little more about what this is for?
<SnoopJeDi>
I mean the knee-jerk reaction is "okay, pick some quantities in terms of which to base the (arbitrary) definition of A, D relative to B"
<SnoopJeDi>
and then proceed with that construction, which will lead you to the expression of r
<SnoopJeDi>
but you can't really define the distance to the midpoint of the chord until the chord is defined :P
<SnoopJeDi>
err, not define, calculate*
<awang>
Let me think about how to describe the actual problem in a sufficiently vague way
<awang>
I mean, I do know the distance to the midpoint of the chord?
<awang>
I know the chord length
<SnoopJeDi>
that's what you called g, right?
<awang>
Yeah
<SnoopJeDi>
okay, that takes care of one of those degrees of freedom I believe
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<SnoopJeDi>
so defining either A or D is sufficient: the "other point" is the intersection of the circle with radius g at that point and the tangent line (if you choose A), or the arc (if you choose D)
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<awang>
Hrm
<awang>
OK, here's my attempt at explaining the problem
<awang>
I need to measure the shape of a pipe, including its bends
<awang>
The tool I use has some length, and contacts the pipe at each end
<awang>
Shaped sort of like a dumbbell
<awang>
The location measurement unit is at the center of that dumbbell
<awang>
So it won't give the precise center location of the pipe around bends
<awang>
I want to write a tool that will compensate for that difference
<awang>
The geometry problem is based on the point where one end of the tool is in a pipe bend, but the other end is not
<SnoopJeDi>
AD is the pipe?
<awang>
A and D are two points on the pipe
<awang>
AD represents the tool
<awang>
The arc + tangent represents the pipe
<SnoopJeDi>
ah so the arc is the pipe itself?
<awang>
Yep
<awang>
Well, technically part of it, but yes
<SnoopJeDi>
yea
<SnoopJeDi>
is it correct then to say that D is defined as "where the bend starts?"
<awang>
No, that's B
<awang>
Scratch that
<SnoopJeDi>
oh, right
<awang>
Wait, no, that's right
<awang>
B is where the bend starts
<SnoopJeDi>
I'd say you probably want to choose either ∠AB or s_AB as the other parameter, then
<SnoopJeDi>
describing how far you've advanced the tool past the start of the bend
<awang>
Part of the problem may be the way I'm formulating this
<awang>
I chose to make this a function of theta because that makes the difference between the true pipe location and the measured pipe location easy
<awang>
Pick a theta and subtract the calculated radii
<awang>
It makes it more difficult for me to know how far along I've traveled along the bend though
<SnoopJeDi>
yea, it seems more natural in terms of tooling to express θ in terms of the locations of A, D and the length g
<SnoopJeDi>
uh, assuming A/D are what you can physically reference against
<SnoopJeDi>
what's the measurement tool at C? A probe that gives you a physical offset from AD to the pipe OD?
<SnoopJeDi>
(so that the distance to the pipe is r+δ?)
<awang>
Unfortunately I don't have the precise locations of A/D
<awang>
C is a IMU
<awang>
So I get location relative to a known starting point
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<SnoopJeDi>
oh, so C's position is an actual datum
<SnoopJeDi>
and you're relying on the contact points (rings?) at A/D to tie that to the pipe?
<awang>
Yep
<SnoopJeDi>
(my labmate does a lot of bends, but kinda the inverse problem)
<awang>
Inverse problem?
<SnoopJeDi>
he's making bends
<awang>
Ah, instead of measuring them
<SnoopJeDi>
so his shape is all determined by his bending and drawing tools
<SnoopJeDi>
I mean he does post-process measurement too, but it's mostly on the front-end
<awang>
Hmm
<SnoopJeDi>
okay so C is an IMU, which means you're *measuring* r (right?), and trying to get...what quantity? ρ?
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<awang>
Well, technically I'm not measuring r directly
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<SnoopJeDi>
you're getting the coordinates of C relative to some datum?
<awang>
Yeah
<SnoopJeDi>
"r is a given" is what I meant, sorry
<SnoopJeDi>
which begs the question of what measurement C is acting as a proxy for
<awang>
I wanted to frame it in terms of (theta, r) because that seemed like it'd make defining a function giving the difference between "true" pipe location and IMU location in terms of theta easy
<awang>
Ideally, C would indicate the "true" pipe location
<SnoopJeDi>
location = geometrical middle of the pipe, yea?
<awang>
Technically, yes
<SnoopJeDi>
I assume your rings take care of "is this ovalled at all"
<SnoopJeDi>
and moreover that this is reasonably planar so you don't have to get elevation involved :P
<SnoopJeDi>
okay, so ρ as a function of θ in terms of a measured r? is that right?
<awang>
bofh: Something to do with that /r/sysadmin post about helium leakage during a MRI magnet ramp-up killing all Apple devices in the hospital?
<bofh>
yes.
<bofh>
I'm amazed these MEMS oscillators break *that badly* in a He atmosphere.
<bofh>
I initially was skeptical b/c it couldn't fuck them up permanently, that seems like an absurd design flaw.
<bofh>
but no, it seems they actually did release a component that can be completely messed up using small quantities of H/He.
<SnoopJeDi>
I haven't poked closely at it but I think adsorption → detuning
<SnoopJeDi>
which is sensible since helium is one adsorption-y boi
<SnoopJeDi>
awang, I assumed what looks like a P was actually ρ, but I mean the radius of the bend as a function of where you are in the bend
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<awang>
SnoopJeDi: I don't think I had a P anywhere?
<awang>
That may be a very poorly written R
<awang>
But yeah, measured radius as a function of location in the bend
<SnoopJeDi>
there's one each along the x-axis, OA, and OB, but R makes sense. They're all ρ anyway ;P
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<awang>
Yeah, those should be R. My bad on the handwriting
<SnoopJeDi>
No worries. Anyway, that's the quantity you're indirectly measuring to determine the pipe geometry?
<awang>
Yeah
<awang>
Little r on the diagram
<awang>
Erm
<awang>
I guess I'll just go with yes
<bofh>
wtf, I bought some Neapolitan cookies from The Numerically Stable Linear Algebra And Cookies Company (Lefèvre Utile/LU) and cat seemed to think my hand was food afterwards and grabbed it (mercifully mostly w/o claws) before deciding it didn't actually want to put it in its mouth).
<bofh>
<shrug>
<awang>
Technically I still need a coordinate transform to go from (x, y, z) to (theta, r), but I'm leaving that as an exercise to the user :P
<SnoopJeDi>
bofh, LMAO
<UmbralRaptop>
bofh: I have multiple questions
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<SnoopJeDi>
o.O a bot from Italian Wikipedia just decided to welcome me (I have not ever edited anything off en.wikipedia.org)
<SnoopJeDi>
((if only there were a shorter form of "not ever" 🤔))
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<oeuf>
bofh: ask whitequark for interpretatino
<oeuf>
s/ino/ion
<Qboid>
oeuf meant to say: bofh: ask whitequark for interpretation
<oeuf>
maybe the cat wanted to play
<oeuf>
maybe the cat saw that you're a moth
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<UmbralRaptop>
I still have questions about the company name.
<SnoopJeDi>
UmbralRaptop, LU decompositions \o/
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