Inversions, insides, atomics, oh my!

arashi- what would the specific section of math that would deal with this topic.. differential geometry? I mean.. I know it can easily be represented graphically, but deals with motion.. He didnt have much time after class to talk with me, but we're going to schedule a time to sit talk more about it later next week... Math is so specialized now that I need something specific to look for lest I do a door to door thing.. and so far the few people I've talked to weren't really sure what to classify it under... apart from my phil of math teacher, it seemed to take a while to explain to people that what I had wasn't a phyics problem... LOL... They dont' seem to understand that I'm more interested in gemoetrical shapes, and not necessarily just objects in motion... I mean the static shape is the product that I can trace out with my poi..

so yeah.. any idea on what area in particular to look at?

i dunno, i got as far as trig and calc II and said I'M OUTTA HERE and set up a cozy couch in the art department and now 8 years later i can barely add. there may be some exact spherical equations which follow these same principles and they may be calculus oriented? but that's a guess, i was content to find an explanation for the spatial orientations.

If you're going for what I want in "Poi Math", you're trying to define your own algebra where the function space takes into account the full range of poi motion around a human body. Your goal is to get to something like "3*f(x) + 2" where f(x) is a forward butterfly, '2' shows that you added two 90 degree rotations in the positive direction and "3*" makes it the '6-beat' version or something. Then you can move on to adding more symbols for other moves or transitions.(absolute value, exponents, derivatives, logarithms, etc) and their relations to each other. This also allows you to express full movements or just 'core' move formulas that can be added onto. For example "3*f(x) +2 -2 +2" equals (in a math sense) the same thing as the first function, but shows how you can add infinite variation internally and transform one type of move to another one step at a time. And that's only for symmetrical moves.. basically, it also shows that a move's equasion doesn't equal 0 if it doesn't start and end in the same place.

The hard part is coming up with the basic operations. They have to work such that something similar to the above type of cancellations can be performed, allowing equasions to be 'simplified' into more basic forms that have less terms or transformed into terms relative to another type of related move. It would be nice to have simple maths for this that are already well understood, but I don't think it's going to magically appear anytime soon. Any solution for realistically modeling poi+body movement should have no problem modelling the poi part, but will make it impossibly hard to get all the possible collisions that a real person can put a body holding poi through. Can you make a math system that describes all posible dance moves in any style? What about one that takes into account the specific muscle tension of each person's body to show that, for example, it's physically possible to spin perfectly upside down or have head-center isolation moves, they're not going to be any easier for you to do once you see them. If all you get new from this are moves that are impossible to actually do, what's the point?

To do it using established maths, you need multi-dimensional topography, Rev. And maybe some 'minimal surfaces' stuff. The way >3 dimensions in topography works is by compressing the 'parameter space' (where each variable is another dimension) which will be able to tell you which types of transitions require more or less effort (either complexity or physical force, or however you set up your 'hill climbing' function). Defining what variables to use and how they should interact is equivalent to the above solution, though, using a new algebra. I don't think you're going to get much from the base math that you don't already know in another form, but if it helps you to empty your preconceptions to come at it bottom up from a new direction, more power to ya.

The best I see anyone getting out of this direction with current technology is a system that will let you visualize poi moves if you already know the math and/or can show the computer the move. It would help out with finding minimal transitions or transitions that involve certain parameters. It'll make for the neatest ever screensavers, but I don't think it will be able to push the level of the art any further than a person can themselves with --- more practice.

-- dut

ok..
when I talked to the math chair, he gave me a list of names..
I did a demonstration for the department head in math and the chair.. and expalined what I was looking for.. now I have an appointment with a guy whose focus is called braid theory..

I heard about the topography thing from like several people outside math, but everyone in math disagrees.

basically differential geometry will do a number of the features that I need, however I know nothing about braid theory.. I never got above diff eq.. and that was back in highschool.. whihc was a WHILE back..

I had a number of the department intrigued when I started explaining my theory of poi.. so I have a few other professors that want to talk to me after I've worked out my current problems.. LOL...

dut- my goal is to learn about the functions, their derivatives and integrals, and the way they act in relation to other variations.. What ways I can alter it and what its limits are.. not much information really... I have to be honest and say that my creativity is kinda bogged at the moment.. its like working a problem but not being able to see your mistake.. I just want to know more about the structure I'm working with... I already kinda see poi in terms of a certain formulation.. Not some specific dx/dy business.. but rather generic groupings that function equivalently... like talking about amplitude generically rather then as some specific operation..

I'll keep you guys updated.. and by the way.. arashi can you send me that link that I think you posted at some point with all these graphical images of inversions?

wasnt there one that had like 20 or so images in different patterns? I think one of them looked like a flat horizontal planed figure 8 and flat vertical planed figure 8 that was linked in the middle.. so that the top circle twisted into the left circle whihc swisted into the bottom and into the right.. etc.. and other pictures like that.. what were those?

well I talked witha math guy... it is differential geometry, and I'm working with two people at the moment, one that does knot theory, and one that does braid theory.. Unfortunately, I'm not going to get very far with them very fast because the times that they are available conflict with my classes, so I might get about 15 minutes a week with them..

If anyone can find more pictures like this:
pic

let me know.. it would be most helpful.. for the math guys at least..

go to google and click the "images" button, and run a search. you'll find more than enough.

LOL... been there done that man... but it only turns up some of the inversions like the one you linked, not like the one I linked (with the exception of the one I linked.. )

the word for the day is "inverse kinematics" ... (?)

• http://hms.upenn.edu/software/ik/ikan_gm.pdf
  
• http://freespace.virgin.net/hugo.elias/models/m_ik.htm
  
• (or the source) http://www.google.com/search?q=inverse+kinematics
  

that was two words, huh?

"crap". you still have to work the poi, hand, and elbow as targetted "joints", but the elbow can be fudged, and the poi can be specified in combinations of planes, I think. that should handle all the math you need, though. =D

umm. and you can use this to model inverse stuff.. lalalala .. (what topic?) lalala..

-- dut

I think I found the hardest inversion that I've learned to date... take the left hand counter clock wall plane btb.. take the right hand counter clock behind the shoulder blades/neck...

be careful not to hurt the shoulder socket of the hand that comes up from the bottom..

ouch
hey i've got some time!
atomics.

just so you know some of these moves are easier if you stick your tongue slightly out like this...

first let's start with the atom itself, {simian, your atomic weave is two atoms woven together so let's start from here first.}for all these basic moves try to keep the atom shape intact and in the same angles.
this isn't the best way to learn atoms, but we need a set of terms first. so the names may appear to jump around and not have any sort of coherency, but just know that the names make more sense as we get on to the atomic weaves.

let's start with a _forward_ inversion/buzzsaw. from here there are 2 inverted atoms. and there's 2 from the reverse buzzsaw too.
here's a pic courtesy of the illustr-ious spiralx... even though the arms are too short and the poi too long... who's counting?
mind blowing graphic of inverted atom

1. open the buzzsaw into an atom by taking the right plane and moving the far side of the circle 45 degrees to the left, and the far side of the left circle 45 degrees to the right. keep both hands inverted. we'll work with this one cause this typewriter only has backslashes and so this atom will always be an X from above.
Code:

---

L---> X  <---R

---

2. open the buzzsaw into an atom by taking the right plane and moving the near side of the circle to the left 45 degrees, and the left plane will move the near side of the left circle to the right 45 degrees.

okay. from here on out let's ONLY work with atom # 1, but all this applies to both, in a reflective way. remember, always go back to that exact atom every time you mess up! it will get confusing...
#1
so now let's try moving it around. first the easy one, move the atom away from you to a full outside.
outside #1
Code:

---

 X

^^

!!

LR

---

now back to #1
it's really simple to half invert it, with your right hand "outside" and your left hand inverted. you can flip your right hand from inverted to outside and you'll be flipping the atom from inverted to half inverted, see?
half inversion #1
Code:

---

L-->X<--

         R

---

now let's do more. lets move the right hand around.
there's lots of places you can put your right hand if you can crane/parallel the poi so they don't hit each other... let's assume you can, and do the moves in order, keeping the left hand still and bringing the right hand's postition more and more around in a clockwise direction. now we have zones: with the left hand in a and the right hand in c
Code:

---

    b

a(L)X(R)c

    d

---

let's go back to the full inversion #1

the hardest one-you pull your right hand toward you, into the space created by the triangle closest to you, zone d, but without changing your right hand at all, iow it looks like it stays "inverted" if you just stare at it as you move it. you'll be essentially putting your left arm in to zone b, forearm at a 45 degree angle. this is a crane half inversion and this one's real crooked. you can do your right hand either inverted or outside and they are the same.
Code:

---

L 

!

v

X

^

!

R

---

but this requires really good "crane control" so you get a cracker if you get it.

move back to inversion #1...
if we continue, keep moving the right hand around to zone a, and you will run into problems. the first option, is to do an outside atom, 5 beat or second degree to be specific. you'll have to be in a 5 beat spider, (so just the arms... they are crooked around each other like the crossover in the middle of a 5 beat weave... left elbow on top, right elbow under, right hand poking up and on top with left hand under) the atom will be fully outside at this point.
Code:

---

L-->   X

r-->          

---

another is to put your right arm in zone a, just next to the close side of the left poi's circle, and the left arm will be crooked 45 degrees in zone b. this is an outside half inversion
Code:

---

    L

    !

    v

R-->X

---

keep doing this one... you can keep going around if you can crane, by pushing your right hand so it sits under the left forearm... your atom is outside again, now your hands are doing the three beat spider, or first degree crossover. this is a 3 bt. crane atom.
Code:

---

L-->X

  /

R

---

if you keep going around, to inside atoms, they are the same as the moves of an atom from a different buzzsaw so let's stop there for now.

Ok so that's a hell of a lot of new stuff arashi, many thanks for taking the time to write it all down! I'm going to have to spend a fair bit of time when I'm not sat at my desk here at work going through it! I've done some stuff with inverted atoms, but just getting the basic inversion to stay there is harder than doing a bloody inverted weave.

One quick clarification - in your first diagram is your body directly below the X? So the two planes at at 45 degrees to your normal wall/wheel planes?

Once again - thanks!

no with the body like this
Code:

---

     X
   /    /<--pretend this is a backslash, so it 
   *body*      looks like a real arm and not some cheap 
                    imitation flailing arm

---

oh even though i b*!ch a lot about circuitous argumentative word misunderstandings you don't have to be so nice... not that i'm complaining but when you're this nice it makes me feel...

like ROYALTY
wait we take it back, you may now grovel to us...
[holds out his ring]

I'm not kissing your ring you know :P

But you seem to be agreeing and disagreeing with me... here, I've drawn a crappy diagram, is this what you mean?


http://www.homeofpoi.com/gallery/display.php?image=/500/1989atom.GIF

The red lines are the planes of the two poi. And yes, I know the end of the arms should be closer to where the planes cross

as the french would say, weewee.
can i put that up there somewhere?

Go for it

Ok, initial thoughts

Written by: arashi

---

let's start with a _forward_ inversion/buzzsaw. from here there are 2 inverted atoms. and there's 2 from the reverse buzzsaw too.
1. open the buzzsaw into an atom by taking the right plane and moving the far side of the circle 45 degrees to the left, and the far side of the left circle 45 degrees to the right. keep both hands inverted. we'll work with this one cause this typewriter only has backslashes and so this atom will always be an X from above.
Code:

---

L---> X  <---R

---

2. open the buzzsaw into an atom by taking the right plane and moving the near side of the circle to the left 45 degrees, and the left plane will move the near side of the left circle to the right 45 degrees.

---

So from #1 the poi are in a plane parallel to the arm holding them, in #2 they're in a plane perpendicular to the arm holding them? Hadn't thought about that difference before, I've done everything in #2 which seems a hell of a lot easier...

Written by:

---

so now let's try moving it around. first the easy one, move the atom away from you to a full outside.
outside #1
Code:

---

 X
^^
!!
LR

---

now back to #1

---

Ok, some clarification needed, doh. In the very first diagram are your forearms pointed towards each other with the centre of the cross in between your hands? And to get the outside you move your arms so they instead point away from your body.... the poi are still spinning in the same place but you've gone from inverted to outside?

Even if that's not what you mean that's something for me to think about already lol