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Forums > Beginner Poi Moves > The maths of the 3 Beat weave

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sinjaxBRONZE Member
Member
28 posts
Location: Southampton, United Kingdom


Posted:
Hi all

Recently i've been working on a 3D-animation coursework within which i decided to add a person doing poi. Course its all rather simple...the poi are made of a cylinder and a sphere and the "person" spinning them is a collection of cylinders to make the arms.

To do it i had to figure out the maths behind the 3 beat weave. Once i got into it, it became rather complicated to think about biggrin, its amazing how the simplist things our bodys can do are so god damn strange to model in maths and on computers. It turned out to be rather interesting if you're into that kinda stuff smile. Thought id slap it on here see if anyone was interested biggrin

I decided to model the situation on a per-poi basis to simplify things. Each poi has their own period which raises in steps of 10 degrees and has a range of 1080 degrees (that is 3 full rotations).

Now the things which make it a 3 beat weave is the points in this period where the poi travels from the left hand side to the right hand side and visa versa. I worked this out as being:

left poi
---------
leftPoiRotate >= 990 || leftPoiRotate <= 90
left poi travels to the left

leftPoiRotate >=270 && leftPoiRotate <= 450
left poi travels to the right


right poi
---------
rightPoiRotate >= 990 || rightPoiRotate <= 90
right poi travels to the right

rightPoiRotate >=270 && rightPoiRotate <= 450
right poi travels to the left

What this gives you is 2 poi spinning, changing position in x to give the affect of the 3 beat. To get a better 3 beat you can also add the change in period of the y which is simply the y portion of a circle at any given period of the poi....something like:

y = sin(poi_rotation)

The time steps the poi remain on the right or left hand side is what gives the movement of the 3 beat. With a bit of tinkering i recon this could be boiled down to a couple of paramteric equations for x,y and z for each poi smile

Hmm, but yeh thats what you're doing when you spin a 3 beat biggrin...or a close approximation where the arms pass through each other anyways wink

Efficient humour: "heh...wang smile"


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
That linky no worky.
EDITED_BY: NYC (1103816573)

Well, shall we go?
Yes, let's go.
[They do not move.]


borismcnorrisprofessional pedant
137 posts
Location: Bristol


Posted:
you need to take the comma off the end of the link. then it's fine

A warrior always returns to the fray. He never does so out of stubbornness, but because he has noticed a change in the weather - Paulo Coelho


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
Cool! Linky worky now!

Fixed Circle Radius: 20
Moving Circle Radius: 5
Moving Circle Offset: 20

Look, I'm nickwithfire! biggrin

Oh whoa! If I change the above MOVING circle radius to -5 I get an ANTISPIN flower trail.

Weeee! Maths!

Well, shall we go?
Yes, let's go.
[They do not move.]


ado-pGOLD Member
Pirate Ninja
3,882 posts
Location: Galway/Ireland


Posted:
this is the geekiest thread on hop

i feel so at home

Love is the law.


Lachienewbie
1 post
Location: Melbourne, Aust.


Posted:
What is it about poi and juggling that attracts this sort of discussion?

I'm part of the Juggling club at uni and there is a disproportionate number of physicists and computer scientists.

Seriously, good work to those of you working this stuff out, I started reading an article on newscientist about the maths of juggling, but don't have a subscription so couldn't read the whole thing, but its fascinating stuff.

"How is education supposed to make me feel smarter? Besides, every time I learn something new, it pushes some old stuff out of my brain. Remember when I took that home winemaking course, and I forgot how to drive?" - Homer Simpson


sinjaxBRONZE Member
Member
28 posts
Location: Southampton, United Kingdom


Posted:
Hmm theres a big geek following of all circus skills, most of the guys at southampton uni's circus soc are comp sci's, electronics and sciency guys also

lets face it, its a pretty geeky hobby ...in a good way wink

Efficient humour: "heh...wang smile"


Disc0annoying boy
160 posts
Location: Sweden


Posted:
but what about the physics og poi? i've been wondering for how many N a poi-string must hold... but a lack so much knowledge that i can't calculate it.... next year i'll read "physics A" and maby it'll work then... smile

anybody knows how to calc this?

fire is just light and heat.
it's you friend!


RicheeBRONZE Member
HOP librarian
1,841 posts
Location: Prague, Czech. Republic


Posted:

https://www.wordsmith.org/~anu/java/spirograph.html

Snake radus 24, moving radius 24, c. offset 65 smile

quarter time ? radius 57, moving 19, offset 65

Square ?? :]:] 28, -21, 70


Still fuunny ;]

POI THEO(R)IST


*HyperLightBRONZE Member
old hand
1,174 posts
Location: Great Malvern [UK]


Posted:
Written by: sinjax

I'm gonna impliment this in my openGL program




What're you coding in? If it's VC++ I can probably lend a hand - my job is basically VC++ / OpenGL! Could I get a copy of your source pretty please with sugar and sparkles and stuff on top? biggrin

Cake or Death?


TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
This thread has inspired me to get back into my little Poibot project.

Last night I coded the first poibot in flash.

I'll post a link next time i log in on my computer in a day or 2.

It has 3 viewports, front, left and top (1st angle orthographic for anyone who cares)

2 poi have x,y,z coordinates and are currently doing a 3bt weave forwards.

I have a counter which counts in degrees, then converts to radians r

y value is sin(r)
z value is cos(r)
this makes circles in the Wheel plane

For the side to side motion of the pattern i've used a series of 'markers' in an array, e.g

-1 = Left side of body
0 = Where you are standing
1 = Right side of body

weaveA=[-1,-1,1,1,1,1]

This tells 1 poi where to be for 6 beats (3 x 2poi) ie [left, left, right, right, right, right]

the pattern for the other poi is opposite side of body, 3 beats out of phase;

weaveB=[-1,-1,-1,1,1,-1]

This tells the other poi where to be for 6 beats (3 x 2poi) ie [left, left, left, right, right, left]

The code then moves the x position from where it is now to where it should be on the next beat.

The 3 beat weave looks pretty good

Next i'll stick the hands in and connect poi to hand. You can easily calculate the pattern for the other poi from the first. ie same or opposite direct, in time or split time and so on.

Then i want to design a little interface so that everyone can program their own patterns on it and ultimately flow from pattern to pattern. It shouldn't take long to nail most of the patterns we already know.

Then i'll have a think about tangles and wraps.

m

Spherculism ~:~ The Act of becoming Spherculish.


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
Right on Matt. smile

You know, if you graphed the path of each ball on the ball chain, you'd have a much better representation of what's happening on wraps and isolations. biggrin

Well, shall we go?
Yes, let's go.
[They do not move.]


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
5 beat weave:

X1 = cos(T+.3sin(T))
Y1 = sin(5T)

X2 = cos(T-.3sin(T))
Y2 = sin(5T-pi)

Also known as "Fun stuff you can do to stay awake at a staff meeting"... wink

Well, shall we go?
Yes, let's go.
[They do not move.]


TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
Okay, so i'm a closet coder....

Anywho, flash actionscript doesn't count smile

Here's how far i've got with poibot:
poibot v0.5

m

Spherculism ~:~ The Act of becoming Spherculish.


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
HOLY CRUMB MATT!

NICE JOB!

*Bows*

Now we can see who can come up with the best theoretical routine without actually having to bother to learn how to do it. wink

Well, shall we go?
Yes, let's go.
[They do not move.]


TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
Cheers NYC,

It's the first time i've managed to get anything in 3d working properly.

I still don't get your parametric equations tho. I'm using cos and sin to make the poi rotate and then adding that to the movement of the Center of Rotation.

Once we get some patterns sorted i can set them up as arrays.

Then it's easy to join all the arrays in to one long combo.

I love poibot, i've been trying to code it for about 2 years but never had the time, or the skills.

Can anyone explain to me how to take the x,y,z components and draw them in perspective from any angle? I kinda understand how to do it but im sure there's some very usseful equations i need to know.

Then I'll make it spin in 3d so you can move the camera around the model.

Need to add some arms as well.

take it easy,

m

Spherculism ~:~ The Act of becoming Spherculish.


GlåssDIAMOND Member
The Ministry of Manipulation
2,523 posts
Location: Bristol, United Kingdom


Posted:
Hi matt

well done smile

on perspective: this is simple explaination
https://www.faust.fr.bw.schule.de/mhb/perspect.htm
If you google:
mapping equations perspective
You'll find lots of sites with the equations on.

TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
cheers drew, that exactly what i need. smile

I dug out an old a-level maths book t'other day to try and swap up.

Once i get the patterns sorted i'll work on 3d camera stuff.

m

Spherculism ~:~ The Act of becoming Spherculish.


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
My parametric equations allow one equation to be used for the entire rotation of a poi within a 3 or 5 beat weave.

They are based on X and Y varying with respect to Time.

I think what you are doing is closer to what actually happens when you spin. When you do a 3 beat weave, you move the poi to one side, then STOP moving it to that side, then move it back. Rather than a continuous flow.

Parametrics allow for the pattern to repeat indefinitely as it's just a continuing equation.

Well, shall we go?
Yes, let's go.
[They do not move.]


TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
I do kinda get what they look like now.

I was just confused because there is only x and y, no z. I'm assuming in that equation for 5bt weave you are looking at the circles sideways on??? If so then it makes sense.

Poibot works on parametric equations as well. Only there are 2 separate components for each axis. The x,y,z movement of the hand PLUS the rotation of the poi. By separating it out it's easy to see which bit changes between different moves and which bit is just the spinning.

It's helped me understand what i'm doing with my poi enormously.

Plus i can modify if pretty easily to work for staff, then maybe club juggling and diablo smile

I'd like to code the proper physics of poi tho, cos then it would just stall the poi if you moved the hand correctly and stuff like that.

NYC, it was totally your enthusiasm for your equations that persuaded me to do this, thanks.

Now we just need to figure out exactly how we want to use this thing and i can code it.

Just thought. I could add loads of patterns by binary, high or low. Then we could check them all out.

m

Spherculism ~:~ The Act of becoming Spherculish.


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
Yes, most of the equations that I posted were as you are looking at the person's chest. The side view would just be a circle, and the top view would be similar to the front view.

I did an XYZ comparison somewhere on this thread.

But otherwise I was just talking about front view.

I felt a bit silly about my initial enthusiasm so thanks for the pat on the head. biggrin

Well, shall we go?
Yes, let's go.
[They do not move.]


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
Well, that's a really easy way of explaining a butterfly weave!

Just flip the red poi direction to "Minus"!

Matt, you rock.

Well, shall we go?
Yes, let's go.
[They do not move.]


TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
yeah, i did that too and was like "so that's a butterfly weave" smile

At the moment there is a maxBeat of 10 (ie 5 beat weave) but that's only cos that's how much space i had. I figured I could just add more in sets of ten once people start to nail a few patterns.

Damn it, i gotta figure out how to allow everyone to save the variables out as txt or php files, Dom????

m

Spherculism ~:~ The Act of becoming Spherculish.


_Clare_BRONZE Member
Still wiggling
5,967 posts
Location: Belfast, Northern Ireland (UK)


Posted:
Hi there lads,

I was just wondering... is anybody on this thread female?

Probably not, but as I said, just wondering biggrin

Have fun
ubblol

Getting to the other side smile


spiralxveteran
1,376 posts
Location: London, UK


Posted:
Surely to change the behaviour to something more realistic you'd need to have the path of each hand an then a set of points along that path where the hand imparts rotation to the poi?

"Moo," said the happy cow.


TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
"I was just wondering... is anybody on this thread female?" smile

I dunno how my hands affect the movement of the poi in terms of forces so i can't code it. I figured i'd just put the poi pattern a fraction behind the hand pattern so it dragged behind a little.

But i'd rather sort the physics out.

Thing is, how on earth does your hand pull the poi upwards whilst isolating. Maybe if someone can figure out the forces in the 'sock' whilst the poi spins round we could code it.

Someone bought me an ubergeeky book for christmas written by a programmer. inspired me to make poibot.

Spherculism ~:~ The Act of becoming Spherculish.


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
Forces in the isolating sock are relatively straight forward.

Your hand is just rotating around the pivot point exactly compensating for the isolation.

I don't think it's much MORE physics than a normal spinning sock. Which ISN"T simply rotating around a fixed point. The sock is being 'pumped' by staying just in front of where it's supposed to be. Otherwise it'd just flop down from friction.

I'll think about this... after Molly leaves. frown

Well, shall we go?
Yes, let's go.
[They do not move.]


NYCNYC
9,232 posts
Location: NYC, NY, USA


Posted:
I hate to say it Matt but....

You defined 'Beat' wrong in your program. biggrin

Your "Max Beat" should read "Max Beat/2".

Stupid Newbies. wink

Well, shall we go?
Yes, let's go.
[They do not move.]


TheWibblerGOLD Member
old hand
920 posts
Location: New Zealand


Posted:
haha

ALmost, it should actually read maxBeat=numberOfPoi*beat, maxBeat and beat are 2 separate variables in the code

It's so that the trasitions, from side to side for example, only occur for half a circle.

Definitely gonna use your idea of modelling separate points down the sock instead of 1 stretched triangle. That way I should be able to code wraps and possibly the holy grail, tangles.

I'm thinking i'll use 5 points along the poi, Hand, 1/4 up from hand, half way, 3/4 up from hand and head. Will that do???

m

Spherculism ~:~ The Act of becoming Spherculish.


spiralxveteran
1,376 posts
Location: London, UK


Posted:
I reckon those points will cover everything smile

"Moo," said the happy cow.


GlåssDIAMOND Member
The Ministry of Manipulation
2,523 posts
Location: Bristol, United Kingdom


Posted:
Yo

How do you figure that out then??

On the default screen it has a 3 beat weave,

which has a total of 6 beats done by the poi, 3 by each

and the beat counter reads 6

perfect smile



What I wonder is why I'm not allowed 4 beats on the maxbeat

And split time and in time are reversed when the poi are spinning in opposite directions !!
EDITED_BY: Glåss (1104930564)

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