Forums > Beginner Poi Moves > The maths of the 3 Beat weave
Login/Join to ParticipateBRONZE Member
Member
28 posts
Location: Southampton, United Kingdom
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
, 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 
. Thought id slap it on here see if anyone was interested
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
Hmm, but yeh thats what you're doing when you spin a 3 beat...or a close approximation where the arms pass through each other anyways 
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
, 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 . Thought id slap it on here see if anyone was interested 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
Hmm, but yeh thats what you're doing when you spin a 3 beat
...or a close approximation where the arms pass through each other anyways Efficient humour: "heh...wang "
stranger
80 posts
Location: Greece-Samos-Athens
80 posts
Location: Greece-Samos-Athens
Posted:
maybe do this butterfly thing? In which program did you do it?
maybe do this butterfly thing? In which program did you do it?
"For once there was an unknown land, full of strange flowers and subtle perfumes,
a land of which it is joy of all joys to dream, a land where all things are perfect and poisonous."
"Put out the torches! Hide the moon! Hide the stars!"
BRONZE Member
Member
28 posts
Location: Southampton, United Kingdom
Member
28 posts
Location: Southampton, United Kingdom
Posted:
I wrote the program in C++ using openGL...the code is pretty messy but the maths is solid i think
I think a butterfly would be easier, left poi and right poi would just be doing an in time rotation but in oposite directions
so the period would be 360 degrees with both poi exactly in the middle...
now mexicans...that might be a problem
I wrote the program in C++ using openGL...the code is pretty messy but the maths is solid i think
I think a butterfly would be easier, left poi and right poi would just be doing an in time rotation but in oposite directions
so the period would be 360 degrees with both poi exactly in the middle...
now mexicans...that might be a problem
Efficient humour: "heh...wang "
GOLD Member
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Posted:
Have you talked to garthy?
I think it was him who was working on something similiar.
Nice work.
Garty is on here somewhere and over in spherculism too.
Have you talked to garthy?
I think it was him who was working on something similiar.
Nice work.
Garty is on here somewhere and over in spherculism too.
Love is the law.
If its got pistons or boobs, its gonna be expensive...
515 posts
Location: Cyprus
515 posts
Location: Cyprus
Posted:
Thats all i have to say on the matter lol
Thats all i have to say on the matter lol
Henry Hill - 'One day the kids from the neighbourhood carried my mothers groceries all the way home, you know why? It was out of respect'...
ahmet_20valve_ahmet(at)hotmail(dot)com
Hope all is well : )
BRONZE Member
Member
28 posts
Location: Southampton, United Kingdom
Member
28 posts
Location: Southampton, United Kingdom
Posted:
Nah havnt talked to garthy...i'll see what he has to say if he reads the post.
At the moment its all rather simplistic...but i recon this is the path to go down for equating poi and from that getting down some sort of site-swap esc notation for poi...perhaps discovering new and exciting moves by analysing maths
who knows
Nah havnt talked to garthy...i'll see what he has to say if he reads the post.
At the moment its all rather simplistic...but i recon this is the path to go down for equating poi and from that getting down some sort of site-swap esc notation for poi...perhaps discovering new and exciting moves by analysing maths
who knows
Efficient humour: "heh...wang "
GOLD Member
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Posted:
The very best of luck to ya
The very best of luck to ya
Love is the law.
member
66 posts
Location: Barnstaple, Devon, UK
66 posts
Location: Barnstaple, Devon, UK
Posted:
yeah i second that...good luck.
Just be glad your not trying 5 beat or hyperloops.
nightmare
yeah i second that...good luck.
Just be glad your not trying 5 beat or hyperloops.
nightmare
If hope can grow from dirt like me.....It can be done.
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
Maybe it's hard to program but it seems pretty straight forward in terms of graphing it's position.
Parametrically, isn't it just:
X = sin (T)
Y = cos (.5T)
Z = cos (T)
So looking down on the X-Y plane, it looks like a figure 8.
Looking from the side on the X-Z plane, it looks like a circle.
Oh crap! Nope! You're right! That's just a two beat weave. Dumbass me.
(Runs off to my graphing calculator...)
Maybe it's hard to program but it seems pretty straight forward in terms of graphing it's position.
Parametrically, isn't it just:
X = sin (T)
Y = cos (.5T)
Z = cos (T)
So looking down on the X-Y plane, it looks like a figure 8.
Looking from the side on the X-Z plane, it looks like a circle.
Oh crap! Nope! You're right! That's just a two beat weave. Dumbass me.
(Runs off to my graphing calculator...)
Well, shall we go?
Yes, let's go.
[They do not move.]
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
Ha!
Wait... Graph this...
X = cos (T + sin(T))
Y = sin (3T)
Isn't that it?
I mean, it's not perfect by any means, but it is an idealized path of one poi doing 3 beat weave.
And why has noone used the word GEEK yet?
Ha!
Wait... Graph this...
X = cos (T + sin(T))
Y = sin (3T)
Isn't that it?
I mean, it's not perfect by any means, but it is an idealized path of one poi doing 3 beat weave.
And why has noone used the word GEEK yet?
Well, shall we go?
Yes, let's go.
[They do not move.]
Pooh-Bah
2,354 posts
Location: Away from home
2,354 posts
Location: Away from home
Posted:
nyc, you are a geek of the highest order
have a gold star
Non-Https Image Link
and a kiss because geeks don't get so many of those
nyc, you are a geek of the highest order
have a gold star
Non-Https Image Link
and a kiss because geeks don't get so many of those
GOLD Member
Pooh-Bah
2,110 posts
Location: Philadelphia, PA - USA
Pooh-Bah
2,110 posts
Location: Philadelphia, PA - USA
Posted:
We were trying to be nice to you NYC
We were trying to be nice to you NYC
Let's turn those old bridges we crossed into ashes.
We'll blaze a new trail,
and torch the rough patches.
-Me
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
OK, I like this one way better...
X = cos (T + 1.5 sin (T))
Z = sin 3T
Then of course the Y would be just going round in circles as well.
That's just about perfect!
OK, I like this one way better...
X = cos (T + 1.5 sin (T))
Z = sin 3T
Then of course the Y would be just going round in circles as well.
That's just about perfect!
Well, shall we go?
Yes, let's go.
[They do not move.]
SILVER Member
Member
82 posts
Location: Netherlands - Hengelo
Member
82 posts
Location: Netherlands - Hengelo
Posted:
*Pulls out graphic calculator to plot graph...
*Finds out that the calculator doesn't support 3D (duh..)*
*Throws calculator around*
Is there a web-based of free-downloadable program which plots 3D parametric graphs ?
PS great plan to try to make a model for poispinning...you might calculate new moves if it's good
*Pulls out graphic calculator to plot graph...
*Finds out that the calculator doesn't support 3D (duh..)*
*Throws calculator around*
Is there a web-based of free-downloadable program which plots 3D parametric graphs ?
PS great plan to try to make a model for poispinning...you might calculate new moves if it's good
Hij die zijn kind benzine voert moet niet roken als het boert.
Love you MyIng 
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
You don't need a 3D calculator. Just do 2D parametric.
X = cos (T + 1.5 sin (T))
Y = sin 3T
...is what it looks like from the front.
I was having some phase issues with 3D but got them worked out most of the way...
My final 3D answer is...
X = cos (T + 0.5*pi*sin (T))
Y = sin (3T + 0.25 pi)
Z = sin (3T - 0.25 pi)
But that's all theoretical projections using my 2D calculator and switching planes.
GRANTED, it's not perfect. But it's idealized. And it's good enough for me. Since I don't really care.
You don't need a 3D calculator. Just do 2D parametric.
X = cos (T + 1.5 sin (T))
Y = sin 3T
...is what it looks like from the front.
I was having some phase issues with 3D but got them worked out most of the way...
My final 3D answer is...
X = cos (T + 0.5*pi*sin (T))
Y = sin (3T + 0.25 pi)
Z = sin (3T - 0.25 pi)
But that's all theoretical projections using my 2D calculator and switching planes.
GRANTED, it's not perfect. But it's idealized. And it's good enough for me. Since I don't really care.
Well, shall we go?
Yes, let's go.
[They do not move.]
BRONZE Member
Member
28 posts
Location: Southampton, United Kingdom
Member
28 posts
Location: Southampton, United Kingdom
Posted:
Wow i didnt realise the thread had moved...
NYC dude im trying to find a prog to easily map those functions you're talking about there....but...are you suuuure that gives 2 spins on one side and one on the other.
I'll try to plot it before saying any more to have a look at it....but i dunno that doesnt seem right...
Cus the graph for that situation would be...well kinda insane.....i couldnt figure it out without delving into crazy fourier analysis to figure out how to get the graph.....
Fourier analysis for poi....maybe its better we stopped....maybe these are things that shouldnt be done to something so pure
--------------
Ok yeh had a look and its what i thought...the x is hoping from positive to negative every perioid with a period being roughly....20 degrees of the poi?
That isnt right to the model of the 3 beat weave. X should be solid positive for 720 degrees then solid negative for 360 degrees. And that nature of it meaaans that we have to do a fourier analysis to get a single parametric function for it. That...or a conditional parametric (which is what i've done in my C program)...
So yeh basically i think i'll just spin poi instead because when things need fourier analysis they stop being fun
EDITED_BY: sinjax (1103025210)
Wow i didnt realise the thread had moved...
NYC dude im trying to find a prog to easily map those functions you're talking about there....but...are you suuuure that gives 2 spins on one side and one on the other.
I'll try to plot it before saying any more to have a look at it....but i dunno that doesnt seem right...
Cus the graph for that situation would be...well kinda insane.....i couldnt figure it out without delving into crazy fourier analysis to figure out how to get the graph.....
Fourier analysis for poi....maybe its better we stopped
....maybe these are things that shouldnt be done to something so pure --------------
Ok yeh had a look and its what i thought...the x is hoping from positive to negative every perioid with a period being roughly....20 degrees of the poi?
That isnt right to the model of the 3 beat weave. X should be solid positive for 720 degrees then solid negative for 360 degrees. And that nature of it meaaans that we have to do a fourier analysis to get a single parametric function for it. That...or a conditional parametric (which is what i've done in my C program)...
So yeh basically i think i'll just spin poi instead because when things need fourier analysis they stop being fun
EDITED_BY: sinjax (1103025210)
Efficient humour: "heh...wang "
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
I know mine is wrong... but not as wrong as you think it is... I think.
I've got my T set for 3 rotations per 360 'degrees'... If you divide everything by 3, you'll have something you like better.
Did you look at the graphs? They're pretty darn good. At least stick this in a graphing calculator and pat me on the head...
X = cos (T + 1.5 sin (T))
Y = sin 3T
... and then tell me it's not good enough.
I know mine is wrong... but not as wrong as you think it is... I think.
I've got my T set for 3 rotations per 360 'degrees'... If you divide everything by 3, you'll have something you like better.
Did you look at the graphs? They're pretty darn good. At least stick this in a graphing calculator and pat me on the head...
X = cos (T + 1.5 sin (T))
Y = sin 3T
... and then tell me it's not good enough.
Well, shall we go?
Yes, let's go.
[They do not move.]
BRONZE Member
Member
28 posts
Location: Southampton, United Kingdom
Member
28 posts
Location: Southampton, United Kingdom
Posted:
TBH i'm putting it into Excel...
no graph calc have i ...
but i'll try again...
the graphs in excel do give truley manic behaviour for X though...beh we'll see
--------
Bloody hell. Just plotted it correctly and that is rather good actually ...nice...
that central point could do with being moved buuuut yeh...thats basically right...nice one dude
EDITED_BY: sinjax (1103031707)
TBH i'm putting it into Excel...
no graph calc have i ...
but i'll try again...
the graphs in excel do give truley manic behaviour for X though...beh we'll see
--------
Bloody hell
. Just plotted it correctly and that is rather good actually ...nice...that central point could do with being moved buuuut yeh...thats basically right
...nice one dude EDITED_BY: sinjax (1103031707)
Efficient humour: "heh...wang "
BRONZE Member
Carpal \'Tunnel
3,750 posts
Location: Europe,Scotland,Both
Carpal \'Tunnel
3,750 posts
Location: Europe,Scotland,Both
Posted:
see, geekism is the discussion of something unterlly unimportant in deadly earnest terms.
this is actually pretty intresting + usefull.
*pats the short american on the head*
T
see, geekism is the discussion of something unterlly unimportant in deadly earnest terms.
this is actually pretty intresting + usefull.
*pats the short american on the head*
T
This is a post by tom, all spelling is deleberate
-><- Kallisti
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
Shouldn't be manic. It looks like a fish swimming to the right. The graphing calculator is nice because you get to actually see it follow the path.
I can't seem to find one online that doesn't suck. But the excell graph should be OK. The only problem is it doesn't "cross" at the center like we would expect on a 3 beat weave.
I tried to get two functions 'weaving' but am not there yet....
Shouldn't be manic. It looks like a fish swimming to the right. The graphing calculator is nice because you get to actually see it follow the path.
I can't seem to find one online that doesn't suck. But the excell graph should be OK. The only problem is it doesn't "cross" at the center like we would expect on a 3 beat weave.
I tried to get two functions 'weaving' but am not there yet....
Well, shall we go?
Yes, let's go.
[They do not move.]
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
Got it.
It's ugly.
But it weaves.
Left poi:
X(t) = cos (t + .5*pi*sin(t))
Y(t) = sin (3t)
Right poi:
X(t) = -cos((T + pi) + .5*pi*sin (T + pi))
Y(t) = sin (3(t+pi))
IF you want to see this, you need a graphing calculator or something else that will graph two functions simultaneously with respect to T (like the TI83 I'm on now... change the settings to 'parametric' and 'simultaneous'). In excell it will look quite messy because it doesn't do it time wise.
The first time I graphed it, I wasn't sure if it was right. But after careful review... the planes aren't perfect, but the timing is quite good.
Maybe we could just hand this formula to the next newbie who's having trouble doing the three beat weave.
The only problem is that it doesn't cross in front of the body. it crosses a bit left (for the right poi) and right (for the left poi) ... but not bad for messing around while eating a burrito.
YAY!
Got it.
It's ugly.
But it weaves.
Left poi:
X(t) = cos (t + .5*pi*sin(t))
Y(t) = sin (3t)
Right poi:
X(t) = -cos((T + pi) + .5*pi*sin (T + pi))
Y(t) = sin (3(t+pi))
IF you want to see this, you need a graphing calculator or something else that will graph two functions simultaneously with respect to T (like the TI83 I'm on now... change the settings to 'parametric' and 'simultaneous'). In excell it will look quite messy because it doesn't do it time wise.
The first time I graphed it, I wasn't sure if it was right. But after careful review... the planes aren't perfect, but the timing is quite good.
Maybe we could just hand this formula to the next newbie who's having trouble doing the three beat weave.
The only problem is that it doesn't cross in front of the body. it crosses a bit left (for the right poi) and right (for the left poi) ... but not bad for messing around while eating a burrito.
YAY!
Well, shall we go?
Yes, let's go.
[They do not move.]
GOLD Member
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Posted:
holy burrito's math man
cool
holy burrito's math man
cool
Love is the law.
BRONZE Member
Member
28 posts
Location: Southampton, United Kingdom
Member
28 posts
Location: Southampton, United Kingdom
Posted:
Yes man absolutely perfect.... The graphs im gettin seem to be exactly right...
I'm gonna impliment this in my openGL program
Soon i'll make it so you can give it arbitrary parametric equations on the command line
Fully functioning poi program anyone?
As long as you can express its parametric equation i should be able to draw it....and as long as it can be drawn, surely it can be done by a human?....oh the possibilities
Yes man absolutely perfect.... The graphs im gettin seem to be exactly right...
I'm gonna impliment this in my openGL program
Soon i'll make it so you can give it arbitrary parametric equations on the command line
Fully functioning poi program anyone?
As long as you can express its parametric equation i should be able to draw it....and as long as it can be drawn, surely it can be done by a human?....oh the possibilities
Efficient humour: "heh...wang "
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
Holy crap, it actually works!
OK... get yourself to a TI-83
Set MODE to PARAMETRIC and SIMULTANEOUS
Window to -1 to 1 for both x and y
t step 0.1 works fine
AND... when you are entering the formulas ... look just to the left of the X1T... you'll see a little frontslash. Click on that and it will eventually change to a circle (JUST a circle)...
Now hit 'graph' and be in awe. Two circles floating around doing a 3 beat weave.
YAAAAAAAAAAAAAAAAAAAAAAAHHHHH!!!
Where's Cole and Glass damnit? I want a cookie from the engineering boys.
Beg, borrow or steal a TI-83.
Holy crap, it actually works!
OK... get yourself to a TI-83
Set MODE to PARAMETRIC and SIMULTANEOUS
Window to -1 to 1 for both x and y
t step 0.1 works fine
AND... when you are entering the formulas ... look just to the left of the X1T... you'll see a little frontslash. Click on that and it will eventually change to a circle (JUST a circle)...
Now hit 'graph' and be in awe. Two circles floating around doing a 3 beat weave.
YAAAAAAAAAAAAAAAAAAAAAAAHHHHH!!!
Where's Cole and Glass damnit? I want a cookie from the engineering boys.
Beg, borrow or steal a TI-83.
Well, shall we go?
Yes, let's go.
[They do not move.]
NYC
9,232 posts
Location: NYC, NY, USA
9,232 posts
Location: NYC, NY, USA
Posted:
YAY!
Written by: sinjax
Yes man absolutely perfect....
YAY!
Well, shall we go?
Yes, let's go.
[They do not move.]
PLATINUM Member
Flying Water Muppet
5,276 posts
Location: Edin-borrow., United Kingdom
Flying Water Muppet
5,276 posts
Location: Edin-borrow., United Kingdom
Posted:
PICTURES!!!!!
please sir, can we have some pictures... (or maybe a video?)
:tantrumsmiley:
PICTURES!!!!!
please sir, can we have some pictures... (or maybe a video?)
:tantrumsmiley:
"the now legendary" - Kaskade
"the still legendary" - Kaskade
I spunked in my friend's aquarium and the fish ate it. I love all fish. Especially the pink ones. They are my bitches. - Anon.
Pooh-Bah
2,354 posts
Location: Away from home
2,354 posts
Location: Away from home
Posted:
but he probably would have given NO thought to costumes and the plot would be lacking...
but he probably would have given NO thought to costumes and the plot would be lacking...
BRONZE Member
HOP librarian
1,841 posts
Location: Prague, Czech. Republic
HOP librarian
1,841 posts
Location: Prague, Czech. Republic
Posted:
NYC: What is TI-83?
NYC: What is TI-83?
POI THEO(R)IST
PLATINUM Member
Flying Water Muppet
5,276 posts
Location: Edin-borrow., United Kingdom
Flying Water Muppet
5,276 posts
Location: Edin-borrow., United Kingdom
Posted:
well, as long as it was in a classroom I would be happy.
Illicit classroom videos made by teachers are the best!
well, as long as it was in a classroom I would be happy.
Illicit classroom videos made by teachers are the best!
"the now legendary" - Kaskade
"the still legendary" - Kaskade
I spunked in my friend's aquarium and the fish ate it. I love all fish. Especially the pink ones. They are my bitches. - Anon.
GOLD Member
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Pirate Ninja
3,882 posts
Location: Galway/Ireland
Posted:
for the math boys
thats real nice work.
(i've never seen you so excited nyc, nothings better than figuring something like that out )
now make with the illustrations
for the math boysthats real nice work.
(i've never seen you so excited nyc, nothings better than figuring something like that out
)now make with the illustrations
Love is the law.
BRONZE Member
HOP librarian
1,841 posts
Location: Prague, Czech. Republic
HOP librarian
1,841 posts
Location: Prague, Czech. Republic
Posted:
NYC what is TI-83?
NYC what is TI-83?
POI THEO(R)IST
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