Closing the AbAbAb braid to make the 6.3.2 knot

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Closing the AbAbAb braid to make the 6.3.2 knot

Postby oarcher on Sun Sep 25, 2011 11:11 am

Hi,
... or openning the 6.3.2 knot (borromean rings) to make the AbAbAb braid.

I've try the command 'cut', 'join', 'open', whithout success.

Can somebody ( Rob ?) give me help ?

Olivier
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Re: Closing the AbAbAb braid to make the 6.3.2 knot

Postby rob on Sun Sep 25, 2011 5:20 pm

hi

there are several ways to do this
Code: Select all
braid (Ab)^3
warp rec2ann 1
join all

The first command creates the braid, you can use parentheses and exponentiation. The second command "warps" a rectangular region to an annulus. You can play with the value (here 1) which is the space left. A value of 0 means the rectangular ends will meet up exactly. The value can be negative. The last command joins each end point to the closest other end point it can find.

The above method is good if you want to get a mostly flat representation of the Borromean Rings. If you just care about getting something that is topologically the correct link, you can try:
Code: Select all
braid -closed (Ab)^3


As you may know, braids can get pretty complicated, for example, see http://knotplot.com/software/ex2.pdf

rob....
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Re: Closing the AbAbAb braid to make the 6.3.2 knot

Postby oarcher on Sun Sep 25, 2011 7:26 pm

Hi Rob,
Many thanks ! The "warp rec2ann 1 " was the command i was searching. But can this instruction be animated ? Like a loop from "warp rec2ann 100" to "warp rec2ann 1" ..

I am reading the documentation you point to me, because i will probably need the 'wrap path' and 'wrap along' instruction soon.

Thanks!

Olivier
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Re: Closing the AbAbAb braid to make the 6.3.2 knot

Postby rob on Mon Sep 26, 2011 4:24 pm

oarcher wrote:But can this instruction be animated ? Like a loop from "warp rec2ann 100" to "warp rec2ann 1" ..r


yes, it can. the "random braid" demo on DemoA does something similar. to see the source code for that (or any other) demo, look in the "demos" folder. The DemoA panel itself is defined in DemoA.kps file and that file will tell you the random braid demo is defined in randbraid2.kps. All .kps files are plain text.

because it's a demo, it might be more complicated than you need. one way to do what you want is something like this:
Code: Select all
reset all
scale=.12
braid (Ab)^3
save |a

frame comm "load |a;warp rec2ann %d;fitto 23;disp t"

frame 100 to 1

you can read about the frame command at http://knotplot.com/man/
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Re: Closing the AbAbAb braid to make the 6.3.2 knot

Postby oarcher on Tue Sep 27, 2011 9:40 pm

Hi Rob,
Thank you , it's awesome !
knotplot has it's own syntax, but it is understandable. I'm now going to try to make something on my own. I want to warp the aBa braid along a moebius rubber, so it can be closed keeping 3 components...

I will probably post questions in a few days about warp install and so...

Olivier
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