Rational 2-string-tangles

How to create figures and illustrations for knot theory papers

Rational 2-string-tangles

Postby Benedikt on Sat Jul 26, 2008 11:55 am

Hello,

I'd like to create some rational 2-string-tangles, like the ones which could be found here on pages 6 and 7.
I tried to work with two given the examples on the KP homepage. But there are some commands I don't understand and I couldn't find them in the manual:
What are the following commads for?

1. mass open
2. ago 200
3. psop clip circ 0 24
psop frame circ 0 24
psop frame linewidth 1.5
psop phantom -25 -25 25 25
I guess these commands create the ring, but I don't know what they exactly do.

When I tried to replace the tangle command in http://www.knotplot.com/postscript/m/3stringTangleA.html with 'tangle 3@2#' I got the numerator of this tangle in a circle. I don't understand why?
Benedikt
 
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Joined: Fri Jul 25, 2008 9:18 am

Re: Rational 2-string-tangles

Postby rob on Sat Jul 26, 2008 9:05 pm

Benedikt wrote:What are the following commads for?

1. mass open
2. ago 200
3. psop clip circ 0 24
psop frame circ 0 24
psop frame linewidth 1.5
psop phantom -25 -25 25 25
I guess these commands create the ring, but I don't know what they exactly do.


mass open sets bead masses (actually reciprocal masses) to 0 for ends of open strings, and to 1 for all other beads. when you then relax the knot, the end points are fixed. unfortunately, the mass command is not documented.

ago 200 does 200 iterations of the relaxation in "a"-mode. if you used go instead of ago then KnotPlot would start relaxing in the background. it would then output the PostScript before the relaxation finishes. or even gets very far. that's not what you want in this example. you want to relaxation to be an atomic operation (i guess that's where the "a" comes from), i.e., finish before anything else happens. unfortunately, the ago command is not documented.

psop clip circ M R sets a clipping circle in the PostScript output. the origin of the circle is at (0,0) in KnotPlot coordinates. the radius of the circle is equal to M*E + R where E is the link extent. so, in this example the radius would just be equal to 24.

psop frame circ M R draws a framing circle in the PostScript output. the origin of the circle is at (0,0) in KnotPlot coordinates. the radius of the circle is equal to M*E + R where E is the link extent. so, in this example the radius would just be equal to 24.

psop frame linewidth 1.5 sets the width of the circular frame

psop phantom -25 -25 25 25 sets the phantom bounding box. normally, the bounding box in KnotPlot's EPS output is set according to the link extent. sometimes this doesn't give you the results you want. in this example, KnotPlot is fooled into thinking that the link extends from (-25,-25) to (25,25).

unfortunately, none of these psop options are documented.

Benedikt wrote:When I tried to replace the tangle command in http://www.knotplot.com/postscript/m/3stringTangleA.html with 'tangle 3@2#' I got the numerator of this tangle in a circle. I don't understand why?


KnotPlot embeds the tangle into a 1*-polyhedron (Conway's terminology) by default. in other words it creates the numerator of the tangle. some info about this can be found by clicking on the "help" button on the Tangle Calculator panel in KnotPlot. if you want just the tangle, then terminate the tangle string with a period, i.e.
Code: Select all
tangle 3@2#.
.

if you want to use the S tangle operator to create three string tangles, it is part installed by default now. the example should be updated to be
Code: Select all
cyl=1.1
ortho

dstep=44

tangle 25z1S   
mass open
ago 200

pserase=3

psop clip circ  0 24
psop frame circ 0 24
psop frame linewidth 1.5
psop phantom -25 -25 25 25

psout 3stringTangle
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rob
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Re: Rational 2-string-tangles

Postby Benedikt on Mon Jul 28, 2008 9:13 am

Many thanks! I think this will help me.

At the moment there is I have just one more question:

What is the function of this clipping cirlce? I don't know if i got this right, but is this some kind of restriction of the tangle to the inside of the circle?
Benedikt
 
Posts: 2
Joined: Fri Jul 25, 2008 9:18 am

Re: Rational 2-string-tangles

Postby rob on Tue Jul 29, 2008 3:57 pm

Benedikt wrote:What is the function of this clipping cirlce? I don't know if i got this right, but is this some kind of restriction of the tangle to the inside of the circle?


The clipping circle is only in effect in the PostScript file. it's for display only. it defines a circular "clipping path" in PostScript terminology. anything outside the clipping path is not drawn.

the EPS file create by the psout command is a plain text file. You open it in any text editor, modify it if you wish, etc.
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