Relaxing while preserving distance between vertices

How to do experimental knot theory using KnotPlot

Relaxing while preserving distance between vertices

Postby whager on Wed Oct 01, 2008 10:20 pm

I would like to relax a knot in KnotPlot without changing the distance between a pair of chosen vertices.

For instance: Given a 30-bead knot, I would like to relax the knot in such a way so that at all times during this relaxation bead #1 and bead #5 are always the same distace apart.

Is there a way to do this?
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Re: Relaxing while preserving distance between vertices

Postby rob on Wed Oct 01, 2008 11:20 pm

hi

probably the simplest way is to enable bead masses. by default, KnotPlot uses beads of unit "mass". due to a history of bad design decisions, the "mass" is actually "inverse mass", but is called "mass" for reasons unknown but time will tell.

here is how to do it:

first assign all beads unit mass:
mass all 1
and then assign a mass (remember it's really inverse mass) of any bead you want to freeze:
mass 1 0
mass 5 0
KnotPlot will echo back what it's doing.

the above will give beads 1 and 5 a "mass" of 0, which because it really is inverse mass, means the bead will not move.

you can turn bead mases on/off with:

mass on
mass off


the solution above is almost certainly not what you want tho, you probably want the beads to move, just maintain a constant distance. is that right?

if so, what you want to do could probably be done with KnotPlot's new plugin mechanism for adding your own dynamics. that feature has only been tested on Linux tho.

rob....
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