C Prior: Downloadable code
Note: all code posted here is free to distribute.
A tool box for evaluating the topology of
ribbons.
The following routines are used for
calculating the net winding of two curves bound
between planes
as well as the polar writhing of a single curve.
This can be used to calculate the open
equivalent of the
Calugareanu-White-Fuller decomposition of the
ribbon detailed in this
paper. I extended this framework in
joint work
with Sebastien
Neukirch in which we allowed for ribbons
which looped over their ends (this motion is the
so-called dirac belt trick)
(the paper can be found here).
The code has recently been modified in order to
deal with less than differentiable curves
following private conversations with Zachary
Sierzega
The first set of routines calculate various
forms of the writhe. First for closed curves
Closed writhe
Here the polar and standard writhe definitions
give the same value. However, with the polar
writhe calculation there
is further information in the decomposition into
local and non local contributions.
On Linux The routine is compiled under g++ by
running
sh makeFileGenClosed.sh
then running
./polarWritheClosed <file>
<file> is assumed to be in the same folder
as the command polarWritheClosed
Open polar writhe
This quantity calculates the angles the
end points of the curve make with the curve
itself. This is the standard definition
(see here
for details).
On
Linux The routine is
compiled under g++ by
running
sh makeFileGenStandard.sh
then running
./polarWritheGen
<file>
Following
conversations with Zacahary Sierzega