Robert Scharein’s method of smoothing the knot seems entirely reasonable to implement. What’s the legality of implementing his methods? Can we just borrow the techniques that he uses in his thesis?
Here’s more of a research question which I just thought of: Regarding the bounding box check referred to on page 125, I wonder if in fact one could just use the Taxi-cab metric instead of the regular Euclidean distance to perform the collision avoidance calculations. Would the relaxation algorithm essentially run the same way (you might have to increase the number of beads to get it to work)? The Taxi-cab metric has the benefit that it is much easier to evaluate, which can allow you to have a lot more beads and get a smoother knot diagram. Scharein says that he got a speed increase of about five-fold by relying mostly on the bounding box method for collision avoidance. Otherwise: Push/Pull rockets described on page 130 could be used to interactively modify the diagram. The user would select a bead with the mouse and give it a push in a given direction. The diagram is 3 dimensional so how the user specifies the direction to move the bead would have to be worked out. However, if we could constrain the diagram to be mostly planar, then we could specify the direction by just pushing the mouse. Also, there is some discussion on this mailing list of getting a Sage app working for tablets. Wouldn’t it be a nice idea to create a knot manipulation interface for a tablet that was touch based? The user could manipulate the knot with his fingers using the Push/Pull rockets idea. On Wednesday, March 5, 2014 4:58:56 AM UTC-5, Miguel Angel Marco wrote: > > Take a look at knotplot. It uses an interactive 3d window. It is > proprietary software, but the methods are described in the author's thesis: > http://www.knotplot.com/thesis/ > In general, it is a nice lecture about the subject of implementing knot > theory into a software. Chapter 7 describes his methods to "relax" a knot > in space. It actually works quite well. > > El martes, 4 de marzo de 2014 13:25:59 UTC+1, Jason Suagee escribió: >> >> Hello Sage mentors and fellow posters, >> >> >> My name Jason Suagee and I'm a 4th year PhD student in mathematics at >> George Washington University in Washington DC. I am primarily interested in >> working on a javascript editor for manipulating knot diagrams as part of >> the knot theory project. My background in knot theory comes mostly from >> Rolfsen's classical Knots and Links book, which was the primary textbook >> for a two semester course in knot theory that I am currently taking this >> academic year. >> >> >> In my own work I focus on symmetric combinatorial decompositions of >> 3-manifolds, which is a cross between low dimensional topology and >> topological graph theory. Where this intersects with knot theory is that >> much of knot theory is actually used as a tool to describe 3-manifolds. In >> particular, one of the most useful methods to present a 3-manifold is by >> performing Dehn surgery on the components of a link in S^3. So manipulation >> of link diagrams can be a big part of what low dimensional topologists do >> on a regular basis. >> >> But manipulating a link diagram on paper can be a real headache, as I >> have found out this year. It would be beneficial if there was a graphical >> way by computer to do these manipulations. I have thought out a rough >> framework with which to approach this design problem and will share it in >> the post below. >> >> >> By the way, I have been a Sage user for the past 4 years and love it! I >> was quite happy to sport a Sage sticker at the joint math meeting this year >> in Baltimore. >> >> >> Best, >> >> Jason >> >> [email protected] >> > -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-gsoc. For more options, visit https://groups.google.com/groups/opt_out.
