Hi Nathann! On Feb 4, 8:43 am, Nathann Cohen <[email protected]> wrote: > Hello !!!! > > Could you be by any chance trying to compute the convex hull of a set > of points ? > > http://en.wikipedia.org/wiki/Convex_hull >
If I imagine the typical shape of a hysteresis (see the pictures at http://en.wikipedia.org/wiki/Hysteresis), I think Convex Hull is not suitable -- simply since the polygonal region is not convex. I think what some people do (this would be a very basic example of persistent homology) is to replace the data points by discs of radius r. If d discs overlap, then join their centre points by a (d-1)- simplex; i.e., if two discs overlap, join them by an edge, if three discs overlap, fill in a triangle. In that way, a simplicial complex emerges (that of course depends on the choice of the radius r). The machinery of persistent homology would now test how long homology elements (geometrically corresponding to circles, spheres, etc) survive when r varies. The circle that survives longest apparently gives you the boundary of the polygon that you are looking for, and it could even cope with some noise in your data. I think there is no persistent homology implemented in Sage, is it? The "persistent group cohomology" in our cohomology spkg has a different scope and wouldn't help here. But back to Eli's question: If the data are sufficiently nice, then it may be worth a try to join each data point with its two nearest neighbours. Perhaps some hand work will be needed to adjust things, but I don't think that there is any algorithm that is as good as the human eye. Cheers, Simon -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
