I know that Mathematica has built-in functions for creating triangulations such as Delaunay and Voronoi. However, I haven’t found a function that would generate a Vietoris - Rips Complex for a finite number of points (x_i,y_i) in R^2. I don’t know how to write such a function myself.
I would be very thankful if anyone has any idea!
Maybe you could adapt code from this WFR function?
Thanks. I found the part in this WFR function that uses Rips complexes, but I’ve been pretty stuck trying to make it a stand alone code for only Rips complexes. I find it a bit complicated since I’m new to mathematica.
I’m also interested, in case anyone codes a vietoris-rips function!
I did not manage to incorporate the Vietoris-Rips with the PersistentHomology WFR, however, after reading the following article, I figured I could use the NearestNeighbor function to build something that works like Vietoris-Rips.
Manipulate[
NearestNeighborGraph[positions, k], {k, 1, 1, 1}]
Make sure to set positions as your set of {x,y} coordinates. Sadly, the functions does not work if I’m using too many coordinates, but that might be on my hardware. The function also only works using whole numbers.