Lib.rs

This crate implements the alpha and weak-alpha filtration of a set of points in the plane. Both are filtrations of the Delaunay triangulation. With the optional lophat feature, the crate also provides a function for computing the boundary matrix of the filtration.

• The alpha filtration is constructed similarly to the Čech filtration. Grow balls of radius r around each point and intersect each ball with the corresponding Voronoi cell. This nerve of this collection of open sets is the alpha filtration at radius r.
• The weak alpha filtration is a sub-filtration of the Vietoris-Rips filtration. Namely, at each filtration value r, the weak alpha filtration is equal to the Vietoris-Rips filtration intersected with the Delaunay triangulation.

Filtrations of the Delauny triangulation are implemented as a DelaunayTriangulation from the spade crate. The filtration value is stored in the data() struct associated to each vertex, undirected edge and inner face.

WARNING: To avoid unecessary square roots, the filtration times are squared from their theoretical value.