Module alpha_complex 

Alpha complex filtration for 2D point clouds

Implements the Bowyer-Watson incremental Delaunay triangulation and uses circumradii as filtration values to build the alpha complex. Persistent homology is then computed via standard boundary-matrix column reduction.

Algorithm

1. Build Delaunay triangulation with Bowyer-Watson.
2. Assign each simplex a filtration value = circumradius of its smallest enclosing circle:
   • 0-simplex (vertex): 0.0
   • 1-simplex (edge): circumradius of the two-point “circle” = half edge length
   • 2-simplex (triangle): circumradius of the circumscribed circle
3. Sort all simplices by filtration value.
4. Reduce the boundary matrix to extract persistence pairs.

Structs

AlphaComplex

Alpha complex built from a 2D point cloud via Delaunay triangulation.

AlphaConfig

Configuration for alpha complex construction.

Simplex

A simplex with an associated filtration value.

Functions

circumradius_2d

Compute the circumradius of the triangle formed by points a, b, c in 2D.

compute_persistence_from_simplices

Compute persistence pairs from a filtered simplicial complex.

sym_diff_sorted

Symmetric difference of two sorted vectors (mod-2 addition of columns).