Struct VietorisRips 

pub struct VietorisRips {
    pub points: Vec<[f64; 2]>,
    pub epsilon: f64,
}

Vietoris–Rips complex construction from a 2-D point cloud.

The complex includes all simplices (vertices, edges, triangles) whose maximum pairwise distance is at most epsilon.

Fields

points: Vec<[f64; 2]>

The 2-D point cloud.

epsilon: f64

Maximum edge length (epsilon radius).

Implementations

impl VietorisRips

pub fn new(points: Vec<[f64; 2]>, epsilon: f64) -> Self

Create a new VietorisRips complex from a point cloud with radius epsilon.

pub fn edges(&self) -> Vec<(usize, usize, f64)>

All edges (pairs) within epsilon distance.

Returns a list of (i, j, distance) tuples.

pub fn triangles(&self) -> Vec<(usize, usize, usize)>

All triangles (triples) where every pair is within epsilon.

Returns a list of (i, j, k) index triples.

pub fn n_vertices(&self) -> usize

Number of vertices (all points are 0-simplices).

pub fn n_edges(&self) -> usize

Number of edges within epsilon.

pub fn n_triangles(&self) -> usize

Number of triangles (2-simplices) within epsilon.

pub fn euler_characteristic(&self) -> i64

Euler characteristic χ = V − E + F.

pub fn betti_numbers(&self) -> BettiNumbers

Betti numbers via the Euler formula and a union-find for β₀.

β₀ is the number of connected components. β₁ is estimated as β₁ = E − V + β₀ (first Betti number from spanning tree). β₂ is estimated from the Euler characteristic.

pub fn persistent_h0(&self) -> Vec<PersistentInterval>

Compute the 0-dimensional persistent homology (H₀) via Kruskal.

Trait Implementations

impl Clone for VietorisRips

fn clone(&self) -> VietorisRips

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for VietorisRips

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.