Struct SimplicialComplex 

pub struct SimplicialComplex {
    pub vertices: Vec<[f64; 3]>,
    pub edges: Vec<[usize; 2]>,
    pub triangles: Vec<[usize; 3]>,
    pub tetrahedra: Vec<[usize; 4]>,
}

Simplicial complex: vertices, edges, triangles, tetrahedra.

A simplicial complex is a set of simplices that satisfies the condition that every face of a simplex is also a simplex in the complex.

Fields

vertices: Vec<[f64; 3]>

Vertices (0-simplices) stored as [x, y, z]

edges: Vec<[usize; 2]>

Edges (1-simplices) as pairs of vertex indices

triangles: Vec<[usize; 3]>

Triangles (2-simplices) as triples of vertex indices

tetrahedra: Vec<[usize; 4]>

Tetrahedra (3-simplices) as quadruples of vertex indices

Implementations

impl SimplicialComplex

pub fn new() -> Self

Creates an empty simplicial complex.

pub fn add_vertex(&mut self, pos: [f64; 3]) -> usize

Adds a vertex and returns its index.

pub fn add_edge(&mut self, i: usize, j: usize)

Adds an edge if it is not already present.

pub fn add_triangle(&mut self, i: usize, j: usize, k: usize)

Adds a triangle.

pub fn add_tetrahedron(&mut self, i: usize, j: usize, k: usize, l: usize)

Adds a tetrahedron.

pub fn euler_characteristic(&self) -> i64

Computes the Euler characteristic χ = V - E + F - T.

pub fn n_vertices(&self) -> usize

Returns the number of vertices V.

pub fn n_edges(&self) -> usize

Returns the number of edges E.

pub fn n_triangles(&self) -> usize

Returns the number of triangles F.

pub fn n_tetrahedra(&self) -> usize

Returns the number of tetrahedra T.

pub fn boundary_1(&self) -> Vec<i32>

Builds the boundary operator ∂_1: edges → vertices as incidence matrix.

Returns a |V| × |E| matrix (flat row-major).

pub fn boundary_2(&self) -> Vec<i32>

Builds the boundary operator ∂_2: triangles → edges.

Returns a |E| × |F| matrix (flat row-major).

pub fn octahedral_sphere() -> Self

Creates the simplicial complex for a triangulated sphere (icosphere-like).

Uses an octahedral approximation: 6 vertices, 12 edges, 8 triangles. Euler characteristic = 6 - 12 + 8 = 2.

pub fn minimal_torus() -> Self

Creates a torus triangulation with Euler characteristic 0.

Minimal triangulation: V=7, E=21, F=14, χ=0. Uses the complete graph K_7 triangulation of the torus.

Trait Implementations

impl Clone for SimplicialComplex

fn clone(&self) -> SimplicialComplex

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SimplicialComplex

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

Formats the value using the given formatter.

impl Default for SimplicialComplex

fn default() -> Self

Returns the “default value” for a type.