Struct EulerCharacteristic 

pub struct EulerCharacteristic;

Euler characteristic and Euler-Poincaré theorem.

Provides utilities for computing the Euler characteristic from cell counts, Betti numbers, and classification of surfaces.

Implementations

impl EulerCharacteristic

pub fn from_cell_counts(counts: &[usize]) -> i64

Euler characteristic from cell counts: χ = V - E + F - … (alternating sum).

pub fn from_betti(betti: &[usize]) -> i64

Euler characteristic from Betti numbers (Euler-Poincaré theorem): χ = Σ_k (-1)^k β_k.

pub fn surface_genus(g: usize) -> i64

Euler characteristic of a compact orientable surface of genus g: χ = 2 - 2g.

pub fn genus_from_chi(chi: i64) -> Option<i64>

Genus of a compact orientable surface from Euler characteristic: g = (2 - χ) / 2. Returns None if χ is odd.

pub fn classify_surface(chi: i64) -> &'static str

Classification: returns a description string for surfaces by χ.

pub fn verify_sphere_triangulation(v: usize, e: usize, f: usize) -> bool

Euler characteristic formula check: for any triangulation of S², V - E + F = 2.

Trait Implementations

impl Clone for EulerCharacteristic

fn clone(&self) -> EulerCharacteristic

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for EulerCharacteristic

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

Formats the value using the given formatter.