Struct Cube 

pub struct Cube {
    pub vertices: Vec<usize>,
    pub dimension: usize,
    pub id: Option<usize>,
}

Represents an individual cube in a cubical complex.

A $k$-cube is represented by its $2^k$ vertices and its dimension. The vertices are ordered according to a binary coordinate system where each vertex corresponds to a corner of the hypercube.

Fields

• vertices: A Vec<usize> containing the vertex indices that define the cube. For a $k$-cube, this contains $2^k$ vertices ordered systematically.
• dimension: The intrinsic dimension of the cube (e.g., 0 for a point, 1 for an edge).
• id: An optional unique identifier assigned when the cube is added to a complex.

Fields

vertices: Vec<usize>

The vertex indices that define this cube.

dimension: usize

The dimension of this cube (e.g., 0 for a point, 1 for an edge, 2 for a face).

id: Option<usize>

An optional unique identifier assigned when the cube is added to a complex.

Implementations

impl Cube

pub fn new(dimension: usize, vertices: Vec<usize>) -> Self

Creates a new cube with the given dimension and vertices.

Arguments

• dimension: The dimension of the cube.
• vertices: The vertex indices that define the cube. For a k-cube, this should contain exactly 2^k vertices.

Panics

Panics if vertices.len() is not equal to 2^dimension.

pub fn vertex(vertex: usize) -> Self

Creates a new 0-cube (vertex) from a single vertex index.

pub fn edge(v0: usize, v1: usize) -> Self

Creates a new 1-cube (edge) from two vertex indices.

pub fn square(vertices: [usize; 4]) -> Self

Creates a new 2-cube (square) from four vertex indices. The vertices should be ordered as: [bottom-left, bottom-right, top-left, top-right] corresponding to binary coordinates (0,0), (1,0), (0,1), (1,1).

pub fn vertices(&self) -> &[usize]

Returns a slice reference to the vertex indices of the cube.

pub const fn dimension(&self) -> usize

Returns the dimension of the cube.

pub const fn id(&self) -> Option<usize>

Returns the ID of the cube if it has been assigned to a complex.

pub fn same_content(&self, other: &Self) -> bool

Checks if this cube has the same mathematical content as another.

Trait Implementations

impl Clone for Cube

fn clone(&self) -> Cube

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ComplexElement for Cube

fn dimension(&self) -> usize

Returns the intrinsic dimension of this element.

fn faces(&self) -> Vec<Self>

Returns all faces (boundary elements) of this element.

fn boundary_with_orientations(&self) -> Vec<(Self, i32)>

Returns the faces with their correct orientation coefficients for boundary computation.

fn id(&self) -> Option<usize>

Returns the ID if this element has been assigned to a complex, None otherwise.

fn same_content(&self, other: &Self) -> bool

Checks if this element has the same mathematical content as another.

fn with_id(&self, new_id: usize) -> Self

Creates a new element with the same content but a specific ID.

impl Debug for Cube

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

Formats the value using the given formatter.

impl Display for Cube

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

Formats the value using the given formatter.

impl Hash for Cube

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Ord for Cube

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for Cube

fn eq(&self, other: &Cube) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for Cube

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Eq for Cube

impl StructuralPartialEq for Cube