Struct Discrete1Form 

pub struct Discrete1Form {
    pub values: HashMap<(usize, usize), f64>,
}

A discrete 1-form on mesh edges, storing one value per directed edge.

A 1-form ω assigns a value ω(e) to each oriented edge such that ω(-e) = -ω(e).

Fields

values: HashMap<(usize, usize), f64>

Values indexed by (vertex_i, vertex_j) with i < j.

Implementations

impl Discrete1Form

pub fn zeros(mesh: &DiscreteMesh) -> Self

Construct a zero 1-form over all mesh edges.

pub fn eval(&self, a: usize, b: usize) -> f64

Evaluate the 1-form on directed edge (a → b).

Returns +val if a < b, else -val.

pub fn integrate_path(&self, path: &[usize]) -> f64

Integrate the 1-form along a path given as a sequence of vertex indices.

pub fn exterior_derivative(&self, mesh: &DiscreteMesh) -> Vec<f64>

Compute the exterior derivative (discrete 2-form = scalar on faces).

Returns a vector of face values dω[f] = ω(e01) + ω(e12) + ω(e20).

Trait Implementations

impl Clone for Discrete1Form

fn clone(&self) -> Discrete1Form

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Discrete1Form

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

Formats the value using the given formatter.