Struct DiscreteMesh 

pub struct DiscreteMesh {
    pub vertices: Vec<[f64; 3]>,
    pub triangles: Vec<[usize; 3]>,
}

A triangle mesh suitable for discrete differential geometry computations.

Stores vertex positions and triangles, with lazy adjacency information.

Fields

vertices: Vec<[f64; 3]>

Vertex positions, indexed by vertex index.

triangles: Vec<[usize; 3]>

Triangle faces, each given as three vertex indices.

Implementations

impl DiscreteMesh

pub fn new(vertices: Vec<[f64; 3]>, triangles: Vec<[usize; 3]>) -> Self

Construct a mesh from vertex positions and face index triples.

pub fn num_vertices(&self) -> usize

Number of vertices.

pub fn num_faces(&self) -> usize

Number of triangular faces.

pub fn one_ring_faces(&self, v: usize) -> Vec<usize>

Returns all triangles that share vertex v.

pub fn one_ring_vertices(&self, v: usize) -> Vec<usize>

Returns all neighbour vertices of vertex v (one-ring).

pub fn vertex_normal(&self, v: usize) -> [f64; 3]

Area-weighted vertex normal at vertex v.

pub fn face_normal(&self, fi: usize) -> [f64; 3]

Face normal for triangle fi.

pub fn voronoi_area(&self, v: usize) -> f64

Voronoi area of vertex v (mixed Voronoi / barycentric area).

Uses the formulation of Meyer et al. (2003).

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

Build the sparse cotangent-weight Laplace-Beltrami matrix as a list of (row, col, weight) triples.

The returned weights satisfy L[i][j] = (cot_alpha + cot_beta) / 2 for adjacent vertices i, j, and L[i][i] = -sum_j L[i][j].

pub fn apply_laplacian(&self, f: &[f64]) -> Vec<f64>

Apply the Laplace-Beltrami operator to a scalar field f (length = n_vertices), returning the Laplacian value at each vertex: (Lf)[i] = sum_j L[i][j] * f[j].

pub fn gaussian_curvature(&self) -> Vec<f64>

Discrete Gaussian curvature (angle defect) at each vertex.

K[v] = (2*pi - sum_angles) / A_v where A_v is the Voronoi area.

pub fn mean_curvature(&self) -> Vec<f64>

Discrete mean curvature at each vertex using the cotangent formula.

Returns the mean curvature H[v] (scalar) at each vertex. H[v] = |Lx[v]| / (2 * A_v) where Lx is the Laplacian of position.

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

Principal curvatures estimated from mean and Gaussian curvature.

Returns (kappa_1, kappa_2) where kappa_1 >= kappa_2.

Trait Implementations

impl Clone for DiscreteMesh

fn clone(&self) -> DiscreteMesh

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DiscreteMesh

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

Formats the value using the given formatter.