Struct LevelSet 

pub struct LevelSet {
    pub tree: QuadTree,
    pub delta: f64,
}

Signed-distance level-set function stored on a QuadTree.

Variable index 0 of each leaf cell contains the level-set value φ. The tree must have been constructed with n_vars >= 1.

The narrow band is the set of cells where |φ| < delta. Only narrow- band cells are updated during reinitialization and advection, which makes these algorithms O(N_interface) rather than O(N_total).

Fields

tree: QuadTree

The underlying quad-tree (n_vars == 1, storing φ).

delta: f64

Narrow-band half-width in physical units.

Implementations

impl LevelSet

pub fn new(tree: QuadTree, phi0: impl Fn(f64, f64) -> f64) -> Self

Create a new level-set by evaluating phi0(x, y) on every leaf of an already-constructed quad-tree (must have n_vars >= 1).

phi0 should return a signed distance (positive outside, negative inside) but any smooth function is accepted.

pub fn set_delta(&mut self, delta: f64)

Override the narrow-band half-width (default: 3 × coarsest cell size).

pub fn phi(&self, id: CellId) -> Option<f64>

Return the level-set value φ at a leaf cell.

pub fn reinitialize(&mut self, n_iters: usize)

Sussman reinitialization: solve ∂φ/∂τ + sign(φ₀)(|∇φ|−1) = 0 for n_iters pseudo-time steps using first-order Godunov upwind.

Only narrow-band cells (|φ| < delta) are updated.

pub fn advect( &mut self, vx: &dyn Fn(f64, f64, f64) -> f64, vy: &dyn Fn(f64, f64, f64) -> f64, t: f64, dt: f64, )

First-order upwind advection: ∂φ/∂t + v·∇φ = 0.

vx(x, y, t) and vy(x, y, t) are the advecting velocity components. Only narrow-band cells are updated. The time step dt must satisfy the CFL condition dt * max(|v|) / dx < 1.

pub fn interface_cells(&self) -> Vec<CellId>

Return the IDs of all interface cells: leaf cells where φ changes sign among the cell and its face-neighbours.

Equivalently: cells where |φ| < delta and at least one neighbour has the opposite sign of φ.

pub fn gradient(&self, id: CellId) -> Option<(f64, f64)>

Compute the first-order centred gradient (∂φ/∂x, ∂φ/∂y) at a leaf cell.

pub fn narrow_band_count(&self) -> usize

Statistics: number of narrow-band leaf cells.

pub fn cell_data(&self, id: CellId) -> Option<&CellData>

Retrieve the CellData of a leaf.