Compute spatial topology and weights for hexagonal smoothing

Finds spatial neighbours and computes Gaussian-based weights for smoothing. Neighbours are computed up to `neighbor_orders` orders (1st-order = touching, 2nd-order = neighbours of neighbours, etc.). Weights decay with order using a Gaussian kernel.

Usage

compute_topology(
  grid,
  projection_crs = NULL,
  neighbor_orders = 2,
  sigma = NULL,
  center_weight = 1,
  neighbor_weights_param = NULL,
  adaptive_sigma_factor = 0.5,
  sample_size = 100
)

Arguments

grid: sf object with polygonal geometries (or a list of sf objects).
projection_crs: CRS used for distance calculations. Default `NULL` selects an appropriate UTM zone via [`get_utm_crs()`].
neighbor_orders: Number of neighbour orders (positive integer).
sigma: Gaussian bandwidth. `NULL` (default) auto-computes from `avg_distance` and `adaptive_sigma_factor`.
center_weight: Weight for the centre cell.
neighbor_weights_param: Optional list of length `neighbor_orders` with per-order weights (overrides Gaussian computation).
adaptive_sigma_factor: Scaling factor for auto-sigma.
sample_size: Cells to sample for the average-distance estimate.

Value

List (or named list of lists if `grid` was a list) containing `neighbors`, `weights`, `avg_distance`, `sigma`, `grid_ids`, `grid_indices`, `neighbor_orders`.

Weight computation

- `sigma = avg_distance * adaptive_sigma_factor` (auto-bandwidth) when `sigma` is `NULL`. - For order N: weight ~ `exp(-N^2 / (2 * sigma^2))`. - All weights (including `center_weight`) are normalised to sum to 1.