Self-fix function for distance calculation parallelization

[sigmafelix]

Distance calculation parallelization with smaller spatial extents than the entire dataset's extent may result in erroneous values if some grids/sub-regions have no target data features or edge cases are present near the boundary of adjacent grids/sub-regions. Gradually expanding grids can be used to fix such edge cases. One challenge is to design a function which determine whether the current calculation is shorter or longer than the actual shortest distance to the nearest feature that would have been found at the full dataset.

Problem statement

Given a grid $G_i$, a point or line target feature set $V$, and a point origin feature set $U$, we want to find $\text{if }\sup {d((U_k \cap G_i ), (V_l \cap G_i))} < \sup {d((U_k \cap G_i ), V)}$, or $\text{if }\inf {d((U_k \cap G_i ), (V_l \cap G_i))} > \sup {d((U_k \cap G_i ), V)}$ $\text{ } \forall k, l$ $\inf$ problem is relevant as we consider calculating the shortest distance to the target feature set.

Hypothesis

• A distance is considered suspicious/sub-optimal when it is longer than the distance from this point to the grid boundary.

• [ ] Hypothesis implementation

• [ ] Gradual increment in search window

• [ ] Check the influence to the performance

[sigmafelix]

A function in the next version will--

• [ ] Use alphahull to identify the outermost points to detect erroneous distance calculation.

library(terra)
library(sf)
library(alphahull)

nc <- vect(system.file("gpkg/nc.gpkg", package = "sf"))
ncp <- spatSample(ncp, 3000)
ncpp <- crds(ncp)
ncp_ahull <- ahull(ncpp[,1], ncpp[,2], 1)

# get the outermost point row indices
ncp_ahull$ashape.obj$alpha.extremes