development of alpha hull algorithm

alphadev.R

nc <- sf::st_read(system.file("shape/nc.shp", package = "sf"))

geo <- sf::st_centroid(nc) |> 
  sf::st_geometry()

tris <- geo |> 
  geos::geos_make_collection() |> 
  geos::geos_delaunay_triangles()

# this is what i would've preferred (and now do)
x <- geos::geos_unnest(tris)

# Identify the circumscribed circle
circumscribe_circle <- function(geom) {
  tri_xy <- sf::st_coordinates(sf::st_as_sf(geom))[1:3,1:2]
  circum_circ <- tripack::circumcircle(tri_xy[,1], tri_xy[,2])
  circum_circ
}


# apply the above function to all triangles
all_circs <- do.call("rbind", lapply(x, circumscribe_circle)) 

# create new wk circles object
circs <- wk::new_wk_crc(
  x = list(x = unlist(all_circs$x),
           y = unlist(all_circs$y),
           r = unlist(all_circs$r)),
  crs = attr(x, "crs")
  )

# pull the radii from the circles
radii <- unclass(circs)[["r"]]

# sort 
radii_sorted <- sort(radii, TRUE)

# calculate alpha
alpha_og <- 1 / radii_sorted[1]

# plot tesselations
plot(x[radii < alpha_og])

Let's not get worked up over triangles and circles. :) I've tried both long lat and projected coords, both work after jittering.

I'm sorry Jos, you know it's just numbers ... I'm not going to participate in any nonsense about it being "non-planar" (when that, while real, is irrelevant)

I don't have any patience for that idiocy and that's why I'll just dip out 🙏