Spherical Voronoi

Generate a Voronoi mesh on spherical coordinates

voronoi_spherical(xyz)

Arguments

xyz	matrix of columns longitude, latitude, and optionally z

Value

list with matrix elements triangles, edges and centroids.

Details

An input matrix of XYZ coordinates is triangulated using convex hull (Delaunay on the sphere), coordinates are assumed to lie on the surface of a sphere.

A list is returned with triangles the index of triangles created from xyz, $edges a matrix of index pairs into $centroids, a matrix of XYZ coordinates that are the centres of the triangles of the convex hull of xyz.

Examples

## does the hard work (convex hull on xyz points is Delaunay triangulation)
library(geometry)
## random longlat coordinates on the (geo)sphere
pts <- geosphere::randomCoordinates(5000)
library(rgl)
#> Error: package or namespace load failed for ‘rgl’:
#>  .onLoad failed in loadNamespace() for 'rgl', details:
#>   call: NULL
#>   error: X11 not found; XQuartz (from www.xquartz.org) is required to run rgl.
vs <- voronoi_spherical(ll2cart(pts))
clear3d()
#> Error in clear3d(): could not find function "clear3d"
segments3d(vs$centroids[t(vs$edges), ], lit = FALSE, lwd = 2)
#> Error in segments3d(vs$centroids[t(vs$edges), ], lit = FALSE, lwd = 2): could not find function "segments3d"
spheres3d(0, 0, 0, 6310000, color = "lightgrey")
#> Error in spheres3d(0, 0, 0, 6310000, color = "lightgrey"): could not find function "spheres3d"
## add the triangles
wire3d(tmesh3d(t(ll2cart(pts, rad = 6350000)), t(vs$triangles),
  homogeneous = FALSE), color = grey(0.3), alpha = .8)
#> Error in wire3d(tmesh3d(t(ll2cart(pts, rad = 6350000)), t(vs$triangles),     homogeneous = FALSE), color = grey(0.3), alpha = 0.8): could not find function "wire3d"


#pts <- do.call(cbind, maps::map(plot = FALSE)[c("x", "y")])
#pts <- pts[!is.na(pts[,1]), ]
#pts <- pts[sort(sample(1:nrow(pts), 8000)), ]