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Fortran implementation of a geospatial K-d Tree for efficient lookup of closest latitude/longitude points
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Fortran implementation of a geospatial K-d Tree for efficient lookup of closest latitude/longitude points.

Once a tree has been constructed by providing it with a list of latitude/longitude points (taking O(n log n) time, where n is the number of points), the tree can then be searched for points closest to a given search point in a fast O(log n) time.

The source file contains more detailed usage information.


Initializing k-d tree

The kd_init() subroutine populates a kd-tree with a list of latitude/longitude points ( lons, lats) and returns a kd-tree object ( type(kd_root)) for use in subsequent calls to subroutines searching the tree

subroutine kd_init(root, lons, lats)
    type(kd_root), intent(out)  :: root
    !! the root node of our kd-tree, used by kd_search_nnearest and kd_search_radius

    real(dp), intent(in), target :: lats(:)
    !! 1-D array of latitudes.
    real(dp), intent(in), target :: lons(:)
    !! 1-D array of longitudes. These can be within any range. Must match the length of lats

Once done with a kd-tree, the memory associated with it should be freed by calling kd_free() on it.

Searching the tree

There are two ways to search the tree and retreive points, by a search radius or by the n-neareast. With both methods, distance can be calculated via great circle distances (exact=.true.), or by a euclidean distance (the default) which is faster. Euclidean distances are close enough for most purposes if the search radius is small comapred with the radius of the earth.

by search radius

subroutine kd_search_radius(root, s_lon, s_lat, s_radius, r_points, r_distance, r_num, exact)

kd_search_radius() searches for all points within a given radius (s_radius) of the search point (s_lon, s_lat). The maximum number of points to search for depends on the size of r_points and r_distance. Once the arrays are full, the subroutine will exit early. The resulting r_points is a list of index values pointing to the corresponding array elements of the orginal lat, lon used to initial the kdtree. r_distance is a corresponding array of distances.

by n-nearest neighbors

subroutine kd_search_nnearest(root, s_lon, s_lat, s_num, r_points, r_distance, r_num, exact)

kd_search_nnearest() finds the s_num neareast points to the given s_lon, s_lat. The variables r_points,r_distance, and r_num have the same meaning as kd_search_radius()


use kdtree

type(kd_root) :: ll_kdtree
real, allocatable :: lons(:), lats(:)
integer, parameter :: s_num = 4
integer :: r_points(s_num), r_num
real    :: r_dist(s_num)

! initialize lons/lats with the model grid

! initialize the kd-tree
call kd_init(ll_kdtree, lons, lats)

! search the kd-tree to find the 4 grid points closest to my house.
call kd_search_nnearest(ll_kdtree, -76.58, 34.28, s_num, r_points, r_distance, r_num)
do i=1,r_num
  print *, "point ", i, "lat: ", lats[r_points[i]], "lon: ", lons[r_points[i]], "distance: ", r_distance[i]
end do

! cleanup
call kd_free(ll_kdtree)
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