Spatial joins
Spatial joins are table joins which are based not on equality, but on some predicate true
or false
. For geometries, the DE-9IM
spatial relationship model is used to determine the spatial relationship between two geometries.
Spatial joins can be done between any geometry types (from geometrycollections to points), just as geometrical predicates can be evaluated on any geometries.
In this tutorial, we will show how to perform a spatial join on first a toy dataset and then two Natural Earth datasets, to show how this can be used in the real world.
In order to perform the spatial join, we use FlexiJoins.jl to perform the join, specifically using its by_pred
joining method. This allows the user to specify a predicate in the following manner, for any kind of table join operation:
using FlexiJoins
innerjoin((table1, table1),
by_pred(:table1_column, predicate_function, :table2_column) # & add other conditions here
)
leftjoin((table1, table1),
by_pred(:table1_column, predicate_function, :table2_column) # & add other conditions here
)
rightjoin((table1, table1),
by_pred(:table1_column, predicate_function, :table2_column) # & add other conditions here
)
outerjoin((table1, table1),
by_pred(:table1_column, predicate_function, :table2_column) # & add other conditions here
)
We have enabled the use of all of GeometryOps' boolean comparisons here. These are:
GO.contains, GO.within, GO.intersects, GO.touches, GO.crosses, GO.disjoint, GO.overlaps, GO.covers, GO.coveredby, GO.equals
Tip
Always place the dataframe with more complex geometries second, as that is the one which will be sorted into a tree.
Simple example
This example demonstrates how to perform a spatial join between two datasets: a set of polygons and a set of randomly generated points.
The polygons are represented as a DataFrame with geometries and colors, while the points are stored in a separate DataFrame.
The spatial join is performed using the contains
predicate from GeometryOps, which checks if each point is contained within any of the polygons. The resulting joined DataFrame is then used to plot the points, colored according to the containing polygon.
First, we generate our data. We create two triangle polygons which, together, span the rectangle (0, 0, 1, 1), and a set of points which are randomly distributed within this rectangle.
import GeoInterface as GI, GeometryOps as GO
using FlexiJoins, DataFrames
using CairoMakie, GeoInterfaceMakie
pl = GI.Polygon([GI.LinearRing([(0, 0), (1, 0), (1, 1), (0, 0)])])
pu = GI.Polygon([GI.LinearRing([(0, 0), (0, 1), (1, 1), (0, 0)])])
poly_df = DataFrame(geometry = [pl, pu], color = [:red, :blue])
f, a, p = poly(poly_df.geometry; color = tuple.(poly_df.color, 0.3))
Here, the upper polygon is blue, and the lower polygon is red. Keep this in mind!
Now, we generate the points.
points = tuple.(rand(1000), rand(1000))
points_df = DataFrame(geometry = points)
scatter!(points_df.geometry)
f
You can see that they are evenly distributed around the box. But how do we know which points are in which polygons?
We have to join the two dataframes based on which polygon (if any) each point lies within.
Now, we can perform the "spatial join" using FlexiJoins. We are performing an outer join here
@time joined_df = FlexiJoins.innerjoin(
(points_df, poly_df),
by_pred(:geometry, GO.within, :geometry)
)
Row | geometry | geometry_1 | color |
---|---|---|---|
Tuple… | Polygon… | Symbol | |
1 | (0.579668, 0.418981) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
2 | (0.870787, 0.862943) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
3 | (0.725779, 0.0271903) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
4 | (0.617383, 0.411257) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
5 | (0.552354, 0.618873) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
6 | (0.637353, 0.107921) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
7 | (0.588094, 0.991052) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
8 | (0.998496, 0.0272512) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
9 | (0.0644319, 0.350338) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
10 | (0.775918, 0.326632) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
11 | (0.00762354, 0.85318) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
12 | (0.811834, 0.538752) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
13 | (0.988829, 0.884951) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
14 | (0.330547, 0.261156) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
15 | (0.278286, 0.71943) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
16 | (0.0534075, 0.864692) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
17 | (0.024719, 0.394339) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
18 | (0.788389, 0.453098) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
19 | (0.691268, 0.0663854) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
20 | (0.39578, 0.75686) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
21 | (0.897274, 0.0489362) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
22 | (0.753282, 0.0869874) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
23 | (0.548988, 0.430035) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
24 | (0.114838, 0.430422) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
25 | (0.426772, 0.240971) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
26 | (0.185415, 0.953978) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
27 | (0.575065, 0.0266779) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
28 | (0.348095, 0.177604) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
29 | (0.552024, 0.329429) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
30 | (0.361157, 0.99895) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
31 | (0.398495, 0.405048) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
32 | (0.243348, 0.827048) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
33 | (0.235185, 0.659998) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
34 | (0.754472, 0.941849) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
35 | (0.404439, 0.680964) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
36 | (0.002662, 0.182011) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
37 | (0.610443, 0.854407) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
38 | (0.563156, 0.964938) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
39 | (0.866182, 0.401861) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
40 | (0.647219, 0.124533) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
41 | (0.854595, 0.558525) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
42 | (0.602683, 0.214484) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
43 | (0.384321, 0.644376) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
44 | (0.884604, 0.944742) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
45 | (0.586309, 0.471658) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
46 | (0.8505, 0.4623) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
47 | (0.997294, 0.0678189) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
48 | (0.317364, 0.615587) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
49 | (0.378618, 0.771186) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
50 | (0.534945, 0.0179853) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
51 | (0.688786, 0.467427) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
52 | (0.722092, 0.378339) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
53 | (0.102092, 0.618318) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
54 | (0.418453, 0.419101) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
55 | (0.0261376, 0.816022) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
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950 | (0.4458, 0.170956) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
951 | (0.471641, 0.407937) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
952 | (0.866939, 0.118715) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
953 | (0.949593, 0.192584) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
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955 | (0.401386, 0.832782) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
956 | (0.715832, 0.122867) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
957 | (0.408207, 0.797291) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
958 | (0.384039, 0.0525275) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
959 | (0.407919, 0.181933) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
960 | (0.961018, 0.209384) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
961 | (0.637144, 0.0519378) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
962 | (0.858008, 0.926193) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
963 | (0.656818, 0.536412) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
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966 | (0.861853, 0.376452) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
967 | (0.42193, 0.54552) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
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969 | (0.824075, 0.439823) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
970 | (0.954337, 0.932345) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
971 | (0.244003, 0.509786) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
972 | (0.338185, 0.0942468) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
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974 | (0.375354, 0.879216) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
975 | (0.687411, 0.616336) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
976 | (0.401855, 0.55862) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
977 | (0.782838, 0.921745) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
978 | (0.723637, 0.701824) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
979 | (0.00127379, 0.250643) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
980 | (0.58876, 0.00379436) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
981 | (0.718404, 0.375573) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
982 | (0.132484, 0.910641) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
983 | (0.846967, 0.52689) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
984 | (0.0245429, 0.249223) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
985 | (0.211491, 0.166168) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
986 | (0.928752, 0.129423) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
987 | (0.101336, 0.913714) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
988 | (0.588685, 0.792643) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
989 | (0.825149, 0.456824) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
990 | (0.955796, 0.0974551) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
991 | (0.845674, 0.191616) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
992 | (0.583933, 0.614775) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
993 | (0.280367, 0.750336) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
994 | (0.80843, 0.0519292) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
995 | (0.922822, 0.314164) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
996 | (0.129179, 0.393819) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
997 | (0.430212, 0.984949) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
998 | (0.997466, 0.709782) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
999 | (0.91426, 0.143988) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (1, 0), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | red |
1000 | (0.0537724, 0.140957) | Polygon{false, false, Vector{LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}}, Nothing, Nothing}(LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}[LinearRing{false, false, Vector{Tuple{Int64, Int64}}, Nothing, Nothing}([(0, 0), (0, 1), (1, 1), (0, 0)], nothing, nothing)], nothing, nothing) | blue |
scatter!(a, joined_df.geometry; color = joined_df.color)
f
Here, you can see that the colors were assigned appropriately to the scattered points!
Real-world example
Suppose I have a list of polygons representing administrative regions (or mining sites, or what have you), and I have a list of polygons for each country. I want to find the country each region is in.
import GeoInterface as GI, GeometryOps as GO
using FlexiJoins, DataFrames, GADM # GADM gives us country and sublevel geometry
using CairoMakie, GeoInterfaceMakie
country_df = GADM.get.(["JPN", "USA", "IND", "DEU", "FRA"]) |> DataFrame
country_df.geometry = GI.GeometryCollection.(GO.tuples.(country_df.geom))
state_doublets = [
("USA", "New York"),
("USA", "California"),
("IND", "Karnataka"),
("DEU", "Berlin"),
("FRA", "Grand Est"),
("JPN", "Tokyo"),
]
state_full_df = (x -> GADM.get(x...)).(state_doublets) |> DataFrame
state_full_df.geom = GO.tuples.(only.(state_full_df.geom))
state_compact_df = state_full_df[:, [:geom, :NAME_1]]
innerjoin((state_compact_df, country_df), by_pred(:geom, GO.within, :geometry))
innerjoin((state_compact_df, view(country_df, 1:1, :)), by_pred(:geom, GO.within, :geometry))
Warning
This is how you would do this, but it doesn't work yet, since the GeometryOps predicates are quite slow on large polygons. If you try this, the code will continue to run for a very, very long time (it took 12 hours on my laptop, but with minimal CPU usage).
Enabling custom predicates
In case you want to use a custom predicate, you only need to define a method to tell FlexiJoins how to use it.
For example, let's suppose you wanted to perform a spatial join on geometries which are some distance away from each other:
my_predicate_function = <(5) ∘ abs ∘ GO.distance
You would need to define FlexiJoins.supports_mode
on your predicate:
FlexiJoins.supports_mode(
::FlexiJoins.Mode.NestedLoopFast,
::FlexiJoins.ByPred{typeof(my_predicate_function)},
datas
) = true
This will enable FlexiJoins to support your custom function, when it's passed to by_pred(:geometry, my_predicate_function, :geometry)
.