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 | (0.672037, 0.783943) | 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 |
2 | (0.701471, 0.924963) | 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 |
3 | (0.762922, 0.640653) | 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 | (0.624508, 0.479962) | 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 | (0.916338, 0.951715) | 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 | (0.155171, 0.155739) | 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 |
7 | (0.630325, 0.0955352) | 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 |
8 | (0.243231, 0.177745) | 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 | (0.614233, 0.138269) | 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 |
10 | (0.354032, 0.270195) | 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 | (0.0796682, 0.38936) | 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 | (0.449371, 0.0509673) | 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 | (0.773453, 0.823363) | 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 |
14 | (0.00206616, 0.635829) | 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 |
15 | (0.0215555, 0.969333) | 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 | (0.389633, 0.93163) | 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 | (0.228039, 0.414152) | 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 | (0.0342937, 0.764733) | 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 |
19 | (0.011401, 0.0287) | 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 |
20 | (0.967381, 0.0166557) | 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 |
21 | (0.225143, 0.623402) | 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 |
22 | (0.253505, 0.285186) | 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 |
23 | (0.0720961, 0.819014) | 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 |
24 | (0.950204, 0.962446) | 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 | (0.109448, 0.477227) | 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 |
26 | (0.353382, 0.661179) | 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 | (0.298076, 0.940517) | 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 |
28 | (0.553315, 0.311698) | 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 | (0.658473, 0.939954) | 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 |
30 | (0.838542, 0.0242648) | 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 |
31 | (0.956272, 0.869915) | 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 |
32 | (0.115847, 0.929739) | 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 | (0.347193, 0.45123) | 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 | (0.325995, 0.753376) | 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 | (0.738303, 0.556584) | 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 |
36 | (0.507187, 0.654961) | 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 | (0.663739, 0.227775) | 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 |
38 | (0.94182, 0.713428) | 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 |
39 | (0.942492, 0.345439) | 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 | (0.312973, 0.159244) | 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 | (0.171714, 0.972181) | 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 |
42 | (0.105142, 0.415505) | 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 |
43 | (0.760067, 0.187069) | 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 |
44 | (0.409095, 0.888506) | 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 | (0.199471, 0.793903) | 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 |
46 | (0.972929, 0.179581) | 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 | (0.417523, 0.788075) | 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 |
48 | (0.349182, 0.0492267) | 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 |
49 | (0.0666313, 0.952176) | 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 | (0.933699, 0.898068) | 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 | (0.147343, 0.876079) | 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 |
52 | (0.376717, 0.683571) | 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 |
53 | (0.861593, 1.15455e-5) | 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 |
54 | (0.433295, 0.0947341) | 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 |
55 | (0.745559, 0.761831) | 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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945 | (0.166821, 0.749783) | 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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948 | (0.973144, 0.938989) | 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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950 | (0.736886, 0.766832) | 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 |
951 | (0.349004, 0.0612676) | 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 | (0.53619, 0.834643) | 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 |
953 | (0.323647, 0.728653) | 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 |
954 | (0.934091, 0.542974) | 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 |
955 | (0.0945247, 0.832001) | 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 | (0.885381, 0.399072) | 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 | (0.67684, 0.577139) | 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 |
958 | (0.905389, 0.493575) | 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 | (0.998364, 0.321842) | 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 | (0.867531, 0.0595527) | 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 | (0.815585, 0.769242) | 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 | (0.553453, 0.878584) | 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 | (0.0145825, 0.451545) | 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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965 | (0.545013, 0.602196) | 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 |
966 | (0.915319, 0.0279173) | 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 | (0.525158, 0.238216) | 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 |
968 | (0.146452, 0.474749) | 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 |
969 | (0.686944, 0.454361) | 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 | (0.375851, 0.757422) | 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 |
971 | (0.284334, 0.000924755) | 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 |
972 | (0.333553, 0.575169) | 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 |
973 | (0.476283, 0.728255) | 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 |
974 | (0.50294, 0.604378) | 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 | (0.880089, 0.483774) | 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 | (0.621958, 0.840255) | 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 | (0.0450995, 0.937587) | 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 | (0.741811, 0.704015) | 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 | (0.561603, 0.89234) | 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 | (0.357168, 0.676498) | 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 |
981 | (0.957779, 0.616702) | 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 | (0.160822, 0.645397) | 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 | (0.308103, 0.244809) | 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 | (0.603669, 0.500973) | 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 |
985 | (0.176755, 0.00158902) | 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 | (0.0280796, 0.420983) | 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 |
987 | (0.424759, 0.113473) | 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 |
988 | (0.274597, 0.834699) | 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 | (0.229766, 0.0056143) | 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 | (0.915998, 0.564949) | 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 | (0.276472, 0.733237) | 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 |
992 | (0.356547, 0.828926) | 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 | (0.513175, 0.0805762) | 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 |
994 | (0.520359, 0.286057) | 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 | (0.729971, 0.295494) | 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 | (0.424679, 0.915423) | 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 | (0.751852, 0.26337) | 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 |
998 | (0.362413, 0.310759) | 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 | (0.906376, 0.318561) | 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 | (0.892589, 0.640933) | 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 |
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)
.