GeoPython 2021 - Mapquadlib: A Python Library for Working with Map Quads

Introduction
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GeoPython 2021 - Mapquadlib

What are MapQuads?
• Quadtree data structure in which each
internal node has exactly four
children.
• Partitions a two-dimensional space by
recursively subdividing it into four
quadrants.

Why using MapQuads?
• Very convenient way to represent some area on the map
• load tiles individually
• Binning spatial data
• Pre-compute tiles

Constructing MapQuads
• Depth-first traversal of a quadtree
• Z-order curve
• Morton Codes

Morton Codes
• Interleaving the binary coordinate
values yields binary z-values
• Connecting the z-values in their
numerical order produces the
recursively Z-shaped curve
• Two-dimensional z-values are also
called quadkey

Morton Codes - Example
Example: A Mapquad of zoom level 10 with column x=754 and row y=531
1. Convert X and Y to binary values
x = 1011110010
y = 1000010011
2. Interleave x and y, with
• x on even and
• y on odd positions
morton_key = 1100 0101 0111 0000 1110
= 11 00 01 01 01 11 10 00 00 11 10
=> 3 0 1 1 1 3 2 0 0 3 2
= 30111320032 = quad_key

Mapquadlib
A Python library for working with MapQuads
• Uses only Python Standard Library => zero dependencies
• Well tested: over 500 tests, 92% test coverage
• Currently, supports MercatorQuads and HereQuads
• To be open-sourced soon

MercatorQuads
• Used at Bing Maps, Mapbox
• Tiling schema with baked in Mercator
projection
•
!
Tile is always a square on the
map surface
•
"
Distortion
•
"
Latitude is limited up to ~85.05
degrees north and ~-85.05 south

HereQuads
• Based on raw, non-projected WGS84
lat/lng coordinate values
• non-square tiles when viewed on
Mercator projected 2D map
•
!
Tile size in degrees does not change
when close to the poles

Mapquadlib - GeoCoordinate
GeoCoordinate
here_office_location = GeoCoordinate(lng=13.3850739, lat=52.5309163)
print(f"GeoJSON: {here_office_location.geojson}")
GeoJSON: {"type": "Point",
"coordinates": [13.3850739, 52.5309163]}
print(f"WKT: {here_office_location.wkt}")
WKT: POINT (13.3850739 52.5309163)

Mapquadlib - BoundingBox
BoundingBox
here_office = BoundingBox(west=13.3839069538,
south=52.5302044945,
east=13.385562377,
north=52.5309703632)
print(f"GeoJSON: {here_office.geojson}")
GeoJSON: {"type": "Polygon",
"coordinates": [
[
[13.3839069538, 52.5302044945],
[13.385562377, 52.5302044945],
[13.385562377, 52.5309703632],
[13.3839069538, 52.5309703632],
[13.3839069538, 52.5302044945]
]
]
}
print(f"WKT: {here_office.wkt}")
WKT: POLYGON (52.5302044945 13.3839069538,
52.5309703632 13.3839069538,
52.5309703632 13.385562377,
52.5302044945 13.385562377,
52.5302044945 13.3839069538)

Mapquadlib - Creating MapQuads
• Generate a MapQuad by
• long key
• quad key
• latitude, longitude and
zoom level
• x, y index and zoom level
my_quad_1 = HereQuad.from_lat_lng_level(lat=52.5309163,
lng=13.3850739,
level=10)
str(my_quad)
str(my_quad_1)
HereQuad [quadKey=1220120312, longKey=1476150, x=550, y=405, level=10]
my_quad_2 = HereQuad(1476150)
my_quad_3 = HereQuad.from_quad_key("1220120312")
my_quad_1 == my_quad_2 == my_quad_3
True

Mapquadlib - Plotting
Draw its bounding box on a map
bbox = my_quad_1.bounding_box
bbox.geojson
{"type": "Polygon",
"coordinates": [
[
[13.359375, 52.3828125],
[13.7109375, 52.3828125],
[13.7109375, 52.734375],
[13.359375, 52.734375],
[13.359375, 52.3828125]
]
]
}

Mapquadlib - Ancestors
Get a MapQuad's ancestor:
ancestor = my_quad.ancestor(7)
ancestor.bounding_box.geojson
{"type": "Polygon",
"coordinates": [
[
[11.25, 50.625],
[14.0625, 50.625],
[14.0625, 53.4375],
[11.25, 53.4375],
[11.25, 50.625]
]
]
}

Mapquadlib - Descendants
Get a MapQuad's descendants:
descendants = my_quad.descendants(14)
geo_collection = {
"type": "GeometryCollection",
"geometries": [d.bounding_box._geojson()
for d in descendants]
}

Mapquadlib - Neighbors
Get a MapQuad's neighbors:
neighbors = my_quad.neighbors()
geo_collection = {
for d in neighbors]
}

Mapquadlib - Neighbors
Get a MapQuad's neighbors at a different
level:
neighbors = my_quad.neighbors(14)
geo_collection = {
for d in neighbors]
}

Mapquadlib - Iterators
Get all MapQuads for a given bounding
box
berlin = BoundingBox(west=13.08835,
south=52.33826,
east=13.76116,
north=52.67551)
quads = MapQuadIterator(HereQuad,level=14,
bounding_box=berlin)
geo_collection = {
"geometries": [q.bounding_box._geojson() for q in quads]
}

Mapquadlib - Conversion
Convert from one MapQuad type to
another
iterator = MapQuadIterator(MercatorQuad,
level=14,
bounding_box=berlin)
geojson = {
"geometries": [q.bounding_box._geojson() for q in iterator]
}
here_quads = set([HereQuad.from_geocoordinate_level(q.bounding_box.center,
level=14) for q in iterator])
geojson = {
"geometries": [q.bounding_box._geojson() for q in here_quads]
}

References
1. Tiled web map
2. Z-order curve
3. Bing Maps Tile System
4. Here Developer Portal

Thank you

GeoPython 2021 - Mapquadlib: A Python Library for Working with Map Quads

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