Geo crash course

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Geo Crash Course
Elena Nikolaeva

smartpuffin.com | @ice_lenor | #geo
Who am I?
● 10 years in Geo
● Started in 2GIS
● Built a distributed scalable
GIS-system called Fiji
○ Tailored to needs of
3000 cartographers
● Allowed the business to
scale world-wide
● 3 years in Geo team in
Booking
● Built GeoObject database
● Built process of data
collection between Tech
and Geo Content
departments

Purpose:
make you familiar
with Geo

What is an integer?
● A whole number
● 4 bytes (nowadays, mostly)
● Unsigned or signed
○ Signed range: [-2,147,483,648 .. 2,147,483,647]
○ Unsigned range: [0, 4,294,967,295]
● If you divide 2 integers, you'll get an integer

Common wisdom
● One doesn't store money in double
● When working with strings, mind the encoding
● Theoretically, π is endless; but practically, first
~10 digits will do
● A very large or small double loses precision
● Array representation in memory depends

Geo data: it's a
data type!

Geometry types

Point
Point(25 10)

MultiPoint
1
2
point1
point2
MultiPoint( (25 10), (32 9) )

LineString
1
2
LineString(5 10, 22 15)
● Consists of ordered points

MultiLineString
1
2
3
4
line1 line2
MultiLineString( (10 10, 20 20), (30 15, 40 12) )

Polygon
1
3
2
4
Polygon((0 0, 2 5, 4 0, 0 0))
● Consists of ordered points; certain direction (i.e., counterclockwise)
● Is closed: Point 1 === Point 4
Depends on
implementation

Polygon with holes
6
7
8
9
1
2
3
4
5
Polygon((0 0, 8 0, 8 5, 0 5, 0 0), (3 2, 4 5, 6 2, 3 2))
● First set - "outer ring" (closed, counterclockwise)
● Other sets - "holes" (closed, clockwise)

1
2
3
4
5
MultiPolygon
10
6
7 8
9
11
12 13
14
15
16
17 18
poly1
poly2
poly3

GeometryCollection
GeometryCollection(
Polygon((...)),
LineString(...),
Point(...),
Polygon((...),(...))
)

● Name: Amsterdam
● Type: city
● Population: 821,752
● Country: The Netherlands
GeoObject / Feature
Geometry
Attributes
+

Coordinates

Who thinks that
Earth is flat?

SHOCK!

(x, y)
Point (0 10)
LineString (0 0, 10 0)
Flat coordinates

(lat, long)
Point (52.373160 4.891999)
52.3680° N, 4.9036° E
Geography coordinates

Flat coordinates
● Computer games
● Building plans
● Large scale maps of small areas
○ One city, one district

Flat coordinates
(0, 0) 5 10 15 20 25
5
10
15
Ficus is at
(23, 8)
x
y

Geographical coordinates
● Map of the whole planet
● Map of a large area of the planet
○ "Small scale"

Small scale: when everything is small

Large scale: when everything is LARGE

Latitude
0°
90° North
-90° South
North Pole
South Pole
30th parallel North
30° N
30°
40th parallel South
40° S
-40°
Equator
0° N

Longitude
0°
-180°
West
180°
East
40th meridian east
40° E
40°20th meridian west
40° W
-40°
Prime meridian
0°

Datums and
Coordinate Systems
How round is Earth, exactly?

Geoid
Earth's shape is a

Spheroid
But we can simplify it to a

WGS84
The latest revision is WGS 84 (also known as WGS
1984, EPSG:4326). The WGS 84 datum surface is
an oblate spheroid with equatorial radius a =
6378137 m at the equator and flattening f =
1/298.257223563. The polar semi-minor axis b
then equals a × (1 − f) = 6356752.3142 m. Currently,
WGS 84 uses the Earth Gravitational Model 1996
(EGM96) geoid, revised in 2004. This geoid defines
the nominal sea level surface by means of a
spherical harmonics series of degree 360 (which
provides about 100 km latitudinal resolution near
the Equator). The deviations of the EGM96 geoid
from the WGS 84 reference ellipsoid range from
about −105 m to about +85 m.[8] EGM96 differs
from the original WGS 84 geoid, referred to as
EGM84.

WGS84
radius
R = 6378 km
flattening
F = 1 / 298.25
● Earth is an ellipsoid
○ flattened from the poles
○ has a certain radius
● (0,0) is specified
● Latitude is [90..-90]
● Longitude is [180..-180]
(0,0) is here

Datum describes Earth's
general shape
(Sphere? Ellipsoid? Spheroid?)

Coordinate system describes
where coordinates start
where they end
and what’s the unit

You must specify
the Coordinate System
to make your math correct!

Formula for distance: flat
Point(0 0) to Point(1 1) = 1.414 (units)
● We all learned it in school
● Derived from the Pythagorean
theorem
● Doesn’t know about Earth
● Just plain old distance.

Formula for distance: haversine
● Uses radius
● Doesn’t use flattening
● => Calculates on sphere!
Point(0 0) to Point(1 1) = 157.2 km

Formula for distance: Vincenty
● Uses radius
● And flattening
● => Calculates on WGS84!
○ Or any ellipsoid provided
● => Millimetre precision!
Point(0 0) to Point(1 1) = 156.899568 km

SRID: Spatial Reference Id
● EPSG - European Petroleum Survey
Group
○ A registry of datums and projections
● WGS84's SRID is EPSG:4326
● There are other SRIDs
● You must specify SRID with your
geometry for correct math
○ I.e., when storing geodata in a database
○ Or using a library or a formula

Why is a SRID like a toothbrush?
Because everyone has got one.
● British National Grid
○ Ellipsoid: Airy 1830
● Amersfoort / RD New -- Netherlands
○ Ellipsoid: Bessel 1841
● Geoscience Australia Lambert
○ Ellipsoid: GRS 1980

Who still thinks
that
Earth is flat?

Projections

"How do we draw
a 3D-Earth
on paper?"
- Gerardus Mercator

Projection
● A means to display a N-dimensional object
in a (N-1)-dimensional space
● For maps:
○ How do we display 3D Earth on a 2D paper?
○ Or a piece of parchment?
○ Or a tapestry?
○ Or a computer screen?

We take a datum
and flatten it!

Projections
● A sphere can't be flattened without problems
○ You have to tug and stretch and shrink
● No projections are "100% accurate depictions"
● One has to choose what traits to preserve
○ direction
○ shape
○ area
○ distance

Specific way of flattening,
shrinking, stretching, fitting
is called
a projection

Mercator Projection
● Preserves angles and shapes of
small objects
● => Good for navigation
● Loses sizes (Greenland larger than
Africa)
● Mercator on WGS84 is popular
(EPSG:3395)
● What does Google use? Read on.

Orthographic
● "Like I'm looking at it from
space!"
● Directions from the central
point are preserved
● The closer to the edge, the
more objects are distorted

Plate Carrée
● longitude => y
● latitude => x
● Preserves angles
● Loses everything
else :)

Equal-area (i.e., Mollweide, Lambert, etc)
● Preserves
relative areas
● Distorts angles
and shapes

Winkel Tripel: A Compromise?
● Tries to preserve all at once
● Minimises distortion of area,
direction, and distance
● Cool name
● Used by

Universal Transverse Mercator (UTM)
● Family of 60 projections ("zones")
○ Slice Earth like an orange
○ Each slice has own coordinates
● => Flat coordinates! In meters!
● Coordinate system AND projection,
in one
● Can't make map of whole planet,
only one slice

There is no single
"best projection"

Each projection
is good
for a specific purpose

Web Mercator: A Cursed Projection :)
● "Invented" by Google
○ They mix sphere and ellipsoid, boo!
○ "The underlying geographic coordinates
are defined using WGS84 [ellipsoid]
(as in 3857), but projected as if they
were defined on a sphere (as in 3785)".
● Wasn't accepted for a long time
● Old unofficial code: EPSG:900913, official: EPSG:3857
● Now - alas! - is used by many online maps

OGC Standard

OGC Standard
● Open Geospatial Consortium: 500+ companies
● De-facto defines the geo-industry
● A set of documents about how to:
○ Define geodata
○ Store geodata (in databases)
○ Index it
○ Manipulate it (in databases and in libraries)
● => Start reading with Simple Features

What can I do with my geodata?
Geo Math:
Spatial Operations

Distance
Point(0 0)
Point(4, 2)
Distance = 222.4 km
(calculated on WGS84)
Distance = 4.472
(calculated on flat coords)

Inside

Touches

Overlaps

Topological operations: Union
∪
poly1
poly2
poly1

Topological operations: Intersection
∩
poly1
poly2

Topological operations: Difference
poly1
poly2

Bounding box
Geometry
Bounding box:
smallest enclosing
rectangle

Buffer(5)
Buffer
5
5

● Coordinates must be within SRID's limits
○ I.e., 95° North latitude is a no-no
● Line:
○ Must have min 2 points
○ Length must be > 0
● Polygon:
○ Must have min 4 points
○ Area must be > 0
○ First and last points must be the same (closed ring)
○ Can't intersect itself
○ Holes must be inside
IsValid

1
5
2
IsValid, MakeValid: Self-Intersection
3
4
● 8-shape polygon
● "Butterfly" geometry
● Is NOT valid!
● Must be stored as
MultiPolygon of 2 polygons
○ MakeValid(geom) may fix
problems

Storing spatial data

Well-known geometry representation
● Defined in OGC standard
● Well-known text
○ "Point(0 0)"
○ "LineString(0 0, 1 0)"
○ "Polygon((0 0, 5 0, 5 5, 0 5, 0 0), (1 1, 1 4, 4 4, 4 1, 1 1))"
● Well-known binary
○ 0x0101000000000000000000f03f0000000000000040
A hole in the
polygon

Spatial databases
● OGC-compliant
● Store and index spatial data
○ Fast and correct querying
○ Geometry validation
● Support spatial operations: Union, Buffer, etc
● Support different SRIDs
○ => Support flat coordinates and geography
○ Support all geo math correctly

Spatial databases
● SQL Server
● Postgres: PostGIS extension
● Oracle Spatial and Graph
● MySQL 8.0+ (perhaps, limited support)
● Column type: Geometry / Geography

Spatial Elasticsearch?
● Supports only geographical coordinates on
WGS84
● Index: GeoHash
● Imprecise operations (only uses index, doesn't
do precise calculations)
● Slow to reindex
● Still, can be useful

Spatial indexes
● Quickly answer questions:
○ "What is close to this place"
○ "What is inside this area"
● Usually rough answer, needs precise
calculation afterwards
● Usually already implemented in database or in
library

Spatial index: Quadtree
● Divides space into 4
squares recursively
● Adding new objects is
easy and cheap
● Good for constantly
changing data

Spatial index: R-tree
● Divides space into
rectangles
● Efficient for reading
● Adding new objects
(reindexing) is
expensive

Spatial index: Z-order Curve
● Efficient for reading
● And for writing
● Harder to comprehend
○ And implement
● Though looks cool :)

File formats
● Download your geodata into a file (like .csv)
● Then upload it somewhere else
● No indexing, no operations, simple plain file
● Standardised file formats:
○ .kml
○ .kmz - zipped kml
○ .geojson
○ shapefile

Libraries
● OGC defines the API
● Can load a geometry from spatial db
● Can operate on it in memory
● Supports all topological operations
○ Java: Java Topology Suite
○ C#: NetTopologySuite
○ Ports to many different languages

GIS-systems
Geographic information
systems: apps for creating
and editing geodata.
● ArcGIS from ESRI
● OpenStreetMap editor
● QGIS
● ... many of them

GIS-systems
● Users: geo-specialists (cartographers)
● Create layers (types of objects: "Buildings", "Rivers",
"Parks")
● Create geoobjects
○ Draw geometry
○ Add attributes (names, tags, etc)
○ Do spatial operations, data validations ("buildings
should not intersect each other")

Common Problems in Geo

new Point (lat, lon)
OR
new Point (lon, lat)
?
● Library-dependent
● Always check!

Units: degrees
● Units of latitude and longitude: degrees
● You CAN'T measure distance in them!

Units: degrees
● Two points on the equator:
● Point 1: latitude 0, longitude 0.
● Distance between them, measured as if they
were flat coordinates: 1. (Units: degrees.)
● Distance between them, measured as if they're
on the planet Earth: 111.19 km.

Units: degrees
● Two points on Amsterdam's latitude (52° N):
● Distance between them, measured as if they
were flat coordinates: still 1. (Units: degrees.)
● Distance between them, measured as if they're
on the planet Earth: 68.46 km.

The closer to the pole,
the less km's fit
in one degree longitude

Degrees latitude
are always the same
in km's

180th Meridian

180th Meridian: Always Check With Fiji!
-16.760, -179.658
-16.712, 179.713
180th Meridian

180th Meridian
● Fiji
● New Zealand
● Russia
● Kiribati
● United States

Poles
● One latitude: 90° or -90°
● All longitudes meet there
=> It's all exactly the same point!
○ Point (lat=90, lon=0)
○ Point (lat=90, lon=100)
○ Point (lat=90, lon=-140)

Poles
● Some projections don't support poles
● I.e., Mercator on WGS84:
○ "World between 80°S and 84°N."
○ Otherwise, poles would be stretched into infinity
● => If you need poles, check if your projection
and datum support them

Spatial operations around problem areas
● Math close to 180th meridian must work
correctly!
● Same goes for poles!

Thank you
Your questions, please!

Geo crash course

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