1. The future of coordinate transformation in geospatial open source software
Kristian Evers
Danish Agency for Data supply and Efficiency
I am a geophysicist at the national mapping authority in Denmark. Work in the geodetic office.
Amongst other things i work on reference frames and coordinate transformations.
Special focus has been on PROJ lately, which we are planning on using as our main transformation software in Denmark.

2. The earth is dynamic.
Continents drift, the sea level and the earth’s crust rise and unstable soil layers collapse.
This is handled in many different ways, which is why coordinate transformation is a tough problem to solve.

3. static
The earth is dynamic.
Continents drift, the sea level and the earth’s crust rise and unstable soil layers collapse.
stay where they are for ever
never ever change
BUT, as always in physics, if we simplify the problem enough, eventually it becomes simple. This trick is used in QGIS and PROJ today.
stay stable

4. Explain the components.
EPSG Guidance note 7-1

5. Earth-centered, Earth-fixed Co-rotating with the Eurasian plate
Details on datums. The connection between the coordinate system and the real world. And what makes transformation difficult.
It’s the box in the middle that we’re interested in today.
Earth-centered, Earth-fixed
Co-rotating with the Eurasian plate
Rigid continental plate
Only defined in Europe
Models the world in 1989
Earth-centered, Earth-fixed
Co-rotating with the Earth
Elastic continents move freely
Globally defined
Models the world today
EPSG Guidance note 7-1

6. Standard method of coordinate transformation today
CRS A
Inverse projection
Inverse grid shift
Geodetic
->
cartesian
7 parameter Helmert
WGS84
The recipe PROJ.4 and thus QGIS follows
7 parameter Helmert
Cartesian
->
geodetic
Grid shift
Projection
CRS B

7. Standard method of coordinate transformation today
CRS A
Inverse projection
Inverse grid shift
Geodetic
->
cartesian
7 parameter Helmert
WGS84
Hub datum
7 parameter Helmert
Cartesian
->
geodetic
Grid shift
Projection
CRS B

8. Standard method of coordinate transformation today
Inverse projection
Inverse grid shift
7 parameter Helmert
Cartesian
->
geodetic
Projection
ED50 /
UTM 32N
ETRS89 /
WGS84
Geodetic
cartesian
Grid shift
+proj=utm +zone=32 +ellps=intl +towgs84=-87,-98,-121,0,0,0,0 +units=m
Hub datum
Example of datum shift ED50 -> ETRS89
+proj=utm +zone=32 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m

9. Okay, so one size doesn’t fit all
Okay, so one size doesn’t fit all. There’s a bunch of problems with this approach. Here’s some of them.

10. (if you care about high accuracy data)
The problem with WGS84
(if you care about high accuracy data)
WGS84 is ill-defined (it’s not, but the way we use it is…)
6 different versions (realizations) exists - which one is never specified
The different versions can differ up to 1 m
Most regional datums are said to be equivalent to WGS84
They are not!
WGS84 moves away from ETRS89 with ~2.5 cm per year (~70 cm out of sync today)
Using WGS84 as a hub datum introduces uncertainties to your data
In principle you add ~2m of uncertainty to your cm accuracy data when transforming with WGS84 as a hub datum
Many coordinate systems are not defined in terms of WGS84
example on next slide
Sorry for the wall of text…

11. System 45 -> ETRS89 / UTM 33 N
Polynomial mapping
Inverse UTM projection on the Hayford ellipsoid
To geodetic coordinates
To cartesian coordiantes
Helmert shift
System45
TC32
ED50
ETRS89
UTM projection on the GRS80 ellipsoid
ETRS89 / UTM 33N

12. The earth IS dynamic

13. Iceland
Iceland is also working on a dynamic datum. The country is moving in two directions and theres a lot of both seismic and vulcanic activity.
Not very suitable for a conventional static datum.

14. Dynamic datums
Coordinates are not ”attached” to the Earth. Geometrically defined by satellite systems, not physical objects on the ground.
Coordinates change with time. The same point on earth will have a different coordinate every time you measure it.
Timestamps are a necesary component in a coordinate.
But coordinates will stay accurate at mm to cm level!
Urgh, another wall of text…

15. Introducing Transformation Pipelines in PROJ
A flexible framework that allows for complex transformations
Transformations are constructed as a set of daisy-chained basic building blocks
Not limited to spatial transformations – pipelines are fully time-aware
More than two geodetic techniques available
14-parameter shift
Velocity and deformation models
Molodensky transform
Polynomial mappings
Affine transformation …
Exposed in a new and more coherent API for PROJ
Last one, I promise!

16. Transformation Pipeline example
proj=pipeline
proj=horner …
proj=utm inv
ellps=intl zone=32
proj=cart inv
ellps=intl
proj=cart
proj=helmert
System45
TC32
ED50
ETRS89
proj=utm
ellps=GRS80 zone=33
ETRS89 / UTM 33N

17. Transformation Pipeline example
+proj=pipeline
+step +init=./s45b.pol:s45b_tc32
+step +proj=utm inv +ellps=intl +zone=32
+step +proj=cart ellps=intl
+step +proj=helmert +ellps=GRS80
+x= y= z=
+rx= ry= rz= s=
+step +proj=cart +inv +ellps=GRS80
+step +proj=utm +ellps=GRS80 +zone=33
proj=pipeline
proj=horner …
proj=utm inv
ellps=intl zone=32
proj=cart inv
ellps=intl
proj=cart
proj=helmert
System45
TC32
ED50
ETRS89
proj=utm
ellps=GRS80 zone=33
ETRS89 / UTM 33N

18. Thanks for your attention!
Questions?