.. courtesy of Adrian Custer on the OpenJUMP mailing list:

> > just one question .. what is this bursa wolf parameter option?

> My impression is that this is scary math I never quite understood.

Well, Bursa was a 9 year old bicyclist from the Alps and...no, no, no, i

lie. Actually it's not particularly scary math and quite easy to

understand. All you really need to remember is that no one has ever been

to the center of the earth.

So everyone started surveying (mostly so the repressive central

governments could exploit taxes from people and have lots of jolly wars

where people could slog through the mud and kill each other so they'd be

blood and suffering for all). Each group started from some random place

on the surface of the earth. Right away, it becomes obvious to everyone

that euclidean rules don't work so well. Some didn't care so much since

taxes are basically arbitrary anyway and getting serious about it means

you'd have to walk through fields and woods and get lots of mud on your

shoes. Others kept at it and resorted to spherical geometry. Once you

start doing that precisely and at continental scales you realize that

doesn't really work either so you decide to try the next hardest thing,

an ellipsoid of rotation. Now how do you know which one to choose? Well

you pick one that minimizes your squared errors. All good and nice but

(1) you are surveying the ground which is anything but an ellipsoid

since it has all those ditches you keep falling into and that keep

getting your clothes covered in mud and (2) you are not perfect

especially with all that mud on your paper. So you have a bunch of

errors. Well everyone that does this comes up with lots of different

ellipsoids that work really nice for their data and everyone is sure

they clearly have found the 'one true ellipsoid' and they decide to use

that for all their work. Then everyone guesses where they actually are

on each of their particular ellipsoids which involves lots of going

outside at night and looking up from the mud at the stars. But then it's

not like the edges of each survey was nice and level on these ellipsoids

either --- think of the eastern USA. You can start nice and clean and

warm and dry at an inn in Boston on the edge of the sea drinking clam

chowder and having a good time but a few months later it will be bitter,

bitter cold in that tiny town of Denver because you are somewhere like a

mile high up in the air and you're wet and covered in mud from slogging

through the plains in a snowstorm. So you've got a pretty good idea that

your data is on a major slant but, well, you'll do your best to make up

for it but it really doesn't help the effort any, especially what with

all that mud that's still itching in your hair. So your errors may be a

wee bit big but hey it's all right: it's good enough to wage lots of

good wars with lots of mud and blood and to keep collecting lots of

taxes so no one cares too much.

Fast forward to more recent times where some people want to talk to lots

of different governments and work with lots of different data. They take

everyone's guess and try to line them up. Well it turns out, when you

try to line everything up, that the center points of all the different

ellipses aren't really the same points and even the orientation of the

three axes are all a bit off because of how everyone guessed where their

were on their ellipsoids. So now, to go from one data set to another so

they line up "the best," you need estimates of how much to rotate each

of the axes and how to shift the center point around; all this beyond

even the obvious stuff of changing between the different definition of

all those "one true" ellipsoids.

When you do this mathematically, you need a bunch of parameters: these

now have the names of the wolf and the bursa. Generally, you can only

come up with good parameters if you have lots of data to compare and

some good software to do the comparing. That's what the EPSG did for

everyone. The guys in the pickup trucks that went out looking for oil

kept falling into ditches along the way and getting mud on their faces

but when they got back to the office they had a good sense of what lined

up with what and could say: "yep, that hill there is the same as this

squiggle here and there's this big ditch right here that cost us our

third flat tire and..." So they collected as much data as they could and

compared it and came up with a database of parameters by which you go

from one data set to another. So that's it. That's why we use their

data; we don't have to fall in any ditches and can avoid getting mud on

our clothes. They give us their parameters and we can mostly line up

data from one survey against data from another. But you do need some

good parameters because the earlier folk had a harder time of the mud

and the data they created don't just line up the way we would like them

to.

Actually doing the math is a bit harder but the concept is pretty

straight forward: geographic data all ultimately gets tied into points

on the earth surface and that requires estimating where the points

really are and how they line up on the estimated ellipsoid being used.

That in turn means none of ellipsoids quite line up and we need

parameters to move between them.

--adrian

## Monday, 17 September 2007

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